FM_Interval_User_Manual.txt
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FM_Interval_User_Manual.txt
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			This file extends the FM_User_Manual.txt file for the files that support the FM interval arithmetic
			package. All of these programs use the 3 basic files discussed there:

			1. FMSAVE.f95 Module for FM internal global variables

			2. FM.f95 Subroutine library for multiple-precision operations

			3. FMZM90.f95 Modules for interfaces and definitions of derived-types

			These are the files included for interval arithmetic.

			4. fm_interval.f95 The routines and interfaces for interval operations

			5. TestFMinterval.f95 Test program for the FM interval routines

			6. SampleFMinterval.f95 Small sample program using fm_interval

			7. IntervalExamplesFM.f95 Code for the example interval calculations that are discussed in the
			paper "A Multiple-Precision Interval Arithmetic Package"


			After the first 3 files have been compiled and the program TestFM.f95 has been compiled and run
			to verify the basic FM package has been installed successfully, as shown in FM_User_Manual.txt,
			files 4 through 7 can be compiled and run.

			The interval arithmetic operations are made available in the user's program by putting
			USE FM_INTERVAL_ARITHMETIC
			at the top of routines using interval arithmetic, and the multiple precision interval variables
			are declared as
			TYPE (FM_INTERVAL)

			Here are sample commands to run the 3 programs in files 5, 6, and 7. These are for the gfortran
			compiler on a Windows PC. Macs are very similar, as are other compilers. See FM_User_Manual.txt.


			gfortran fm_interval.f95 -c -O3


			gfortran TestFMinterval.f95 -c -O3

			gfortran fmsave.o FM.o FMZM90.o fm_interval.o TestFMinterval.o -o TestFMinterval.exe

			./TestFMinterval


			gfortran SampleFMinterval.f95 -c -O3

			gfortran fmsave.o FM.o FMZM90.o fm_interval.o SampleFMinterval.o -o SampleFMinterval.exe

			./SampleFMinterval


			gfortran IntervalExamplesFM.f95 -c -O3

			gfortran fmsave.o FM.o FMZM90.o fm_interval.o IntervalExamplesFM.o -o IntervalExamplesFM.exe

			./IntervalExamplesFM


			TestFMinterval is a program that tests all the interval operations defined in the FM interval
			arithmetic package. Run it first to make sure that the interval package has been successfully
			installed. At the end of the run, it should say:

			1044 cases tested. No errors were found.


			SampleFMinterval is a small program showing how to do some interval calculations. It checks a
			sum for stability and accuracy using 4 methods and compares the results:

			1. Do the sum in double precision
			2. Use FM with increasing precision
			3. Use FM with different rounding modes
			4. Use FM with interval arithmetic

			SampleFMinterval also tests a recurrence that is horribly unstable using FM vs FM interval
			arithmetic. The results are saved in the file SampleFMinterval.out.


			IntervalExamplesFM is a program that runs the example interval calculations that are discussed
			in the paper "A Multiple-Precision Interval Arithmetic Package". The results are saved in file
			IntervalExamplesFM.out.

			The program also produces 7 other output files that contain the data on how the width of the
			intervals increase at each step of the calculation for different examples in the paper. These
			files were used to produce the graphs in the paper showing rate of increase for interval width.

			The basic arithmetic operations are provided, along with assignments and logical comparisons.
			Here are the functions that are available for the FM_INTERVAL type variables:

			ABS
			ACOS
			ACOSH
			AINT
			ANINT
			ASIN
			ASINH
			ATAN
			ATANH
			ATAN2
			BESSEL_J0
			BESSEL_J1
			BESSEL_JN
			BESSEL_Y0
			BESSEL_Y1
			BESSEL_YN
			BETA
			BINOMIAL
			CEILING
			COS
			COSH
			COS_INTEGRAL
			COSH_INTEGRAL
			DBLE
			DIGITS
			DIM
			DINT
			DOT_PRODUCT
			EPSILON
			ERF
			ERFC
			EXP
			EXPONENT
			EXP_INTEGRAL_EI
			EXP_INTEGRAL_EN
			FACTORIAL
			FLOOR
			FRACTION
			FRESNEL_C
			FRESNEL_S
			GAMMA
			HUGE
			INCOMPLETE_BETA
			INCOMPLETE_GAMMA1
			INCOMPLETE_GAMMA2
			INT
			IS_OVERFLOW
			IS_UNDERFLOW
			IS_UNKNOWN
			LEFT_ENDPOINT
			LOG
			LOG10
			LOG_ERFC
			LOG_GAMMA
			LOG_INTEGRAL
			MATMUL
			MAX
			MAXEXPONENT
			MAXVAL
			MIN
			MINEXPONENT
			MINVAL
			MOD
			MODULO
			NEAREST
			NINT
			POCHHAMMER
			POLYGAMMA
			PRECISION
			PRODUCT
			PSI
			RADIX
			RANGE
			REAL
			RIGHT_ENDPOINT
			RRSPACING
			SCALE
			SETEXPONENT
			SIGN
			SIN
			SINH
			SIN_INTEGRAL
			SINH_INTEGRAL
			SPACING
			SQRT
			SUM
			TAN
			TANH
			TO_FM
			TO_IM
			TO_ZM
			TINY

cosolver/FM/FMinterval/FM_Interval_User_Manual.txt565bccac0d42new_coulomb

FM_Interval_User_Manual.txtView Options

cosolver/FM/FMinterval/FM_Interval_User_Manual.txt
565bccac0d42new_coulomb

FM_Interval_User_Manual.txt
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