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cosolver/FM/src/fmsave.f90
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fmsave.f90
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MODULE FMVALS
! These are the global and saved variables used by the FM package.
! See the FM_User_Manual.txt file for further description of some of these variables.
! They are initialized assuming the program will run on a 32-bit computer with variables in
! FM.f95 having names beginning with 'M' being declared as having 64-bit representations
! (DOUBLE PRECISION).
! For a machine with a different architecture, or for setting the precision level to a different
! value, CALL FMSET(NPREC) before doing any multiple precision operations. FMSET tries to
! initialize the variables to the best values for the given machine. To have the values chosen
! by FMSET written on unit KW, CALL FMVARS.
! Base and precision will be set to give slightly more than 50 decimal digits of precision, giving
! the user 50 significant digits of precision along with several base ten guard digits.
! MBASE is set to 10**7.
! JFORM1 and JFORM2 are set to ES format displaying 50 significant digits.
! The trace option is set off.
! The mode for angles in trig functions is set to radians.
! The rounding mode is set to symmetric rounding (to nearest).
! Warning error message level is set to 1.
! Cancellation error monitor is set off.
! Screen width for output is set to 80 columns.
! The exponent character for FM output is set to 'M'.
! Debug error checking is set off.
! KW, the unit number for all FM output, is set to 6.
PRIVATE AINT, CEILING, DIGITS, EPSILON, HUGE, INT, LOG, MAX, MIN, SQRT
REAL (KIND(1.0D0)), PARAMETER :: M_TWO = 2
DOUBLE PRECISION, PARAMETER :: DP_TWO = 2
INTEGER, PARAMETER :: I_TWO = 2
REAL, PARAMETER :: R_TWO = 2
! KW is the unit number for standard output from the FM package.
! This includes trace output and error messages.
INTEGER, SAVE :: KW = 6
! The min below is needed when m-variables have more precision than double,
! as with 64-bit integer m-variables and 64-bit doubles (53-bit precision).
REAL (KIND(1.0D0)), PARAMETER :: MAX_REPRESENTABLE_M_VAR = &
( (M_TWO ** (MIN(DIGITS(M_TWO),DIGITS(DP_TWO))-1)) - 1 ) * 2 + 1
! MAXINT should be set to a very large integer, possibly the largest representable
! integer for the current machine. For most 32-bit machines, MAXINT is set
! to 2**53 - 1 = 9.007D+15 when double precision arithmetic is used for
! M-variables. Using integer M-variables usually gives
! MAXINT = 2**31 - 1 = 2147483647.
! Setting MAXINT to a smaller number is ok, but this unnecessarily restricts
! the permissible range of MBASE and MXEXP.
REAL (KIND(1.0D0)), SAVE :: MAXINT = MAX_REPRESENTABLE_M_VAR
! INTMAX is a large value close to the overflow threshold for integer variables.
! It is usually 2**31 - 1 for machines with 32-bit integer arithmetic.
INTEGER, SAVE :: INTMAX = HUGE(I_TWO)
! DPMAX should be set to a value near the machine's double precision overflow threshold,
! so that DPMAX and 1.0D0/DPMAX are both representable in double precision.
DOUBLE PRECISION, SAVE :: DPMAX = HUGE(DP_TWO)/5
! SPMAX should be set to a value near the machine's single precision overflow threshold,
! so that 1.01*SPMAX and 1.0/SPMAX are both representable in single precision.
REAL, SAVE :: SPMAX = HUGE(R_TWO)/5
! MXBASE is the maximum value for MBASE.
REAL (KIND(1.0D0)), PARAMETER :: MAX_BASE = AINT(SQRT(MAX_REPRESENTABLE_M_VAR + 1.0D-9))
REAL (KIND(1.0D0)), SAVE :: MXBASE = MAX_BASE
! MBASE is the currently used base for arithmetic.
REAL (KIND(1.0D0)), PARAMETER :: M_TEN = 10
REAL (KIND(1.0D0)), SAVE :: MBASE = M_TEN ** AINT(LOG(MAX_BASE/4.0D0) / LOG(10.0D0))
! NDIG is the number of digits currently being carried.
INTEGER, SAVE :: NDIG = CEILING( 52.0D0 / AINT(LOG(MAX_BASE/4.0D0)/LOG(10.0D0)) ) + 1
! KFLAG is the flag for error conditions.
INTEGER, SAVE :: KFLAG = 0
! NTRACE is the trace switch. Default is no printing.
INTEGER, SAVE :: NTRACE = 0
! LVLTRC is the trace level. Default is to trace only routines called directly
! by the user.
INTEGER, SAVE :: LVLTRC = 1
! NCALL is the call stack pointer.
INTEGER, SAVE :: NCALL = 0
! RAISE_NDIG is set to 1 when one FM routine calls another and the second one needs
! to use more guard digits.
INTEGER, SAVE :: RAISE_NDIG = 0
! NAMEST is the call stack.
INTEGER, PRIVATE :: I
CHARACTER(9), SAVE :: NAMEST(0:50) = (/ ('MAIN ' , I = 0, 50) /)
! Some constants that are often needed are stored with the maximum precision to which
! they have been computed in the currently used base. This speeds up the trig, log,
! power, and exponential functions.
! NDIGPI is the number of digits available in the currently stored value of pi (MPISAV).
INTEGER, SAVE :: NDIGPI = 0
! MBSPI is the value of MBASE for the currently stored value of pi.
REAL (KIND(1.0D0)), SAVE :: MBSPI = 0
! NDIGE is the number of digits available in the currently stored value of e (MESAV).
INTEGER, SAVE :: NDIGE = 0
! MBSE is the value of MBASE for the currently stored value of e.
REAL (KIND(1.0D0)), SAVE :: MBSE = 0
! NDIGLB is the number of digits available in the currently stored value of LN(MBASE)
! (MLBSAV).
INTEGER, SAVE :: NDIGLB = 0
! MBSLB is the value of MBASE for the currently stored value of LN(MBASE).
REAL (KIND(1.0D0)), SAVE :: MBSLB = 0
! NDIGLI is the number of digits available in the currently stored values of the four
! logarithms used by FMLNI: MLN2, MLN3, MLN5, MLN7.
INTEGER, SAVE :: NDIGLI = 0
! MBSLI is the value of MBASE for the currently stored values of MLN2, MLN3, MLN5, MLN7.
REAL (KIND(1.0D0)), SAVE :: MBSLI = 0
! MXEXP is the current maximum exponent.
! MXEXP2 is the internal maximum exponent. This is used to define the overflow and
! underflow thresholds.
!
! These values are chosen so that FM routines can raise the overflow/underflow limit
! temporarily while computing intermediate results. MXEXP2 satisfies these conditions:
! 1. EXP(INTMAX) > MXBASE**(MXEXP2+1)
! 2. MXEXP2 < MAXINT/20
!
! The overflow threshold is MBASE**(MXEXP+1), and the underflow threshold is
! MBASE**(-MXEXP-1). This means the valid exponents in the first word of an FM
! number can range from -MXEXP to MXEXP+1 (inclusive).
REAL (KIND(1.0D0)), PARAMETER :: MAX_EXPONENT = AINT( MIN( &
MAX(HUGE(INTMAX) / LOG(MAX_BASE+1.0D-9) , 117496405.0D0), &
MAX_REPRESENTABLE_M_VAR / 20.0D0) )
REAL (KIND(1.0D0)), SAVE :: MXEXP = AINT( MAX_EXPONENT / 2.01D0 + 0.5D0 )
REAL (KIND(1.0D0)), SAVE :: MXEXP2 = MAX_EXPONENT
! KACCSW is a switch used to enable cancellation error monitoring. Routines where
! cancellation is not a problem run faster by skipping the cancellation monitor
! calculations.
! KACCSW = 0 means no error monitoring,
! = 1 means error monitoring is done.
INTEGER, SAVE :: KACCSW = 0
! MEXPUN is the exponent used as a special symbol for underflowed results.
REAL (KIND(1.0D0)), SAVE :: MEXPUN = AINT( -MAX_EXPONENT * 1.01D0 )
! MEXPOV is the exponent used as a special symbol for overflowed results.
REAL (KIND(1.0D0)), SAVE :: MEXPOV = AINT( MAX_EXPONENT * 1.01D0 )
! MUNKNO is the exponent used as a special symbol for unknown FM results
! (1/0, SQRT(-3.0), ...). When changing this value, also change the three
! TYPE FM, IM, ZM initializations in FMZM90.f95.
REAL (KIND(1.0D0)), SAVE :: MUNKNO = AINT( MAX_EXPONENT * 1.0201D0 )
! RUNKNO is returned from FM to real or double conversion routines when no valid result
! can be expressed in real or double precision. On systems that provide a value
! for undefined results (e.g., Not A Number) setting RUNKNO to that value is
! reasonable. On other systems set it to a value that is likely to make any
! subsequent results obviously wrong that use it. In either case a KFLAG = -4
! condition is also returned.
REAL, SAVE :: RUNKNO = -1.01*(HUGE(R_TWO)/3.0)
! IUNKNO is returned from FM to integer conversion routines when no valid result can be
! expressed as a one word integer. KFLAG = -4 is also set.
INTEGER, SAVE :: IUNKNO = -HUGE(I_TWO)/18
! JFORM1 indicates the format used by FMOUT.
INTEGER, SAVE :: JFORM1 = 1
! JFORM2 indicates the number of digits used in FMOUT.
INTEGER, SAVE :: JFORM2 = 50
! KRAD = 1 indicates that trig functions use radians,
! = 0 means use degrees.
INTEGER, SAVE :: KRAD = 1
! KWARN = 0 indicates that no warning message is printed and execution continues when
! UNKNOWN or another exception is produced.
! = 1 means print a warning message and continue.
! = 2 means print a warning message and stop.
INTEGER, SAVE :: KWARN = 1
! KROUND = 1 causes all results to be rounded to the nearest FM number, or to the
! value with an even last digit if the result is halfway between two
! FM numbers.
! = 0 causes all results to be rounded toward zero (chopped).
! = -1 causes all results to be rounded toward minus infinity.
! = 2 causes all results to be rounded toward plus infinity.
INTEGER, SAVE :: KROUND = 1
! KRPERF = 1 causes more guard digits to be used, to get perfect rounding in the mode
! set by KROUND.
! = 0 causes a smaller number of guard digits used, to give nearly perfect
! rounding. This number is chosen so that the last intermediate result
! should have error less than 0.001 unit in the last place of the final
! rounded result.
! Beginning with version 1.3 KRPERF is not used, since perfect rounding is always done.
! The variable has been left in the package for compatibility with earlier versions.
INTEGER, SAVE :: KRPERF = 0
! KSWIDE defines the maximum screen width to be used for all unit KW output.
INTEGER, SAVE :: KSWIDE = 80
! KESWCH = 1 causes input to FMINP with no digits before the exponent letter to be
! treated as if there were a leading '1'. This is sometimes better for
! interactive input: 'E7' converts to 10.0**7.
! = 0 causes a leading zero to be assumed. This gives compatibility with
! Fortran: 'E7' converts to 0.0.
INTEGER, SAVE :: KESWCH = 1
! CMCHAR defines the exponent letter to be used for FM variable output from FMOUT,
! as in 1.2345M+678.
! Change it to 'E' for output to be read by a non-FM program.
CHARACTER, SAVE :: CMCHAR = 'M'
! KDEBUG = 0 Error checking is not done for valid input arguments and parameters
! like NDIG and MBASE upon entry to each routine.
! = 1 Error checking is done.
INTEGER, SAVE :: KDEBUG = 0
! KROUND_RETRY is an internal flag controlling cases where the result has close to
! 1/2 ulp of error and the operation should be done again with more
! guard digits to insure perfect rounding.
INTEGER, SAVE :: KROUND_RETRY = 0
! KSUB is an internal flag set during subtraction so that the addition routine will
! negate its second argument.
INTEGER, SAVE :: KSUB = 0
! KSQR is an internal flag set during squaring so that at high precision the
! multiplication routine will not need to compute the fft of its second argument.
INTEGER, SAVE :: KSQR = 0
! KREM is an internal flag set during high precision integer division operations to
! indicate that the remainder in IMDIVR need not be computed.
INTEGER, SAVE :: KREM = 1
! JRSIGN is an internal flag set during arithmetic operations so that the rounding
! routine will know the sign of the final result.
INTEGER, SAVE :: JRSIGN = 0
! LHASH is a flag variable used to indicate when to initialize two hash tables that are
! used for character look-up during input conversion.
! LHASH = 1 means that the tables have been built.
! LHASH1 and LHASH2 are the array dimensions of the tables.
! KHASHT and KHASHV are the two tables.
INTEGER, SAVE :: LHASH = 0
INTEGER, PARAMETER :: LHASH1 = 0
INTEGER, PARAMETER :: LHASH2 = 256
INTEGER, SAVE :: KHASHT(LHASH1:LHASH2),KHASHV(LHASH1:LHASH2)
! DPEPS is the approximate machine precision.
DOUBLE PRECISION, SAVE :: DPEPS = EPSILON(DP_TWO)
! LJSUMS is the maximum number of concurrent sums to use in function evaluation.
INTEGER, PARAMETER :: LJSUMS = 1000
! Saved constants that depend on MBASE.
REAL (KIND(1.0D0)), SAVE :: MBLOGS = 0
! (Setting MBLOGS to zero here will cause the other variables that depend on MBASE
! to automatically be defined when the first FM operation is done.)
REAL, SAVE :: ALOGMB = 1.611810E+1
REAL, SAVE :: ALOGM2 = 2.325350E+1
REAL, SAVE :: ALOGMX = 3.673680E+1
REAL, SAVE :: ALOGMT = 7.0E0
INTEGER, SAVE :: NGRD21 = 1
INTEGER, SAVE :: NGRD52 = 2
INTEGER, SAVE :: NGRD22 = 2
REAL (KIND(1.0D0)), SAVE :: MEXPAB = AINT(MAX_EXPONENT / 5.0D0)
DOUBLE PRECISION, SAVE :: DLOGMB = 1.611809565095832D+1
DOUBLE PRECISION, SAVE :: DLOGTN = 2.302585092994046D+0
DOUBLE PRECISION, SAVE :: DLOGTW = 6.931471805599453D-1
DOUBLE PRECISION, SAVE :: DPPI = 3.141592653589793D+0
DOUBLE PRECISION, SAVE :: DLOGTP = 1.837877066409345D+0
DOUBLE PRECISION, SAVE :: DLOGPI = 1.144729885849400D+0
DOUBLE PRECISION, SAVE :: DLOGEB = 2.236222824932432D+0
REAL (KIND(1.0D0)), SAVE :: MBASEL = 0
REAL (KIND(1.0D0)), SAVE :: MBASEN = 0
REAL (KIND(1.0D0)), SAVE :: M_VAL, M_VAL1, M_VAL2, M_VAL3, M_VAL4
INTEGER, SAVE :: NDIGL = 0
INTEGER, SAVE :: NDIGN = 0
INTEGER, SAVE :: NGUARL = 0
INTEGER, SAVE :: N21
INTEGER, SAVE :: NGRDN
! These variables are used by FM_RANDOM_NUMBER.
! MBRAND is the base used for the random number arithmetic.
! It needs to remain the same even if the user changes MBASE.
REAL (KIND(1.0D0)), SAVE :: MBRAND = M_TEN ** AINT(LOG(MAX_BASE/4.0D0) / LOG(10.0D0))
INTEGER, SAVE :: MRNX = -3
INTEGER, SAVE :: MRNA = -3
INTEGER, SAVE :: MRNM = -3
INTEGER, SAVE :: MRNC = -3
INTEGER, SAVE :: START_RANDOM_SEQUENCE = -1
INTEGER, SAVE :: LAST_DIGIT_OF_M_M1
DOUBLE PRECISION, SAVE :: DPM
! Work area for FM numbers, and related variables.
INTEGER, SAVE :: SIZE_OF_MWK = 0
REAL (KIND(1.0D0)), SAVE, DIMENSION(:), ALLOCATABLE :: MWK, MOVE_MWK, MOVE_F
INTEGER, PARAMETER :: START_RESIZE = 200000 ! default 100 000
INTEGER, SAVE :: SIZE_OF_START = START_RESIZE
LOGICAL, SAVE :: IN_USER_FUNCTION = .FALSE.
INTEGER, SAVE :: USER_FUNCTION_LEVEL = 0
INTEGER, SAVE :: LEVEL_OF_RECURSION = 0
INTEGER, SAVE :: NUMBER_USED_AT_LEVEL(1000)
INTEGER, SAVE, DIMENSION(:), ALLOCATABLE :: START, TEMPV, RESIZE, SIZE_OF, TEMP7
INTEGER, PARAMETER :: SIZE_OF_TEMP6 = 100
INTEGER, SAVE :: FMTEMP6(SIZE_OF_TEMP6), NMAX_FMTEMP6 = 0, N_FMTEMP6 = 0, TOTAL_FMTEMP6 = 0
INTEGER, SAVE :: IMTEMP6(SIZE_OF_TEMP6), NMAX_IMTEMP6 = 0, N_IMTEMP6 = 0, TOTAL_IMTEMP6 = 0
INTEGER, SAVE :: TOTAL_TEMP7 = 0
INTEGER, SAVE :: LOWEST_SAVED_AREA_INDEX = 2*START_RESIZE + 1
INTEGER, SAVE :: START_OF_MWK_SAVED_AREA = 0
INTEGER, SAVE :: MINIMUM_SAVED_CONSTANTS_USED = 10**9
INTEGER, SAVE :: NUMBER_USED = 0
INTEGER, SAVE :: MAXIMUM_NUMBER_USED = 0
INTEGER, SAVE :: MAXIMUM_MWK_USED = 0
INTEGER, SAVE :: RESULT_SIZE = 0
INTEGER, SAVE :: TEMPV_CALL_STACK = 0
INTEGER, SAVE :: MWA = -4
INTEGER, SAVE :: MWD = -4
INTEGER, SAVE :: MWE = -4
INTEGER, SAVE :: MPA = -3
INTEGER, SAVE :: MPB = -3
INTEGER, SAVE :: MPC = -3
INTEGER, SAVE :: MPD = -3
INTEGER, SAVE :: MWI = -3
INTEGER, SAVE :: MPMA = -3
INTEGER, SAVE :: MPMB = -3
INTEGER, SAVE :: MPX(2) = (/ -3, -3 /)
INTEGER, SAVE :: MPY(2) = (/ -3, -3 /)
INTEGER, SAVE :: MPZ(2) = (/ -3, -3 /)
! Variables related to input/output and formatting.
INTEGER, SAVE :: LMBUFF = 0
INTEGER, SAVE :: LMBUFZ = 0
CHARACTER, SAVE, DIMENSION(:), ALLOCATABLE :: CMBUFF,CMBUFZ,MOVE_CMBUFF
! Saved FM constants.
INTEGER, SAVE :: MPISAV = -3
INTEGER, SAVE :: MESAV = -3
INTEGER, SAVE :: MLBSAV = -3
INTEGER, SAVE :: MLN2 = -3
INTEGER, SAVE :: MLN3 = -3
INTEGER, SAVE :: MLN5 = -3
INTEGER, SAVE :: MLN7 = -3
! Set the default value of JFORMZ to give ' 1.23 + 4.56 i ' style format for output
! of complex variables.
INTEGER, SAVE :: JFORMZ = 1
! Set the default value of JPRNTZ to print real and imaginary parts on one line
! whenever possible.
INTEGER, SAVE :: JPRNTZ = 1
! MBERN is the array used to save Bernoulli numbers so they do not have to be
! re-computed on subsequent calls.
! NDBERN is the array used to save the number of digits in the current base for
! each of the saved Bernoulli numbers.
! MBSBRN is the value of MBASE for the currently saved Bernoulli numbers.
REAL (KIND(1.0D0)), SAVE :: MBSBRN = 0
! NUMBRN is the number of the largest Bernoulli number saved using base MBSBRN.
INTEGER, SAVE :: NUMBRN = 0
! LMBERN is the size of the arrays MBERN and NDBERN.
INTEGER, PARAMETER :: LMBERN = 60000
INTEGER, SAVE, DIMENSION(LMBERN) :: MBERN = (/ (-3 , I = 1, LMBERN) /)
INTEGER, SAVE, DIMENSION(LMBERN) :: NDBERN = 0
! B(2N) is stored in MBERN(N) for 2N >= 28.
! M_EULER is the saved value of Euler's constant.
! M_GAMMA_MA is the last input value to FMGAM, and
! M_GAMMA_MB is the corresponding output value.
! M_LN_2PI holds the saved value of LN(2*pi).
INTEGER, SAVE :: M_EULER = -3
INTEGER, SAVE :: M_GAMMA_MA = -3
INTEGER, SAVE :: M_GAMMA_MB = -3
INTEGER, SAVE :: M_LN_2PI = -3
! MBSGAM is the value of MBASE used in the currently stored value of
! M_GAMMA_MA and M_GAMMA_MB.
! NDGGAM is the maximum NDIG used in the currently stored value of
! M_GAMMA_MA and M_GAMMA_MB.
REAL (KIND(1.0D0)), SAVE :: MBSGAM = 0
INTEGER, SAVE :: NDGGAM = 0
! MBS2PI is the value of MBASE used in the currently stored value of LN(2*pi).
! NDG2PI is the maximum NDIG used in the currently stored value of LN(2*pi).
REAL (KIND(1.0D0)), SAVE :: MBS2PI = 0
INTEGER, SAVE :: NDG2PI = 0
! MBSEUL is the value of MBASE used in the currently stored value of M_EULER.
! NDGEUL is the maximum NDIG used in the currently stored value of M_EULER.
REAL (KIND(1.0D0)), SAVE :: MBSEUL = 0
INTEGER, SAVE :: NDGEUL = 0
END MODULE FMVALS
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