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MODULE FM_RATIONAL_ARITHMETIC_1
! FM_rational 1.3 David M. Smith Rational Arithmetic
! This module extends the definition of basic Fortran arithmetic and function operations so
! they also apply to multiple precision rationals, using version 1.3 of FM.
! The multiple precision rational data type is called
! TYPE (FM_RATIONAL)
! Each FM rational number A/B consists of two values, with A and B being TYPE(IM) integer multiple
! precision numbers. Negative rationals are represented with A being negative.
! This module supports assignment, arithmetic, comparison, and functions involving FM_RATIONAL
! numbers.
! Mixed-mode operations, such as adding FM_RATIONAL to IM or machine integer types, are supported.
! In general, operations where both the arguments and results are mathematically rational (machine
! precision integers, TYPE(IM), or TYPE (FM_RATIONAL)) are supported, such as A = 1, A = B - 3, or
! A = B / X_IM, where A and B are FM_RATIONAL, and X_IM is type IM.
! Array operations are also supported, so A, B, and X_IM could be 1- or 2-dimensional arrays in the
! examples above.
! Mixed-mode comparisons are also supported, as with IF (A == 1), IF (A <= B - 3), or
! IF (A > B / X_IM).
! TO_FM_RATIONAL is a function for creating a number of type FM_RATIONAL.
! This function can have one argument, for the common case of creating a rational number with an
! integer value. For TO_FM_RATIONAL(A), A can be a machine integer or array of integers, a type
! IM value or array, or a character string.
! There is also a two argument form, TO_FM_RATIONAL(A,B), that can be used to create the fraction
! A/B when A and B are both machine precision integers, TYPE(IM) multiple precision integers, or
! character strings representing integers.
! The one argument character form can be used with a single input string having both parts of the
! fraction present and separated by '/', as in TO_FM_RATIONAL(' 41 / 314 '). This might be more
! readable than the equivalent forms TO_FM_RATIONAL( 41, 314 ) or TO_FM_RATIONAL( '41', '314' ).
! The TO_FM function from the basic FM package has been extended to convert a type FM_RATIONAL to
! a type FM number. The result is an approximation accurate to the current FM precision.
! RATIONAL_APPROX(A, DIGITS) is a function that converts an FM number A to a rational approximation
! of type FM_RATIONAL that has no more than DIGITS decimal digits in the top and bottom.
! Ex: A = pi, DIGITS = 2 returns the FM_RATIONAL result 22 / 7
! A = pi, DIGITS = 3 returns the FM_RATIONAL result 355 / 113
! A = pi, DIGITS = 6 returns the FM_RATIONAL result 833719 / 265381
! The rational result usually approximates A to about 2*DIGITS significant digits, so
! DIGITS should not be more than about half the precision carried for A.
! Ex: 833719 / 265381 = 3.141592653581077771204419306..., and agrees with pi to about 11 s.d.
! The standard Fortran functions that are available for FM_RATIONAL arguments are the ones that
! give exact rational results. So if A and B are type FM_RATIONAL variables, A**B, EXP(A), etc.,
! are not provided since the results are not generally exact rational numbers.
! But INT(A), FLOOR(A), MAX(A,B), MOD(A,B), etc., do give rational result and are provided.
! AVAILABLE OPERATONS:
! =
! +
! -
! *
! /
! ** A ** J is provided for FM_RATIONAL A and machine integer J.
! ==
! /=
! <
! <=
! >
! >=
! ABS(A)
! CEILING(A)
! DIM(A,B) Positive difference. Returns A - B if A > B, zero if not.
! FLOOR(A)
! INT(A)
! IS_UNKNOWN(A) Returns true if A is unknown.
! MAX(A,B,...) Can have from 2 to 10 arguments.
! MIN(A,B,...) Can have from 2 to 10 arguments.
! MOD(A,B) Result is A - int(A/B) * B
! MODULO(A,B) Result is A - floor(A/B) * B
! NINT(A)
! Array operations for functions.
! ABS, CEILING, FLOOR, INT, and NINT can each have a 1- or 2-dimensional array argument.
! They will return a vector or matrix with the function applied to each element of the
! argument.
! DIM, MOD, MODULO work the same way, but the two array arguments for these functions must
! have the same size and shape.
! IS_UNKNOWN is a logical function that can be used with an array argument but does not return
! an array result. It returns "true" if any element of the input array is FM's special UNKNOWN
! value, which comes from undefined operations such as dividing by zero.
! Functions that operate only on arrays.
! DOT_PRODUCT(X,Y) Dot product of rank 1 vectors.
! MATMUL(X,Y) Matrix multiplication of arrays
! Cases for valid argument shapes:
! (1) (n,m) * (m,k) --> (n,k)
! (2) (m) * (m,k) --> (k)
! (3) (n,m) * (m) --> (n)
! MAXVAL(X) Maximum value in the array
! MINVAL(X) Minimum value in the array
! PRODUCT(X) Product of all values in the array
! SUM(X) Sum of all values in the array
! TRANSPOSE(X) Matrix transposition. If X is a rank 2 array with shape (n,m), then
! Y = TRANSPOSE(X) has shape (m,n) with Y(i,j) = X(j,i).
USE FMZM
TYPE FM_RATIONAL
INTEGER :: NUMERATOR = -1
INTEGER :: DENOMINATOR = -1
END TYPE
! Work variables for derived type operations.
TYPE (IM), SAVE :: R_1 = IM(-3), R_2 = IM(-3), R_3 = IM(-3), R_4 = IM(-3), &
R_5 = IM(-3), R_6 = IM(-3)
TYPE (FM), SAVE :: F_1 = FM(-3), F_2 = FM(-3)
TYPE (FM_RATIONAL), SAVE :: MT_RM = FM_RATIONAL(-3,-3), MU_RM = FM_RATIONAL(-3,-3)
INTEGER, SAVE :: RATIONAL_EXP_MAX = 0, RATIONAL_SKIP_MAX = 100
LOGICAL, SAVE :: SKIP_GCD = .FALSE.
INTERFACE TO_FM_RATIONAL
MODULE PROCEDURE FM_RATIONAL_I
MODULE PROCEDURE FM_RATIONAL_II
MODULE PROCEDURE FM_RATIONAL_I1
MODULE PROCEDURE FM_RATIONAL_I2
MODULE PROCEDURE FM_RATIONAL_IM
MODULE PROCEDURE FM_RATIONAL_IMIM
MODULE PROCEDURE FM_RATIONAL_IM1
MODULE PROCEDURE FM_RATIONAL_IM2
MODULE PROCEDURE FM_RATIONAL_ST
MODULE PROCEDURE FM_RATIONAL_STST
END INTERFACE
INTERFACE FM_UNDEF_INP
MODULE PROCEDURE FM_UNDEF_INP_RATIONAL_RM0
MODULE PROCEDURE FM_UNDEF_INP_RATIONAL_RM1
MODULE PROCEDURE FM_UNDEF_INP_RATIONAL_RM2
END INTERFACE
INTERFACE FMEQ_INDEX_RATIONAL
MODULE PROCEDURE FMEQ_INDEX_RATIONAL_RM0
MODULE PROCEDURE FMEQ_INDEX_RATIONAL_RM1
MODULE PROCEDURE FMEQ_INDEX_RATIONAL_RM2
END INTERFACE
INTERFACE RATIONAL_NUMERATOR
MODULE PROCEDURE RATIONAL_NUMERATOR_IM
END INTERFACE
INTERFACE RATIONAL_DENOMINATOR
MODULE PROCEDURE RATIONAL_DENOMINATOR_IM
END INTERFACE
INTERFACE FM_DEALLOCATE
MODULE PROCEDURE FM_DEALLOCATE_RM1
MODULE PROCEDURE FM_DEALLOCATE_RM2
END INTERFACE
INTERFACE ASSIGNMENT (=)
MODULE PROCEDURE FMEQ_RATIONAL_RMRM
MODULE PROCEDURE FMEQ_RATIONAL_RMI
MODULE PROCEDURE FMEQ_RATIONAL_RMIM
MODULE PROCEDURE FMEQ_RATIONAL_RM1RM
MODULE PROCEDURE FMEQ_RATIONAL_RM1RM1
MODULE PROCEDURE FMEQ_RATIONAL_RM1I
MODULE PROCEDURE FMEQ_RATIONAL_RM1I1
MODULE PROCEDURE FMEQ_RATIONAL_RM1IM
MODULE PROCEDURE FMEQ_RATIONAL_RM1IM1
MODULE PROCEDURE FMEQ_RATIONAL_RM2RM
MODULE PROCEDURE FMEQ_RATIONAL_RM2RM2
MODULE PROCEDURE FMEQ_RATIONAL_RM2I
MODULE PROCEDURE FMEQ_RATIONAL_RM2I2
MODULE PROCEDURE FMEQ_RATIONAL_RM2IM
MODULE PROCEDURE FMEQ_RATIONAL_RM2IM2
END INTERFACE
! These routines are called to let the FMEQ_ subroutines know that a function subprogram has been
! called in the user's program. That means temporary FM, IM, or ZM variables created by this
! interface should not be discarded until the user's function ends and one of the FMEQ_ routines
! is called elsewhere in the user's program.
INTERFACE FM_ENTER_USER_FUNCTION
MODULE PROCEDURE FM_ENTER_FUNCTION_RATIONAL_FM
MODULE PROCEDURE FM_ENTER_FUNCTION_RATIONAL_FM1
MODULE PROCEDURE FM_ENTER_FUNCTION_RATIONAL_FM2
END INTERFACE
INTERFACE FM_EXIT_USER_FUNCTION
MODULE PROCEDURE FM_EXIT_FUNCTION_RATIONAL_FM
MODULE PROCEDURE FM_EXIT_FUNCTION_RATIONAL_FM1
MODULE PROCEDURE FM_EXIT_FUNCTION_RATIONAL_FM2
END INTERFACE
CONTAINS
SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: F_NAME
IN_USER_FUNCTION = .TRUE.
CALL IMDEFINE(F_NAME%NUMERATOR,5)
CALL IMDEFINE(F_NAME%DENOMINATOR,5)
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL + 1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) = NUMBER_USED
TEMPV(NUMBER_USED-1) = -2
TEMPV(NUMBER_USED) = -2
END SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM
SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM1(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: F_NAME
INTEGER :: J
IN_USER_FUNCTION = .TRUE.
DO J = 1, SIZE(F_NAME)
F_NAME(J)%NUMERATOR = -1
F_NAME(J)%DENOMINATOR = -1
CALL IMDEFINE(F_NAME(J)%NUMERATOR,5)
CALL IMDEFINE(F_NAME(J)%DENOMINATOR,5)
TEMPV(NUMBER_USED-1) = -2
TEMPV(NUMBER_USED) = -2
ENDDO
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL + 1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) = NUMBER_USED
END SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM1
SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM2(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: F_NAME
INTEGER :: J,K
IN_USER_FUNCTION = .TRUE.
DO J = 1, SIZE(F_NAME,DIM=1)
DO K = 1, SIZE(F_NAME,DIM=2)
F_NAME(J,K)%NUMERATOR = -1
F_NAME(J,K)%DENOMINATOR = -1
CALL IMDEFINE(F_NAME(J,K)%NUMERATOR,5)
CALL IMDEFINE(F_NAME(J,K)%DENOMINATOR,5)
TEMPV(NUMBER_USED-1) = -2
TEMPV(NUMBER_USED) = -2
ENDDO
ENDDO
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL + 1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) = NUMBER_USED
END SUBROUTINE FM_ENTER_FUNCTION_RATIONAL_FM2
! The exit routines for functions record the fact that a user function has finished,
! and also check to see if the multiple precision value associated with the function name
! has been moved during the function.
SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: F_NAME
INTEGER :: J,K,NEW_K
IF (USER_FUNCTION_LEVEL <= 0) THEN
WRITE (KW,*) ' '
WRITE (KW,*) ' Error in routine FM_EXIT_USER_FUNCTION.'
WRITE (KW,*) ' USER_FUNCTION_LEVEL is not positive.'
WRITE (KW,*) ' Check that all user function subprograms call FM_ENTER_USER_FUNCTION'
WRITE (KW,*) ' on entry and FM_EXIT_USER_FUNCTION before any RETURN or END statement.'
WRITE (KW,*) ' '
STOP
ENDIF
IF (F_NAME%NUMERATOR > NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1 .OR. &
F_NAME%DENOMINATOR > NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)) THEN
IF (F_NAME%NUMERATOR < F_NAME%DENOMINATOR) THEN
J = F_NAME%NUMERATOR
NEW_K = START(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1) - 1
DO K = START(J), START(J)+SIZE_OF(J)-1
NEW_K = NEW_K + 1
MWK(NEW_K) = MWK(K)
ENDDO
TEMPV(J) = -1
F_NAME%NUMERATOR = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) - 1
SIZE_OF(F_NAME%NUMERATOR) = SIZE_OF(J)
START(F_NAME%NUMERATOR) = START(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1)
J = F_NAME%DENOMINATOR
F_NAME%DENOMINATOR = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)
SIZE_OF(F_NAME%DENOMINATOR) = SIZE_OF(J)
START(F_NAME%DENOMINATOR) = NEW_K + 1
DO K = START(J), START(J)+SIZE_OF(J)-1
NEW_K = NEW_K + 1
MWK(NEW_K) = MWK(K)
ENDDO
TEMPV(J) = -1
DO J = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1, NUMBER_USED
IF (TEMPV(J) == -6) TEMPV(J) = -1
ENDDO
ELSE
J = F_NAME%DENOMINATOR
NEW_K = START(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1) - 1
DO K = START(J), START(J)+SIZE_OF(J)-1
NEW_K = NEW_K + 1
MWK(NEW_K) = MWK(K)
ENDDO
TEMPV(J) = -1
F_NAME%DENOMINATOR = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) - 1
SIZE_OF(F_NAME%DENOMINATOR) = SIZE_OF(J)
START(F_NAME%DENOMINATOR) = START(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1)
J = F_NAME%NUMERATOR
F_NAME%NUMERATOR = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)
SIZE_OF(F_NAME%NUMERATOR) = SIZE_OF(J)
START(F_NAME%NUMERATOR) = NEW_K + 1
DO K = START(J), START(J)+SIZE_OF(J)-1
NEW_K = NEW_K + 1
MWK(NEW_K) = MWK(K)
ENDDO
TEMPV(J) = -1
DO J = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1, NUMBER_USED
IF (TEMPV(J) == -6) TEMPV(J) = -1
ENDDO
ENDIF
ENDIF
TEMPV(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)-1) = -1
TEMPV(NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)) = -1
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL - 1
IF (USER_FUNCTION_LEVEL == 0) IN_USER_FUNCTION = .FALSE.
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM
SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM1(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: F_NAME
INTEGER :: J,K,KL,L,NEW_MAX_F,NPT,TOTAL_SIZE
IF (USER_FUNCTION_LEVEL <= 0) THEN
WRITE (KW,*) ' '
WRITE (KW,*) ' Error in routine FM_EXIT_USER_FUNCTION.'
WRITE (KW,*) ' USER_FUNCTION_LEVEL is not positive.'
WRITE (KW,*) ' Check that all user function subprograms call FM_ENTER_USER_FUNCTION'
WRITE (KW,*) ' on entry and FM_EXIT_USER_FUNCTION before any RETURN or END statement.'
WRITE (KW,*) ' '
STOP
ENDIF
NEW_MAX_F = 0
TOTAL_SIZE = 0
DO J = 1, SIZE(F_NAME)
NEW_MAX_F = MAX(NEW_MAX_F,F_NAME(J)%NUMERATOR)
TOTAL_SIZE = TOTAL_SIZE + SIZE_OF(F_NAME(J)%NUMERATOR)
NEW_MAX_F = MAX(NEW_MAX_F,F_NAME(J)%DENOMINATOR)
TOTAL_SIZE = TOTAL_SIZE + SIZE_OF(F_NAME(J)%DENOMINATOR)
ENDDO
IF (NEW_MAX_F > NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)) THEN
ALLOCATE(MOVE_F(TOTAL_SIZE+2*SIZE(F_NAME)),STAT=J)
IF (J /= 0) THEN
CALL FMDEFINE_ERROR(1)
ENDIF
L = 0
DO J = 1, SIZE(F_NAME)
L = L + 1
MOVE_F(L) = SIZE_OF(F_NAME(J)%NUMERATOR)
DO K = 1, SIZE_OF(F_NAME(J)%NUMERATOR)
L = L + 1
MOVE_F(L) = MWK(START(F_NAME(J)%NUMERATOR)+K-1)
ENDDO
L = L + 1
MOVE_F(L) = SIZE_OF(F_NAME(J)%DENOMINATOR)
DO K = 1, SIZE_OF(F_NAME(J)%DENOMINATOR)
L = L + 1
MOVE_F(L) = MWK(START(F_NAME(J)%DENOMINATOR)+K-1)
ENDDO
ENDDO
L = 0
NPT = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) - 2*SIZE(F_NAME)
DO J = 1, SIZE(F_NAME)
L = L + 1
NPT = NPT + 1
SIZE_OF(NPT) = MOVE_F(L)
IF (NPT > 1) THEN
START(NPT) = START(NPT-1) + SIZE_OF(NPT-1)
ELSE
START(NPT) = 1
ENDIF
KL = MOVE_F(L)
DO K = 1, KL
L = L + 1
MWK(START(NPT)+K-1) = MOVE_F(L)
ENDDO
TEMPV(F_NAME(J)%NUMERATOR) = -1
F_NAME(J)%NUMERATOR = NPT
TEMPV(F_NAME(J)%NUMERATOR) = -1
L = L + 1
NPT = NPT + 1
SIZE_OF(NPT) = MOVE_F(L)
IF (NPT > 1) THEN
START(NPT) = START(NPT-1) + SIZE_OF(NPT-1)
ELSE
START(NPT) = 1
ENDIF
KL = MOVE_F(L)
DO K = 1, KL
L = L + 1
MWK(START(NPT)+K-1) = MOVE_F(L)
ENDDO
TEMPV(F_NAME(J)%DENOMINATOR) = -1
F_NAME(J)%DENOMINATOR = NPT
TEMPV(F_NAME(J)%DENOMINATOR) = -1
ENDDO
DO J = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL), NUMBER_USED
IF (TEMPV(J) == -6) TEMPV(J) = -1
ENDDO
DEALLOCATE(MOVE_F)
ELSE
DO J = 1, SIZE(F_NAME)
TEMPV(F_NAME(J)%NUMERATOR) = -1
TEMPV(F_NAME(J)%DENOMINATOR) = -1
ENDDO
ENDIF
CALL FMEQ_TEMP
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL - 1
IF (USER_FUNCTION_LEVEL == 0) IN_USER_FUNCTION = .FALSE.
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM1
SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM2(F_NAME)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: F_NAME
INTEGER :: I,J,K,KL,L,NEW_MAX_F,NPT,TOTAL_SIZE
IF (USER_FUNCTION_LEVEL <= 0) THEN
WRITE (KW,*) ' '
WRITE (KW,*) ' Error in routine FM_EXIT_USER_FUNCTION.'
WRITE (KW,*) ' USER_FUNCTION_LEVEL is not positive.'
WRITE (KW,*) ' Check that all user function subprograms call FM_ENTER_USER_FUNCTION'
WRITE (KW,*) ' on entry and FM_EXIT_USER_FUNCTION before any RETURN or END statement.'
WRITE (KW,*) ' '
STOP
ENDIF
NEW_MAX_F = 0
TOTAL_SIZE = 0
DO I = 1, SIZE(F_NAME,DIM=1)
DO J = 1, SIZE(F_NAME,DIM=2)
NEW_MAX_F = MAX(NEW_MAX_F,F_NAME(I,J)%NUMERATOR)
TOTAL_SIZE = TOTAL_SIZE + SIZE_OF(F_NAME(I,J)%NUMERATOR)
NEW_MAX_F = MAX(NEW_MAX_F,F_NAME(I,J)%DENOMINATOR)
TOTAL_SIZE = TOTAL_SIZE + SIZE_OF(F_NAME(I,J)%DENOMINATOR)
ENDDO
ENDDO
IF (NEW_MAX_F > NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL)) THEN
ALLOCATE(MOVE_F(TOTAL_SIZE+2*SIZE(F_NAME)),STAT=J)
IF (J /= 0) THEN
CALL FMDEFINE_ERROR(1)
ENDIF
L = 0
DO I = 1, SIZE(F_NAME,DIM=1)
DO J = 1, SIZE(F_NAME,DIM=2)
L = L + 1
MOVE_F(L) = SIZE_OF(F_NAME(I,J)%NUMERATOR)
DO K = 1, SIZE_OF(F_NAME(I,J)%NUMERATOR)
L = L + 1
MOVE_F(L) = MWK(START(F_NAME(I,J)%NUMERATOR)+K-1)
ENDDO
L = L + 1
MOVE_F(L) = SIZE_OF(F_NAME(I,J)%DENOMINATOR)
DO K = 1, SIZE_OF(F_NAME(I,J)%DENOMINATOR)
L = L + 1
MOVE_F(L) = MWK(START(F_NAME(I,J)%DENOMINATOR)+K-1)
ENDDO
ENDDO
ENDDO
L = 0
NPT = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) - 2*SIZE(F_NAME)
DO I = 1, SIZE(F_NAME,DIM=1)
DO J = 1, SIZE(F_NAME,DIM=2)
L = L + 1
NPT = NPT + 1
SIZE_OF(NPT) = MOVE_F(L)
IF (NPT > 1) THEN
START(NPT) = START(NPT-1) + SIZE_OF(NPT-1)
ELSE
START(NPT) = 1
ENDIF
KL = MOVE_F(L)
DO K = 1, KL
L = L + 1
MWK(START(NPT)+K-1) = MOVE_F(L)
ENDDO
TEMPV(F_NAME(I,J)%NUMERATOR) = -1
F_NAME(I,J)%NUMERATOR = NPT
TEMPV(F_NAME(I,J)%NUMERATOR) = -1
L = L + 1
NPT = NPT + 1
SIZE_OF(NPT) = MOVE_F(L)
IF (NPT > 1) THEN
START(NPT) = START(NPT-1) + SIZE_OF(NPT-1)
ELSE
START(NPT) = 1
ENDIF
KL = MOVE_F(L)
DO K = 1, KL
L = L + 1
MWK(START(NPT)+K-1) = MOVE_F(L)
ENDDO
TEMPV(F_NAME(I,J)%DENOMINATOR) = -1
F_NAME(I,J)%DENOMINATOR = NPT
TEMPV(F_NAME(I,J)%DENOMINATOR) = -1
ENDDO
ENDDO
DO J = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL), NUMBER_USED
IF (TEMPV(J) == -6) TEMPV(J) = -1
ENDDO
DEALLOCATE(MOVE_F)
ELSE
DO I = 1, SIZE(F_NAME,DIM=1)
DO J = 1, SIZE(F_NAME,DIM=2)
TEMPV(F_NAME(I,J)%NUMERATOR) = -1
TEMPV(F_NAME(I,J)%DENOMINATOR) = -1
ENDDO
ENDDO
ENDIF
CALL FMEQ_TEMP
USER_FUNCTION_LEVEL = USER_FUNCTION_LEVEL - 1
IF (USER_FUNCTION_LEVEL == 0) IN_USER_FUNCTION = .FALSE.
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FM_EXIT_FUNCTION_RATIONAL_FM2
! TO_FM_RATIONAL
FUNCTION FM_RATIONAL_I(TOP)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_I
INTEGER :: TOP,N1,N2
INTENT (IN) :: TOP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
IF (TOP == 0) THEN
CALL IMST2M('0',FM_RATIONAL_I%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_I%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
N1 = ABS(TOP)
N2 = 1
IF (TOP > 0) THEN
CALL IMI2M(N1,FM_RATIONAL_I%NUMERATOR)
ELSE
CALL IMI2M(-N1,FM_RATIONAL_I%NUMERATOR)
ENDIF
CALL IMI2M(N2,FM_RATIONAL_I%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_I)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_I
FUNCTION FM_RATIONAL_II(TOP,BOT)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_II
INTEGER :: TOP,BOT,N1,N2
INTENT (IN) :: TOP,BOT
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
IF (BOT == 0) THEN
CALL IMST2M('UNKNOWN',FM_RATIONAL_II%NUMERATOR)
CALL IMST2M('UNKNOWN',FM_RATIONAL_II%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (TOP == 0) THEN
CALL IMST2M('0',FM_RATIONAL_II%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_II%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
N1 = ABS(TOP)
N2 = ABS(BOT)
CALL FMGCDI(N1,N2)
IF ((TOP > 0 .AND. BOT > 0) .OR. (TOP < 0 .AND. BOT < 0)) THEN
CALL IMI2M(N1,FM_RATIONAL_II%NUMERATOR)
ELSE
CALL IMI2M(-N1,FM_RATIONAL_II%NUMERATOR)
ENDIF
CALL IMI2M(N2,FM_RATIONAL_II%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_II)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_II
FUNCTION FM_RATIONAL_I1(IVAL)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: IVAL
TYPE (FM_RATIONAL), DIMENSION(SIZE(IVAL)) :: FM_RATIONAL_I1
INTEGER :: J
FM_RATIONAL_I1%NUMERATOR = -1
FM_RATIONAL_I1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
DO J = 1, SIZE(IVAL)
CALL IMI2M(IVAL(J),FM_RATIONAL_I1(J)%NUMERATOR)
CALL IMI2M(1,FM_RATIONAL_I1(J)%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_I1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_I1
FUNCTION FM_RATIONAL_I2(IVAL)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: IVAL
TYPE (FM_RATIONAL), DIMENSION(SIZE(IVAL,DIM=1),SIZE(IVAL,DIM=2)) :: FM_RATIONAL_I2
INTEGER :: J,K
FM_RATIONAL_I2%NUMERATOR = -1
FM_RATIONAL_I2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
DO J = 1, SIZE(IVAL,DIM=1)
DO K = 1, SIZE(IVAL,DIM=2)
CALL IMI2M(IVAL(J,K),FM_RATIONAL_I2(J,K)%NUMERATOR)
CALL IMI2M(1,FM_RATIONAL_I2(J,K)%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_I2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_I2
FUNCTION FM_RATIONAL_IM(TOP)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_IM
INTEGER :: R_SIGN
TYPE (IM) :: TOP
INTENT (IN) :: TOP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(TOP)
CALL IMEQ(TOP%MIM,R_1%MIM)
CALL IMI2M(1,R_2%MIM)
IF (IS_UNKNOWN(R_1) .OR. IS_OVERFLOW(R_1)) THEN
CALL IMST2M('UNKNOWN',FM_RATIONAL_IM%NUMERATOR)
CALL IMST2M('UNKNOWN',FM_RATIONAL_IM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (R_1 == 0) THEN
CALL IMST2M('0',FM_RATIONAL_IM%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_IM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
R_SIGN = 1
IF (R_1 < 0) THEN
R_SIGN = -1
ENDIF
CALL IM_ABS(R_1,R_4)
CALL IM_ABS(R_2,R_5)
CALL FM_MAX_EXP_IM(R_4,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_4%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
IF (R_SIGN == -1) MWK(START(R_4%MIM)) = -1
CALL IMEQ(R_4%MIM,FM_RATIONAL_IM%NUMERATOR)
CALL IMEQ(R_5%MIM,FM_RATIONAL_IM%DENOMINATOR)
ELSE
CALL IM_GCD(R_4,R_5,R_3)
CALL IM_DIV(R_4,R_3,R_1)
CALL IM_DIV(R_5,R_3,R_2)
IF (R_SIGN == -1) MWK(START(R_1%MIM)) = -1
CALL IMEQ(R_1%MIM,FM_RATIONAL_IM%NUMERATOR)
CALL IMEQ(R_2%MIM,FM_RATIONAL_IM%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_IM
FUNCTION FM_RATIONAL_IMIM(TOP,BOT)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_IMIM
INTEGER :: R_SIGN
TYPE (IM) :: TOP,BOT
INTENT (IN) :: TOP,BOT
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(TOP)
CALL FM_UNDEF_INP(BOT)
CALL IMEQ(TOP%MIM,R_1%MIM)
CALL IMEQ(BOT%MIM,R_2%MIM)
IF (R_2 == 0 .OR. IS_UNKNOWN(R_1) .OR. IS_OVERFLOW(R_1) .OR. &
IS_UNKNOWN(R_2) .OR. IS_OVERFLOW(R_2) ) THEN
CALL IMST2M('UNKNOWN',FM_RATIONAL_IMIM%NUMERATOR)
CALL IMST2M('UNKNOWN',FM_RATIONAL_IMIM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (R_1 == 0) THEN
CALL IMST2M('0',FM_RATIONAL_IMIM%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_IMIM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
R_SIGN = 1
IF ((R_1 > 0 .AND. R_2 < 0) .OR. (R_1 < 0 .AND. R_2 > 0)) THEN
R_SIGN = -1
ENDIF
CALL IM_ABS(R_1,R_4)
CALL IM_ABS(R_2,R_5)
CALL FM_MAX_EXP_IM(R_4,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_4%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
IF (R_SIGN == -1) MWK(START(R_4%MIM)) = -1
CALL IMEQ(R_4%MIM,FM_RATIONAL_IMIM%NUMERATOR)
CALL IMEQ(R_5%MIM,FM_RATIONAL_IMIM%DENOMINATOR)
ELSE
CALL IM_GCD(R_4,R_5,R_3)
CALL IM_DIV(R_4,R_3,R_1)
CALL IM_DIV(R_5,R_3,R_2)
IF (R_SIGN == -1) MWK(START(R_1%MIM)) = -1
CALL IMEQ(R_1%MIM,FM_RATIONAL_IMIM%NUMERATOR)
CALL IMEQ(R_2%MIM,FM_RATIONAL_IMIM%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_IMIM
FUNCTION FM_RATIONAL_IM1(TOP)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: TOP
TYPE (FM_RATIONAL), DIMENSION(SIZE(TOP)) :: FM_RATIONAL_IM1
INTEGER :: J
FM_RATIONAL_IM1%NUMERATOR = -1
FM_RATIONAL_IM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
DO J = 1, SIZE(TOP)
CALL IMEQ(TOP(J)%MIM,FM_RATIONAL_IM1(J)%NUMERATOR)
CALL IMI2M(1,FM_RATIONAL_IM1(J)%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_IM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_IM1
FUNCTION FM_RATIONAL_IM2(TOP)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: TOP
TYPE (FM_RATIONAL), DIMENSION(SIZE(TOP,DIM=1),SIZE(TOP,DIM=2)) :: FM_RATIONAL_IM2
INTEGER :: J,K
FM_RATIONAL_IM2%NUMERATOR = -1
FM_RATIONAL_IM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
DO J = 1, SIZE(TOP,DIM=1)
DO K = 1, SIZE(TOP,DIM=2)
CALL IMEQ(TOP(J,K)%MIM,FM_RATIONAL_IM2(J,K)%NUMERATOR)
CALL IMI2M(1,FM_RATIONAL_IM2(J,K)%DENOMINATOR)
CALL FM_MAX_EXP_RM(FM_RATIONAL_IM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_IM2
FUNCTION FM_RATIONAL_ST(TOP)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_ST
INTEGER :: K,R_SIGN
CHARACTER(*) :: TOP
INTENT (IN) :: TOP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
K = INDEX(TOP,'/')
IF (K > 0) THEN
CALL IMST2M(TOP(1:K-1),R_1%MIM)
CALL IMST2M(TOP(K+1:LEN(TOP)),R_2%MIM)
ELSE
CALL IMST2M(TOP,R_1%MIM)
CALL IMI2M(1,R_2%MIM)
ENDIF
IF (R_2 == 0 .OR. IS_UNKNOWN(R_1) .OR. IS_OVERFLOW(R_1) .OR. &
IS_UNKNOWN(R_2) .OR. IS_OVERFLOW(R_2) ) THEN
CALL IMST2M('UNKNOWN',FM_RATIONAL_ST%NUMERATOR)
CALL IMST2M('UNKNOWN',FM_RATIONAL_ST%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (R_1 == 0) THEN
CALL IMST2M('0',FM_RATIONAL_ST%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_ST%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
R_SIGN = 1
IF ((R_1 > 0 .AND. R_2 < 0) .OR. (R_1 < 0 .AND. R_2 > 0)) THEN
R_SIGN = -1
ENDIF
CALL IM_ABS(R_1,R_4)
CALL IM_ABS(R_2,R_5)
CALL FM_MAX_EXP_IM(R_4,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_4%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
IF (R_SIGN == -1) MWK(START(R_4%MIM)) = -1
CALL IMEQ(R_4%MIM,FM_RATIONAL_ST%NUMERATOR)
CALL IMEQ(R_5%MIM,FM_RATIONAL_ST%DENOMINATOR)
ELSE
CALL IM_GCD(R_4,R_5,R_3)
CALL IM_DIV(R_4,R_3,R_1)
CALL IM_DIV(R_5,R_3,R_2)
IF (R_SIGN == -1) MWK(START(R_1%MIM)) = -1
CALL IMEQ(R_1%MIM,FM_RATIONAL_ST%NUMERATOR)
CALL IMEQ(R_2%MIM,FM_RATIONAL_ST%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_ST
FUNCTION FM_RATIONAL_STST(TOP,BOT)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: FM_RATIONAL_STST
INTEGER :: R_SIGN
CHARACTER(*) :: TOP,BOT
INTENT (IN) :: TOP,BOT
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M(TOP,R_1%MIM)
CALL IMST2M(BOT,R_2%MIM)
IF (R_2 == 0 .OR. IS_UNKNOWN(R_1) .OR. IS_OVERFLOW(R_1) .OR. &
IS_UNKNOWN(R_2) .OR. IS_OVERFLOW(R_2) ) THEN
CALL IMST2M('UNKNOWN',FM_RATIONAL_STST%NUMERATOR)
CALL IMST2M('UNKNOWN',FM_RATIONAL_STST%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (R_1 == 0) THEN
CALL IMST2M('0',FM_RATIONAL_STST%NUMERATOR)
CALL IMST2M('1',FM_RATIONAL_STST%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
R_SIGN = 1
IF ((R_1 > 0 .AND. R_2 < 0) .OR. (R_1 < 0 .AND. R_2 > 0)) THEN
R_SIGN = -1
ENDIF
CALL IM_ABS(R_1,R_4)
CALL IM_ABS(R_2,R_5)
CALL FM_MAX_EXP_IM(R_4,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_4%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
IF (R_SIGN == -1) MWK(START(R_4%MIM)) = -1
CALL IMEQ(R_4%MIM,FM_RATIONAL_STST%NUMERATOR)
CALL IMEQ(R_5%MIM,FM_RATIONAL_STST%DENOMINATOR)
ELSE
CALL IM_GCD(R_4,R_5,R_3)
CALL IM_DIV(R_4,R_3,R_1)
CALL IM_DIV(R_5,R_3,R_2)
IF (R_SIGN == -1) MWK(START(R_1%MIM)) = -1
CALL IMEQ(R_1%MIM,FM_RATIONAL_STST%NUMERATOR)
CALL IMEQ(R_2%MIM,FM_RATIONAL_STST%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_STST
! RATIONAL_NUMERATOR
FUNCTION RATIONAL_NUMERATOR_IM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM) :: RATIONAL_NUMERATOR_IM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMEQ(MA%NUMERATOR,RATIONAL_NUMERATOR_IM%MIM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION RATIONAL_NUMERATOR_IM
! RATIONAL_DENOMINATOR
FUNCTION RATIONAL_DENOMINATOR_IM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM) :: RATIONAL_DENOMINATOR_IM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMEQ(MA%DENOMINATOR,RATIONAL_DENOMINATOR_IM%MIM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION RATIONAL_DENOMINATOR_IM
SUBROUTINE FM_MAX_EXP_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER :: NT, NB
NT = MWK(START(MA%NUMERATOR)+2)
NB = MWK(START(MA%DENOMINATOR)+2)
IF (NT < MEXPOV .AND. NT > RATIONAL_EXP_MAX) RATIONAL_EXP_MAX = NT
IF (NB < MEXPOV .AND. NB > RATIONAL_EXP_MAX) RATIONAL_EXP_MAX = NB
END SUBROUTINE FM_MAX_EXP_RM
SUBROUTINE FM_MAX_EXP_IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA,MB
INTEGER :: NT
NT = MWK(START(MA%MIM)+2)
IF (NT < MEXPOV .AND. NT > RATIONAL_EXP_MAX) RATIONAL_EXP_MAX = NT
NT = MWK(START(MB%MIM)+2)
IF (NT < MEXPOV .AND. NT > RATIONAL_EXP_MAX) RATIONAL_EXP_MAX = NT
END SUBROUTINE FM_MAX_EXP_IM
! FM_PRINT_RATIONAL
SUBROUTINE FM_PRINT_RATIONAL(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
CHARACTER(100) :: ST1, ST2
CHARACTER(203) :: STR
INTENT (IN) :: MA
INTEGER :: J,KPT
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
! If the top and bottom integers can be printed on one line, as 12 / 7
! in fewer than KSWIDE characters, do it. Otherwise call IMPRINT twice.
CALL IMABS(MA%NUMERATOR,R_1%MIM)
CALL IMABS(MA%DENOMINATOR,R_2%MIM)
CALL IMMPY(R_1%MIM,R_2%MIM,R_3%MIM)
IF (TO_IM(10)**(KSWIDE-11) > R_3 .AND. R_1 < TO_IM('1E+99') .AND. R_2 < TO_IM('1E+99')) THEN
CALL IMFORM('I100',MA%NUMERATOR,ST1)
CALL IMFORM('I100',MA%DENOMINATOR,ST2)
STR = ' '
KPT = 0
DO J = 1, 100
IF (ST1(J:J) /= ' ') THEN
KPT = KPT + 1
STR(KPT:KPT) = ST1(J:J)
ENDIF
ENDDO
STR(KPT+1:KPT+3) = ' / '
KPT = KPT + 3
DO J = 1, 100
IF (ST2(J:J) /= ' ') THEN
KPT = KPT + 1
STR(KPT:KPT) = ST2(J:J)
ENDIF
ENDDO
IF (MWK(START(MA%NUMERATOR)) < 0) THEN
WRITE (KW,"(6X,A)") STR(1:KPT)
ELSE
WRITE (KW,"(7X,A)") STR(1:KPT)
ENDIF
ELSE
CALL IMPRINT(MA%NUMERATOR)
WRITE (KW,"(A)") ' /'
CALL IMPRINT(MA%DENOMINATOR)
ENDIF
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FM_PRINT_RATIONAL
! FMEQ_INDEX
! Check to see if the multiple precision number MA being defined is previously undefined
! and has a default index value of -1. If so, since it is a user variable and not a
! compiler-generated temporary number, change the index to -3 so that the variable is
! stored in the saved area in MWK and not treated as a temporary variable.
SUBROUTINE FMEQ_INDEX_RATIONAL_RM0(MA)
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTENT (INOUT) :: MA
IF (MA%NUMERATOR == -1) MA%NUMERATOR = -3
IF (MA%DENOMINATOR == -1) MA%DENOMINATOR = -3
END SUBROUTINE FMEQ_INDEX_RATIONAL_RM0
SUBROUTINE FMEQ_INDEX_RATIONAL_RM1(MA)
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: J
INTENT (INOUT) :: MA
DO J = 1, SIZE(MA)
IF (MA(J)%NUMERATOR == -1) MA(J)%NUMERATOR = -3
IF (MA(J)%DENOMINATOR == -1) MA(J)%DENOMINATOR = -3
ENDDO
END SUBROUTINE FMEQ_INDEX_RATIONAL_RM1
SUBROUTINE FMEQ_INDEX_RATIONAL_RM2(MA)
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: J,K
INTENT (INOUT) :: MA
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
IF (MA(J,K)%NUMERATOR == -1) MA(J,K)%NUMERATOR = -3
IF (MA(J,K)%DENOMINATOR == -1) MA(J,K)%DENOMINATOR = -3
ENDDO
ENDDO
END SUBROUTINE FMEQ_INDEX_RATIONAL_RM2
SUBROUTINE FM_UNDEF_INP_RATIONAL_RM0(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTENT (IN) :: MA
IF (MA%NUMERATOR <= 0) CALL FM_INPUT_ERROR
IF (MA%NUMERATOR > NUMBER_USED .AND. &
MA%NUMERATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR
IF (MA%NUMERATOR > SIZE_OF_START) CALL FM_INPUT_ERROR
IF (MA%DENOMINATOR <= 0) CALL FM_INPUT_ERROR
IF (MA%DENOMINATOR > NUMBER_USED .AND. &
MA%DENOMINATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR
IF (MA%DENOMINATOR > SIZE_OF_START) CALL FM_INPUT_ERROR
END SUBROUTINE FM_UNDEF_INP_RATIONAL_RM0
SUBROUTINE FM_UNDEF_INP_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: J
INTENT (IN) :: MA
DO J = 1, SIZE(MA)
IF (MA(J)%NUMERATOR <= 0) CALL FM_INPUT_ERROR1(J)
IF (MA(J)%NUMERATOR > NUMBER_USED .AND. &
MA(J)%NUMERATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR1(J)
IF (MA(J)%NUMERATOR > SIZE_OF_START) CALL FM_INPUT_ERROR1(J)
IF (MA(J)%DENOMINATOR <= 0) CALL FM_INPUT_ERROR1(J)
IF (MA(J)%DENOMINATOR > NUMBER_USED .AND. &
MA(J)%DENOMINATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR1(J)
IF (MA(J)%DENOMINATOR > SIZE_OF_START) CALL FM_INPUT_ERROR1(J)
ENDDO
END SUBROUTINE FM_UNDEF_INP_RATIONAL_RM1
SUBROUTINE FM_UNDEF_INP_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: J,K
INTENT (IN) :: MA
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
IF (MA(J,K)%NUMERATOR <= 0) CALL FM_INPUT_ERROR2(J,K)
IF (MA(J,K)%NUMERATOR > NUMBER_USED .AND. &
MA(J,K)%NUMERATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR2(J,K)
IF (MA(J,K)%NUMERATOR > SIZE_OF_START) CALL FM_INPUT_ERROR2(J,K)
IF (MA(J,K)%DENOMINATOR <= 0) CALL FM_INPUT_ERROR2(J,K)
IF (MA(J,K)%DENOMINATOR > NUMBER_USED .AND. &
MA(J,K)%DENOMINATOR < LOWEST_SAVED_AREA_INDEX) CALL FM_INPUT_ERROR2(J,K)
IF (MA(J,K)%DENOMINATOR > SIZE_OF_START) CALL FM_INPUT_ERROR2(J,K)
ENDDO
ENDDO
END SUBROUTINE FM_UNDEF_INP_RATIONAL_RM2
SUBROUTINE FMEQ_RATIONAL_TEMP
! Check to see if the last few FM numbers are temporaries.
! If so, re-set NUMBER_USED so that space in MWK can be re-claimed.
USE FMVALS
IMPLICIT NONE
INTEGER :: J,K,L
IF (USER_FUNCTION_LEVEL == 0) THEN
L = 1
ELSE
L = NUMBER_USED_AT_LEVEL(USER_FUNCTION_LEVEL) + 1
ENDIF
K = NUMBER_USED
DO J = K, L, -1
IF (TEMPV(J) == -1 .OR. TEMPV(J) <= -6) THEN
NUMBER_USED = NUMBER_USED - 1
TEMPV(J) = -2
ELSE
EXIT
ENDIF
ENDDO
END SUBROUTINE FMEQ_RATIONAL_TEMP
SUBROUTINE FM_DEALLOCATE_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: J
INTENT (INOUT) :: MA
DO J = 1, SIZE(MA)
IF (MA(J)%NUMERATOR >= LOWEST_SAVED_AREA_INDEX) THEN
TEMPV(MA(J)%NUMERATOR) = -6
TOTAL_IMTEMP6 = TOTAL_IMTEMP6 + 1
IF (NMAX_IMTEMP6 >= SIZE_OF_TEMP6) THEN
N_IMTEMP6 = MOD( TOTAL_IMTEMP6, SIZE_OF_TEMP6 ) + 1
IMTEMP6(N_IMTEMP6) = MA(J)%NUMERATOR
ELSE
NMAX_IMTEMP6 = NMAX_IMTEMP6 + 1
IMTEMP6(NMAX_IMTEMP6) = MA(J)%NUMERATOR
ENDIF
ENDIF
IF (MA(J)%DENOMINATOR >= LOWEST_SAVED_AREA_INDEX) THEN
TEMPV(MA(J)%DENOMINATOR) = -6
TOTAL_IMTEMP6 = TOTAL_IMTEMP6 + 1
IF (NMAX_IMTEMP6 >= SIZE_OF_TEMP6) THEN
N_IMTEMP6 = MOD( TOTAL_IMTEMP6, SIZE_OF_TEMP6 ) + 1
IMTEMP6(N_IMTEMP6) = MA(J)%DENOMINATOR
ELSE
NMAX_IMTEMP6 = NMAX_IMTEMP6 + 1
IMTEMP6(NMAX_IMTEMP6) = MA(J)%DENOMINATOR
ENDIF
ENDIF
ENDDO
CALL FMDEFINE_RESIZE(0)
END SUBROUTINE FM_DEALLOCATE_RM1
SUBROUTINE FM_DEALLOCATE_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: J,K
INTENT (INOUT) :: MA
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
IF (MA(J,K)%NUMERATOR >= LOWEST_SAVED_AREA_INDEX) THEN
TEMPV(MA(J,K)%NUMERATOR) = -6
TOTAL_IMTEMP6 = TOTAL_IMTEMP6 + 1
IF (NMAX_IMTEMP6 >= SIZE_OF_TEMP6) THEN
N_IMTEMP6 = MOD( TOTAL_IMTEMP6, SIZE_OF_TEMP6 ) + 1
IMTEMP6(N_IMTEMP6) = MA(J,K)%NUMERATOR
ELSE
NMAX_IMTEMP6 = NMAX_IMTEMP6 + 1
IMTEMP6(NMAX_IMTEMP6) = MA(J,K)%NUMERATOR
ENDIF
ENDIF
IF (MA(J,K)%DENOMINATOR >= LOWEST_SAVED_AREA_INDEX) THEN
TEMPV(MA(J,K)%DENOMINATOR) = -6
TOTAL_IMTEMP6 = TOTAL_IMTEMP6 + 1
IF (NMAX_IMTEMP6 >= SIZE_OF_TEMP6) THEN
N_IMTEMP6 = MOD( TOTAL_IMTEMP6, SIZE_OF_TEMP6 ) + 1
IMTEMP6(N_IMTEMP6) = MA(J,K)%DENOMINATOR
ELSE
NMAX_IMTEMP6 = NMAX_IMTEMP6 + 1
IMTEMP6(NMAX_IMTEMP6) = MA(J,K)%DENOMINATOR
ENDIF
ENDIF
ENDDO
ENDDO
CALL FMDEFINE_RESIZE(0)
END SUBROUTINE FM_DEALLOCATE_RM2
SUBROUTINE FMEQ_RATIONAL(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA
INTENT (INOUT) :: MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMEQ(MA%NUMERATOR,MB%NUMERATOR)
CALL IMEQ(MA%DENOMINATOR,MB%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMEQ_RATIONAL
! =
SUBROUTINE FMEQ_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB
INTENT (INOUT) :: MA
INTENT (IN) :: MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FMEQ_INDEX_RATIONAL(MA)
CALL FM_UNDEF_INP(MB)
CALL FMEQ_RATIONAL(MB,MA)
CALL FMEQ_RATIONAL_TEMP
CALL FM_MAX_EXP_RM(MA)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMEQ_RATIONAL_RMRM
SUBROUTINE FMEQ_RATIONAL_RMI(MA,IVAL)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER :: IVAL
INTENT (INOUT) :: MA
INTENT (IN) :: IVAL
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FMEQ_INDEX_RATIONAL(MA)
CALL IMI2M(IVAL,MA%NUMERATOR)
CALL IMI2M(1,MA%DENOMINATOR)
CALL FMEQ_RATIONAL_TEMP
CALL FM_MAX_EXP_RM(MA)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMEQ_RATIONAL_RMI
SUBROUTINE FMEQ_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM) :: MB
INTENT (INOUT) :: MA
INTENT (IN) :: MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FMEQ_INDEX_RATIONAL(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%MIM,MA%NUMERATOR)
CALL IMI2M(1,MA%DENOMINATOR)
CALL FMEQ_RATIONAL_TEMP
CALL FM_MAX_EXP_RM(MA)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMEQ_RATIONAL_RMIM
! Array equal assignments for RM.
! (1) rank 1 = rank 0
SUBROUTINE FMEQ_RATIONAL_RM1I(MA,IVAL)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: IVAL,J
INTENT (INOUT) :: MA
INTENT (IN) :: IVAL
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL_RMI(MA(J),IVAL)
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM1I
SUBROUTINE FMEQ_RATIONAL_RM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
INTEGER :: J
INTENT (INOUT) :: MA
INTENT (IN) :: MB
CALL FMEQ_RATIONAL_RMRM(MT_RM,MB)
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL_RMRM(MA(J),MT_RM)
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM1RM
SUBROUTINE FMEQ_RATIONAL_RM1IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM) :: MB
INTEGER :: J
INTENT (INOUT) :: MA
INTENT (IN) :: MB
CALL IMEQ(MB%MIM,R_1%MIM)
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL_RMIM(MA(J),R_1)
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM1IM
! (2) rank 1 = rank 1
SUBROUTINE FMEQ_RATIONAL_RM1I1(MA,IVAL)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER, DIMENSION(:) :: IVAL
INTEGER :: J
INTENT (INOUT) :: MA
INTENT (IN) :: IVAL
IF (SIZE(MA) /= SIZE(IVAL)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,MA(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J)%DENOMINATOR)
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL_RMI(MA(J),IVAL(J))
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM1I1
SUBROUTINE FMEQ_RATIONAL_RM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), ALLOCATABLE, DIMENSION(:) :: TEMP
INTEGER :: J,N
INTENT (INOUT) :: MA
INTENT (IN) :: MB
IF (SIZE(MA) /= SIZE(MB)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,MA(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J)%DENOMINATOR)
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
N = SIZE(MA)
! To avoid problems when lhs and rhs are overlapping parts of the same array, move MB
! to a temporary array before re-defining any of MA.
ALLOCATE(TEMP(N))
CALL FMEQ_INDEX_RATIONAL(TEMP)
DO J = 1, N
CALL IMEQ(MB(J)%NUMERATOR,TEMP(J)%NUMERATOR)
CALL IMEQ(MB(J)%DENOMINATOR,TEMP(J)%DENOMINATOR)
ENDDO
DO J = 1, N
CALL FMEQ_RATIONAL_RMRM(MA(J),TEMP(J))
ENDDO
CALL FM_DEALLOCATE(TEMP)
DEALLOCATE(TEMP)
END SUBROUTINE FMEQ_RATIONAL_RM1RM1
SUBROUTINE FMEQ_RATIONAL_RM1IM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (IM), ALLOCATABLE, DIMENSION(:) :: TEMP
INTEGER :: J,N
INTENT (INOUT) :: MA
INTENT (IN) :: MB
IF (SIZE(MA) /= SIZE(MB)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,MA(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J)%DENOMINATOR)
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
N = SIZE(MA)
ALLOCATE(TEMP(N))
CALL FMEQ_INDEX(TEMP)
DO J = 1, SIZE(MA)
CALL IMEQ(MB(J)%MIM,TEMP(J)%MIM)
ENDDO
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL_RMIM(MA(J),TEMP(J))
ENDDO
CALL FM_DEALLOCATE(TEMP)
DEALLOCATE(TEMP)
END SUBROUTINE FMEQ_RATIONAL_RM1IM1
! (3) rank 2 = rank 0
SUBROUTINE FMEQ_RATIONAL_RM2I(MA,IVAL)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: IVAL,J,K
INTENT (INOUT) :: MA
INTENT (IN) :: IVAL
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMI(MA(J,K),IVAL)
ENDDO
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM2I
SUBROUTINE FMEQ_RATIONAL_RM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
INTEGER :: J,K
INTENT (INOUT) :: MA
INTENT (IN) :: MB
CALL FMEQ_RATIONAL_RMRM(MT_RM,MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMRM(MA(J,K),MT_RM)
ENDDO
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM2RM
SUBROUTINE FMEQ_RATIONAL_RM2IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM) :: MB
INTEGER :: J,K
INTENT (INOUT) :: MA
INTENT (IN) :: MB
CALL IMEQ(MB%MIM,R_1%MIM)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMIM(MA(J,K),R_1)
ENDDO
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM2IM
! (4) rank 2 = rank 2
SUBROUTINE FMEQ_RATIONAL_RM2I2(MA,IVAL)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER, DIMENSION(:,:) :: IVAL
INTEGER :: J,K
INTENT (INOUT) :: MA
INTENT (IN) :: IVAL
IF (SIZE(MA,DIM=1) /= SIZE(IVAL,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(IVAL,DIM=2)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,MA(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J,K)%DENOMINATOR)
ENDDO
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMI(MA(J,K),IVAL(J,K))
ENDDO
ENDDO
END SUBROUTINE FMEQ_RATIONAL_RM2I2
SUBROUTINE FMEQ_RATIONAL_RM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), ALLOCATABLE, DIMENSION(:,:) :: TEMP
INTEGER :: J,K
INTENT (INOUT) :: MA
INTENT (IN) :: MB
CALL FMEQ_INDEX_RATIONAL(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,MA(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J,K)%DENOMINATOR)
ENDDO
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
! To avoid problems when lhs and rhs are overlapping parts of the same array, move MB
! to a temporary array before re-defining any of MA.
ALLOCATE(TEMP(SIZE(MA,DIM=1),SIZE(MA,DIM=2)))
CALL FMEQ_INDEX_RATIONAL(TEMP)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MB(J,K)%NUMERATOR,TEMP(J,K)%NUMERATOR)
CALL IMEQ(MB(J,K)%DENOMINATOR,TEMP(J,K)%DENOMINATOR)
ENDDO
ENDDO
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMRM(MA(J,K),TEMP(J,K))
ENDDO
ENDDO
CALL FM_DEALLOCATE(TEMP)
DEALLOCATE(TEMP)
END SUBROUTINE FMEQ_RATIONAL_RM2RM2
SUBROUTINE FMEQ_RATIONAL_RM2IM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (IM), ALLOCATABLE, DIMENSION(:,:) :: TEMP
INTEGER :: J,K
INTENT (INOUT) :: MA
INTENT (IN) :: MB
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,MA(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,MA(J,K)%DENOMINATOR)
ENDDO
ENDDO
CALL FMEQ_RATIONAL_TEMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
ALLOCATE(TEMP(SIZE(MA,DIM=1),SIZE(MA,DIM=2)))
CALL FMEQ_INDEX(TEMP)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MB(J,K)%MIM,TEMP(J,K)%MIM)
ENDDO
ENDDO
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL_RMIM(MA(J,K),TEMP(J,K))
ENDDO
ENDDO
CALL FM_DEALLOCATE(TEMP)
DEALLOCATE(TEMP)
END SUBROUTINE FMEQ_RATIONAL_RM2IM2
SUBROUTINE FMADD_RATIONAL_RMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
CALL IM_ADD(R_1,R_5,R_3)
CALL IM_MPY(R_2,R_4,R_5)
CALL FM_MAX_EXP_IM(R_3,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_3%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_3%MIM,MC%NUMERATOR)
CALL IMEQ(R_5%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_3,R_5,R_1)
CALL IMDIV(R_3%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_5%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMADD_RATIONAL_RMRM_0
SUBROUTINE FMSUB_RATIONAL_RMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
CALL IM_SUB(R_5,R_1,R_3)
CALL IM_MPY(R_2,R_4,R_5)
CALL FM_MAX_EXP_IM(R_3,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_3%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_3%MIM,MC%NUMERATOR)
CALL IMEQ(R_5%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_3,R_5,R_1)
CALL IMDIV(R_3%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_5%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMSUB_RATIONAL_RMRM_0
SUBROUTINE FMMPY_RATIONAL_RMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
INTEGER :: IDIV
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_3,R_5)
CALL IM_MPY(R_2,R_4,R_3)
CALL FM_MAX_EXP_IM(R_3,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_3%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_5%MIM,MC%NUMERATOR)
CALL IMEQ(R_3%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_3,R_5,R_1)
IF (MWK(START(R_1%MIM)+2) == 1 .AND. MWK(START(R_1%MIM)+3) == 1) THEN
CALL IMEQ(R_5%MIM,MC%NUMERATOR)
CALL IMEQ(R_3%MIM,MC%DENOMINATOR)
ELSE IF (MWK(START(R_1%MIM)+2) == 1 .AND. MWK(START(R_1%MIM)+3) < MXBASE) THEN
IDIV = MWK(START(R_1%MIM)+3)
CALL IMDIVI(R_5%MIM,IDIV,MC%NUMERATOR)
CALL IMDIVI(R_3%MIM,IDIV,MC%DENOMINATOR)
ELSE
CALL IMDIV(R_5%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_3%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMPY_RATIONAL_RMRM_0
SUBROUTINE FMDIV_RATIONAL_RMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (MWK(START(MA%NUMERATOR)+2) == MUNKNO .OR. MWK(START(MA%DENOMINATOR)+2) == MUNKNO .OR. &
MWK(START(MB%NUMERATOR)+2) == MUNKNO .OR. MWK(START(MB%DENOMINATOR)+2) == MUNKNO .OR. &
MWK(START(MB%NUMERATOR)+3) == 0 ) THEN
CALL IMST2M('UNKNOWN',MC%NUMERATOR)
CALL IMST2M('UNKNOWN',MC%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_4)
CALL FM_MAX_EXP_IM(R_4,R_5)
IF (SKIP_GCD .AND. MAX(MWK(START(R_4%MIM)+2),MWK(START(R_5%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_5%MIM,MC%NUMERATOR)
CALL IMEQ(R_4%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_4,R_5,R_1)
CALL IMDIV(R_5%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMDIV_RATIONAL_RMRM_0
END MODULE FM_RATIONAL_ARITHMETIC_1
MODULE FM_RATIONAL_ARITHMETIC_2
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (+)
MODULE PROCEDURE FMADD_RATIONAL_RM
MODULE PROCEDURE FMADD_RATIONAL_RM1
MODULE PROCEDURE FMADD_RATIONAL_RM2
MODULE PROCEDURE FMADD_RATIONAL_RMRM
MODULE PROCEDURE FMADD_RATIONAL_IRM
MODULE PROCEDURE FMADD_RATIONAL_RMI
MODULE PROCEDURE FMADD_RATIONAL_IMRM
MODULE PROCEDURE FMADD_RATIONAL_RMIM
MODULE PROCEDURE FMADD_RATIONAL_RM1RM1
MODULE PROCEDURE FMADD_RATIONAL_RM1RM
MODULE PROCEDURE FMADD_RATIONAL_RMRM1
MODULE PROCEDURE FMADD_RATIONAL_I1RM1
MODULE PROCEDURE FMADD_RATIONAL_RM1I1
MODULE PROCEDURE FMADD_RATIONAL_I1RM
MODULE PROCEDURE FMADD_RATIONAL_RMI1
MODULE PROCEDURE FMADD_RATIONAL_IRM1
MODULE PROCEDURE FMADD_RATIONAL_RM1I
MODULE PROCEDURE FMADD_RATIONAL_IM1RM1
MODULE PROCEDURE FMADD_RATIONAL_IM1RM
MODULE PROCEDURE FMADD_RATIONAL_IMRM1
MODULE PROCEDURE FMADD_RATIONAL_RM1IM1
MODULE PROCEDURE FMADD_RATIONAL_RM1IM
MODULE PROCEDURE FMADD_RATIONAL_RMIM1
MODULE PROCEDURE FMADD_RATIONAL_RM2RM2
MODULE PROCEDURE FMADD_RATIONAL_RM2RM
MODULE PROCEDURE FMADD_RATIONAL_RMRM2
MODULE PROCEDURE FMADD_RATIONAL_I2RM2
MODULE PROCEDURE FMADD_RATIONAL_I2RM
MODULE PROCEDURE FMADD_RATIONAL_IRM2
MODULE PROCEDURE FMADD_RATIONAL_RM2I2
MODULE PROCEDURE FMADD_RATIONAL_RM2I
MODULE PROCEDURE FMADD_RATIONAL_RMI2
MODULE PROCEDURE FMADD_RATIONAL_IM2RM2
MODULE PROCEDURE FMADD_RATIONAL_IM2RM
MODULE PROCEDURE FMADD_RATIONAL_IMRM2
MODULE PROCEDURE FMADD_RATIONAL_RM2IM2
MODULE PROCEDURE FMADD_RATIONAL_RM2IM
MODULE PROCEDURE FMADD_RATIONAL_RMIM2
END INTERFACE
CONTAINS
! +
FUNCTION FMADD_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMADD_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FMEQ_RATIONAL(MA,FMADD_RATIONAL_RM)
IF (MWK(START(FMADD_RATIONAL_RM%DENOMINATOR)) < 0) THEN
MWK(START(FMADD_RATIONAL_RM%DENOMINATOR)) = 1
MWK(START(FMADD_RATIONAL_RM%NUMERATOR)) = -MWK(START(FMADD_RATIONAL_RM%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM
FUNCTION FMADD_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMADD_RATIONAL_RM1%NUMERATOR = -1
FMADD_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL(MA(J),FMADD_RATIONAL_RM1(J))
IF (MWK(START(FMADD_RATIONAL_RM1(J)%DENOMINATOR)) < 0) THEN
MWK(START(FMADD_RATIONAL_RM1(J)%DENOMINATOR)) = 1
MWK(START(FMADD_RATIONAL_RM1(J)%NUMERATOR)) = &
-MWK(START(FMADD_RATIONAL_RM1(J)%NUMERATOR))
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1
FUNCTION FMADD_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMADD_RATIONAL_RM2%NUMERATOR = -1
FMADD_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL(MA(J,K),FMADD_RATIONAL_RM2(J,K))
IF (MWK(START(FMADD_RATIONAL_RM2(J,K)%DENOMINATOR)) < 0) THEN
MWK(START(FMADD_RATIONAL_RM2(J,K)%DENOMINATOR)) = 1
MWK(START(FMADD_RATIONAL_RM2(J,K)%NUMERATOR)) = &
-MWK(START(FMADD_RATIONAL_RM2(J,K)%NUMERATOR))
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2
FUNCTION FMADD_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMADD_RATIONAL_RMRM
INTENT (IN) :: MA,MB
CALL FMADD_RATIONAL_RMRM_0(MA,MB,FMADD_RATIONAL_RMRM)
END FUNCTION FMADD_RATIONAL_RMRM
SUBROUTINE FMADD_RATIONAL_RMI_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
INTEGER :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_ADD(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMADD_RATIONAL_RMI_0
FUNCTION FMADD_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMADD_RATIONAL_RMI
INTEGER :: MB
INTENT (IN) :: MA,MB
CALL FMADD_RATIONAL_RMI_0(MA,MB,FMADD_RATIONAL_RMI)
END FUNCTION FMADD_RATIONAL_RMI
SUBROUTINE FMADD_RATIONAL_IRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
INTEGER :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_ADD(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMADD_RATIONAL_IRM_0
FUNCTION FMADD_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMADD_RATIONAL_IRM
INTEGER :: MA
INTENT (IN) :: MA,MB
CALL FMADD_RATIONAL_IRM_0(MA,MB,FMADD_RATIONAL_IRM)
END FUNCTION FMADD_RATIONAL_IRM
SUBROUTINE FMADD_RATIONAL_RMIM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_ADD(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMADD_RATIONAL_RMIM_0
FUNCTION FMADD_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMADD_RATIONAL_RMIM
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
CALL FMADD_RATIONAL_RMIM_0(MA,MB,FMADD_RATIONAL_RMIM)
END FUNCTION FMADD_RATIONAL_RMIM
SUBROUTINE FMADD_RATIONAL_IMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_ADD(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMADD_RATIONAL_IMRM_0
FUNCTION FMADD_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMADD_RATIONAL_IMRM
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
CALL FMADD_RATIONAL_IMRM_0(MA,MB,FMADD_RATIONAL_IMRM)
END FUNCTION FMADD_RATIONAL_IMRM
FUNCTION FMADD_RATIONAL_RM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1RM1%NUMERATOR = -1
FMADD_RATIONAL_RM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMRM_0(MA(J),MB(J),FMADD_RATIONAL_RM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1RM1
FUNCTION FMADD_RATIONAL_RM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1RM%NUMERATOR = -1
FMADD_RATIONAL_RM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMRM_0(MA(J),MB,FMADD_RATIONAL_RM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1RM
FUNCTION FMADD_RATIONAL_RMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMADD_RATIONAL_RMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMRM1%NUMERATOR = -1
FMADD_RATIONAL_RMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMADD_RATIONAL_RMRM_0(MA,MB(J),FMADD_RATIONAL_RMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMRM1
FUNCTION FMADD_RATIONAL_I1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_I1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_I1RM1%NUMERATOR = -1
FMADD_RATIONAL_I1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_I1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_I1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_IRM_0(MA(J),MB(J),FMADD_RATIONAL_I1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_I1RM1
FUNCTION FMADD_RATIONAL_RM1I1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1I1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1I1%NUMERATOR = -1
FMADD_RATIONAL_RM1I1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM1I1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM1I1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMI_0(MA(J),MB(J),FMADD_RATIONAL_RM1I1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1I1
FUNCTION FMADD_RATIONAL_IRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMADD_RATIONAL_IRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IRM1%NUMERATOR = -1
FMADD_RATIONAL_IRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMADD_RATIONAL_IRM_0(MA,MB(J),FMADD_RATIONAL_IRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IRM1
FUNCTION FMADD_RATIONAL_RM1I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1I
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1I%NUMERATOR = -1
FMADD_RATIONAL_RM1I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMI_0(MA(J),MB,FMADD_RATIONAL_RM1I(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1I
FUNCTION FMADD_RATIONAL_RMI1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMADD_RATIONAL_RMI1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMI1%NUMERATOR = -1
FMADD_RATIONAL_RMI1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB)
CALL FMADD_RATIONAL_RMI_0(MA,MB(J),FMADD_RATIONAL_RMI1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMI1
FUNCTION FMADD_RATIONAL_I1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_I1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_I1RM%NUMERATOR = -1
FMADD_RATIONAL_I1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_IRM_0(MA(J),MB,FMADD_RATIONAL_I1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_I1RM
FUNCTION FMADD_RATIONAL_IM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_IM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IM1RM1%NUMERATOR = -1
FMADD_RATIONAL_IM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_IM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_IM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_IMRM_0(MA(J),MB(J),FMADD_RATIONAL_IM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IM1RM1
FUNCTION FMADD_RATIONAL_RM1IM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1IM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1IM1%NUMERATOR = -1
FMADD_RATIONAL_RM1IM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM1IM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM1IM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMIM_0(MA(J),MB(J),FMADD_RATIONAL_RM1IM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1IM1
FUNCTION FMADD_RATIONAL_IMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMADD_RATIONAL_IMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IMRM1%NUMERATOR = -1
FMADD_RATIONAL_IMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMADD_RATIONAL_IMRM_0(MA,MB(J),FMADD_RATIONAL_IMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IMRM1
FUNCTION FMADD_RATIONAL_RM1IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_RM1IM
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM1IM%NUMERATOR = -1
FMADD_RATIONAL_RM1IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_RMIM_0(MA(J),MB,FMADD_RATIONAL_RM1IM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM1IM
FUNCTION FMADD_RATIONAL_RMIM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMADD_RATIONAL_RMIM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMIM1%NUMERATOR = -1
FMADD_RATIONAL_RMIM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMADD_RATIONAL_RMIM_0(MA,MB(J),FMADD_RATIONAL_RMIM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMIM1
FUNCTION FMADD_RATIONAL_IM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMADD_RATIONAL_IM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IM1RM%NUMERATOR = -1
FMADD_RATIONAL_IM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMADD_RATIONAL_IMRM_0(MA(J),MB,FMADD_RATIONAL_IM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IM1RM
FUNCTION FMADD_RATIONAL_RM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2RM2%NUMERATOR = -1
FMADD_RATIONAL_RM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMRM_0(MA(J,K),MB(J,K),FMADD_RATIONAL_RM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2RM2
FUNCTION FMADD_RATIONAL_RM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2RM%NUMERATOR = -1
FMADD_RATIONAL_RM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMRM_0(MA(J,K),MB,FMADD_RATIONAL_RM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2RM
FUNCTION FMADD_RATIONAL_RMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMADD_RATIONAL_RMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMRM2%NUMERATOR = -1
FMADD_RATIONAL_RMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMADD_RATIONAL_RMRM_0(MA,MB(J,K),FMADD_RATIONAL_RMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMRM2
FUNCTION FMADD_RATIONAL_I2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_I2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_I2RM2%NUMERATOR = -1
FMADD_RATIONAL_I2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_I2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_I2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_IRM_0(MA(J,K),MB(J,K),FMADD_RATIONAL_I2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_I2RM2
FUNCTION FMADD_RATIONAL_RM2I2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2I2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2I2%NUMERATOR = -1
FMADD_RATIONAL_RM2I2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM2I2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM2I2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMI_0(MA(J,K),MB(J,K),FMADD_RATIONAL_RM2I2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2I2
FUNCTION FMADD_RATIONAL_IRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMADD_RATIONAL_IRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IRM2%NUMERATOR = -1
FMADD_RATIONAL_IRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMADD_RATIONAL_IRM_0(MA,MB(J,K),FMADD_RATIONAL_IRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IRM2
FUNCTION FMADD_RATIONAL_RM2I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2I
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2I%NUMERATOR = -1
FMADD_RATIONAL_RM2I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMI_0(MA(J,K),MB,FMADD_RATIONAL_RM2I(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2I
FUNCTION FMADD_RATIONAL_RMI2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMADD_RATIONAL_RMI2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMI2%NUMERATOR = -1
FMADD_RATIONAL_RMI2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMADD_RATIONAL_RMI_0(MA,MB(J,K),FMADD_RATIONAL_RMI2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMI2
FUNCTION FMADD_RATIONAL_I2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_I2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_I2RM%NUMERATOR = -1
FMADD_RATIONAL_I2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_IRM_0(MA(J,K),MB,FMADD_RATIONAL_I2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_I2RM
FUNCTION FMADD_RATIONAL_IM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_IM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IM2RM2%NUMERATOR = -1
FMADD_RATIONAL_IM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_IM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_IM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_IMRM_0(MA(J,K),MB(J,K),FMADD_RATIONAL_IM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IM2RM2
FUNCTION FMADD_RATIONAL_RM2IM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2IM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2IM2%NUMERATOR = -1
FMADD_RATIONAL_RM2IM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMADD_RATIONAL_RM2IM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMADD_RATIONAL_RM2IM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMIM_0(MA(J,K),MB(J,K),FMADD_RATIONAL_RM2IM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2IM2
FUNCTION FMADD_RATIONAL_IMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMADD_RATIONAL_IMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IMRM2%NUMERATOR = -1
FMADD_RATIONAL_IMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMADD_RATIONAL_IMRM_0(MA,MB(J,K),FMADD_RATIONAL_IMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IMRM2
FUNCTION FMADD_RATIONAL_RM2IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_RM2IM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RM2IM%NUMERATOR = -1
FMADD_RATIONAL_RM2IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_RMIM_0(MA(J,K),MB,FMADD_RATIONAL_RM2IM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RM2IM
FUNCTION FMADD_RATIONAL_RMIM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMADD_RATIONAL_RMIM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_RMIM2%NUMERATOR = -1
FMADD_RATIONAL_RMIM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMADD_RATIONAL_RMIM_0(MA,MB(J,K),FMADD_RATIONAL_RMIM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_RMIM2
FUNCTION FMADD_RATIONAL_IM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMADD_RATIONAL_IM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMADD_RATIONAL_IM2RM%NUMERATOR = -1
FMADD_RATIONAL_IM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMADD_RATIONAL_IMRM_0(MA(J,K),MB,FMADD_RATIONAL_IM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMADD_RATIONAL_IM2RM
END MODULE FM_RATIONAL_ARITHMETIC_2
MODULE FM_RATIONAL_ARITHMETIC_3
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (-)
MODULE PROCEDURE FMSUB_RATIONAL_RM
MODULE PROCEDURE FMSUB_RATIONAL_RM1
MODULE PROCEDURE FMSUB_RATIONAL_RM2
MODULE PROCEDURE FMSUB_RATIONAL_RMRM
MODULE PROCEDURE FMSUB_RATIONAL_IRM
MODULE PROCEDURE FMSUB_RATIONAL_RMI
MODULE PROCEDURE FMSUB_RATIONAL_IMRM
MODULE PROCEDURE FMSUB_RATIONAL_RMIM
MODULE PROCEDURE FMSUB_RATIONAL_RM1RM1
MODULE PROCEDURE FMSUB_RATIONAL_RM1RM
MODULE PROCEDURE FMSUB_RATIONAL_RMRM1
MODULE PROCEDURE FMSUB_RATIONAL_I1RM1
MODULE PROCEDURE FMSUB_RATIONAL_RM1I1
MODULE PROCEDURE FMSUB_RATIONAL_I1RM
MODULE PROCEDURE FMSUB_RATIONAL_RMI1
MODULE PROCEDURE FMSUB_RATIONAL_IRM1
MODULE PROCEDURE FMSUB_RATIONAL_RM1I
MODULE PROCEDURE FMSUB_RATIONAL_IM1RM1
MODULE PROCEDURE FMSUB_RATIONAL_IM1RM
MODULE PROCEDURE FMSUB_RATIONAL_IMRM1
MODULE PROCEDURE FMSUB_RATIONAL_RM1IM1
MODULE PROCEDURE FMSUB_RATIONAL_RM1IM
MODULE PROCEDURE FMSUB_RATIONAL_RMIM1
MODULE PROCEDURE FMSUB_RATIONAL_RM2RM2
MODULE PROCEDURE FMSUB_RATIONAL_RM2RM
MODULE PROCEDURE FMSUB_RATIONAL_RMRM2
MODULE PROCEDURE FMSUB_RATIONAL_I2RM2
MODULE PROCEDURE FMSUB_RATIONAL_I2RM
MODULE PROCEDURE FMSUB_RATIONAL_IRM2
MODULE PROCEDURE FMSUB_RATIONAL_RM2I2
MODULE PROCEDURE FMSUB_RATIONAL_RM2I
MODULE PROCEDURE FMSUB_RATIONAL_RMI2
MODULE PROCEDURE FMSUB_RATIONAL_IM2RM2
MODULE PROCEDURE FMSUB_RATIONAL_IM2RM
MODULE PROCEDURE FMSUB_RATIONAL_IMRM2
MODULE PROCEDURE FMSUB_RATIONAL_RM2IM2
MODULE PROCEDURE FMSUB_RATIONAL_RM2IM
MODULE PROCEDURE FMSUB_RATIONAL_RMIM2
END INTERFACE
CONTAINS
! -
FUNCTION FMSUB_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMSUB_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FMEQ_RATIONAL(MA,FMSUB_RATIONAL_RM)
MWK(START(FMSUB_RATIONAL_RM%NUMERATOR)) = -MWK(START(FMSUB_RATIONAL_RM%NUMERATOR))
IF (MWK(START(FMSUB_RATIONAL_RM%DENOMINATOR)) < 0) THEN
MWK(START(FMSUB_RATIONAL_RM%DENOMINATOR)) = 1
MWK(START(FMSUB_RATIONAL_RM%NUMERATOR)) = -MWK(START(FMSUB_RATIONAL_RM%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM
FUNCTION FMSUB_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMSUB_RATIONAL_RM1%NUMERATOR = -1
FMSUB_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMEQ_RATIONAL(MA(J),FMSUB_RATIONAL_RM1(J))
IF (MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR)+2) /= MUNKNO .AND. &
MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR)+3) /= 0) THEN
MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR)) = &
-MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR))
ENDIF
IF (MWK(START(FMSUB_RATIONAL_RM1(J)%DENOMINATOR)) < 0) THEN
MWK(START(FMSUB_RATIONAL_RM1(J)%DENOMINATOR)) = 1
MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR)) = &
-MWK(START(FMSUB_RATIONAL_RM1(J)%NUMERATOR))
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1
FUNCTION FMSUB_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMSUB_RATIONAL_RM2%NUMERATOR = -1
FMSUB_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMEQ_RATIONAL(MA(J,K),FMSUB_RATIONAL_RM2(J,K))
IF (MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR)+2) /= MUNKNO .AND. &
MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR)+3) /= 0) THEN
MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR)) = &
-MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR))
ENDIF
IF (MWK(START(FMSUB_RATIONAL_RM2(J,K)%DENOMINATOR)) < 0) THEN
MWK(START(FMSUB_RATIONAL_RM2(J,K)%DENOMINATOR)) = 1
MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR)) = &
-MWK(START(FMSUB_RATIONAL_RM2(J,K)%NUMERATOR))
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2
FUNCTION FMSUB_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMSUB_RATIONAL_RMRM
INTENT (IN) :: MA,MB
CALL FMSUB_RATIONAL_RMRM_0(MA,MB,FMSUB_RATIONAL_RMRM)
END FUNCTION FMSUB_RATIONAL_RMRM
SUBROUTINE FMSUB_RATIONAL_RMI_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
INTEGER :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_SUB(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMSUB_RATIONAL_RMI_0
FUNCTION FMSUB_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMSUB_RATIONAL_RMI
INTEGER :: MB
INTENT (IN) :: MA,MB
CALL FMSUB_RATIONAL_RMI_0(MA,MB,FMSUB_RATIONAL_RMI)
END FUNCTION FMSUB_RATIONAL_RMI
SUBROUTINE FMSUB_RATIONAL_IRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
INTEGER :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_SUB(R_5,R_1,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMSUB_RATIONAL_IRM_0
FUNCTION FMSUB_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMSUB_RATIONAL_IRM
INTEGER :: MA
INTENT (IN) :: MA,MB
CALL FMSUB_RATIONAL_IRM_0(MA,MB,FMSUB_RATIONAL_IRM)
END FUNCTION FMSUB_RATIONAL_IRM
SUBROUTINE FMSUB_RATIONAL_RMIM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_SUB(R_1,R_5,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMSUB_RATIONAL_RMIM_0
FUNCTION FMSUB_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMSUB_RATIONAL_RMIM
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
CALL FMSUB_RATIONAL_RMIM_0(MA,MB,FMSUB_RATIONAL_RMIM)
END FUNCTION FMSUB_RATIONAL_RMIM
SUBROUTINE FMSUB_RATIONAL_IMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
CALL IM_SUB(R_5,R_1,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMSUB_RATIONAL_IMRM_0
FUNCTION FMSUB_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMSUB_RATIONAL_IMRM
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
CALL FMSUB_RATIONAL_IMRM_0(MA,MB,FMSUB_RATIONAL_IMRM)
END FUNCTION FMSUB_RATIONAL_IMRM
FUNCTION FMSUB_RATIONAL_RM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1RM1%NUMERATOR = -1
FMSUB_RATIONAL_RM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMRM_0(MA(J),MB(J),FMSUB_RATIONAL_RM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1RM1
FUNCTION FMSUB_RATIONAL_RM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1RM%NUMERATOR = -1
FMSUB_RATIONAL_RM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMRM_0(MA(J),MB,FMSUB_RATIONAL_RM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1RM
FUNCTION FMSUB_RATIONAL_RMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMSUB_RATIONAL_RMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMRM1%NUMERATOR = -1
FMSUB_RATIONAL_RMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMSUB_RATIONAL_RMRM_0(MA,MB(J),FMSUB_RATIONAL_RMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMRM1
FUNCTION FMSUB_RATIONAL_I1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_I1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_I1RM1%NUMERATOR = -1
FMSUB_RATIONAL_I1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_I1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_I1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_IRM_0(MA(J),MB(J),FMSUB_RATIONAL_I1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_I1RM1
FUNCTION FMSUB_RATIONAL_RM1I1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1I1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1I1%NUMERATOR = -1
FMSUB_RATIONAL_RM1I1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM1I1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM1I1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMI_0(MA(J),MB(J),FMSUB_RATIONAL_RM1I1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1I1
FUNCTION FMSUB_RATIONAL_IRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMSUB_RATIONAL_IRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IRM1%NUMERATOR = -1
FMSUB_RATIONAL_IRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMSUB_RATIONAL_IRM_0(MA,MB(J),FMSUB_RATIONAL_IRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IRM1
FUNCTION FMSUB_RATIONAL_RM1I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1I
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1I%NUMERATOR = -1
FMSUB_RATIONAL_RM1I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMI_0(MA(J),MB,FMSUB_RATIONAL_RM1I(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1I
FUNCTION FMSUB_RATIONAL_RMI1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMSUB_RATIONAL_RMI1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMI1%NUMERATOR = -1
FMSUB_RATIONAL_RMI1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB)
CALL FMSUB_RATIONAL_RMI_0(MA,MB(J),FMSUB_RATIONAL_RMI1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMI1
FUNCTION FMSUB_RATIONAL_I1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_I1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_I1RM%NUMERATOR = -1
FMSUB_RATIONAL_I1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_IRM_0(MA(J),MB,FMSUB_RATIONAL_I1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_I1RM
FUNCTION FMSUB_RATIONAL_IM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_IM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IM1RM1%NUMERATOR = -1
FMSUB_RATIONAL_IM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_IM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_IM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_IMRM_0(MA(J),MB(J),FMSUB_RATIONAL_IM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IM1RM1
FUNCTION FMSUB_RATIONAL_RM1IM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1IM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1IM1%NUMERATOR = -1
FMSUB_RATIONAL_RM1IM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM1IM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM1IM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMIM_0(MA(J),MB(J),FMSUB_RATIONAL_RM1IM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1IM1
FUNCTION FMSUB_RATIONAL_IMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMSUB_RATIONAL_IMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IMRM1%NUMERATOR = -1
FMSUB_RATIONAL_IMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMSUB_RATIONAL_IMRM_0(MA,MB(J),FMSUB_RATIONAL_IMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IMRM1
FUNCTION FMSUB_RATIONAL_RM1IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_RM1IM
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM1IM%NUMERATOR = -1
FMSUB_RATIONAL_RM1IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMIM_0(MA(J),MB,FMSUB_RATIONAL_RM1IM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM1IM
FUNCTION FMSUB_RATIONAL_RMIM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMSUB_RATIONAL_RMIM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMIM1%NUMERATOR = -1
FMSUB_RATIONAL_RMIM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMSUB_RATIONAL_RMIM_0(MA,MB(J),FMSUB_RATIONAL_RMIM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMIM1
FUNCTION FMSUB_RATIONAL_IM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMSUB_RATIONAL_IM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IM1RM%NUMERATOR = -1
FMSUB_RATIONAL_IM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_IMRM_0(MA(J),MB,FMSUB_RATIONAL_IM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IM1RM
FUNCTION FMSUB_RATIONAL_RM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2RM2%NUMERATOR = -1
FMSUB_RATIONAL_RM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMRM_0(MA(J,K),MB(J,K),FMSUB_RATIONAL_RM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2RM2
FUNCTION FMSUB_RATIONAL_RM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2RM%NUMERATOR = -1
FMSUB_RATIONAL_RM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMRM_0(MA(J,K),MB,FMSUB_RATIONAL_RM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2RM
FUNCTION FMSUB_RATIONAL_RMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMSUB_RATIONAL_RMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMRM2%NUMERATOR = -1
FMSUB_RATIONAL_RMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMSUB_RATIONAL_RMRM_0(MA,MB(J,K),FMSUB_RATIONAL_RMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMRM2
FUNCTION FMSUB_RATIONAL_I2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_I2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_I2RM2%NUMERATOR = -1
FMSUB_RATIONAL_I2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_I2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_I2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_IRM_0(MA(J,K),MB(J,K),FMSUB_RATIONAL_I2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_I2RM2
FUNCTION FMSUB_RATIONAL_RM2I2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2I2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2I2%NUMERATOR = -1
FMSUB_RATIONAL_RM2I2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM2I2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM2I2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMI_0(MA(J,K),MB(J,K),FMSUB_RATIONAL_RM2I2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2I2
FUNCTION FMSUB_RATIONAL_IRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMSUB_RATIONAL_IRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IRM2%NUMERATOR = -1
FMSUB_RATIONAL_IRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMSUB_RATIONAL_IRM_0(MA,MB(J,K),FMSUB_RATIONAL_IRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IRM2
FUNCTION FMSUB_RATIONAL_RM2I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2I
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2I%NUMERATOR = -1
FMSUB_RATIONAL_RM2I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMI_0(MA(J,K),MB,FMSUB_RATIONAL_RM2I(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2I
FUNCTION FMSUB_RATIONAL_RMI2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMSUB_RATIONAL_RMI2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMI2%NUMERATOR = -1
FMSUB_RATIONAL_RMI2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMSUB_RATIONAL_RMI_0(MA,MB(J,K),FMSUB_RATIONAL_RMI2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMI2
FUNCTION FMSUB_RATIONAL_I2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_I2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_I2RM%NUMERATOR = -1
FMSUB_RATIONAL_I2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_IRM_0(MA(J,K),MB,FMSUB_RATIONAL_I2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_I2RM
FUNCTION FMSUB_RATIONAL_IM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_IM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IM2RM2%NUMERATOR = -1
FMSUB_RATIONAL_IM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_IM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_IM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_IMRM_0(MA(J,K),MB(J,K),FMSUB_RATIONAL_IM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IM2RM2
FUNCTION FMSUB_RATIONAL_RM2IM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2IM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2IM2%NUMERATOR = -1
FMSUB_RATIONAL_RM2IM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMSUB_RATIONAL_RM2IM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMSUB_RATIONAL_RM2IM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMIM_0(MA(J,K),MB(J,K),FMSUB_RATIONAL_RM2IM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2IM2
FUNCTION FMSUB_RATIONAL_IMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMSUB_RATIONAL_IMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IMRM2%NUMERATOR = -1
FMSUB_RATIONAL_IMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMSUB_RATIONAL_IMRM_0(MA,MB(J,K),FMSUB_RATIONAL_IMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IMRM2
FUNCTION FMSUB_RATIONAL_RM2IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_RM2IM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RM2IM%NUMERATOR = -1
FMSUB_RATIONAL_RM2IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMIM_0(MA(J,K),MB,FMSUB_RATIONAL_RM2IM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RM2IM
FUNCTION FMSUB_RATIONAL_RMIM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMSUB_RATIONAL_RMIM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_RMIM2%NUMERATOR = -1
FMSUB_RATIONAL_RMIM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMSUB_RATIONAL_RMIM_0(MA,MB(J,K),FMSUB_RATIONAL_RMIM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_RMIM2
FUNCTION FMSUB_RATIONAL_IM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMSUB_RATIONAL_IM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMSUB_RATIONAL_IM2RM%NUMERATOR = -1
FMSUB_RATIONAL_IM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_IMRM_0(MA(J,K),MB,FMSUB_RATIONAL_IM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUB_RATIONAL_IM2RM
END MODULE FM_RATIONAL_ARITHMETIC_3
MODULE FM_RATIONAL_ARITHMETIC_4
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (*)
MODULE PROCEDURE FMMPY_RATIONAL_RMRM
MODULE PROCEDURE FMMPY_RATIONAL_IRM
MODULE PROCEDURE FMMPY_RATIONAL_RMI
MODULE PROCEDURE FMMPY_RATIONAL_IMRM
MODULE PROCEDURE FMMPY_RATIONAL_RMIM
MODULE PROCEDURE FMMPY_RATIONAL_RM1RM1
MODULE PROCEDURE FMMPY_RATIONAL_RM1RM
MODULE PROCEDURE FMMPY_RATIONAL_RMRM1
MODULE PROCEDURE FMMPY_RATIONAL_I1RM1
MODULE PROCEDURE FMMPY_RATIONAL_RM1I1
MODULE PROCEDURE FMMPY_RATIONAL_I1RM
MODULE PROCEDURE FMMPY_RATIONAL_RMI1
MODULE PROCEDURE FMMPY_RATIONAL_IRM1
MODULE PROCEDURE FMMPY_RATIONAL_RM1I
MODULE PROCEDURE FMMPY_RATIONAL_IM1RM1
MODULE PROCEDURE FMMPY_RATIONAL_IM1RM
MODULE PROCEDURE FMMPY_RATIONAL_IMRM1
MODULE PROCEDURE FMMPY_RATIONAL_RM1IM1
MODULE PROCEDURE FMMPY_RATIONAL_RM1IM
MODULE PROCEDURE FMMPY_RATIONAL_RMIM1
MODULE PROCEDURE FMMPY_RATIONAL_RM2RM2
MODULE PROCEDURE FMMPY_RATIONAL_RM2RM
MODULE PROCEDURE FMMPY_RATIONAL_RMRM2
MODULE PROCEDURE FMMPY_RATIONAL_I2RM2
MODULE PROCEDURE FMMPY_RATIONAL_I2RM
MODULE PROCEDURE FMMPY_RATIONAL_IRM2
MODULE PROCEDURE FMMPY_RATIONAL_RM2I2
MODULE PROCEDURE FMMPY_RATIONAL_RM2I
MODULE PROCEDURE FMMPY_RATIONAL_RMI2
MODULE PROCEDURE FMMPY_RATIONAL_IM2RM2
MODULE PROCEDURE FMMPY_RATIONAL_IM2RM
MODULE PROCEDURE FMMPY_RATIONAL_IMRM2
MODULE PROCEDURE FMMPY_RATIONAL_RM2IM2
MODULE PROCEDURE FMMPY_RATIONAL_RM2IM
MODULE PROCEDURE FMMPY_RATIONAL_RMIM2
END INTERFACE
CONTAINS
! *
FUNCTION FMMPY_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMMPY_RATIONAL_RMRM
INTENT (IN) :: MA,MB
CALL FMMPY_RATIONAL_RMRM_0(MA,MB,FMMPY_RATIONAL_RMRM)
END FUNCTION FMMPY_RATIONAL_RMRM
SUBROUTINE FMMPY_RATIONAL_RMI_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
INTEGER :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_1,R_3,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMPY_RATIONAL_RMI_0
FUNCTION FMMPY_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMMPY_RATIONAL_RMI
INTEGER :: MB
INTENT (IN) :: MA,MB
CALL FMMPY_RATIONAL_RMI_0(MA,MB,FMMPY_RATIONAL_RMI)
END FUNCTION FMMPY_RATIONAL_RMI
SUBROUTINE FMMPY_RATIONAL_IRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
INTEGER :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_1,R_3,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMPY_RATIONAL_IRM_0
FUNCTION FMMPY_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMMPY_RATIONAL_IRM
INTEGER :: MA
INTENT (IN) :: MA,MB
CALL FMMPY_RATIONAL_IRM_0(MA,MB,FMMPY_RATIONAL_IRM)
END FUNCTION FMMPY_RATIONAL_IRM
SUBROUTINE FMMPY_RATIONAL_RMIM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_1,R_3,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMPY_RATIONAL_RMIM_0
FUNCTION FMMPY_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMMPY_RATIONAL_RMIM
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
CALL FMMPY_RATIONAL_RMIM_0(MA,MB,FMMPY_RATIONAL_RMIM)
END FUNCTION FMMPY_RATIONAL_RMIM
SUBROUTINE FMMPY_RATIONAL_IMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_1,R_3,R_4)
CALL FM_MAX_EXP_IM(R_2,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_2%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_2%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_2,R_4,R_1)
CALL IMDIV(R_4%MIM,R_1%MIM,MC%NUMERATOR)
CALL IMDIV(R_2%MIM,R_1%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMPY_RATIONAL_IMRM_0
FUNCTION FMMPY_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMMPY_RATIONAL_IMRM
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
CALL FMMPY_RATIONAL_IMRM_0(MA,MB,FMMPY_RATIONAL_IMRM)
END FUNCTION FMMPY_RATIONAL_IMRM
FUNCTION FMMPY_RATIONAL_RM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1RM1%NUMERATOR = -1
FMMPY_RATIONAL_RM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMRM_0(MA(J),MB(J),FMMPY_RATIONAL_RM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1RM1
FUNCTION FMMPY_RATIONAL_RM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1RM%NUMERATOR = -1
FMMPY_RATIONAL_RM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMRM_0(MA(J),MB,FMMPY_RATIONAL_RM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1RM
FUNCTION FMMPY_RATIONAL_RMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMMPY_RATIONAL_RMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMRM1%NUMERATOR = -1
FMMPY_RATIONAL_RMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMMPY_RATIONAL_RMRM_0(MA,MB(J),FMMPY_RATIONAL_RMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMRM1
FUNCTION FMMPY_RATIONAL_I1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_I1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_I1RM1%NUMERATOR = -1
FMMPY_RATIONAL_I1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_I1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_I1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_IRM_0(MA(J),MB(J),FMMPY_RATIONAL_I1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_I1RM1
FUNCTION FMMPY_RATIONAL_RM1I1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1I1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1I1%NUMERATOR = -1
FMMPY_RATIONAL_RM1I1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM1I1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM1I1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMI_0(MA(J),MB(J),FMMPY_RATIONAL_RM1I1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1I1
FUNCTION FMMPY_RATIONAL_IRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMMPY_RATIONAL_IRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IRM1%NUMERATOR = -1
FMMPY_RATIONAL_IRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMMPY_RATIONAL_IRM_0(MA,MB(J),FMMPY_RATIONAL_IRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IRM1
FUNCTION FMMPY_RATIONAL_RM1I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1I
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1I%NUMERATOR = -1
FMMPY_RATIONAL_RM1I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMI_0(MA(J),MB,FMMPY_RATIONAL_RM1I(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1I
FUNCTION FMMPY_RATIONAL_RMI1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMMPY_RATIONAL_RMI1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMI1%NUMERATOR = -1
FMMPY_RATIONAL_RMI1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB)
CALL FMMPY_RATIONAL_RMI_0(MA,MB(J),FMMPY_RATIONAL_RMI1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMI1
FUNCTION FMMPY_RATIONAL_I1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_I1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_I1RM%NUMERATOR = -1
FMMPY_RATIONAL_I1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_IRM_0(MA(J),MB,FMMPY_RATIONAL_I1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_I1RM
FUNCTION FMMPY_RATIONAL_IM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_IM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IM1RM1%NUMERATOR = -1
FMMPY_RATIONAL_IM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_IM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_IM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_IMRM_0(MA(J),MB(J),FMMPY_RATIONAL_IM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IM1RM1
FUNCTION FMMPY_RATIONAL_RM1IM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1IM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1IM1%NUMERATOR = -1
FMMPY_RATIONAL_RM1IM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM1IM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM1IM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMIM_0(MA(J),MB(J),FMMPY_RATIONAL_RM1IM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1IM1
FUNCTION FMMPY_RATIONAL_IMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMMPY_RATIONAL_IMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IMRM1%NUMERATOR = -1
FMMPY_RATIONAL_IMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMMPY_RATIONAL_IMRM_0(MA,MB(J),FMMPY_RATIONAL_IMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IMRM1
FUNCTION FMMPY_RATIONAL_RM1IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_RM1IM
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM1IM%NUMERATOR = -1
FMMPY_RATIONAL_RM1IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_RMIM_0(MA(J),MB,FMMPY_RATIONAL_RM1IM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM1IM
FUNCTION FMMPY_RATIONAL_RMIM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMMPY_RATIONAL_RMIM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMIM1%NUMERATOR = -1
FMMPY_RATIONAL_RMIM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMMPY_RATIONAL_RMIM_0(MA,MB(J),FMMPY_RATIONAL_RMIM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMIM1
FUNCTION FMMPY_RATIONAL_IM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMPY_RATIONAL_IM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IM1RM%NUMERATOR = -1
FMMPY_RATIONAL_IM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMMPY_RATIONAL_IMRM_0(MA(J),MB,FMMPY_RATIONAL_IM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IM1RM
FUNCTION FMMPY_RATIONAL_RM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2RM2%NUMERATOR = -1
FMMPY_RATIONAL_RM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMRM_0(MA(J,K),MB(J,K),FMMPY_RATIONAL_RM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2RM2
FUNCTION FMMPY_RATIONAL_RM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2RM%NUMERATOR = -1
FMMPY_RATIONAL_RM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMRM_0(MA(J,K),MB,FMMPY_RATIONAL_RM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2RM
FUNCTION FMMPY_RATIONAL_RMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMMPY_RATIONAL_RMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMRM2%NUMERATOR = -1
FMMPY_RATIONAL_RMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMMPY_RATIONAL_RMRM_0(MA,MB(J,K),FMMPY_RATIONAL_RMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMRM2
FUNCTION FMMPY_RATIONAL_I2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_I2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_I2RM2%NUMERATOR = -1
FMMPY_RATIONAL_I2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_I2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_I2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_IRM_0(MA(J,K),MB(J,K),FMMPY_RATIONAL_I2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_I2RM2
FUNCTION FMMPY_RATIONAL_RM2I2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2I2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2I2%NUMERATOR = -1
FMMPY_RATIONAL_RM2I2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM2I2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM2I2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMI_0(MA(J,K),MB(J,K),FMMPY_RATIONAL_RM2I2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2I2
FUNCTION FMMPY_RATIONAL_IRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMMPY_RATIONAL_IRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IRM2%NUMERATOR = -1
FMMPY_RATIONAL_IRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMMPY_RATIONAL_IRM_0(MA,MB(J,K),FMMPY_RATIONAL_IRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IRM2
FUNCTION FMMPY_RATIONAL_RM2I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2I
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2I%NUMERATOR = -1
FMMPY_RATIONAL_RM2I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMI_0(MA(J,K),MB,FMMPY_RATIONAL_RM2I(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2I
FUNCTION FMMPY_RATIONAL_RMI2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMMPY_RATIONAL_RMI2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMI2%NUMERATOR = -1
FMMPY_RATIONAL_RMI2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMMPY_RATIONAL_RMI_0(MA,MB(J,K),FMMPY_RATIONAL_RMI2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMI2
FUNCTION FMMPY_RATIONAL_I2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_I2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_I2RM%NUMERATOR = -1
FMMPY_RATIONAL_I2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_IRM_0(MA(J,K),MB,FMMPY_RATIONAL_I2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_I2RM
FUNCTION FMMPY_RATIONAL_IM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_IM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IM2RM2%NUMERATOR = -1
FMMPY_RATIONAL_IM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_IM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_IM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_IMRM_0(MA(J,K),MB(J,K),FMMPY_RATIONAL_IM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IM2RM2
FUNCTION FMMPY_RATIONAL_RM2IM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2IM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2IM2%NUMERATOR = -1
FMMPY_RATIONAL_RM2IM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMMPY_RATIONAL_RM2IM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMPY_RATIONAL_RM2IM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMIM_0(MA(J,K),MB(J,K),FMMPY_RATIONAL_RM2IM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2IM2
FUNCTION FMMPY_RATIONAL_IMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMMPY_RATIONAL_IMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IMRM2%NUMERATOR = -1
FMMPY_RATIONAL_IMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMMPY_RATIONAL_IMRM_0(MA,MB(J,K),FMMPY_RATIONAL_IMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IMRM2
FUNCTION FMMPY_RATIONAL_RM2IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_RM2IM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RM2IM%NUMERATOR = -1
FMMPY_RATIONAL_RM2IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_RMIM_0(MA(J,K),MB,FMMPY_RATIONAL_RM2IM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RM2IM
FUNCTION FMMPY_RATIONAL_RMIM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMMPY_RATIONAL_RMIM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_RMIM2%NUMERATOR = -1
FMMPY_RATIONAL_RMIM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMMPY_RATIONAL_RMIM_0(MA,MB(J,K),FMMPY_RATIONAL_RMIM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_RMIM2
FUNCTION FMMPY_RATIONAL_IM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMPY_RATIONAL_IM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMMPY_RATIONAL_IM2RM%NUMERATOR = -1
FMMPY_RATIONAL_IM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMMPY_RATIONAL_IMRM_0(MA(J,K),MB,FMMPY_RATIONAL_IM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMPY_RATIONAL_IM2RM
END MODULE FM_RATIONAL_ARITHMETIC_4
MODULE FM_RATIONAL_ARITHMETIC_5
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (/)
MODULE PROCEDURE FMDIV_RATIONAL_RMRM
MODULE PROCEDURE FMDIV_RATIONAL_IRM
MODULE PROCEDURE FMDIV_RATIONAL_RMI
MODULE PROCEDURE FMDIV_RATIONAL_IMRM
MODULE PROCEDURE FMDIV_RATIONAL_RMIM
MODULE PROCEDURE FMDIV_RATIONAL_RM1RM1
MODULE PROCEDURE FMDIV_RATIONAL_RM1RM
MODULE PROCEDURE FMDIV_RATIONAL_RMRM1
MODULE PROCEDURE FMDIV_RATIONAL_I1RM1
MODULE PROCEDURE FMDIV_RATIONAL_RM1I1
MODULE PROCEDURE FMDIV_RATIONAL_I1RM
MODULE PROCEDURE FMDIV_RATIONAL_RMI1
MODULE PROCEDURE FMDIV_RATIONAL_IRM1
MODULE PROCEDURE FMDIV_RATIONAL_RM1I
MODULE PROCEDURE FMDIV_RATIONAL_IM1RM1
MODULE PROCEDURE FMDIV_RATIONAL_IM1RM
MODULE PROCEDURE FMDIV_RATIONAL_IMRM1
MODULE PROCEDURE FMDIV_RATIONAL_RM1IM1
MODULE PROCEDURE FMDIV_RATIONAL_RM1IM
MODULE PROCEDURE FMDIV_RATIONAL_RMIM1
MODULE PROCEDURE FMDIV_RATIONAL_RM2RM2
MODULE PROCEDURE FMDIV_RATIONAL_RM2RM
MODULE PROCEDURE FMDIV_RATIONAL_RMRM2
MODULE PROCEDURE FMDIV_RATIONAL_I2RM2
MODULE PROCEDURE FMDIV_RATIONAL_I2RM
MODULE PROCEDURE FMDIV_RATIONAL_IRM2
MODULE PROCEDURE FMDIV_RATIONAL_RM2I2
MODULE PROCEDURE FMDIV_RATIONAL_RM2I
MODULE PROCEDURE FMDIV_RATIONAL_RMI2
MODULE PROCEDURE FMDIV_RATIONAL_IM2RM2
MODULE PROCEDURE FMDIV_RATIONAL_IM2RM
MODULE PROCEDURE FMDIV_RATIONAL_IMRM2
MODULE PROCEDURE FMDIV_RATIONAL_RM2IM2
MODULE PROCEDURE FMDIV_RATIONAL_RM2IM
MODULE PROCEDURE FMDIV_RATIONAL_RMIM2
END INTERFACE
CONTAINS
! /
FUNCTION FMDIV_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMDIV_RATIONAL_RMRM
INTENT (IN) :: MA,MB
CALL FMDIV_RATIONAL_RMRM_0(MA,MB,FMDIV_RATIONAL_RMRM)
END FUNCTION FMDIV_RATIONAL_RMRM
SUBROUTINE FMDIV_RATIONAL_RMI_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
INTEGER :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_4)
CALL FM_MAX_EXP_IM(R_1,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_1%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_1%MIM,MC%NUMERATOR)
CALL IMEQ(R_4%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_1,R_4,R_5)
CALL IMDIV(R_1%MIM,R_5%MIM,MC%NUMERATOR)
CALL IMDIV(R_4%MIM,R_5%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMDIV_RATIONAL_RMI_0
FUNCTION FMDIV_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMDIV_RATIONAL_RMI
INTEGER :: MB
INTENT (IN) :: MA,MB
CALL FMDIV_RATIONAL_RMI_0(MA,MB,FMDIV_RATIONAL_RMI)
END FUNCTION FMDIV_RATIONAL_RMI
SUBROUTINE FMDIV_RATIONAL_IRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
INTEGER :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_4)
CALL FM_MAX_EXP_IM(R_1,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_1%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_1%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_1,R_4,R_5)
CALL IMDIV(R_4%MIM,R_5%MIM,MC%NUMERATOR)
CALL IMDIV(R_1%MIM,R_5%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMDIV_RATIONAL_IRM_0
FUNCTION FMDIV_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMDIV_RATIONAL_IRM
INTEGER :: MA
INTENT (IN) :: MA,MB
CALL FMDIV_RATIONAL_IRM_0(MA,MB,FMDIV_RATIONAL_IRM)
END FUNCTION FMDIV_RATIONAL_IRM
SUBROUTINE FMDIV_RATIONAL_RMIM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MC
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_4)
CALL FM_MAX_EXP_IM(R_1,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_1%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_1%MIM,MC%NUMERATOR)
CALL IMEQ(R_4%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_1,R_4,R_5)
CALL IMDIV(R_1%MIM,R_5%MIM,MC%NUMERATOR)
CALL IMDIV(R_4%MIM,R_5%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMDIV_RATIONAL_RMIM_0
FUNCTION FMDIV_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMDIV_RATIONAL_RMIM
TYPE (IM) :: MB
INTENT (IN) :: MA,MB
CALL FMDIV_RATIONAL_RMIM_0(MA,MB,FMDIV_RATIONAL_RMIM)
END FUNCTION FMDIV_RATIONAL_RMIM
SUBROUTINE FMDIV_RATIONAL_IMRM_0(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,MC
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_4)
CALL FM_MAX_EXP_IM(R_1,R_4)
IF (SKIP_GCD .AND. MAX(MWK(START(R_1%MIM)+2),MWK(START(R_4%MIM)+2)) < RATIONAL_SKIP_MAX) THEN
CALL IMEQ(R_4%MIM,MC%NUMERATOR)
CALL IMEQ(R_1%MIM,MC%DENOMINATOR)
ELSE
CALL IM_GCD(R_1,R_4,R_5)
CALL IMDIV(R_4%MIM,R_5%MIM,MC%NUMERATOR)
CALL IMDIV(R_1%MIM,R_5%MIM,MC%DENOMINATOR)
ENDIF
IF (MWK(START(MC%DENOMINATOR)) < 0) THEN
MWK(START(MC%DENOMINATOR)) = 1
MWK(START(MC%NUMERATOR)) = -MWK(START(MC%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMDIV_RATIONAL_IMRM_0
FUNCTION FMDIV_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MB,FMDIV_RATIONAL_IMRM
TYPE (IM) :: MA
INTENT (IN) :: MA,MB
CALL FMDIV_RATIONAL_IMRM_0(MA,MB,FMDIV_RATIONAL_IMRM)
END FUNCTION FMDIV_RATIONAL_IMRM
FUNCTION FMDIV_RATIONAL_RM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1RM1%NUMERATOR = -1
FMDIV_RATIONAL_RM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMRM_0(MA(J),MB(J),FMDIV_RATIONAL_RM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1RM1
FUNCTION FMDIV_RATIONAL_RM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1RM%NUMERATOR = -1
FMDIV_RATIONAL_RM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMRM_0(MA(J),MB,FMDIV_RATIONAL_RM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1RM
FUNCTION FMDIV_RATIONAL_RMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMDIV_RATIONAL_RMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMRM1%NUMERATOR = -1
FMDIV_RATIONAL_RMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMDIV_RATIONAL_RMRM_0(MA,MB(J),FMDIV_RATIONAL_RMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMRM1
FUNCTION FMDIV_RATIONAL_I1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_I1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_I1RM1%NUMERATOR = -1
FMDIV_RATIONAL_I1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_I1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_I1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_IRM_0(MA(J),MB(J),FMDIV_RATIONAL_I1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_I1RM1
FUNCTION FMDIV_RATIONAL_RM1I1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1I1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1I1%NUMERATOR = -1
FMDIV_RATIONAL_RM1I1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM1I1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM1I1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMI_0(MA(J),MB(J),FMDIV_RATIONAL_RM1I1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1I1
FUNCTION FMDIV_RATIONAL_IRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMDIV_RATIONAL_IRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IRM1%NUMERATOR = -1
FMDIV_RATIONAL_IRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMDIV_RATIONAL_IRM_0(MA,MB(J),FMDIV_RATIONAL_IRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IRM1
FUNCTION FMDIV_RATIONAL_RM1I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1I
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1I%NUMERATOR = -1
FMDIV_RATIONAL_RM1I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMI_0(MA(J),MB,FMDIV_RATIONAL_RM1I(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1I
FUNCTION FMDIV_RATIONAL_RMI1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMDIV_RATIONAL_RMI1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMI1%NUMERATOR = -1
FMDIV_RATIONAL_RMI1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB)
CALL FMDIV_RATIONAL_RMI_0(MA,MB(J),FMDIV_RATIONAL_RMI1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMI1
FUNCTION FMDIV_RATIONAL_I1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_I1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_I1RM%NUMERATOR = -1
FMDIV_RATIONAL_I1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_IRM_0(MA(J),MB,FMDIV_RATIONAL_I1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_I1RM
FUNCTION FMDIV_RATIONAL_IM1RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_IM1RM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IM1RM1%NUMERATOR = -1
FMDIV_RATIONAL_IM1RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_IM1RM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_IM1RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_IMRM_0(MA(J),MB(J),FMDIV_RATIONAL_IM1RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IM1RM1
FUNCTION FMDIV_RATIONAL_RM1IM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1IM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1IM1%NUMERATOR = -1
FMDIV_RATIONAL_RM1IM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) /= SIZE(MB)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM1IM1(J)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM1IM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMIM_0(MA(J),MB(J),FMDIV_RATIONAL_RM1IM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1IM1
FUNCTION FMDIV_RATIONAL_IMRM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMDIV_RATIONAL_IMRM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IMRM1%NUMERATOR = -1
FMDIV_RATIONAL_IMRM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMDIV_RATIONAL_IMRM_0(MA,MB(J),FMDIV_RATIONAL_IMRM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IMRM1
FUNCTION FMDIV_RATIONAL_RM1IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_RM1IM
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM1IM%NUMERATOR = -1
FMDIV_RATIONAL_RM1IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMIM_0(MA(J),MB,FMDIV_RATIONAL_RM1IM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM1IM
FUNCTION FMDIV_RATIONAL_RMIM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB)) :: FMDIV_RATIONAL_RMIM1
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMIM1%NUMERATOR = -1
FMDIV_RATIONAL_RMIM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB)
CALL FMDIV_RATIONAL_RMIM_0(MA,MB(J),FMDIV_RATIONAL_RMIM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMIM1
FUNCTION FMDIV_RATIONAL_IM1RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIV_RATIONAL_IM1RM
INTEGER :: J
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IM1RM%NUMERATOR = -1
FMDIV_RATIONAL_IM1RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_IMRM_0(MA(J),MB,FMDIV_RATIONAL_IM1RM(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IM1RM
FUNCTION FMDIV_RATIONAL_RM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2RM2%NUMERATOR = -1
FMDIV_RATIONAL_RM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMRM_0(MA(J,K),MB(J,K),FMDIV_RATIONAL_RM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2RM2
FUNCTION FMDIV_RATIONAL_RM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2RM%NUMERATOR = -1
FMDIV_RATIONAL_RM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMRM_0(MA(J,K),MB,FMDIV_RATIONAL_RM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2RM
FUNCTION FMDIV_RATIONAL_RMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMDIV_RATIONAL_RMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMRM2%NUMERATOR = -1
FMDIV_RATIONAL_RMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMDIV_RATIONAL_RMRM_0(MA,MB(J,K),FMDIV_RATIONAL_RMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMRM2
FUNCTION FMDIV_RATIONAL_I2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_I2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_I2RM2%NUMERATOR = -1
FMDIV_RATIONAL_I2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_I2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_I2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_IRM_0(MA(J,K),MB(J,K),FMDIV_RATIONAL_I2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_I2RM2
FUNCTION FMDIV_RATIONAL_RM2I2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2I2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2I2%NUMERATOR = -1
FMDIV_RATIONAL_RM2I2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM2I2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM2I2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMI_0(MA(J,K),MB(J,K),FMDIV_RATIONAL_RM2I2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2I2
FUNCTION FMDIV_RATIONAL_IRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMDIV_RATIONAL_IRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IRM2%NUMERATOR = -1
FMDIV_RATIONAL_IRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMDIV_RATIONAL_IRM_0(MA,MB(J,K),FMDIV_RATIONAL_IRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IRM2
FUNCTION FMDIV_RATIONAL_RM2I(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2I
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2I%NUMERATOR = -1
FMDIV_RATIONAL_RM2I%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMI_0(MA(J,K),MB,FMDIV_RATIONAL_RM2I(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2I
FUNCTION FMDIV_RATIONAL_RMI2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
INTEGER, DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMDIV_RATIONAL_RMI2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMI2%NUMERATOR = -1
FMDIV_RATIONAL_RMI2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMDIV_RATIONAL_RMI_0(MA,MB(J,K),FMDIV_RATIONAL_RMI2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMI2
FUNCTION FMDIV_RATIONAL_I2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
INTEGER, DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_I2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_I2RM%NUMERATOR = -1
FMDIV_RATIONAL_I2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_IRM_0(MA(J,K),MB,FMDIV_RATIONAL_I2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_I2RM
FUNCTION FMDIV_RATIONAL_IM2RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_IM2RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IM2RM2%NUMERATOR = -1
FMDIV_RATIONAL_IM2RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_IM2RM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_IM2RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_IMRM_0(MA(J,K),MB(J,K),FMDIV_RATIONAL_IM2RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IM2RM2
FUNCTION FMDIV_RATIONAL_RM2IM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2IM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2IM2%NUMERATOR = -1
FMDIV_RATIONAL_RM2IM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA,DIM=1) /= SIZE(MB,DIM=1) .OR. SIZE(MA,DIM=2) /= SIZE(MB,DIM=2)) THEN
CALL IMST2M('UNKNOWN',MT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MT_RM%NUMERATOR,FMDIV_RATIONAL_RM2IM2(J,K)%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMDIV_RATIONAL_RM2IM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMIM_0(MA(J,K),MB(J,K),FMDIV_RATIONAL_RM2IM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2IM2
FUNCTION FMDIV_RATIONAL_IMRM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM) :: MA
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMDIV_RATIONAL_IMRM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IMRM2%NUMERATOR = -1
FMDIV_RATIONAL_IMRM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMDIV_RATIONAL_IMRM_0(MA,MB(J,K),FMDIV_RATIONAL_IMRM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IMRM2
FUNCTION FMDIV_RATIONAL_RM2IM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (IM) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_RM2IM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RM2IM%NUMERATOR = -1
FMDIV_RATIONAL_RM2IM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMIM_0(MA(J,K),MB,FMDIV_RATIONAL_RM2IM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RM2IM
FUNCTION FMDIV_RATIONAL_RMIM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (IM), DIMENSION(:,:) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=1),SIZE(MB,DIM=2)) :: FMDIV_RATIONAL_RMIM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_RMIM2%NUMERATOR = -1
FMDIV_RATIONAL_RMIM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MB,DIM=1)
DO K = 1, SIZE(MB,DIM=2)
CALL FMDIV_RATIONAL_RMIM_0(MA,MB(J,K),FMDIV_RATIONAL_RMIM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_RMIM2
FUNCTION FMDIV_RATIONAL_IM2RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (IM), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL) :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIV_RATIONAL_IM2RM
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMDIV_RATIONAL_IM2RM%NUMERATOR = -1
FMDIV_RATIONAL_IM2RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_IMRM_0(MA(J,K),MB,FMDIV_RATIONAL_IM2RM(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIV_RATIONAL_IM2RM
END MODULE FM_RATIONAL_ARITHMETIC_5
MODULE FM_RATIONAL_ARITHMETIC_6
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (==)
MODULE PROCEDURE FMLEQ_RATIONAL_RMRM
MODULE PROCEDURE FMLEQ_RATIONAL_RMI
MODULE PROCEDURE FMLEQ_RATIONAL_IRM
MODULE PROCEDURE FMLEQ_RATIONAL_RMIM
MODULE PROCEDURE FMLEQ_RATIONAL_IMRM
END INTERFACE
INTERFACE OPERATOR (/=)
MODULE PROCEDURE FMLNE_RATIONAL_RMRM
MODULE PROCEDURE FMLNE_RATIONAL_RMI
MODULE PROCEDURE FMLNE_RATIONAL_IRM
MODULE PROCEDURE FMLNE_RATIONAL_RMIM
MODULE PROCEDURE FMLNE_RATIONAL_IMRM
END INTERFACE
INTERFACE OPERATOR (<)
MODULE PROCEDURE FMLLT_RATIONAL_RMRM
MODULE PROCEDURE FMLLT_RATIONAL_RMI
MODULE PROCEDURE FMLLT_RATIONAL_IRM
MODULE PROCEDURE FMLLT_RATIONAL_RMIM
MODULE PROCEDURE FMLLT_RATIONAL_IMRM
END INTERFACE
INTERFACE OPERATOR (<=)
MODULE PROCEDURE FMLLE_RATIONAL_RMRM
MODULE PROCEDURE FMLLE_RATIONAL_RMI
MODULE PROCEDURE FMLLE_RATIONAL_IRM
MODULE PROCEDURE FMLLE_RATIONAL_RMIM
MODULE PROCEDURE FMLLE_RATIONAL_IMRM
END INTERFACE
INTERFACE OPERATOR (>)
MODULE PROCEDURE FMLGT_RATIONAL_RMRM
MODULE PROCEDURE FMLGT_RATIONAL_RMI
MODULE PROCEDURE FMLGT_RATIONAL_IRM
MODULE PROCEDURE FMLGT_RATIONAL_RMIM
MODULE PROCEDURE FMLGT_RATIONAL_IMRM
END INTERFACE
INTERFACE OPERATOR (>=)
MODULE PROCEDURE FMLGE_RATIONAL_RMRM
MODULE PROCEDURE FMLGE_RATIONAL_RMI
MODULE PROCEDURE FMLGE_RATIONAL_IRM
MODULE PROCEDURE FMLGE_RATIONAL_RMIM
MODULE PROCEDURE FMLGE_RATIONAL_IMRM
END INTERFACE
CONTAINS
! Logical ==
FUNCTION FMLEQ_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLEQ_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
FMLEQ_RATIONAL_RMRM = IM_COMP(R_5,'==',R_1)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLEQ_RATIONAL_RMRM
FUNCTION FMLEQ_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLEQ_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLEQ_RATIONAL_RMI = IM_COMP(R_1,'==',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLEQ_RATIONAL_RMI
FUNCTION FMLEQ_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLEQ_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLEQ_RATIONAL_IRM = IM_COMP(R_1,'==',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLEQ_RATIONAL_IRM
FUNCTION FMLEQ_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLEQ_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLEQ_RATIONAL_RMIM = IM_COMP(R_1,'==',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLEQ_RATIONAL_RMIM
FUNCTION FMLEQ_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLEQ_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLEQ_RATIONAL_IMRM = IM_COMP(R_1,'==',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLEQ_RATIONAL_IMRM
! Logical /=
FUNCTION FMLNE_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLNE_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
FMLNE_RATIONAL_RMRM = IM_COMP(R_5,'/=',R_1)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLNE_RATIONAL_RMRM
FUNCTION FMLNE_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLNE_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLNE_RATIONAL_RMI = IM_COMP(R_1,'/=',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLNE_RATIONAL_RMI
FUNCTION FMLNE_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLNE_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLNE_RATIONAL_IRM = IM_COMP(R_1,'/=',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLNE_RATIONAL_IRM
FUNCTION FMLNE_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLNE_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLNE_RATIONAL_RMIM = IM_COMP(R_1,'/=',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLNE_RATIONAL_RMIM
FUNCTION FMLNE_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLNE_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
FMLNE_RATIONAL_IMRM = IM_COMP(R_1,'/=',R_5)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLNE_RATIONAL_IMRM
! Logical <
FUNCTION FMLLT_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLT_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
FMLLT_RATIONAL_RMRM = IM_COMP(R_5,'<',R_1)
ELSE
FMLLT_RATIONAL_RMRM = IM_COMP(R_5,'>',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLT_RATIONAL_RMRM
FUNCTION FMLLT_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLT_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLT_RATIONAL_RMI = IM_COMP(R_1,'<',R_5)
ELSE
FMLLT_RATIONAL_RMI = IM_COMP(R_1,'>',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLT_RATIONAL_RMI
FUNCTION FMLLT_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLT_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLT_RATIONAL_IRM = IM_COMP(R_5,'<',R_1)
ELSE
FMLLT_RATIONAL_IRM = IM_COMP(R_5,'>',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLT_RATIONAL_IRM
FUNCTION FMLLT_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLT_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLT_RATIONAL_RMIM = IM_COMP(R_1,'<',R_5)
ELSE
FMLLT_RATIONAL_RMIM = IM_COMP(R_1,'>',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLT_RATIONAL_RMIM
FUNCTION FMLLT_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLT_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLT_RATIONAL_IMRM = IM_COMP(R_5,'<',R_1)
ELSE
FMLLT_RATIONAL_IMRM = IM_COMP(R_5,'>',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLT_RATIONAL_IMRM
! Logical <=
FUNCTION FMLLE_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLE_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
FMLLE_RATIONAL_RMRM = IM_COMP(R_5,'<=',R_1)
ELSE
FMLLE_RATIONAL_RMRM = IM_COMP(R_5,'>=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLE_RATIONAL_RMRM
FUNCTION FMLLE_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLE_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLE_RATIONAL_RMI = IM_COMP(R_1,'<=',R_5)
ELSE
FMLLE_RATIONAL_RMI = IM_COMP(R_1,'>=',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLE_RATIONAL_RMI
FUNCTION FMLLE_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLE_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLE_RATIONAL_IRM = IM_COMP(R_5,'<=',R_1)
ELSE
FMLLE_RATIONAL_IRM = IM_COMP(R_5,'>=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLE_RATIONAL_IRM
FUNCTION FMLLE_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLE_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLE_RATIONAL_RMIM = IM_COMP(R_1,'<=',R_5)
ELSE
FMLLE_RATIONAL_RMIM = IM_COMP(R_1,'>=',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLE_RATIONAL_RMIM
FUNCTION FMLLE_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLLE_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLLE_RATIONAL_IMRM = IM_COMP(R_5,'<=',R_1)
ELSE
FMLLE_RATIONAL_IMRM = IM_COMP(R_5,'>=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLLE_RATIONAL_IMRM
! Logical >
FUNCTION FMLGT_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGT_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
FMLGT_RATIONAL_RMRM = IM_COMP(R_5,'>',R_1)
ELSE
FMLGT_RATIONAL_RMRM = IM_COMP(R_5,'<',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGT_RATIONAL_RMRM
FUNCTION FMLGT_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGT_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGT_RATIONAL_RMI = IM_COMP(R_1,'>',R_5)
ELSE
FMLGT_RATIONAL_RMI = IM_COMP(R_1,'<',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGT_RATIONAL_RMI
FUNCTION FMLGT_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGT_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGT_RATIONAL_IRM = IM_COMP(R_5,'>',R_1)
ELSE
FMLGT_RATIONAL_IRM = IM_COMP(R_5,'<',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGT_RATIONAL_IRM
FUNCTION FMLGT_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGT_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGT_RATIONAL_RMIM = IM_COMP(R_1,'>',R_5)
ELSE
FMLGT_RATIONAL_RMIM = IM_COMP(R_1,'<',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGT_RATIONAL_RMIM
FUNCTION FMLGT_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGT_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGT_RATIONAL_IMRM = IM_COMP(R_5,'>',R_1)
ELSE
FMLGT_RATIONAL_IMRM = IM_COMP(R_5,'<',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGT_RATIONAL_IMRM
! Logical >=
FUNCTION FMLGE_RATIONAL_RMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGE_RATIONAL_RMRM
TYPE (FM_RATIONAL) :: MA,MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
FMLGE_RATIONAL_RMRM = IM_COMP(R_5,'>=',R_1)
ELSE
FMLGE_RATIONAL_RMRM = IM_COMP(R_5,'<=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGE_RATIONAL_RMRM
FUNCTION FMLGE_RATIONAL_RMI(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGE_RATIONAL_RMI
TYPE (FM_RATIONAL) :: MA
INTEGER :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGE_RATIONAL_RMI = IM_COMP(R_1,'>=',R_5)
ELSE
FMLGE_RATIONAL_RMI = IM_COMP(R_1,'<=',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGE_RATIONAL_RMI
FUNCTION FMLGE_RATIONAL_IRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGE_RATIONAL_IRM
TYPE (FM_RATIONAL) :: MB
INTEGER :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMI2M(MA, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGE_RATIONAL_IRM = IM_COMP(R_5,'>=',R_1)
ELSE
FMLGE_RATIONAL_IRM = IM_COMP(R_5,'<=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGE_RATIONAL_IRM
FUNCTION FMLGE_RATIONAL_RMIM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGE_RATIONAL_RMIM
TYPE (FM_RATIONAL) :: MA
TYPE(IM) :: MB
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGE_RATIONAL_RMIM = IM_COMP(R_1,'>=',R_5)
ELSE
FMLGE_RATIONAL_RMIM = IM_COMP(R_1,'<=',R_5)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGE_RATIONAL_RMIM
FUNCTION FMLGE_RATIONAL_IMRM(MA,MB)
USE FMVALS
IMPLICIT NONE
LOGICAL :: FMLGE_RATIONAL_IMRM
TYPE (FM_RATIONAL) :: MB
TYPE(IM) :: MA
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MB%NUMERATOR, R_1%MIM)
CALL IMEQ(MB%DENOMINATOR,R_2%MIM)
CALL IMEQ(MA%MIM, R_3%MIM)
CALL IM_MPY(R_2,R_3,R_5)
IF (MWK(START(R_2%MIM)) > 0) THEN
FMLGE_RATIONAL_IMRM = IM_COMP(R_5,'>=',R_1)
ELSE
FMLGE_RATIONAL_IMRM = IM_COMP(R_5,'<=',R_1)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMLGE_RATIONAL_IMRM
END MODULE FM_RATIONAL_ARITHMETIC_6
MODULE FM_RATIONAL_ARITHMETIC_7
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE OPERATOR (**)
MODULE PROCEDURE FMIPWR_RATIONAL_RM
MODULE PROCEDURE FMIPWR_RATIONAL_RM1
MODULE PROCEDURE FMIPWR_RATIONAL_RM2
END INTERFACE
INTERFACE ABS
MODULE PROCEDURE FMABS_RATIONAL_RM
MODULE PROCEDURE FMABS_RATIONAL_RM1
MODULE PROCEDURE FMABS_RATIONAL_RM2
END INTERFACE
INTERFACE CEILING
MODULE PROCEDURE FMCEILING_RATIONAL_RM
MODULE PROCEDURE FMCEILING_RATIONAL_RM1
MODULE PROCEDURE FMCEILING_RATIONAL_RM2
END INTERFACE
INTERFACE DIM
MODULE PROCEDURE FMDIM_RATIONAL_RM
MODULE PROCEDURE FMDIM_RATIONAL_RM1
MODULE PROCEDURE FMDIM_RATIONAL_RM2
END INTERFACE
INTERFACE FLOOR
MODULE PROCEDURE FMFLOOR_RATIONAL_RM
MODULE PROCEDURE FMFLOOR_RATIONAL_RM1
MODULE PROCEDURE FMFLOOR_RATIONAL_RM2
END INTERFACE
INTERFACE INT
MODULE PROCEDURE FMINT_RATIONAL_RM
MODULE PROCEDURE FMINT_RATIONAL_RM1
MODULE PROCEDURE FMINT_RATIONAL_RM2
END INTERFACE
INTERFACE IS_UNKNOWN
MODULE PROCEDURE RM_IS_UNKNOWN
MODULE PROCEDURE RM_IS_UNKNOWN1
MODULE PROCEDURE RM_IS_UNKNOWN2
END INTERFACE
INTERFACE MAX
MODULE PROCEDURE FMMAX_RATIONAL_RM
END INTERFACE
INTERFACE MIN
MODULE PROCEDURE FMMIN_RATIONAL_RM
END INTERFACE
INTERFACE MOD
MODULE PROCEDURE FMMOD_RATIONAL_RM
MODULE PROCEDURE FMMOD_RATIONAL_RM1
MODULE PROCEDURE FMMOD_RATIONAL_RM2
END INTERFACE
INTERFACE MODULO
MODULE PROCEDURE FMMODULO_RATIONAL_RM
MODULE PROCEDURE FMMODULO_RATIONAL_RM1
MODULE PROCEDURE FMMODULO_RATIONAL_RM2
END INTERFACE
INTERFACE NINT
MODULE PROCEDURE FMNINT_RATIONAL_RM
MODULE PROCEDURE FMNINT_RATIONAL_RM1
MODULE PROCEDURE FMNINT_RATIONAL_RM2
END INTERFACE
CONTAINS
! ABS
FUNCTION FMABS_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMABS_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMABS(MA%NUMERATOR,FMABS_RATIONAL_RM%NUMERATOR)
CALL IMABS(MA%DENOMINATOR,FMABS_RATIONAL_RM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMABS_RATIONAL_RM
FUNCTION FMABS_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMABS_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMABS_RATIONAL_RM1%NUMERATOR = -1
FMABS_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMABS(MA(J)%NUMERATOR,FMABS_RATIONAL_RM1(J)%NUMERATOR)
CALL IMABS(MA(J)%DENOMINATOR,FMABS_RATIONAL_RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMABS_RATIONAL_RM1
FUNCTION FMABS_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMABS_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMABS_RATIONAL_RM2%NUMERATOR = -1
FMABS_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMABS(MA(J,K)%NUMERATOR,FMABS_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMABS(MA(J,K)%DENOMINATOR,FMABS_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMABS_RATIONAL_RM2
! CEILING
FUNCTION FMCEILING_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMCEILING_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMDIVR(MA%NUMERATOR,MA%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM%NUMERATOR)
ELSE
CALL IMI2M(1,R_2%MIM)
CALL IMADD(R_1%MIM,R_2%MIM,FMCEILING_RATIONAL_RM%NUMERATOR)
ENDIF
CALL IMI2M(1,FMCEILING_RATIONAL_RM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMCEILING_RATIONAL_RM
FUNCTION FMCEILING_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMCEILING_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMCEILING_RATIONAL_RM1%NUMERATOR = -1
FMCEILING_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMDIVR(MA(J)%NUMERATOR,MA(J)%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM1(J)%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM1(J)%NUMERATOR)
ELSE
CALL IMI2M(1,R_2%MIM)
CALL IMADD(R_1%MIM,R_2%MIM,FMCEILING_RATIONAL_RM1(J)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMCEILING_RATIONAL_RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMCEILING_RATIONAL_RM1
FUNCTION FMCEILING_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMCEILING_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMCEILING_RATIONAL_RM2%NUMERATOR = -1
FMCEILING_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMDIVR(MA(J,K)%NUMERATOR,MA(J,K)%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM2(J,K)%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMEQ(R_1%MIM,FMCEILING_RATIONAL_RM2(J,K)%NUMERATOR)
ELSE
CALL IMI2M(1,R_2%MIM)
CALL IMADD(R_1%MIM,R_2%MIM,FMCEILING_RATIONAL_RM2(J,K)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMCEILING_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMCEILING_RATIONAL_RM2
! DIM
FUNCTION FMDIM_RATIONAL_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMDIM_RATIONAL_RM
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL FMSUB_RATIONAL_RMRM_0(MA,MB,FMDIM_RATIONAL_RM)
IF (MWK(START(FMDIM_RATIONAL_RM%NUMERATOR)) < 0) THEN
CALL IMI2M(0,FMDIM_RATIONAL_RM%NUMERATOR)
CALL IMI2M(1,FMDIM_RATIONAL_RM%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIM_RATIONAL_RM
FUNCTION FMDIM_RATIONAL_RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMDIM_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMDIM_RATIONAL_RM1%NUMERATOR = -1
FMDIM_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMSUB_RATIONAL_RMRM_0(MA(J),MB(J),FMDIM_RATIONAL_RM1(J))
IF (MWK(START(FMDIM_RATIONAL_RM1(J)%NUMERATOR)) < 0) THEN
CALL IMI2M(0,FMDIM_RATIONAL_RM1(J)%NUMERATOR)
CALL IMI2M(1,FMDIM_RATIONAL_RM1(J)%DENOMINATOR)
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIM_RATIONAL_RM1
FUNCTION FMDIM_RATIONAL_RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMDIM_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMDIM_RATIONAL_RM2%NUMERATOR = -1
FMDIM_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMSUB_RATIONAL_RMRM_0(MA(J,K),MB(J,K),FMDIM_RATIONAL_RM2(J,K))
IF (MWK(START(FMDIM_RATIONAL_RM2(J,K)%NUMERATOR)) < 0) THEN
CALL IMI2M(0,FMDIM_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMI2M(1,FMDIM_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDIM_RATIONAL_RM2
! FLOOR
FUNCTION FMFLOOR_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMFLOOR_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMDIVR(MA%NUMERATOR,MA%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMI2M(1,R_2%MIM)
CALL IMSUB(R_1%MIM,R_2%MIM,FMFLOOR_RATIONAL_RM%NUMERATOR)
ELSE
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM%NUMERATOR)
ENDIF
CALL IMI2M(1,FMFLOOR_RATIONAL_RM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMFLOOR_RATIONAL_RM
FUNCTION FMFLOOR_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMFLOOR_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMFLOOR_RATIONAL_RM1%NUMERATOR = -1
FMFLOOR_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMDIVR(MA(J)%NUMERATOR,MA(J)%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM1(J)%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMI2M(1,R_2%MIM)
CALL IMSUB(R_1%MIM,R_2%MIM,FMFLOOR_RATIONAL_RM1(J)%NUMERATOR)
ELSE
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM1(J)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMFLOOR_RATIONAL_RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMFLOOR_RATIONAL_RM1
FUNCTION FMFLOOR_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMFLOOR_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMFLOOR_RATIONAL_RM2%NUMERATOR = -1
FMFLOOR_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMDIVR(MA(J,K)%NUMERATOR,MA(J,K)%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(R_2%MIM)+3) == 0) THEN
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM2(J,K)%NUMERATOR)
ELSE IF (MWK(START(R_2%MIM)) < 0) THEN
CALL IMI2M(1,R_2%MIM)
CALL IMSUB(R_1%MIM,R_2%MIM,FMFLOOR_RATIONAL_RM2(J,K)%NUMERATOR)
ELSE
CALL IMEQ(R_1%MIM,FMFLOOR_RATIONAL_RM2(J,K)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMFLOOR_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMFLOOR_RATIONAL_RM2
! INT
FUNCTION FMINT_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMINT_RATIONAL_RM
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMDIVR(MA%NUMERATOR,MA%DENOMINATOR,R_1%MIM,R_2%MIM)
CALL IMEQ(R_1%MIM,FMINT_RATIONAL_RM%NUMERATOR)
CALL IMI2M(1,FMINT_RATIONAL_RM%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMINT_RATIONAL_RM
FUNCTION FMINT_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMINT_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMINT_RATIONAL_RM1%NUMERATOR = -1
FMINT_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMDIVR(MA(J)%NUMERATOR,MA(J)%DENOMINATOR,R_1%MIM,R_2%MIM)
CALL IMEQ(R_1%MIM,FMINT_RATIONAL_RM1(J)%NUMERATOR)
CALL IMI2M(1,FMINT_RATIONAL_RM1(J)%DENOMINATOR)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMINT_RATIONAL_RM1
FUNCTION FMINT_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMINT_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMINT_RATIONAL_RM2%NUMERATOR = -1
FMINT_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMDIVR(MA(J,K)%NUMERATOR,MA(J,K)%DENOMINATOR,R_1%MIM,R_2%MIM)
CALL IMEQ(R_1%MIM,FMINT_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMI2M(1,FMINT_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMINT_RATIONAL_RM2
! IS_UNKNOWN
FUNCTION RM_IS_UNKNOWN(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
LOGICAL :: RM_IS_UNKNOWN
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
RM_IS_UNKNOWN = .FALSE.
IF (MWK(START(MA%NUMERATOR)+2) == MUNKNO) RM_IS_UNKNOWN = .TRUE.
IF (MWK(START(MA%DENOMINATOR)+2) == MUNKNO) RM_IS_UNKNOWN = .TRUE.
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION RM_IS_UNKNOWN
FUNCTION RM_IS_UNKNOWN1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
LOGICAL :: RM_IS_UNKNOWN1
INTEGER :: J,N
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
N = SIZE(MA)
RM_IS_UNKNOWN1 = .FALSE.
DO J = 1, N
IF (MWK(START(MA(J)%NUMERATOR)+2) == MUNKNO) RM_IS_UNKNOWN1 = .TRUE.
IF (MWK(START(MA(J)%DENOMINATOR)+2) == MUNKNO) RM_IS_UNKNOWN1 = .TRUE.
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION RM_IS_UNKNOWN1
FUNCTION RM_IS_UNKNOWN2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
LOGICAL :: RM_IS_UNKNOWN2
INTEGER :: J,K
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
RM_IS_UNKNOWN2 = .FALSE.
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
IF (MWK(START(MA(J,K)%NUMERATOR)+2) == MUNKNO) RM_IS_UNKNOWN2 = .TRUE.
IF (MWK(START(MA(J,K)%DENOMINATOR)+2) == MUNKNO) RM_IS_UNKNOWN2 = .TRUE.
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION RM_IS_UNKNOWN2
! MAX
SUBROUTINE FMMAX_RATIONAL(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
LOGICAL :: MA_LT_MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
MA_LT_MB = IM_COMP(R_5,'<',R_1)
ELSE
MA_LT_MB = IM_COMP(R_5,'>',R_1)
ENDIF
IF (MA_LT_MB) THEN
CALL IMEQ(MB%NUMERATOR, MC%NUMERATOR)
CALL IMEQ(MB%DENOMINATOR,MC%DENOMINATOR)
ELSE
CALL IMEQ(MA%NUMERATOR, MC%NUMERATOR)
CALL IMEQ(MA%DENOMINATOR,MC%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMAX_RATIONAL
FUNCTION FMMAX_RATIONAL_RM(MA,MB,MC,MD,ME,MF,MG,MH,MI,MJ)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMMAX_RATIONAL_RM
TYPE (FM_RATIONAL), OPTIONAL :: MC,MD,ME,MF,MG,MH,MI,MJ
INTENT (IN) :: MA,MB,MC,MD,ME,MF,MG,MH,MI,MJ
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL FMMAX_RATIONAL(MA,MB,MT_RM)
IF (PRESENT(MC)) THEN
CALL FM_UNDEF_INP(MC)
CALL FMMAX_RATIONAL(MT_RM,MC,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MD)) THEN
CALL FM_UNDEF_INP(MD)
CALL FMMAX_RATIONAL(MT_RM,MD,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(ME)) THEN
CALL FM_UNDEF_INP(ME)
CALL FMMAX_RATIONAL(MT_RM,ME,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MF)) THEN
CALL FM_UNDEF_INP(MF)
CALL FMMAX_RATIONAL(MT_RM,MF,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MG)) THEN
CALL FM_UNDEF_INP(MG)
CALL FMMAX_RATIONAL(MT_RM,MG,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MH)) THEN
CALL FM_UNDEF_INP(MH)
CALL FMMAX_RATIONAL(MT_RM,MH,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MI)) THEN
CALL FM_UNDEF_INP(MI)
CALL FMMAX_RATIONAL(MT_RM,MI,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MJ)) THEN
CALL FM_UNDEF_INP(MJ)
CALL FMMAX_RATIONAL(MT_RM,MJ,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
CALL FMEQ_RATIONAL(MT_RM,FMMAX_RATIONAL_RM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMAX_RATIONAL_RM
! MIN
SUBROUTINE FMMIN_RATIONAL(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,MC
LOGICAL :: MA_LT_MB
INTENT (IN) :: MA,MB
INTENT (INOUT) :: MC
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMEQ(MB%NUMERATOR, R_3%MIM)
CALL IMEQ(MB%DENOMINATOR,R_4%MIM)
CALL IM_MPY(R_1,R_4,R_5)
CALL IM_MPY(R_2,R_3,R_1)
IF (MWK(START(R_2%MIM)) * MWK(START(R_4%MIM)) > 0) THEN
MA_LT_MB = IM_COMP(R_5,'<',R_1)
ELSE
MA_LT_MB = IM_COMP(R_5,'>',R_1)
ENDIF
IF (MA_LT_MB) THEN
CALL IMEQ(MA%NUMERATOR, MC%NUMERATOR)
CALL IMEQ(MA%DENOMINATOR,MC%DENOMINATOR)
ELSE
CALL IMEQ(MB%NUMERATOR, MC%NUMERATOR)
CALL IMEQ(MB%DENOMINATOR,MC%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END SUBROUTINE FMMIN_RATIONAL
FUNCTION FMMIN_RATIONAL_RM(MA,MB,MC,MD,ME,MF,MG,MH,MI,MJ)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMMIN_RATIONAL_RM
TYPE (FM_RATIONAL), OPTIONAL :: MC,MD,ME,MF,MG,MH,MI,MJ
INTENT (IN) :: MA,MB,MC,MD,ME,MF,MG,MH,MI,MJ
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL FMMIN_RATIONAL(MA,MB,MT_RM)
IF (PRESENT(MC)) THEN
CALL FM_UNDEF_INP(MC)
CALL FMMIN_RATIONAL(MT_RM,MC,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MD)) THEN
CALL FM_UNDEF_INP(MD)
CALL FMMIN_RATIONAL(MT_RM,MD,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(ME)) THEN
CALL FM_UNDEF_INP(ME)
CALL FMMIN_RATIONAL(MT_RM,ME,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MF)) THEN
CALL FM_UNDEF_INP(MF)
CALL FMMIN_RATIONAL(MT_RM,MF,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MG)) THEN
CALL FM_UNDEF_INP(MG)
CALL FMMIN_RATIONAL(MT_RM,MG,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MH)) THEN
CALL FM_UNDEF_INP(MH)
CALL FMMIN_RATIONAL(MT_RM,MH,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MI)) THEN
CALL FM_UNDEF_INP(MI)
CALL FMMIN_RATIONAL(MT_RM,MI,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
IF (PRESENT(MJ)) THEN
CALL FM_UNDEF_INP(MJ)
CALL FMMIN_RATIONAL(MT_RM,MJ,MU_RM)
CALL FMEQ_RATIONAL(MU_RM,MT_RM)
ENDIF
CALL FMEQ_RATIONAL(MT_RM,FMMIN_RATIONAL_RM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMIN_RATIONAL_RM
! MOD
FUNCTION FMMOD_RATIONAL_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMMOD_RATIONAL_RM
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL FMDIV_RATIONAL_RMRM_0(MA,MB,MT_RM)
CALL IMDIV(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(R_1%MIM,MB%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA,MT_RM,FMMOD_RATIONAL_RM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMOD_RATIONAL_RM
FUNCTION FMMOD_RATIONAL_RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMOD_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMMOD_RATIONAL_RM1%NUMERATOR = -1
FMMOD_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMRM_0(MA(J),MB(J),MT_RM)
CALL IMDIV(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(R_1%MIM,MB(J)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB(J)%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA(J),MT_RM,FMMOD_RATIONAL_RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMOD_RATIONAL_RM1
FUNCTION FMMOD_RATIONAL_RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMOD_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMMOD_RATIONAL_RM2%NUMERATOR = -1
FMMOD_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMRM_0(MA(J,K),MB(J,K),MT_RM)
CALL IMDIV(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(R_1%MIM,MB(J,K)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB(J,K)%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA(J,K),MT_RM,FMMOD_RATIONAL_RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMOD_RATIONAL_RM2
! MODULO
FUNCTION FMMODULO_RATIONAL_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,MB,FMMODULO_RATIONAL_RM
INTENT (IN) :: MA,MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
CALL FMDIV_RATIONAL_RMRM_0(MA,MB,MT_RM)
CALL IMDIVR(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(MT_RM%NUMERATOR)) < 0 .AND. MWK(START(R_2%MIM)+3) /= 0) THEN
CALL IMI2M(1,R_3%MIM)
CALL IMSUB(R_1%MIM,R_3%MIM,R_4%MIM)
CALL IMEQ(R_4%MIM,R_1%MIM)
ENDIF
CALL IMMPY(R_1%MIM,MB%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA,MT_RM,FMMODULO_RATIONAL_RM)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMODULO_RATIONAL_RM
FUNCTION FMMODULO_RATIONAL_RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMMODULO_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
FMMODULO_RATIONAL_RM1%NUMERATOR = -1
FMMODULO_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA)
CALL FMDIV_RATIONAL_RMRM_0(MA(J),MB(J),MT_RM)
CALL IMDIVR(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(MT_RM%NUMERATOR)) < 0 .AND. MWK(START(R_2%MIM)+3) /= 0) THEN
CALL IMI2M(1,R_3%MIM)
CALL IMSUB(R_1%MIM,R_3%MIM,R_4%MIM)
CALL IMEQ(R_4%MIM,R_1%MIM)
ENDIF
CALL IMMPY(R_1%MIM,MB(J)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB(J)%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA(J),MT_RM,FMMODULO_RATIONAL_RM1(J))
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMODULO_RATIONAL_RM1
FUNCTION FMMODULO_RATIONAL_RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA,MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMMODULO_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
FMMODULO_RATIONAL_RM2%NUMERATOR = -1
FMMODULO_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL FMDIV_RATIONAL_RMRM_0(MA(J,K),MB(J,K),MT_RM)
CALL IMDIVR(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM,R_2%MIM)
IF (MWK(START(MT_RM%NUMERATOR)) < 0 .AND. MWK(START(R_2%MIM)+3) /= 0) THEN
CALL IMI2M(1,R_3%MIM)
CALL IMSUB(R_1%MIM,R_3%MIM,R_4%MIM)
CALL IMEQ(R_4%MIM,R_1%MIM)
ENDIF
CALL IMMPY(R_1%MIM,MB(J,K)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MB(J,K)%DENOMINATOR,MT_RM%DENOMINATOR)
CALL FMSUB_RATIONAL_RMRM_0(MA(J,K),MT_RM,FMMODULO_RATIONAL_RM2(J,K))
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMODULO_RATIONAL_RM2
! NINT
FUNCTION FMNINT_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMNINT_RATIONAL_RM
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMABS(MA%NUMERATOR,R_1%MIM)
CALL IMABS(MA%DENOMINATOR,R_2%MIM)
CALL IMDIVR(R_1%MIM,R_2%MIM,R_3%MIM,R_4%MIM)
CALL IMMPYI(R_4%MIM,2,R_5%MIM)
IF (IMCOMP(R_5%MIM,'>=',MA%DENOMINATOR)) THEN
CALL IMI2M(1,R_4%MIM)
CALL IMADD(R_3%MIM,R_4%MIM,FMNINT_RATIONAL_RM%NUMERATOR)
ELSE
CALL IMEQ(R_3%MIM,FMNINT_RATIONAL_RM%NUMERATOR)
ENDIF
CALL IMI2M(1,FMNINT_RATIONAL_RM%DENOMINATOR)
IF (MWK(START(MA%NUMERATOR)) < 0) MWK(START(FMNINT_RATIONAL_RM%NUMERATOR)) = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMNINT_RATIONAL_RM
FUNCTION FMNINT_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMNINT_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
FMNINT_RATIONAL_RM1%NUMERATOR = -1
FMNINT_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMABS(MA(J)%NUMERATOR,R_1%MIM)
CALL IMABS(MA(J)%DENOMINATOR,R_2%MIM)
CALL IMDIVR(R_1%MIM,R_2%MIM,R_3%MIM,R_4%MIM)
CALL IMMPYI(R_4%MIM,2,R_5%MIM)
IF (IMCOMP(R_5%MIM,'>=',MA(J)%DENOMINATOR)) THEN
CALL IMI2M(1,R_4%MIM)
CALL IMADD(R_3%MIM,R_4%MIM,FMNINT_RATIONAL_RM1(J)%NUMERATOR)
ELSE
CALL IMEQ(R_3%MIM,FMNINT_RATIONAL_RM1(J)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMNINT_RATIONAL_RM1(J)%DENOMINATOR)
IF (MWK(START(MA(J)%NUMERATOR)) < 0) MWK(START(FMNINT_RATIONAL_RM1(J)%NUMERATOR)) = -1
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMNINT_RATIONAL_RM1
FUNCTION FMNINT_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMNINT_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
FMNINT_RATIONAL_RM2%NUMERATOR = -1
FMNINT_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMABS(MA(J,K)%NUMERATOR,R_1%MIM)
CALL IMABS(MA(J,K)%DENOMINATOR,R_2%MIM)
CALL IMDIVR(R_1%MIM,R_2%MIM,R_3%MIM,R_4%MIM)
CALL IMMPYI(R_4%MIM,2,R_5%MIM)
IF (IMCOMP(R_5%MIM,'>=',MA(J,K)%DENOMINATOR)) THEN
CALL IMI2M(1,R_4%MIM)
CALL IMADD(R_3%MIM,R_4%MIM,FMNINT_RATIONAL_RM2(J,K)%NUMERATOR)
ELSE
CALL IMEQ(R_3%MIM,FMNINT_RATIONAL_RM2(J,K)%NUMERATOR)
ENDIF
CALL IMI2M(1,FMNINT_RATIONAL_RM2(J,K)%DENOMINATOR)
IF (MWK(START(MA(J,K)%NUMERATOR)) < 0) &
MWK(START(FMNINT_RATIONAL_RM2(J,K)%NUMERATOR)) = -1
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMNINT_RATIONAL_RM2
! ** integer power
FUNCTION FMIPWR_RATIONAL_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA,FMIPWR_RATIONAL_RM
INTEGER :: MB
INTENT (IN) :: MA, MB
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA%NUMERATOR, R_1%MIM)
CALL IMEQ(MA%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
IF (MB > 0) THEN
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM%NUMERATOR)
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM%DENOMINATOR)
ELSE IF (MB < 0) THEN
MWK(START(R_3%MIM)) = 1
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM%NUMERATOR)
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM%DENOMINATOR)
ELSE
CALL IMI2M(1,FMIPWR_RATIONAL_RM%NUMERATOR)
CALL IMI2M(1,FMIPWR_RATIONAL_RM%DENOMINATOR)
ENDIF
CALL FM_MAX_EXP_RM(FMIPWR_RATIONAL_RM)
IF (MWK(START(FMIPWR_RATIONAL_RM%DENOMINATOR)) < 0) THEN
MWK(START(FMIPWR_RATIONAL_RM%DENOMINATOR)) = 1
MWK(START(FMIPWR_RATIONAL_RM%NUMERATOR)) = -MWK(START(FMIPWR_RATIONAL_RM%NUMERATOR))
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMIPWR_RATIONAL_RM
FUNCTION FMIPWR_RATIONAL_RM1(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA)) :: FMIPWR_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA, MB
FMIPWR_RATIONAL_RM1%NUMERATOR = -1
FMIPWR_RATIONAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA)
CALL IMEQ(MA(J)%NUMERATOR, R_1%MIM)
CALL IMEQ(MA(J)%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
IF (MB > 0) THEN
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM1(J)%NUMERATOR)
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM1(J)%DENOMINATOR)
ELSE IF (MB < 0) THEN
MWK(START(R_3%MIM)) = 1
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM1(J)%NUMERATOR)
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM1(J)%DENOMINATOR)
ELSE
CALL IMI2M(1,FMIPWR_RATIONAL_RM1(J)%NUMERATOR)
CALL IMI2M(1,FMIPWR_RATIONAL_RM1(J)%DENOMINATOR)
ENDIF
CALL FM_MAX_EXP_RM(FMIPWR_RATIONAL_RM1(J))
IF (MWK(START(FMIPWR_RATIONAL_RM1(J)%DENOMINATOR)) < 0) THEN
MWK(START(FMIPWR_RATIONAL_RM1(J)%DENOMINATOR)) = 1
MWK(START(FMIPWR_RATIONAL_RM1(J)%NUMERATOR)) = &
-MWK(START(FMIPWR_RATIONAL_RM1(J)%NUMERATOR))
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMIPWR_RATIONAL_RM1
FUNCTION FMIPWR_RATIONAL_RM2(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
INTEGER :: MB
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FMIPWR_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA,MB
FMIPWR_RATIONAL_RM2%NUMERATOR = -1
FMIPWR_RATIONAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMEQ(MA(J,K)%NUMERATOR, R_1%MIM)
CALL IMEQ(MA(J,K)%DENOMINATOR,R_2%MIM)
CALL IMI2M(MB, R_3%MIM)
IF (MB > 0) THEN
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM2(J,K)%DENOMINATOR)
ELSE IF (MB < 0) THEN
MWK(START(R_3%MIM)) = 1
CALL IMPWR(R_2%MIM,R_3%MIM,FMIPWR_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMPWR(R_1%MIM,R_3%MIM,FMIPWR_RATIONAL_RM2(J,K)%DENOMINATOR)
ELSE
CALL IMI2M(1,FMIPWR_RATIONAL_RM2(J,K)%NUMERATOR)
CALL IMI2M(1,FMIPWR_RATIONAL_RM2(J,K)%DENOMINATOR)
ENDIF
CALL FM_MAX_EXP_RM(FMIPWR_RATIONAL_RM2(J,K))
IF (MWK(START(FMIPWR_RATIONAL_RM2(J,K)%DENOMINATOR)) < 0) THEN
MWK(START(FMIPWR_RATIONAL_RM2(J,K)%DENOMINATOR)) = 1
MWK(START(FMIPWR_RATIONAL_RM2(J,K)%NUMERATOR)) = &
-MWK(START(FMIPWR_RATIONAL_RM2(J,K)%NUMERATOR))
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMIPWR_RATIONAL_RM2
END MODULE FM_RATIONAL_ARITHMETIC_7
MODULE FM_RATIONAL_ARITHMETIC_8
USE FM_RATIONAL_ARITHMETIC_1
INTERFACE TO_FM
MODULE PROCEDURE FM_RATIONAL_RM
MODULE PROCEDURE FM_RATIONAL_RM1
MODULE PROCEDURE FM_RATIONAL_RM2
END INTERFACE
INTERFACE RATIONAL_APPROX
MODULE PROCEDURE FM_RATIONAL_APPROX_RM
END INTERFACE
INTERFACE DOT_PRODUCT
MODULE PROCEDURE FMDOTPRODUCT_RM
END INTERFACE
INTERFACE MATMUL
MODULE PROCEDURE FMMATMUL22_RM
MODULE PROCEDURE FMMATMUL12_RM
MODULE PROCEDURE FMMATMUL21_RM
END INTERFACE
INTERFACE MAXLOC
MODULE PROCEDURE FMMAXLOC_RM1
MODULE PROCEDURE FMMAXLOC_RM2
END INTERFACE
INTERFACE MAXVAL
MODULE PROCEDURE FMMAXVAL_RM1
MODULE PROCEDURE FMMAXVAL_RM2
END INTERFACE
INTERFACE MINLOC
MODULE PROCEDURE FMMINLOC_RM1
MODULE PROCEDURE FMMINLOC_RM2
END INTERFACE
INTERFACE MINVAL
MODULE PROCEDURE FMMINVAL_RM1
MODULE PROCEDURE FMMINVAL_RM2
END INTERFACE
INTERFACE PRODUCT
MODULE PROCEDURE FMPRODUCT_RM1
MODULE PROCEDURE FMPRODUCT_RM2
END INTERFACE
INTERFACE SUM
MODULE PROCEDURE FMSUM_RM1
MODULE PROCEDURE FMSUM_RM2
END INTERFACE
INTERFACE TRANSPOSE
MODULE PROCEDURE FMTRANSPOSE_RM
END INTERFACE
CONTAINS
! TO_FM
FUNCTION FM_RATIONAL_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA
TYPE (FM) :: FM_RATIONAL_RM
INTENT (IN) :: MA
INTEGER :: NDSAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
NDSAVE = NDIG
NDIG = NDIG + NGRD21
CALL IMI2FM(MA%NUMERATOR,F_1%MFM)
CALL IMI2FM(MA%DENOMINATOR,F_2%MFM)
CALL FMDIV(F_1%MFM,F_2%MFM,FM_RATIONAL_RM%MFM)
CALL FMEQU_R1(FM_RATIONAL_RM%MFM,NDIG,NDSAVE)
NDIG = NDSAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_RM
FUNCTION FM_RATIONAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:) :: MA
TYPE (FM), DIMENSION(SIZE(MA)) :: FM_RATIONAL_RM1
INTEGER :: J
INTENT (IN) :: MA
INTEGER :: NDSAVE
FM_RATIONAL_RM1%MFM = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
NDSAVE = NDIG
NDIG = NDIG + NGRD21
DO J = 1, SIZE(MA)
CALL IMI2FM(MA(J)%NUMERATOR,F_1%MFM)
CALL IMI2FM(MA(J)%DENOMINATOR,F_2%MFM)
CALL FMDIV(F_1%MFM,F_2%MFM,FM_RATIONAL_RM1(J)%MFM)
CALL FMEQU_R1(FM_RATIONAL_RM1(J)%MFM,NDIG,NDSAVE)
ENDDO
NDIG = NDSAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_RM1
FUNCTION FM_RATIONAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL), DIMENSION(:,:) :: MA
TYPE (FM), DIMENSION(SIZE(MA,DIM=1),SIZE(MA,DIM=2)) :: FM_RATIONAL_RM2
INTEGER :: J,K
INTENT (IN) :: MA
INTEGER :: NDSAVE
FM_RATIONAL_RM2%MFM = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
NDSAVE = NDIG
NDIG = NDIG + NGRD21
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
CALL IMI2FM(MA(J,K)%NUMERATOR,F_1%MFM)
CALL IMI2FM(MA(J,K)%DENOMINATOR,F_2%MFM)
CALL FMDIV(F_1%MFM,F_2%MFM,FM_RATIONAL_RM2(J,K)%MFM)
CALL FMEQU_R1(FM_RATIONAL_RM2(J,K)%MFM,NDIG,NDSAVE)
ENDDO
ENDDO
NDIG = NDSAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_RM2
! Rational approximation
FUNCTION FM_RATIONAL_APPROX_RM(MA,DIGITS)
! Return a TYPE (FM_RATIONAL) result that approximates TYPE (FM) input MA so that the
! numerator and denominator of the result have no more than DIGITS digits in base 10.
! Ex: MA = pi, DIGITS = 2 gives 22 / 7
! MA = pi, DIGITS = 3 gives 355 / 113
! MA = pi, DIGITS = 6 gives 833719 / 265381
! The rational result usually approximates MA to about 2*DIGITS significant digits, so
! DIGITS should not be more than about half the precision carried for the FM result.
! Ex: 833719 / 265381 = 3.141592653581077771204419306... agrees with pi to about 11 s.d.
USE FMVALS
IMPLICIT NONE
TYPE (FM) :: MA
INTEGER :: DIGITS,J,N
INTEGER, SAVE :: A = -3, B = -3, B1 = -3, RA1 = -3, RA2 = -3, RA3 = -3, RB1 = -3, &
RB2 = -3, RB3 = -3, CF = -3
TYPE (FM_RATIONAL) :: FM_RATIONAL_APPROX_RM
LOGICAL, EXTERNAL :: FMCOMP
INTENT (IN) :: MA,DIGITS
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FMABS(MA%MFM,A)
N = DIGITS
N = MAX(N,1)
J = (ALOGMT*NDIG)/2
N = MIN(N,J)
CALL FMI2M(10,B1)
CALL FMIPWR(B1,N,B)
CALL FMINT(A,RA1)
CALL FMI2M(1,RA2)
CALL FMI2M(0,RA3)
CALL FMI2M(1,RB1)
CALL FMI2M(0,RB2)
CALL FMI2M(1,RB3)
CALL FMSUB_R1(A,RA1)
DO J = 1, 1000
IF (FMCOMP(RA1,'>=',B) .OR. FMCOMP(RB1,'>=',B) .OR. MWK(START(A)+3) == 0) THEN
IF (J > 1 .AND. MWK(START(A)+3) /= 0) THEN
CALL FMEQ(RA2,FM_RATIONAL_APPROX_RM%NUMERATOR)
CALL FMEQ(RB2,FM_RATIONAL_APPROX_RM%DENOMINATOR)
ELSE
CALL FMEQ(RA1,FM_RATIONAL_APPROX_RM%NUMERATOR)
CALL FMEQ(RB1,FM_RATIONAL_APPROX_RM%DENOMINATOR)
ENDIF
IF (MA < 0) MWK(START(FM_RATIONAL_APPROX_RM%NUMERATOR)) = -1
EXIT
ENDIF
CALL FMI2M(1,B1)
CALL FMDIV_R2(B1,A)
CALL FMINT(A,CF)
CALL FMEQ(RA2,RA3)
CALL FMEQ(RA1,RA2)
CALL FMMPY(CF,RA2,B1)
CALL FMADD(B1,RA3,RA1)
CALL FMEQ(RB2,RB3)
CALL FMEQ(RB1,RB2)
CALL FMMPY(CF,RB2,B1)
CALL FMADD(B1,RB3,RB1)
CALL FMSUB_R1(A,CF)
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FM_RATIONAL_APPROX_RM
! DOT_PRODUCT
FUNCTION FMDOTPRODUCT_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),MB(:),FMDOTPRODUCT_RM
INTEGER :: J,JA,JB
INTENT (IN) :: MA,MB
FMDOTPRODUCT_RM%NUMERATOR = -1
FMDOTPRODUCT_RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
IF (SIZE(MA) == SIZE(MB)) THEN
CALL IMI2M(0,FMDOTPRODUCT_RM%NUMERATOR)
CALL IMI2M(1,FMDOTPRODUCT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MB,DIM=1) + J - 1
CALL FMMPY_RATIONAL_RMRM_0(MA(JA),MB(JB),MT_RM)
CALL FMADD_RATIONAL_RMRM_0(FMDOTPRODUCT_RM,MT_RM,MU_RM)
CALL IMEQ(MU_RM%NUMERATOR,FMDOTPRODUCT_RM%NUMERATOR)
CALL IMEQ(MU_RM%DENOMINATOR,FMDOTPRODUCT_RM%DENOMINATOR)
ENDDO
ELSE
CALL IMST2M('UNKNOWN',FMDOTPRODUCT_RM%NUMERATOR)
CALL IMST2M('UNKNOWN',FMDOTPRODUCT_RM%DENOMINATOR)
ENDIF
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMDOTPRODUCT_RM
! MATMUL
FUNCTION FMMATMUL22_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),MB(:,:)
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1),SIZE(MB,DIM=2)) :: FMMATMUL22_RM
INTEGER :: I,J,K,MXSAVE
LOGICAL :: SKIP_GCD_SAVE
INTENT (IN) :: MA,MB
FMMATMUL22_RM%NUMERATOR = -1
FMMATMUL22_RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
SKIP_GCD_SAVE = SKIP_GCD
IF (SIZE(MA,DIM=2) == SIZE(MB,DIM=1)) THEN
MXSAVE = MXEXP
DO I = 1, SIZE(MA,DIM=1)
DO J = 1, SIZE(MB,DIM=2)
MXEXP = MXEXP2
CALL IMI2M(0,MT_RM%NUMERATOR)
CALL IMI2M(1,MT_RM%DENOMINATOR)
DO K = 1, SIZE(MA,DIM=2)
SKIP_GCD = .TRUE.
CALL FMMPY_RATIONAL_RMRM_0(MA(I,K),MB(K,J),MU_RM)
IF (K == SIZE(MA,DIM=2)) SKIP_GCD = .FALSE.
CALL FMADD_RATIONAL_RMRM_0(MT_RM,MU_RM,FMMATMUL22_RM(I,J))
CALL IMEQ(FMMATMUL22_RM(I,J)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(FMMATMUL22_RM(I,J)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDDO
MXEXP = MXSAVE
ENDDO
ENDDO
ELSE
DO I = 1, SIZE(MA,DIM=1)
DO J = 1, SIZE(MB,DIM=2)
CALL IMST2M('UNKNOWN',FMMATMUL22_RM(I,J)%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMATMUL22_RM(I,J)%DENOMINATOR)
ENDDO
ENDDO
ENDIF
SKIP_GCD = SKIP_GCD_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMATMUL22_RM
FUNCTION FMMATMUL12_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),MB(:,:)
TYPE (FM_RATIONAL), DIMENSION(SIZE(MB,DIM=2)) :: FMMATMUL12_RM
INTEGER :: J,K,MXSAVE
LOGICAL :: SKIP_GCD_SAVE
INTENT (IN) :: MA,MB
FMMATMUL12_RM%NUMERATOR = -1
FMMATMUL12_RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
SKIP_GCD_SAVE = SKIP_GCD
IF (SIZE(MA) == SIZE(MB,DIM=1)) THEN
MXSAVE = MXEXP
DO J = 1, SIZE(MB,DIM=2)
MXEXP = MXEXP2
CALL IMI2M(0,MT_RM%NUMERATOR)
CALL IMI2M(1,MT_RM%DENOMINATOR)
DO K = 1, SIZE(MA,DIM=1)
SKIP_GCD = .TRUE.
CALL FMMPY_RATIONAL_RMRM_0(MA(K),MB(K,J),MU_RM)
IF (K == SIZE(MA,DIM=1)) SKIP_GCD = .FALSE.
CALL FMADD_RATIONAL_RMRM_0(MT_RM,MU_RM,FMMATMUL12_RM(J))
CALL IMEQ(FMMATMUL12_RM(J)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(FMMATMUL12_RM(J)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDDO
MXEXP = MXSAVE
ENDDO
ELSE
DO J = 1, SIZE(MB,DIM=2)
CALL IMST2M('UNKNOWN',FMMATMUL12_RM(J)%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMATMUL12_RM(J)%DENOMINATOR)
ENDDO
ENDIF
SKIP_GCD = SKIP_GCD_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMATMUL12_RM
FUNCTION FMMATMUL21_RM(MA,MB)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),MB(:)
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=1)) :: FMMATMUL21_RM
INTEGER :: J,K,MXSAVE
LOGICAL :: SKIP_GCD_SAVE
INTENT (IN) :: MA,MB
FMMATMUL21_RM%NUMERATOR = -1
FMMATMUL21_RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL FM_UNDEF_INP(MB)
SKIP_GCD_SAVE = SKIP_GCD
IF (SIZE(MB) == SIZE(MA,DIM=2)) THEN
MXSAVE = MXEXP
DO J = 1, SIZE(MA,DIM=1)
MXEXP = MXEXP2
CALL IMI2M(0,MT_RM%NUMERATOR)
CALL IMI2M(1,MT_RM%DENOMINATOR)
DO K = 1, SIZE(MB,DIM=1)
SKIP_GCD = .TRUE.
CALL FMMPY_RATIONAL_RMRM_0(MA(J,K),MB(K),MU_RM)
IF (K == SIZE(MB,DIM=1)) SKIP_GCD = .FALSE.
CALL FMADD_RATIONAL_RMRM_0(MT_RM,MU_RM,FMMATMUL21_RM(J))
CALL IMEQ(FMMATMUL21_RM(J)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(FMMATMUL21_RM(J)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDDO
MXEXP = MXSAVE
ENDDO
ELSE
DO J = 1, SIZE(MA,DIM=1)
CALL IMST2M('UNKNOWN',FMMATMUL21_RM(J)%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMATMUL21_RM(J)%DENOMINATOR)
ENDDO
ENDIF
SKIP_GCD = SKIP_GCD_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMATMUL21_RM
! MAXLOC
FUNCTION FMMAXLOC_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:)
INTEGER :: FMMAXLOC_RM1
INTEGER :: J,JA
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
FMMAXLOC_RM1 = LBOUND(MA,DIM=1)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
FMMAXLOC_RM1 = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL IMMPY(MA(JA)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'>',R_2)) THEN
CALL IMEQ(MA(JA)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA)%DENOMINATOR,MT_RM%DENOMINATOR)
FMMAXLOC_RM1 = JA
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMAXLOC_RM1
FUNCTION FMMAXLOC_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:)
INTEGER :: FMMAXLOC_RM2(2)
INTEGER :: J,K,JA,JB
LOGICAL, EXTERNAL :: IMCOMP
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
FMMAXLOC_RM2 = (/ LBOUND(MA,DIM=1), LBOUND(MA,DIM=2) /)
DO K = 1, SIZE(MA,DIM=2)
DO J = 1, SIZE(MA,DIM=1)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
FMMAXLOC_RM2 = (/ -1, -1 /)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
CALL IMMPY(MA(JA,JB)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA,JB)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'>',R_2)) THEN
CALL IMEQ(MA(JA,JB)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA,JB)%DENOMINATOR,MT_RM%DENOMINATOR)
FMMAXLOC_RM2 = (/ JA, JB /)
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMAXLOC_RM2
! MAXVAL
FUNCTION FMMAXVAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),FMMAXVAL_RM1
INTEGER :: J,JA
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
FMMAXVAL_RM1%NUMERATOR = -1
FMMAXVAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMMAXVAL_RM1%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMAXVAL_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL IMMPY(MA(JA)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'>',R_2)) THEN
CALL IMEQ(MA(JA)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDIF
ENDDO
CALL IMEQ(MT_RM%NUMERATOR,FMMAXVAL_RM1%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMAXVAL_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMAXVAL_RM1
FUNCTION FMMAXVAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),FMMAXVAL_RM2
INTEGER :: J,K,JA,JB
LOGICAL, EXTERNAL :: IMCOMP
INTENT (IN) :: MA
FMMAXVAL_RM2%NUMERATOR = -1
FMMAXVAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMMAXVAL_RM2%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMAXVAL_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
CALL IMMPY(MA(JA,JB)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA,JB)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'>',R_2)) THEN
CALL IMEQ(MA(JA,JB)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA,JB)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDIF
ENDDO
ENDDO
CALL IMEQ(MT_RM%NUMERATOR,FMMAXVAL_RM2%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMAXVAL_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMAXVAL_RM2
! MINLOC
FUNCTION FMMINLOC_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:)
INTEGER :: FMMINLOC_RM1
INTEGER :: J,JA
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
FMMINLOC_RM1 = LBOUND(MA,DIM=1)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
FMMINLOC_RM1 = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL IMMPY(MA(JA)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'<',R_2)) THEN
CALL IMEQ(MA(JA)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA)%DENOMINATOR,MT_RM%DENOMINATOR)
FMMINLOC_RM1 = JA
ENDIF
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMINLOC_RM1
FUNCTION FMMINLOC_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:)
INTEGER :: FMMINLOC_RM2(2)
INTEGER :: J,K,JA,JB
LOGICAL, EXTERNAL :: IMCOMP
INTENT (IN) :: MA
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
FMMINLOC_RM2 = (/ LBOUND(MA,DIM=1), LBOUND(MA,DIM=2) /)
DO K = 1, SIZE(MA,DIM=2)
DO J = 1, SIZE(MA,DIM=1)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
FMMINLOC_RM2 = (/ -1, -1 /)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
CALL IMMPY(MA(JA,JB)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA,JB)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'<',R_2)) THEN
CALL IMEQ(MA(JA,JB)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA,JB)%DENOMINATOR,MT_RM%DENOMINATOR)
FMMINLOC_RM2 = (/ JA, JB /)
ENDIF
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMINLOC_RM2
! MINVAL
FUNCTION FMMINVAL_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),FMMINVAL_RM1
INTEGER :: J,JA
INTENT (IN) :: MA
LOGICAL, EXTERNAL :: IMCOMP
FMMINVAL_RM1%NUMERATOR = -1
FMMINVAL_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMMINVAL_RM1%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMINVAL_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL IMMPY(MA(JA)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'<',R_2)) THEN
CALL IMEQ(MA(JA)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDIF
ENDDO
CALL IMEQ(MT_RM%NUMERATOR,FMMINVAL_RM1%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMINVAL_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMINVAL_RM1
FUNCTION FMMINVAL_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),FMMINVAL_RM2
INTEGER :: J,K,JA,JB
LOGICAL, EXTERNAL :: IMCOMP
INTENT (IN) :: MA
FMMINVAL_RM2%NUMERATOR = -1
FMMINVAL_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMMINVAL_RM2%NUMERATOR)
CALL IMST2M('UNKNOWN',FMMINVAL_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
CALL IMMPY(MA(JA,JB)%NUMERATOR,MT_RM%DENOMINATOR,R_1%MIM)
CALL IMMPY(MA(JA,JB)%DENOMINATOR,MT_RM%NUMERATOR,R_2%MIM)
IF (IM_COMP(R_1,'<',R_2)) THEN
CALL IMEQ(MA(JA,JB)%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(JA,JB)%DENOMINATOR,MT_RM%DENOMINATOR)
ENDIF
ENDDO
ENDDO
CALL IMEQ(MT_RM%NUMERATOR,FMMINVAL_RM2%NUMERATOR)
CALL IMEQ(MT_RM%DENOMINATOR,FMMINVAL_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMMINVAL_RM2
! PRODUCT
FUNCTION FMPRODUCT_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),FMPRODUCT_RM1
INTEGER :: J,JA
INTENT (IN) :: MA
FMPRODUCT_RM1%NUMERATOR = -1
FMPRODUCT_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMPRODUCT_RM1%NUMERATOR)
CALL IMST2M('UNKNOWN',FMPRODUCT_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL IMMPY(MA(JA)%NUMERATOR,MT_RM%NUMERATOR,R_1%MIM)
CALL IMMPY(MA(JA)%DENOMINATOR,MT_RM%DENOMINATOR,R_2%MIM)
CALL IMEQ(R_1%MIM,MT_RM%NUMERATOR)
CALL IMEQ(R_2%MIM,MT_RM%DENOMINATOR)
ENDDO
CALL IMGCD(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_3%MIM)
CALL IMDIV(MT_RM%NUMERATOR,R_3%MIM,FMPRODUCT_RM1%NUMERATOR)
CALL IMDIV(MT_RM%DENOMINATOR,R_3%MIM,FMPRODUCT_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMPRODUCT_RM1
FUNCTION FMPRODUCT_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),FMPRODUCT_RM2
INTEGER :: J,K,JA,JB
INTENT (IN) :: MA
FMPRODUCT_RM2%NUMERATOR = -1
FMPRODUCT_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMPRODUCT_RM2%NUMERATOR)
CALL IMST2M('UNKNOWN',FMPRODUCT_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
CALL IMMPY(MA(JA,JB)%NUMERATOR,MT_RM%NUMERATOR,R_1%MIM)
CALL IMMPY(MA(JA,JB)%DENOMINATOR,MT_RM%DENOMINATOR,R_2%MIM)
CALL IMEQ(R_1%MIM,MT_RM%NUMERATOR)
CALL IMEQ(R_2%MIM,MT_RM%DENOMINATOR)
ENDDO
ENDDO
CALL IMGCD(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_3%MIM)
CALL IMDIV(MT_RM%NUMERATOR,R_3%MIM,FMPRODUCT_RM2%NUMERATOR)
CALL IMDIV(MT_RM%DENOMINATOR,R_3%MIM,FMPRODUCT_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMPRODUCT_RM2
! SUM
FUNCTION FMSUM_RM1(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:),FMSUM_RM1
INTEGER :: J,JA
LOGICAL :: SKIP_GCD_SAVE
INTENT (IN) :: MA
FMSUM_RM1%NUMERATOR = -1
FMSUM_RM1%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
SKIP_GCD_SAVE = SKIP_GCD
CALL IMEQ(MA(LBOUND(MA,DIM=1))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1))%DENOMINATOR,MT_RM%DENOMINATOR)
SKIP_GCD = .TRUE.
DO J = 1, SIZE(MA)
JA = LBOUND(MA,DIM=1) + J - 1
IF (MWK(START(MA(JA)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMSUM_RM1%NUMERATOR)
CALL IMST2M('UNKNOWN',FMSUM_RM1%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1) CYCLE
CALL FMADD_RATIONAL_RMRM_0(MT_RM,MA(JA),MU_RM)
CALL IMEQ(MU_RM%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MU_RM%DENOMINATOR,MT_RM%DENOMINATOR)
ENDDO
SKIP_GCD = .FALSE.
CALL IMGCD(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_3%MIM)
CALL IMDIV(MT_RM%NUMERATOR,R_3%MIM,FMSUM_RM1%NUMERATOR)
CALL IMDIV(MT_RM%DENOMINATOR,R_3%MIM,FMSUM_RM1%DENOMINATOR)
SKIP_GCD = SKIP_GCD_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUM_RM1
FUNCTION FMSUM_RM2(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:),FMSUM_RM2
INTEGER :: J,K,JA,JB
LOGICAL :: SKIP_GCD_SAVE
INTENT (IN) :: MA
FMSUM_RM2%NUMERATOR = -1
FMSUM_RM2%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
SKIP_GCD_SAVE = SKIP_GCD
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MA(LBOUND(MA,DIM=1),LBOUND(MA,DIM=2))%DENOMINATOR,MT_RM%DENOMINATOR)
DO J = 1, SIZE(MA,DIM=1)
DO K = 1, SIZE(MA,DIM=2)
JA = LBOUND(MA,DIM=1) + J - 1
JB = LBOUND(MA,DIM=2) + K - 1
IF (MWK(START(MA(JA,JB)%NUMERATOR)+2) == MUNKNO .OR. &
MWK(START(MA(JA,JB)%DENOMINATOR)+2) == MUNKNO) THEN
CALL IMST2M('UNKNOWN',FMSUM_RM2%NUMERATOR)
CALL IMST2M('UNKNOWN',FMSUM_RM2%DENOMINATOR)
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
IF (J == 1 .AND. K == 1) CYCLE
SKIP_GCD = .TRUE.
IF (K == 1) SKIP_GCD = .FALSE.
CALL FMADD_RATIONAL_RMRM_0(MT_RM,MA(JA,JB),MU_RM)
CALL IMEQ(MU_RM%NUMERATOR,MT_RM%NUMERATOR)
CALL IMEQ(MU_RM%DENOMINATOR,MT_RM%DENOMINATOR)
ENDDO
ENDDO
SKIP_GCD = .FALSE.
CALL IMGCD(MT_RM%NUMERATOR,MT_RM%DENOMINATOR,R_3%MIM)
CALL IMDIV(MT_RM%NUMERATOR,R_3%MIM,FMSUM_RM2%NUMERATOR)
CALL IMDIV(MT_RM%DENOMINATOR,R_3%MIM,FMSUM_RM2%DENOMINATOR)
SKIP_GCD = SKIP_GCD_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMSUM_RM2
! TRANSPOSE
FUNCTION FMTRANSPOSE_RM(MA)
USE FMVALS
IMPLICIT NONE
TYPE (FM_RATIONAL) :: MA(:,:)
TYPE (FM_RATIONAL), DIMENSION(SIZE(MA,DIM=2),SIZE(MA,DIM=1)) :: FMTRANSPOSE_RM
INTEGER :: I,J
INTENT (IN) :: MA
FMTRANSPOSE_RM%NUMERATOR = -1
FMTRANSPOSE_RM%DENOMINATOR = -1
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
CALL FM_UNDEF_INP(MA)
DO I = 1, SIZE(MA,DIM=1)
DO J = 1, SIZE(MA,DIM=2)
CALL IMEQ(MA(I,J)%NUMERATOR,FMTRANSPOSE_RM(J,I)%NUMERATOR)
CALL IMEQ(MA(I,J)%DENOMINATOR,FMTRANSPOSE_RM(J,I)%DENOMINATOR)
ENDDO
ENDDO
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
END FUNCTION FMTRANSPOSE_RM
END MODULE FM_RATIONAL_ARITHMETIC_8
MODULE FM_RATIONAL_ARITHMETIC
USE FM_RATIONAL_ARITHMETIC_1
USE FM_RATIONAL_ARITHMETIC_2
USE FM_RATIONAL_ARITHMETIC_3
USE FM_RATIONAL_ARITHMETIC_4
USE FM_RATIONAL_ARITHMETIC_5
USE FM_RATIONAL_ARITHMETIC_6
USE FM_RATIONAL_ARITHMETIC_7
USE FM_RATIONAL_ARITHMETIC_8
CONTAINS
! Since finding exact inverse matrices and solutions to linear systems are such common
! applications for the rational arithmetic package, they are included here in the basic
! module file rather than in a separate file like FM_LIN_SOLVE and its related routines.
SUBROUTINE RM_LIN_SOLVE(A,X,B,N,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Find the exact rational solution to the linear system A X = B, where:
! A is the matrix of the system, containing the N x N coefficient matrix.
! B is the N x 1 right-hand-side vector.
! X is the returned N x 1 solution vector.
! DET is returned as the determinant of A.
! Nonzero DET means a solution was found.
! DET = 0 is returned if the system is singular.
! A,X,B,DET are all TYPE (FM_RATIONAL) multiprecision rational variables.
! This routine uses modular integer arithmetic to solve related integer systems A1 x1 = b1 Mod p
! for many different primes p, then these solutions are combined using the Chinese Remainder
! Theorem to recover the original rational solution X.
INTEGER :: N
TYPE (FM_RATIONAL) :: A(N,N), B(N), X(N), DET
TYPE (IM), SAVE :: PC, ABMPY, G, T, DET_IM, LAST_DET_IM, PRIME_PRODUCT
TYPE (IM), ALLOCATABLE :: A1(:,:), XT(:), PRIME_MK(:)
DOUBLE PRECISION, ALLOCATABLE :: A2(:,:), MOD_SOLUTION(:,:), PRIMES(:), DET_P(:), Y(:), &
Z_MS(:,:), Z_P(:), Z_D(:)
DOUBLE PRECISION :: P, R
LOGICAL :: SINGULAR
INTEGER :: I, I_EXTRA, J, JP, K, L, MAX_PRIMES, PRIMES_USED
CALL FM_ENTER_USER_ROUTINE
IF (N <= 0) THEN
DET = 0
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
IF (N == 1) THEN
DET = A(1,1)
IF (A(1,1) /= 0) THEN
X(1) = B(1) / A(1,1)
ELSE
X(1) = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
ENDIF
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
MAX_PRIMES = 1001
ALLOCATE(A1(N,N+1),A2(N,N+1),XT(N),PRIME_MK(MAX_PRIMES),MOD_SOLUTION(N,MAX_PRIMES), &
PRIMES(MAX_PRIMES),DET_P(MAX_PRIMES),Y(MAX_PRIMES),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in RM_LIN_SOLVE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
A1 = 0
XT = 0
G = 0
T = 0
! Copy A and B to augmented matrix A1 and convert to integer coefficients.
DET = 1
DO I = 1, N
ABMPY = 1
DO J = 1, N
IF (MWK(START(A(I,J)%DENOMINATOR)+2) == 1 .AND. &
MWK(START(A(I,J)%DENOMINATOR)+3) == 1) CYCLE
CALL IMGCD(ABMPY%MIM,A(I,J)%DENOMINATOR,G%MIM)
CALL IMMPY(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
IF (MWK(START(G%MIM)+2) == 1 .AND. MWK(START(G%MIM)+3) == 1) THEN
CALL IMEQ(T%MIM,ABMPY%MIM)
ELSE
CALL IMDIV(T%MIM,G%MIM,ABMPY%MIM)
ENDIF
ENDDO
CALL IMGCD(ABMPY%MIM,B(I)%DENOMINATOR,G%MIM)
CALL IMMPY(ABMPY%MIM,B(I)%DENOMINATOR,T%MIM)
CALL IMDIV(T%MIM,G%MIM,ABMPY%MIM)
IF (MWK(START(ABMPY%MIM)+2) == 1 .AND. MWK(START(ABMPY%MIM)+3) == 1) THEN
DO J = 1, N
CALL IMEQ(A(I,J)%NUMERATOR,A1(I,J)%MIM)
ENDDO
CALL IMEQ(B(I)%NUMERATOR,A1(I,N+1)%MIM)
ELSE
DO J = 1, N
CALL IMDIV(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
CALL IMMPY(A(I,J)%NUMERATOR,T%MIM,A1(I,J)%MIM)
ENDDO
CALL IMDIV(ABMPY%MIM,B(I)%DENOMINATOR,T%MIM)
CALL IMMPY(B(I)%NUMERATOR,T%MIM,A1(I,N+1)%MIM)
DET = DET / ABMPY
ENDIF
ENDDO
! Find the determinant of the integer matrix A1, by finding modular solutions using
! a collection of prime moduli.
I = 0
I_EXTRA = 3
PRIMES_USED = 0
LAST_DET_IM = 0
P = FLOOR(MXBASE/10)
JP = 0
110 JP = JP + 1
IF (PRIMES_USED >= MAX_PRIMES) THEN
ALLOCATE(Z_MS(N,MAX_PRIMES),Z_P(MAX_PRIMES),Z_D(MAX_PRIMES),STAT=L)
IF (L /= 0) THEN
WRITE (*,"(/' Error in RM_LIN_SOLVE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
DO L = 1, PRIMES_USED
DO K = 1, N
Z_MS(K,L) = MOD_SOLUTION(K,L)
ENDDO
Z_P(L) = PRIMES(L)
Z_D(L) = DET_P(L)
ENDDO
CALL FM_DEALLOCATE(PRIME_MK)
DEALLOCATE(PRIME_MK,MOD_SOLUTION,PRIMES,DET_P,Y)
ALLOCATE(PRIME_MK(2*MAX_PRIMES),MOD_SOLUTION(N,2*MAX_PRIMES),PRIMES(2*MAX_PRIMES), &
DET_P(2*MAX_PRIMES),Y(2*MAX_PRIMES),STAT=L)
IF (L /= 0) THEN
WRITE (*,"(/' Error in RM_LIN_SOLVE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
DO L = 1, PRIMES_USED
DO K = 1, N
MOD_SOLUTION(K,L) = Z_MS(K,L)
ENDDO
PRIMES(L) = Z_P(L)
DET_P(L) = Z_D(L)
ENDDO
DEALLOCATE(Z_MS,Z_P,Z_D)
MAX_PRIMES = 2 * MAX_PRIMES
ENDIF
CALL RM_NEXT_PRIME(P)
CALL RM_MOD_LIN_SOLVE(A1, A2, DET_P(PRIMES_USED+1), N, P, SINGULAR)
IF (PRIMES_USED == 0 .AND. JP > 100) THEN
DET = 0
IF (KWARN > 0) THEN
WRITE (KW,"(/' Error in RM_LIN_SOLVE. The matrix is singular.'/)")
ENDIF
IF (KWARN >= 2) STOP
X = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
GO TO 200
ENDIF
IF (SINGULAR) GO TO 110
PRIMES_USED = PRIMES_USED + 1
MOD_SOLUTION(1:N , PRIMES_USED) = A2(1:N , N+1)
PRIMES(PRIMES_USED) = P
IF (PRIMES_USED == 1) THEN
DET_IM = DET_P(1)
PC = 1
ELSE
LAST_DET_IM = DET_IM
CALL RM_SOLVE_MOD(DET_P(PRIMES_USED), P, DET_IM, PC)
ENDIF
PC = PC * INT(P)
IF (LAST_DET_IM == DET_IM) THEN
I = I + 1
ELSE
I = 0
ENDIF
IF (I < I_EXTRA) GO TO 110
! Solve the simultaneous congruences to get the rational solution of
! the original system.
PRIME_PRODUCT = INT(PRIMES(1))
DO J = 2, PRIMES_USED
IF (J == PRIMES_USED) PRIME_MK(J) = PRIME_PRODUCT
PRIME_PRODUCT = PRIME_PRODUCT * INT(PRIMES(J))
ENDDO
DO J = 1, PRIMES_USED-1
PRIME_MK(J) = PRIME_PRODUCT / INT(PRIMES(J))
ENDDO
DO J = 1, PRIMES_USED
CALL RM_MOD_ONE(PRIME_MK(J)%MIM,PRIMES(J),R)
CALL RM_INV_MOD_P(R,PRIMES(J),Y(J))
IF (Y(J)*2.0D0 > PRIMES(J)) Y(J) = Y(J) - PRIMES(J)
ENDDO
DO J = 1, PRIMES_USED
PRIME_MK(J) = ( PRIME_MK(J) * INT(Y(J)) ) * INT(DET_P(J))
ENDDO
DO I = 1, N
XT(I) = 0
DO J = 1, PRIMES_USED
XT(I) = XT(I) + PRIME_MK(J) * INT(MOD_SOLUTION(I,J))
ENDDO
XT(I) = MODULO( XT(I), PRIME_PRODUCT )
IF (2*XT(I) > PRIME_PRODUCT) XT(I) = XT(I) - PRIME_PRODUCT
ENDDO
DO J = 1, N
X(J) = TO_FM_RATIONAL( XT(J), DET_IM )
ENDDO
DET = DET_IM * DET
! This modular method can fail if PRIME_PRODUCT is too small or if
! gcd(PRIME_PRODUCT,DET_IM) is not 1 -- see Cetin K. Koc, "A Parallel Algorithm
! for Exact Solutions of Linear Equations via Congruence Technique",
! Computers Math. Applic., Vol. 23, No. 12, pp. 13-24, 1992.
! Check these conditions and also check that the solution solves the linear system.
! If not, first try adding more primes and modular solutions, and if that doesn't
! help, use the slower method in RM_LIN_SOLVE2.
IF (PRIME_PRODUCT < 2*DET_IM .OR. PRIME_PRODUCT < MAXVAL(ABS(A1)) .OR. &
GCD(PRIME_PRODUCT,DET_IM) /= 1) THEN
CALL RM_LIN_SOLVE2(A,X,B,N,DET)
GO TO 200
ENDIF
DO I = 1, N
G = 0
DO J = 1, N
G = G + A1(I,J) * XT(J)
ENDDO
IF (G /= A1(I,N+1) * DET_IM) THEN
I_EXTRA = I_EXTRA + 10
IF (I_EXTRA < 30) GO TO 110
CALL RM_LIN_SOLVE2(A,X,B,N,DET)
GO TO 200
ENDIF
ENDDO
200 CALL FM_DEALLOCATE(XT)
CALL FM_DEALLOCATE(PRIME_MK)
CALL FM_DEALLOCATE(A1)
DEALLOCATE(XT,PRIME_MK,A1,A2,MOD_SOLUTION,PRIMES,DET_P,Y)
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE RM_LIN_SOLVE
SUBROUTINE RM_LIN_SOLVE2(A,X,B,N,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Gauss elimination with exact rational arithmetic to solve the linear system A X = B, where:
! A is the matrix of the system, containing the N x N coefficient matrix.
! B is the N x 1 right-hand-side vector.
! X is the returned N x 1 solution vector.
! DET is returned as the determinant of A.
! Nonzero DET means a solution was found.
! DET = 0 is returned if the system is singular.
! A,X,B,DET are all TYPE (FM_RATIONAL) multiprecision rational variables.
INTEGER :: N
TYPE (FM_RATIONAL) :: A(N,N), B(N), X(N), DET
TYPE (IM), SAVE :: ABMPY, G, T
TYPE (IM), ALLOCATABLE :: A1(:,:)
TYPE (FM), ALLOCATABLE :: A2(:,:), B2(:), X2(:)
INTEGER, ALLOCATABLE :: KSWAP(:)
TYPE (FM), SAVE :: DET_FM, T_FM
INTEGER :: I, J, K, NDSAVE
CALL FM_ENTER_USER_ROUTINE
ALLOCATE(A1(N,N+1),A2(N,N),B2(N),X2(N),KSWAP(N),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in RM_LIN_SOLVE2. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
A1 = 0
A2 = 0
B2 = 0
X2 = 0
G = 0
T = 0
! Copy A and B to A1 and convert to integer coefficients.
DET = 1
DO I = 1, N
ABMPY = 1
DO J = 1, N
IF (MWK(START(A(I,J)%DENOMINATOR)+2) == 1 .AND. &
MWK(START(A(I,J)%DENOMINATOR)+3) == 1) CYCLE
CALL IMGCD(ABMPY%MIM,A(I,J)%DENOMINATOR,G%MIM)
CALL IMMPY(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
IF (MWK(START(G%MIM)+2) == 1 .AND. MWK(START(G%MIM)+3) == 1) THEN
CALL IMEQ(T%MIM,ABMPY%MIM)
ELSE
CALL IMDIV(T%MIM,G%MIM,ABMPY%MIM)
ENDIF
ENDDO
CALL IMGCD(ABMPY%MIM,B(I)%DENOMINATOR,G%MIM)
CALL IMMPY(ABMPY%MIM,B(I)%DENOMINATOR,T%MIM)
CALL IMDIV(T%MIM,G%MIM,ABMPY%MIM)
IF (MWK(START(ABMPY%MIM)+2) == 1 .AND. MWK(START(ABMPY%MIM)+3) == 1) THEN
DO J = 1, N
CALL IMEQ(A(I,J)%NUMERATOR,A1(I,J)%MIM)
ENDDO
CALL IMEQ(B(I)%NUMERATOR,A1(I,N+1)%MIM)
ELSE
DO J = 1, N
CALL IMDIV(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
CALL IMMPY(A(I,J)%NUMERATOR,T%MIM,A1(I,J)%MIM)
ENDDO
CALL IMDIV(ABMPY%MIM,B(I)%DENOMINATOR,T%MIM)
CALL IMMPY(B(I)%NUMERATOR,T%MIM,A1(I,N+1)%MIM)
DET = DET / ABMPY
ENDIF
ENDDO
CALL IMEQ(DET%DENOMINATOR,ABMPY%MIM)
! Set precision level for type FM variables.
NDSAVE = NDIG
CALL FM_SET(50)
110 DO I = 1, N
DO J = 1, N
A2(I,J) = A1(I,J)
ENDDO
B2(I) = A1(I,N+1)
ENDDO
! Factor the matrix.
CALL FM_FACTOR_LU_RM(A2,N,DET_FM,KSWAP)
DET = TO_IM(NINT(DET_FM))
DET = DET / ABMPY
IF (DET_FM == 0 .OR. IS_UNKNOWN(DET_FM)) THEN
IF (KWARN > 0) THEN
WRITE (KW,"(/' Error in RM_LIN_SOLVE2. The matrix is singular.'/)")
ENDIF
IF (KWARN >= 2) STOP
X = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
GO TO 200
ENDIF
IF ((NDIG-1)*DLOGMB/DLOGTN < MWK(START(DET_FM%MFM)+2)*DLOGMB/DLOGTN + 20) THEN
NDIG = MWK(START(DET_FM%MFM)+2) + 20*DLOGTN/DLOGMB + 2
GO TO 110
ENDIF
IF (ABS(DET_FM - NINT(DET_FM)) > 1.0D-10) THEN
NDIG = 1.5D0 * NDIG
GO TO 110
ENDIF
! Solve the system.
CALL FM_SOLVE_LU_RM(A2,N,B2,X2,KSWAP)
G = TO_IM(NINT( DET_FM ))
DO J = 1, N
T_FM = X2(J) * DET_FM
IF (ABS(T_FM - NINT(T_FM)) > 1.0D-10) THEN
NDIG = 1.5D0 * NDIG
GO TO 110
ENDIF
T = TO_IM(NINT( T_FM ))
X(J) = TO_FM_RATIONAL( T, G )
ENDDO
200 CALL FM_DEALLOCATE(B2)
CALL FM_DEALLOCATE(X2)
CALL FM_DEALLOCATE(A1)
CALL FM_DEALLOCATE(A2)
DEALLOCATE(A1,A2,B2,X2,KSWAP)
NDIG = NDSAVE
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE RM_LIN_SOLVE2
SUBROUTINE RM_MOD_LIN_SOLVE(A1, A2, DET_P, N, P, SINGULAR)
! Solve the NxN linear system with augmented coefficient matrix A1 with modular arithmetic mod P.
! A2 is A1 mod P, and the modular solution vector is returned in A2( 1:N, N+1 ).
! DET_P is returned as the modular determinant.
! SINGULAR is returned true if the system is singular.
USE FMVALS
USE FMZM
IMPLICIT NONE
INTEGER :: N, I, J, JD, JR, JC
TYPE (IM) :: A1(N,N+1)
DOUBLE PRECISION :: A2(N,N+1), DET_P, A2JDJD, AMULT, P, T
LOGICAL :: SINGULAR
SINGULAR = .FALSE.
! Copy A1 to A2 Mod P.
DO I = 1, N
DO J = 1, N+1
CALL RM_MOD_ONE(A1(I,J)%MIM,P,A2(I,J))
IF (MWK(START(A1(I,J)%MIM)) < 0) A2(I,J) = -A2(I,J) + P
ENDDO
ENDDO
! Gauss Elimination.
DET_P = 1
DO JD = 1, N-1
IF (A2(JD,JD) == 0.0D0) THEN
DO JR = JD+1, N
IF (A2(JR,JD) /= 0.0D0) THEN
DO JC = JD, N+1
T = A2(JD,JC)
A2(JD,JC) = A2(JR,JC)
A2(JR,JC) = T
ENDDO
EXIT
ENDIF
ENDDO
DET_P = -DET_P
ENDIF
IF (A2(JD,JD) == 0.0D0) THEN
SINGULAR = .TRUE.
RETURN
ENDIF
A2JDJD = A2(JD,JD)
CALL RM_INV_MOD_P(A2(JD,JD),P,T)
DET_P = MODULO( DET_P * A2JDJD, P )
DO JR = JD+1, N
AMULT = MODULO( A2(JR,JD) * T , P )
DO JC = JD, N+1
A2(JR,JC) = MODULO( A2(JR,JC) - AMULT * A2(JD,JC) , P )
ENDDO
ENDDO
ENDDO
DET_P = MODULO( DET_P * A2(N,N), P )
IF (DET_P == 0) THEN
SINGULAR = .TRUE.
RETURN
ENDIF
! Back substitution.
DO JR = N, 1, -1
DO JC = JR+1, N
A2(JR,N+1) = MODULO( A2(JR,N+1) - A2(JR,JC) * A2(JC,N+1) , P )
ENDDO
CALL RM_INV_MOD_P(A2(JR,JR),P,T)
A2(JR,N+1) = MODULO( A2(JR,N+1) * T , P )
ENDDO
END SUBROUTINE RM_MOD_LIN_SOLVE
SUBROUTINE RM_INVERSE(A,N,B,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Return B as the exact rational inverse of the N x N matrix A, and DET as the exact rational
! determinant of A.
! A,B,DET are all TYPE (FM_RATIONAL) multiprecision rational variables.
! This routine uses modular integer arithmetic to find modular inverse matrices for related
! integer matrices, B1 = inverse( A1 ) Mod p, for many different primes p. These solutions are
! then combined using the Chinese Remainder Theorem to recover the original rational inverse B.
INTEGER :: N
TYPE (FM_RATIONAL) :: A(N,N), B(N,N), DET
TYPE (IM), SAVE :: PC, ABDET, ABMPY, G, T, DET_IM, LAST_DET_IM, PRIME_PRODUCT
TYPE (IM), ALLOCATABLE :: A1(:,:), BT(:,:), PRIME_MK(:)
DOUBLE PRECISION, ALLOCATABLE :: A2(:,:), MOD_SOLUTION(:,:,:), PRIMES(:), DET_P(:), Y(:), &
Z_MS(:,:,:), Z_P(:), Z_D(:)
DOUBLE PRECISION :: P, R
LOGICAL :: SINGULAR
INTEGER :: I, I_EXTRA, J, JP, K, L, MAX_PRIMES, PRIMES_USED
CALL FM_ENTER_USER_ROUTINE
IF (N <= 0) THEN
DET = 0
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
IF (N == 1) THEN
DET = A(1,1)
IF (A(1,1) /= 0) THEN
B(1,1) = 1 / A(1,1)
ELSE
B(1,1) = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
ENDIF
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
MAX_PRIMES = 101
ALLOCATE(A1(N,2*N),A2(N,2*N),BT(N,N),PRIME_MK(MAX_PRIMES),MOD_SOLUTION(N,N,MAX_PRIMES), &
PRIMES(MAX_PRIMES),DET_P(MAX_PRIMES),Y(MAX_PRIMES),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in RM_INVERSE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
A1 = 0
BT = 0
G = 0
T = 0
A2 = 0
! Copy A to augmented matrix A1 and convert to integer coefficients.
DET = 1
ABDET = 1
DO I = 1, N
ABMPY = 1
DO J = 1, N
IF (MWK(START(A(I,J)%DENOMINATOR)+2) == 1 .AND. &
MWK(START(A(I,J)%DENOMINATOR)+3) == 1) CYCLE
CALL IMGCD(ABMPY%MIM,A(I,J)%DENOMINATOR,G%MIM)
CALL IMMPY(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
IF (MWK(START(G%MIM)+2) == 1 .AND. MWK(START(G%MIM)+3) == 1) THEN
CALL IMEQ(T%MIM,ABMPY%MIM)
ELSE
CALL IMDIV(T%MIM,G%MIM,ABMPY%MIM)
ENDIF
ENDDO
IF (MWK(START(ABMPY%MIM)+2) == 1 .AND. MWK(START(ABMPY%MIM)+3) == 1) THEN
DO J = 1, N
CALL IMEQ(A(I,J)%NUMERATOR,A1(I,J)%MIM)
ENDDO
A1(I,I+N) = 1
ELSE
DO J = 1, N
CALL IMDIV(ABMPY%MIM,A(I,J)%DENOMINATOR,T%MIM)
CALL IMMPY(A(I,J)%NUMERATOR,T%MIM,A1(I,J)%MIM)
ENDDO
A1(I,I+N) = ABMPY
DET = DET / ABMPY
ENDIF
ENDDO
CALL IMEQ(DET%DENOMINATOR,ABDET%MIM)
! Find the determinant of the integer matrix A1, by finding modular solutions using
! a collection of prime moduli.
I = 0
I_EXTRA = 3
PRIMES_USED = 0
LAST_DET_IM = 0
P = FLOOR(MXBASE/10)
JP = 0
110 JP = JP + 1
IF (PRIMES_USED >= MAX_PRIMES) THEN
ALLOCATE(Z_MS(N,N,MAX_PRIMES),Z_P(MAX_PRIMES),Z_D(MAX_PRIMES),STAT=L)
IF (L /= 0) THEN
WRITE (*,"(/' Error in RM_INVERSE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
DO L = 1, PRIMES_USED
DO K = 1, N
Z_MS(K,1:N,L) = MOD_SOLUTION(K,1:N,L)
ENDDO
Z_P(L) = PRIMES(L)
Z_D(L) = DET_P(L)
ENDDO
CALL FM_DEALLOCATE(PRIME_MK)
DEALLOCATE(PRIME_MK,MOD_SOLUTION,PRIMES,DET_P,Y)
ALLOCATE(PRIME_MK(2*MAX_PRIMES),MOD_SOLUTION(N,N,2*MAX_PRIMES),PRIMES(2*MAX_PRIMES), &
DET_P(2*MAX_PRIMES),Y(2*MAX_PRIMES),STAT=L)
IF (L /= 0) THEN
WRITE (*,"(/' Error in RM_INVERSE. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
DO L = 1, PRIMES_USED
DO K = 1, N
MOD_SOLUTION(K,1:N,L) = Z_MS(K,1:N,L)
ENDDO
PRIMES(L) = Z_P(L)
DET_P(L) = Z_D(L)
ENDDO
DEALLOCATE(Z_MS,Z_P,Z_D)
MAX_PRIMES = 2 * MAX_PRIMES
ENDIF
CALL RM_NEXT_PRIME(P)
CALL RM_MOD_INVERSE(A1, A2, DET_P(PRIMES_USED+1), N, P, SINGULAR)
IF (PRIMES_USED == 0 .AND. JP > 100) THEN
DET = 0
IF (KWARN > 0) THEN
WRITE (KW,"(/' Error in RM_INVERSE. The matrix is singular.'/)")
ENDIF
IF (KWARN >= 2) STOP
B = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
GO TO 200
ENDIF
IF (SINGULAR) GO TO 110
PRIMES_USED = PRIMES_USED + 1
MOD_SOLUTION(1:N , 1:N , PRIMES_USED) = A2(1:N , N+1:2*N)
PRIMES(PRIMES_USED) = P
IF (PRIMES_USED == 1) THEN
DET_IM = DET_P(1)
PC = 1
ELSE
LAST_DET_IM = DET_IM
CALL RM_SOLVE_MOD(DET_P(PRIMES_USED), P, DET_IM, PC)
ENDIF
PC = PC * INT(P)
IF (LAST_DET_IM == DET_IM) THEN
I = I + 1
ELSE
I = 0
ENDIF
IF (I < I_EXTRA) GO TO 110
! Solve the simultaneous congruences to get the rational solution of
! the original system.
PRIME_PRODUCT = INT(PRIMES(1))
DO J = 2, PRIMES_USED
IF (J == PRIMES_USED) PRIME_MK(J) = PRIME_PRODUCT
PRIME_PRODUCT = PRIME_PRODUCT * INT(PRIMES(J))
ENDDO
DO J = 1, PRIMES_USED-1
PRIME_MK(J) = PRIME_PRODUCT / INT(PRIMES(J))
ENDDO
DO J = 1, PRIMES_USED
CALL RM_MOD_ONE(PRIME_MK(J)%MIM,PRIMES(J),R)
CALL RM_INV_MOD_P(R,PRIMES(J),Y(J))
IF (Y(J)*2.0D0 > PRIMES(J)) Y(J) = Y(J) - PRIMES(J)
ENDDO
DO J = 1, PRIMES_USED
PRIME_MK(J) = ( PRIME_MK(J) * INT(Y(J)) ) * INT(DET_P(J))
ENDDO
DO I = 1, N
BT(I,1:N) = 0
DO J = 1, PRIMES_USED
BT(I,1:N) = BT(I,1:N) + PRIME_MK(J) * INT(MOD_SOLUTION(I,1:N,J))
ENDDO
DO K = 1, N
BT(I,K) = MODULO( BT(I,K), PRIME_PRODUCT )
IF (2*BT(I,K) > PRIME_PRODUCT) BT(I,K) = BT(I,K) - PRIME_PRODUCT
ENDDO
ENDDO
DO J = 1, N
DO K = 1, N
B(J,K) = TO_FM_RATIONAL( BT(J,K), DET_IM )
ENDDO
ENDDO
DET = DET_IM * DET
! This modular method can fail if PRIME_PRODUCT is too small or if
! gcd(PRIME_PRODUCT,DET_IM) is not 1 -- see Cetin K. Koc, "A Parallel Algorithm
! for Exact Solutions of Linear Equations via Congruence Technique",
! Computers Math. Applic., Vol. 23, No. 12, pp. 13-24, 1992.
! Check these conditions and also check that the solution solves the linear system.
! If not, first try adding more primes and modular solutions, and if that doesn't
! help, use the slower method in RM_INVERSE2.
IF (PRIME_PRODUCT < 2*DET_IM .OR. PRIME_PRODUCT < MAXVAL(ABS(A1)) .OR. &
GCD(PRIME_PRODUCT,DET_IM) /= 1) THEN
CALL RM_INVERSE2(A1,N,B,DET)
GO TO 200
ENDIF
DO I = 1, N
DO K = 1, N
G = 0
DO J = 1, N
G = G + A1(I,J) * BT(J,K)
ENDDO
IF ( ( I == K .AND. G /= DET_IM * A1(I,I+N) ) .OR. ( I /= K .AND. G /= 0 )) THEN
I_EXTRA = I_EXTRA + 10
DET = TO_FM_RATIONAL( TO_IM(1), ABDET )
IF (I_EXTRA < 30) GO TO 110
CALL RM_INVERSE2(A1,N,B,DET)
GO TO 200
ENDIF
ENDDO
ENDDO
200 CALL FM_DEALLOCATE(BT)
CALL FM_DEALLOCATE(PRIME_MK)
CALL FM_DEALLOCATE(A1)
DEALLOCATE(BT,PRIME_MK,A1,A2,MOD_SOLUTION,PRIMES,DET_P,Y)
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE RM_INVERSE
SUBROUTINE RM_INVERSE2(A1,N,B,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Gauss elimination to find the exact rational inverse of A1.
! A1 is the augmented type(im) N x 2N matrix of the system, scaled to have integer coefficients.
! B is the returned rational N x N inverse matrix.
! DET is returned as the rational determinant of A, the A1 matrix before scaling.
! Nonzero DET means a solution was found.
! DET = 0 is returned if the system is singular.
! B,DET are TYPE (FM_RATIONAL) multiprecision rational variables.
INTEGER :: N
TYPE (IM) :: A1(N,2*N)
TYPE (FM_RATIONAL) :: B(N,N), DET
TYPE (IM), SAVE :: ABMPY, G, T
TYPE (FM), ALLOCATABLE :: A2(:,:), B2(:), X2(:)
INTEGER, ALLOCATABLE :: KSWAP(:)
TYPE (FM), SAVE :: DET_FM, T_FM
INTEGER :: I, J, K, NDSAVE
CALL FM_ENTER_USER_ROUTINE
ALLOCATE(A2(N,N),B2(N),X2(N),KSWAP(N),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in RM_INVERSE2. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
A2 = 0
B2 = 0
X2 = 0
G = 0
T = 0
! Set precision level for type FM variables.
NDSAVE = NDIG
CALL FM_SET(50)
110 DO I = 1, N
DO J = 1, N
A2(I,J) = A1(I,J)
ENDDO
ENDDO
! Factor the matrix.
CALL FM_FACTOR_LU_RM(A2,N,DET_FM,KSWAP)
DET = TO_IM(NINT(DET_FM))
DO I = 1, N
DET = DET / A1(I,I+N)
ENDDO
IF (DET_FM == 0 .OR. IS_UNKNOWN(DET_FM)) THEN
B = TO_FM_RATIONAL(' UNKNOWN ', ' UNKNOWN ')
GO TO 200
ENDIF
IF ((NDIG-1)*DLOGMB/DLOGTN < MWK(START(DET_FM%MFM)+2)*DLOGMB/DLOGTN + 20) THEN
NDIG = MWK(START(DET_FM%MFM)+2) + 20*DLOGTN/DLOGMB + 2
GO TO 110
ENDIF
IF (ABS(DET_FM - NINT(DET_FM)) > 1.0D-10) THEN
NDIG = 1.5D0 * NDIG
GO TO 110
ENDIF
! Solve for the inverse matrix.
G = TO_IM(NINT( DET_FM ))
DO J = 1, N
B2 = 0
B2(J) = A1(J,J+N)
CALL FM_SOLVE_LU_RM(A2,N,B2,X2,KSWAP)
DO K = 1, N
B(K,J) = TO_FM_RATIONAL( TO_IM( NINT( X2(K) * DET_FM ) ) , G )
ENDDO
ENDDO
200 CALL FM_DEALLOCATE(B2)
CALL FM_DEALLOCATE(X2)
CALL FM_DEALLOCATE(A2)
DEALLOCATE(A2,B2,X2,KSWAP)
NDIG = NDSAVE
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE RM_INVERSE2
! The next several routines, with FM_* names, are the same as the ones in the
! standard FM sample routine file. Some are used in special cases by the RM
! routines in this package, and some are used in the SampleFMrational.f95
! program to compare the exact rational routines with their floating-point
! counterparts. To avoid name conflicts in a program that might use both
! the FM rational package and the FM sample routine file, these names have
! an extra "_RM" at the end.
SUBROUTINE FM_INVERSE_RM(A,N,B,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Return B as the inverse of the N x N matrix A, and DET as the determinant of A.
! A and B are type (fm) (real) multiprecision arrays.
INTEGER :: N
TYPE (FM) :: A(N,N), B(N,N), DET
TYPE (FM), SAVE :: TOL
TYPE (FM), ALLOCATABLE :: A1(:,:), A2(:,:), B1(:), R1(:), X1(:)
INTEGER, ALLOCATABLE :: KSWAP(:)
INTEGER :: I, J, K, KWARN_SAVE, NDSAVE
CALL FM_ENTER_USER_ROUTINE
TOL = EPSILON(TO_FM(1))/MBASE/TO_FM(10)**10
N = SIZE(A,DIM=1)
ALLOCATE(A1(N,N),A2(N,N),B1(N),R1(N),X1(N),KSWAP(N),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in FM_INVERSE_RM. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
! Raise precision.
NDSAVE = NDIG
NDIG = 2*NDIG
KWARN_SAVE = KWARN
KWARN = 0
! Copy A to A1 with higher precision.
110 CALL FM_EQU_R1(TOL,NDSAVE,NDIG)
DO I = 1, N
DO J = 1, N
CALL FM_EQU(A(I,J),A1(I,J),NDSAVE,NDIG)
ENDDO
ENDDO
A2 = A1
! Factor A into L*U form.
CALL FM_FACTOR_LU_RM(A1,N,DET,KSWAP)
IF (DET == 0 .OR. IS_UNKNOWN(DET)) THEN
IF (KWARN > 0) THEN
WRITE (KW,"(/' Error in FM_INVERSE_RM. The matrix is singular.'/)")
ENDIF
IF (KWARN >= 2) STOP
B = TO_FM(' UNKNOWN ')
GO TO 120
ENDIF
! Solve for the inverse matrix one column at a time.
DO K = 1, N
B1 = 0
B1(K) = 1
CALL FM_SOLVE_LU_RM(A1,N,B1,X1,KSWAP)
! Do an iterative refinement.
R1 = MATMUL(A2,X1) - B1
CALL FM_SOLVE_LU_RM(A1,N,R1,B1,KSWAP)
X1 = X1 - B1
! Check for accuracy at the user's precision.
IF (SQRT( DOT_PRODUCT( B1 , B1 ) ) > TOL) THEN
NDIG = 2*NDIG
GO TO 110
ENDIF
! Round the results and store column K in the B matrix.
DO I = 1, N
CALL FM_EQU(X1(I),B(I,K),NDIG,NDSAVE)
ENDDO
ENDDO
120 CALL FM_EQU_R1(DET,NDIG,NDSAVE)
CALL FM_DEALLOCATE(A1)
CALL FM_DEALLOCATE(A2)
CALL FM_DEALLOCATE(B1)
CALL FM_DEALLOCATE(R1)
CALL FM_DEALLOCATE(X1)
DEALLOCATE(A1,A2,B1,R1,X1,KSWAP)
NDIG = NDSAVE
KWARN = KWARN_SAVE
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_INVERSE_RM
SUBROUTINE FM_LIN_SOLVE_RM(A,X,B,N,DET)
USE FMVALS
USE FMZM
IMPLICIT NONE
! Gauss elimination to solve the linear system A X = B, where:
! A is the matrix of the system, containing the N x N coefficient matrix.
! B is the N x 1 right-hand-side vector.
! X is the returned N x 1 solution vector.
! DET is returned as the determinant of A.
! Nonzero DET means a solution was found.
! DET = 0 is returned if the system is singular.
! A,X,B,DET are all type (fm) multiprecision variables.
INTEGER :: N
TYPE (FM) :: A(N,N), B(N), X(N), DET
TYPE (FM), SAVE :: TOL
TYPE (FM), ALLOCATABLE :: A1(:,:), A2(:,:), B1(:), R1(:), X1(:)
INTEGER, ALLOCATABLE :: KSWAP(:)
INTEGER :: I, J, NDSAVE
CALL FM_ENTER_USER_ROUTINE
ALLOCATE(A1(N,N),A2(N,N),B1(N),R1(N),X1(N),KSWAP(N),STAT=J)
IF (J /= 0) THEN
WRITE (*,"(/' Error in FM_LIN_SOLVE_RM. Unable to allocate arrays with N = ',I8/)") N
STOP
ENDIF
TOL = EPSILON(B(1))/MBASE/TO_FM(10)**10
NDSAVE = NDIG
NDIG = 2*NDIG
! Copy A and B to A1 and B1 with higher precision.
110 CALL FM_EQU_R1(TOL,NDSAVE,NDIG)
DO I = 1, N
DO J = 1, N
CALL FM_EQU(A(I,J),A1(I,J),NDSAVE,NDIG)
CALL FM_EQ(A1(I,J),A2(I,J))
ENDDO
CALL FM_EQU(B(I),B1(I),NDSAVE,NDIG)
ENDDO
! Solve the system.
CALL FM_FACTOR_LU_RM(A1,N,DET,KSWAP)
IF (DET == 0 .OR. IS_UNKNOWN(DET)) THEN
IF (KWARN > 0) THEN
WRITE (KW,"(/' Error in FM_LIN_SOLVE_RM. The matrix is singular.'/)")
ENDIF
IF (KWARN >= 2) STOP
X1 = TO_FM(' UNKNOWN ')
GO TO 120
ENDIF
CALL FM_SOLVE_LU_RM(A1,N,B1,X1,KSWAP)
! Do an iterative refinement.
R1 = MATMUL(A2,X1) - B1
CALL FM_SOLVE_LU_RM(A1,N,R1,B1,KSWAP)
X1 = X1 - B1
! Check for accuracy at the user's precision.
IF (SQRT( DOT_PRODUCT( B1 , B1 ) ) > TOL) THEN
NDIG = 2*NDIG
GO TO 110
ENDIF
! Round and return X and DET.
120 DO I = 1, N
CALL FM_EQU(X1(I),X(I),NDIG,NDSAVE)
ENDDO
CALL FM_EQU_R1(DET,NDIG,NDSAVE)
NDIG = NDSAVE
CALL FM_DEALLOCATE(A1)
CALL FM_DEALLOCATE(A2)
CALL FM_DEALLOCATE(B1)
CALL FM_DEALLOCATE(R1)
CALL FM_DEALLOCATE(X1)
DEALLOCATE(A1,A2,B1,R1,X1,KSWAP)
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_LIN_SOLVE_RM
SUBROUTINE FM_FACTOR_LU_RM(A,N,DET,KSWAP)
USE FMZM
IMPLICIT NONE
! Gauss elimination to factor the NxN matrix A (LU decomposition).
! The time is proportional to N**3.
! Once this factorization has been done, a linear system A x = b
! with the same coefficient matrix A and Nx1 vector b can be solved
! for x using routine FM_SOLVE_LU_RM in time proportional to N**2.
! DET is returned as the determinant of A.
! Nonzero DET means there is a unique solution.
! DET = 0 is returned if the system is singular.
! KSWAP is a list of row interchanges made by the partial pivoting strategy during the
! elimination phase.
! After returning, the values in matrix A have been replaced by the multipliers
! used during elimination. This is equivalent to factoring the A matrix into
! a lower triangular matrix L times an upper triangular matrix U.
INTEGER :: N
INTEGER :: JCOL, JDIAG, JMAX, JROW, KSWAP(N)
TYPE (FM) :: A(N,N), DET
TYPE (FM), SAVE :: AMAX, AMULT, TEMP
CALL FM_ENTER_USER_ROUTINE
DET = 1
KSWAP(1:N) = 1
IF (N <= 0) THEN
DET = 0
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
IF (N == 1) THEN
KSWAP(1) = 1
DET = A(1,1)
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
! Do the elimination phase.
! JDIAG is the current diagonal element below which the elimination proceeds.
DO JDIAG = 1, N-1
! Pivot to put the element with the largest absolute value on the diagonal.
AMAX = ABS(A(JDIAG,JDIAG))
JMAX = JDIAG
DO JROW = JDIAG+1, N
IF (ABS(A(JROW,JDIAG)) > AMAX) THEN
AMAX = ABS(A(JROW,JDIAG))
JMAX = JROW
ENDIF
ENDDO
! If AMAX is zero here then the system is singular.
IF (AMAX == 0.0) THEN
DET = 0
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
! Swap rows JDIAG and JMAX unless they are the same row.
KSWAP(JDIAG) = JMAX
IF (JMAX /= JDIAG) THEN
DET = -DET
DO JCOL = JDIAG, N
TEMP = A(JDIAG,JCOL)
A(JDIAG,JCOL) = A(JMAX,JCOL)
A(JMAX,JCOL) = TEMP
ENDDO
ENDIF
DET = DET * A(JDIAG,JDIAG)
! For JROW = JDIAG+1, ..., N, eliminate A(JROW,JDIAG) by replacing row JROW by
! row JROW - A(JROW,JDIAG) * row JDIAG / A(JDIAG,JDIAG)
DO JROW = JDIAG+1, N
IF (A(JROW,JDIAG) == 0) CYCLE
AMULT = A(JROW,JDIAG)/A(JDIAG,JDIAG)
! Save the multiplier for use later by FM_SOLVE_LU_RM.
A(JROW,JDIAG) = AMULT
DO JCOL = JDIAG+1, N
CALL FMMPY_SUB_RM(A(JROW,JCOL)%MFM,AMULT%MFM,A(JDIAG,JCOL)%MFM)
ENDDO
ENDDO
ENDDO
DET = DET * A(N,N)
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_FACTOR_LU_RM
SUBROUTINE FM_SOLVE_LU_RM(A,N,B,X,KSWAP)
USE FMZM
IMPLICIT NONE
! Solve a linear system A x = b.
! A is the NxN coefficient matrix, after having been factored by FM_FACTOR_LU_RM.
! B is the Nx1 right-hand-side vector.
! X is returned with the solution of the linear system.
! KSWAP is a list of row interchanges made by the partial pivoting strategy during the
! elimination phase in FM_FACTOR_LU_RM.
! Time for this call is proportional to N**2.
INTEGER :: N, KSWAP(N)
TYPE (FM) :: A(N,N), B(N), X(N)
INTEGER :: J, JDIAG, JMAX
TYPE (FM), SAVE :: TEMP
CALL FM_ENTER_USER_ROUTINE
IF (N <= 0) THEN
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
IF (N == 1) THEN
X(1) = B(1) / A(1,1)
CALL FM_EXIT_USER_ROUTINE
RETURN
ENDIF
DO J = 1, N
X(J) = B(J)
ENDDO
! Do the elimination phase operations only on X.
! JDIAG is the current diagonal element below which the elimination proceeds.
DO JDIAG = 1, N-1
! Pivot to put the element with the largest absolute value on the diagonal.
JMAX = KSWAP(JDIAG)
! Swap rows JDIAG and JMAX unless they are the same row.
IF (JMAX /= JDIAG) THEN
TEMP = X(JDIAG)
X(JDIAG) = X(JMAX)
X(JMAX) = TEMP
ENDIF
! For JROW = JDIAG+1, ..., N, eliminate A(JROW,JDIAG) by replacing row JROW by
! row JROW - A(JROW,JDIAG) * row JDIAG / A(JDIAG,JDIAG)
! After factoring, A(JROW,JDIAG) is the original A(JROW,JDIAG) / A(JDIAG,JDIAG).
DO J = JDIAG+1, N
X(J) = X(J) - A(J,JDIAG) * X(JDIAG)
ENDDO
ENDDO
! Do the back substitution.
DO JDIAG = N, 1, -1
! Divide row JDIAG by the diagonal element.
X(JDIAG) = X(JDIAG) / A(JDIAG,JDIAG)
! Zero above the diagonal in column JDIAG by replacing row JROW by
! row JROW - A(JROW,JDIAG) * row JDIAG
! For JROW = 1, ..., JDIAG-1.
IF (JDIAG == 1) EXIT
DO J = 1, JDIAG-1
X(J) = X(J) - A(J,JDIAG) * X(JDIAG)
ENDDO
ENDDO
CALL FM_EXIT_USER_ROUTINE
END SUBROUTINE FM_SOLVE_LU_RM
SUBROUTINE FMMPY_SUB_RM(MA,MB,MC)
USE FMVALS
IMPLICIT NONE
! Fused multiply-subtract operation. Return MA = MA - MB*MC
! This is an internal FM routine used by FM_FACTOR_LU_RM. It doesn't always return correctly
! rounded results, since precision will have already been raised by FM_LIN_SOLVE_RM before
! calling FM_FACTOR_LU_RM.
INTEGER :: MA,MB,MC
INTEGER :: J,K,K1,KPTA,KPTC,MXY,NUMBER_USED_SAVE,MA_VS_MBMC
DOUBLE PRECISION :: A1,A2,B,B1,B2,C1,C2,DPA,DPBC
REAL (KIND(1.0D0)) :: MBJ, MGD
! Special cases.
IF (MWK(START(MB)+3) == 0 .OR. MWK(START(MC)+3) == 0 .OR. &
MWK(START(MA)+2) - 1 > MWK(START(MB)+2) + MWK(START(MC)+2) + NDIG) THEN
RETURN
ENDIF
IF (MWK(START(MA)+3) == 0 .OR. &
MWK(START(MB)+2) + MWK(START(MC)+2) - 1 > MWK(START(MA)+2) + NDIG) THEN
CALL FMMPY(MB,MC,MA)
IF (MWK(START(MA)+2) /= MUNKNO) MWK(START(MA)) = -MWK(START(MA))
RETURN
ENDIF
IF (ABS(MWK(START(MA)+2)) > MEXPAB .OR. ABS(MWK(START(MB)+2)) > MEXPAB .OR. &
ABS(MWK(START(MC)+2)) > MEXPAB .OR. MBASE < 1000 .OR. MBASE**2 > MAXINT .OR. &
NDIG > 900 .OR. NDIG > MAXINT/MBASE**2) THEN
GO TO 110
ENDIF
! Determine which of abs(MA) and abs(MB*MC) is larger.
MA_VS_MBMC = 0
B = MBASE
IF (MWK(START(MA)+2) <= MWK(START(MB)+2) + MWK(START(MC)+2) - 2) THEN
MA_VS_MBMC = -1
GO TO 120
ENDIF
IF (MWK(START(MA)+2) >= MWK(START(MB)+2) + MWK(START(MC)+2) + 1) THEN
MA_VS_MBMC = 1
GO TO 120
ENDIF
A1 = MWK(START(MA)+3)
A2 = MWK(START(MA)+4)
B1 = MWK(START(MB)+3)
B2 = MWK(START(MB)+4)
C1 = MWK(START(MC)+3)
C2 = MWK(START(MC)+4)
IF (MWK(START(MA)+2) == MWK(START(MB)+2) + MWK(START(MC)+2) - 1) THEN
DPA = A1 * B + A2 + 1
DPBC = B1 * C1 * B + B1 * C2 + B2 * C1 + C2 * B2 / B
IF (DPA < DPBC) THEN
MA_VS_MBMC = -1
GO TO 120
ENDIF
DPA = A1 * B + A2
DPBC = B1 * C1 * B + B1 * (C2+1) + (B2+1) * C1 + (C2+1) * (B2+1) / B
IF (DPA > DPBC) THEN
MA_VS_MBMC = 1
GO TO 120
ENDIF
ELSE IF (MWK(START(MA)+2) == MWK(START(MB)+2) + MWK(START(MC)+2)) THEN
DPA = A1 * B + A2 + 1
DPBC = B1 * C1 + ( B1 * C2 + B2 * C1 ) / B + C2 * B2 / B**2
IF (DPA < DPBC) THEN
MA_VS_MBMC = -1
GO TO 120
ENDIF
DPA = A1 * B + A2
DPBC = B1 * C1 + ( B1 * (C2+1) + (B2+1) * C1 ) / B + (C2+1) * (B2+1) / B**2
IF (DPA > DPBC) THEN
MA_VS_MBMC = 1
GO TO 120
ENDIF
ENDIF
! If it is not easy to determine which term is larger, make separate calls to
! multiply and subtract.
110 NUMBER_USED_SAVE = NUMBER_USED
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
MXY = -2
CALL FMMPY(MB,MC,MXY)
CALL FMSUB_R1(MA,MXY)
NUMBER_USED = NUMBER_USED_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
! Handle the operation using 4 cases, depending on which term is larger and whether
! MA and MB*MC have opposite signs or not.
120 IF (MWK(START(MA)) * MWK(START(MB)) * MWK(START(MC)) < 0) THEN
IF (MA_VS_MBMC == 1) THEN
MGD = 0
K1 = 2 + MWK(START(MA)+2) - MWK(START(MB)+2) - MWK(START(MC)+2)
DO J = K1, NDIG
MBJ = MWK(START(MB)+3+J-K1)
KPTA = START(MA)+2+J
KPTC = START(MC)+3
DO K = J, NDIG
MWK(KPTA) = MWK(KPTA) + MBJ * MWK(KPTC)
KPTA = KPTA + 1
KPTC = KPTC + 1
ENDDO
IF (KPTC <= START(MC)+2+NDIG) MGD = MGD + MBJ * MWK(KPTC)
ENDDO
K1 = MWK(START(MA)+2)
MWK(START(MA)+2) = 0
KPTA = START(MA)+3+NDIG
MWK(KPTA-1) = MWK(KPTA-1) + NINT( MGD / MBASE )
DO J = NDIG, 1, -1
KPTA = KPTA - 1
IF (MWK(KPTA) >= MBASE) THEN
K = MWK(KPTA) / MBASE
MWK(KPTA) = MWK(KPTA) - K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) + K
ENDIF
ENDDO
IF (MWK(START(MA)+2) > 0) THEN
DO J = NDIG, 1, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K1 = K1 + 1
ENDIF
MWK(START(MA)+2) = K1
IF (MWK(START(MA)+3) >= MBASE) THEN
DO J = NDIG, 3, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K = MWK(START(MA)+3) / MBASE
MWK(START(MA)+4) = MWK(START(MA)+3) - K * MBASE
MWK(START(MA)+3) = K
MWK(START(MA)+2) = MWK(START(MA)+2) + 1
ENDIF
ENDIF
IF (MA_VS_MBMC == -1) THEN
MGD = 0
K1 = MWK(START(MB)+2) + MWK(START(MC)+2) - 1
K = MWK(START(MB)+2) + MWK(START(MC)+2) - MWK(START(MA)+2) - 1
MWK(START(MA)+2) = 0
IF (K > 0) THEN
IF (K <= NDIG) MGD = MWK(START(MA)+2+NDIG+1-K)
DO J = NDIG, K+1, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-K)
ENDDO
DO J = 1, MIN(K,NDIG)
MWK(START(MA)+2+J) = 0
ENDDO
ELSE IF (K == -1) THEN
DO J = 1, NDIG
MWK(START(MA)+1+J) = MWK(START(MA)+1+J+1)
ENDDO
MWK(START(MA)+2+NDIG) = 0
ENDIF
DO J = 1, NDIG
MBJ = MWK(START(MB)+2+J)
KPTA = START(MA)+2+J
KPTC = START(MC)+3
DO K = J, NDIG
MWK(KPTA) = MWK(KPTA) + MBJ * MWK(KPTC)
KPTA = KPTA + 1
KPTC = KPTC + 1
ENDDO
IF (KPTC <= START(MC)+2+NDIG) MGD = MGD + MBJ * MWK(KPTC)
ENDDO
KPTA = START(MA)+3+NDIG
MWK(KPTA-1) = MWK(KPTA-1) + NINT( MGD / MBASE )
DO J = NDIG, 1, -1
KPTA = KPTA - 1
IF (MWK(KPTA) >= MBASE) THEN
K = MWK(KPTA) / MBASE
MWK(KPTA) = MWK(KPTA) - K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) + K
ENDIF
ENDDO
IF (MWK(START(MA)+2) > 0) THEN
DO J = NDIG, 1, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K1 = K1 + 1
ENDIF
MWK(START(MA)+2) = K1
IF (MWK(START(MA)+3) >= MBASE) THEN
DO J = NDIG, 3, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K = MWK(START(MA)+3) / MBASE
MWK(START(MA)+4) = MWK(START(MA)+3) - K * MBASE
MWK(START(MA)+3) = K
MWK(START(MA)+2) = MWK(START(MA)+2) + 1
ENDIF
ENDIF
ELSE
NUMBER_USED_SAVE = NUMBER_USED
TEMPV_CALL_STACK = TEMPV_CALL_STACK + 1
MXY = -2
CALL FMEQ(MA,MXY)
IF (MA_VS_MBMC == 1) THEN
MGD = 0
K1 = 2 + MWK(START(MA)+2) - MWK(START(MB)+2) - MWK(START(MC)+2)
DO J = K1, NDIG
MBJ = MWK(START(MB)+3+J-K1)
KPTA = START(MA)+2+J
KPTC = START(MC)+3
DO K = J, NDIG
MWK(KPTA) = MWK(KPTA) - MBJ * MWK(KPTC)
KPTA = KPTA + 1
KPTC = KPTC + 1
ENDDO
IF (KPTC <= START(MC)+2+NDIG) MGD = MGD - MBJ * MWK(KPTC)
ENDDO
K1 = MWK(START(MA)+2)
MWK(START(MA)+2) = 0
KPTA = START(MA)+3+NDIG
MWK(KPTA-1) = MWK(KPTA-1) + NINT( MGD / MBASE )
DO J = NDIG, 1, -1
KPTA = KPTA - 1
IF (MWK(KPTA) < 0) THEN
K = (-MWK(KPTA)-1) / MBASE + 1
MWK(KPTA) = MWK(KPTA) + K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) - K
ELSE IF (MWK(KPTA) >= MBASE) THEN
K = MWK(KPTA) / MBASE
MWK(KPTA) = MWK(KPTA) - K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) + K
ENDIF
ENDDO
IF (MWK(START(MA)+2) > 0) THEN
DO J = NDIG, 1, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K1 = K1 + 1
ENDIF
MWK(START(MA)+2) = K1
IF (MWK(START(MA)+3) == 0) THEN
CALL FMMPY(MB,MC,MA)
CALL FMSUB_R2(MXY,MA)
NUMBER_USED = NUMBER_USED_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
ENDIF
IF (MA_VS_MBMC == -1) THEN
MGD = 0
K1 = MWK(START(MB)+2) + MWK(START(MC)+2) - 1
K = MWK(START(MB)+2) + MWK(START(MC)+2) - MWK(START(MA)+2) - 1
MWK(START(MA)+2) = 0
IF (K > 0) THEN
IF (K <= NDIG) MGD = -MWK(START(MA)+2+NDIG+1-K)
DO J = NDIG, K+1, -1
MWK(START(MA)+2+J) = -MWK(START(MA)+2+J-K)
ENDDO
DO J = 1, MIN(K,NDIG)
MWK(START(MA)+2+J) = 0
ENDDO
ELSE IF (K == -1) THEN
DO J = 1, NDIG
MWK(START(MA)+1+J) = -MWK(START(MA)+1+J+1)
ENDDO
MWK(START(MA)+2+NDIG) = 0
ELSE IF (K == 0) THEN
DO J = 1, NDIG
MWK(START(MA)+2+J) = -MWK(START(MA)+2+J)
ENDDO
ENDIF
DO J = 1, NDIG
MBJ = MWK(START(MB)+2+J)
KPTA = START(MA)+2+J
KPTC = START(MC)+3
DO K = J, NDIG
MWK(KPTA) = MWK(KPTA) + MBJ * MWK(KPTC)
KPTA = KPTA + 1
KPTC = KPTC + 1
ENDDO
IF (KPTC <= START(MC)+2+NDIG) MGD = MGD + MBJ * MWK(KPTC)
ENDDO
KPTA = START(MA)+3+NDIG
MWK(KPTA-1) = MWK(KPTA-1) + NINT( MGD / MBASE )
DO J = NDIG, 1, -1
KPTA = KPTA - 1
IF (MWK(KPTA) >= MBASE) THEN
K = MWK(KPTA) / MBASE
MWK(KPTA) = MWK(KPTA) - K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) + K
ELSE IF (MWK(KPTA) < 0) THEN
K = (-MWK(KPTA)-1) / MBASE + 1
MWK(KPTA) = MWK(KPTA) + K * MBASE
MWK(KPTA-1) = MWK(KPTA-1) - K
ENDIF
ENDDO
IF (MWK(START(MA)+2) > 0) THEN
DO J = NDIG, 1, -1
MWK(START(MA)+2+J) = MWK(START(MA)+2+J-1)
ENDDO
K1 = K1 + 1
ENDIF
MWK(START(MA)+2) = K1
MWK(START(MA)) = -MWK(START(MA))
IF (MWK(START(MA)+3) == 0) THEN
CALL FMMPY(MB,MC,MA)
CALL FMSUB_R2(MXY,MA)
NUMBER_USED = NUMBER_USED_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
ENDIF
NUMBER_USED = NUMBER_USED_SAVE
TEMPV_CALL_STACK = TEMPV_CALL_STACK - 1
RETURN
ENDIF
END SUBROUTINE FMMPY_SUB_RM
SUBROUTINE RM_MOD_INVERSE(A1, A2, DET_P, N, P, SINGULAR)
! Find the NxN inverse matrix of A1 with modular arithmetic mod P.
! A2 is initially A1 mod P, and the modular inverse matrix is returned in A2.
! DET_P is returned as the modular determinant.
! SINGULAR is returned true if the system is singular.
USE FMVALS
USE FMZM
IMPLICIT NONE
INTEGER :: N, I, J, JD, JR, JC
TYPE (IM) :: A1(N,2*N)
DOUBLE PRECISION :: A2(N,2*N), DET_P, A2JDJD, AMULT, P, T
LOGICAL :: SINGULAR
SINGULAR = .FALSE.
! Copy A1 to A2 Mod P.
DO I = 1, N
DO J = 1, N
CALL RM_MOD_ONE(A1(I,J)%MIM,P,A2(I,J))
IF (MWK(START(A1(I,J)%MIM)) < 0) A2(I,J) = -A2(I,J) + P
A2(I,J+N) = 0
ENDDO
CALL RM_MOD_ONE(A1(I,I+N)%MIM,P,A2(I,I+N))
ENDDO
! Gauss Elimination.
DET_P = 1
DO JD = 1, N-1
IF (A2(JD,JD) == 0.0D0) THEN
DO JR = JD+1, N
IF (A2(JR,JD) /= 0.0D0) THEN
DO JC = JD, 2*N
T = A2(JD,JC)
A2(JD,JC) = A2(JR,JC)
A2(JR,JC) = T
ENDDO
EXIT
ENDIF
ENDDO
DET_P = -DET_P
ENDIF
IF (A2(JD,JD) == 0.0D0) THEN
SINGULAR = .TRUE.
RETURN
ENDIF
A2JDJD = A2(JD,JD)
CALL RM_INV_MOD_P(A2(JD,JD),P,T)
DET_P = MODULO( DET_P * A2JDJD, P )
DO JR = JD+1, N
AMULT = MODULO( A2(JR,JD) * T , P )
DO JC = JD, 2*N
A2(JR,JC) = MODULO( A2(JR,JC) - AMULT * A2(JD,JC) , P )
ENDDO
ENDDO
ENDDO
DET_P = MODULO( DET_P * A2(N,N), P )
IF (DET_P == 0) THEN
SINGULAR = .TRUE.
RETURN
ENDIF
! Back substitution.
DO JR = N, 1, -1
DO J = 1, N
DO JC = JR+1, N
A2(JR,N+J) = MODULO( A2(JR,N+J) - A2(JR,JC) * A2(JC,N+J) , P )
ENDDO
CALL RM_INV_MOD_P(A2(JR,JR),P,T)
A2(JR,N+J) = MODULO( A2(JR,N+J) * T , P )
ENDDO
ENDDO
END SUBROUTINE RM_MOD_INVERSE
SUBROUTINE RM_SOLVE_MOD(A2, P2, A3, P3)
! Solve for smallest magnitude x such that x = a2 mod p2 and x = a3 mod p3.
! A3 is returned as that x between -p2*p3/2 and +p2*p3/2
! A2 and P2 are double precision, A3 and P3 are type (im).
USE FMVALS
USE FMZM
IMPLICIT NONE
INTEGER :: I2, IR
INTEGER, SAVE :: KPT
TYPE (IM) :: A3, P3
TYPE (IM), SAVE :: Q3, T(0:2)
DOUBLE PRECISION :: A2, P2, A, B, Q, R
! Use the Euclidean algorithm to solve the modular equations.
KPT = 0
I2 = P2
T(2) = 0
Q3 = 0
CALL IMDVIR(P3%MIM,I2,T(2)%MIM,IR)
B = P2
A = IR
T(0) = 1
T(1) = -T(2)
DO WHILE (A > 0)
Q = AINT(B/A)
R = B - Q * A
IF (Q /= 1.0D0) THEN
CALL IMMPYI(T(MOD(KPT+1,3))%MIM,INT(Q),Q3%MIM)
CALL IMSUB(T(KPT)%MIM,Q3%MIM,T(MOD(KPT+2,3))%MIM)
KPT = MOD(KPT+1,3)
ELSE
CALL IMSUB(T(KPT)%MIM,T(MOD(KPT+1,3))%MIM,T(MOD(KPT+2,3))%MIM)
KPT = MOD(KPT+1,3)
ENDIF
B = A
A = R
ENDDO
Q3 = MODULO( (A3 - INT(A2)) * T(KPT), P3 )
A3 = INT(A2) + Q3 * INT(P2)
Q3 = INT(P2) * P3
IF (2*A3 > Q3) A3 = A3 - Q3
END SUBROUTINE RM_SOLVE_MOD
SUBROUTINE RM_INV_MOD_P(X,P,X_INVERSE)
! Return X_INVERSE as the multiplicative inverse of x mod p. I.e., x * x_inverse mod p = 1.
IMPLICIT NONE
DOUBLE PRECISION :: X,P,X_INVERSE, Q,R0,R1,R2,S0,S1,S2
R0 = P
R1 = X
S0 = 0
S1 = 1
DO WHILE (R1 > 0)
Q = AINT(R0 / R1)
R2 = R0 - Q * R1
S2 = S0 - Q * S1
R0 = R1
R1 = R2
S0 = S1
S1 = S2
ENDDO
IF (S0 < 0) S0 = S0 + P
X_INVERSE = S0
END SUBROUTINE RM_INV_MOD_P
SUBROUTINE RM_MOD_ONE(NUM,P,REM)
! Return integer REM = mod( NUM , P )
! NUM is an IM-format multiple precision integer
! P is a one-word integer.
USE FMVALS
IMPLICIT NONE
INTEGER :: NUM, J, KPT, N
DOUBLE PRECISION :: P, REM
REAL (KIND(1.0D0)) :: MDIV, MREM
MDIV = P
KPT = START(NUM) + 3
N = MWK(KPT-1)
MREM = 0.0D0
DO J = 1, N
MREM = MOD( MBASE*MREM + MWK(KPT) , MDIV )
KPT = KPT + 1
ENDDO
REM = MREM
END SUBROUTINE RM_MOD_ONE
SUBROUTINE RM_NEXT_PRIME(P)
IMPLICIT NONE
INTEGER :: J
DOUBLE PRECISION :: P, D
! Find the next prime after P and return it in P.
110 P = P + 1
IF (MOD(P,2.0D0) == 0) GO TO 110
IF (MOD(P,3.0D0) == 0) GO TO 110
DO J = 5, INT(SQRT(P))+7, 6
D = J
IF (MOD(P,D) == 0) GO TO 110
IF (MOD(P,D+2.0D0) == 0) GO TO 110
ENDDO
END SUBROUTINE RM_NEXT_PRIME
END MODULE FM_RATIONAL_ARITHMETIC
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