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1992-11-17
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CEPHES MATHEMATICAL FUNCTION LIBRARY
This computer software library is a collection of more than
400 high quality mathematical routines for scientific and
engineering applications. All are written entirely in C
language. Many of the functions are supplied in six different
arithmetic precisions: 32 bit single (24-bit significand), 64 bit
IEEE double (53-bit), 64 bit DEC (56-bit), 80 or 96 bit IEEE long
double (64-bit), and extended precision formats having 144-bit
and 336-bit significands. The extended precision arithmetic is
included with the function library.
The library treats about 180 different mathematical
functions. In addition to the elementary arithmetic and
transcendental routines, the library includes a substantial
collection of probability integrals, Bessel functions, and higher
transcendental functions.
There are complex variable routines covering complex
arithmetic, complex logarithm and exponential, and complex
trigonometric functions.
Each function subroutine has been tested by comparing at a
large number of points against high precision check routines.
The test programs use floating point arithmetic having 144 bit
(43 decimal) precision. Thus the actual accuracy of each program
is reported, not merely the result of a consistency test. Test
results are given with the description of each routine.
The routines have been characterized and tested in IEEE Std
754 double precision arithmetic (both Intel and Motorola
formats), used on IBM PC and a growing number of other computers,
and also in the popular DEC/IBM double precision format.
For DEC and IEEE arithmetic, numerical constants and
approximation coefficients are supplied as integer arrays in
order to eliminate conversion errors that might be introduced by
the language compiler. All coefficients are also supplied in the
normal decimal scientific notation so that the routines can be
compiled and used on other machines that do not support either of
the above numeric formats.
A single, common error handling routine is supplied. Error
conditions produce a display of the function name and error type.
The user may easily insert modifications to implement any desired
action on specified types of error.
The following table summarizes the current contents of the
double precision library. See also the corresponding
documentation for the single and long double precision libraries.
Accuracies reported for DEC and IEEE arithmetic are with
arithmetic rounding precision limited to 56 and 53 bits,
respectively. Higher precision may be realized if an arithmetic
unit such as the 8087 or 68881 is used in conjunction with an
optimizing compiler. The accuracy figures are experimentally
measured; they are not guaranteed maximum errors.
Documentation is included on the distribution media as
Unix-style manual pages that describe the functions and their
invocation. The primary documentation for the library functions
is the book by Moshier, Methods and Programs for Mathematical
Functions, Prentice-Hall, 1989.
Function Name Accuracy
-------- ---- DEC IEEE
---- ----
Arithmetic and Algebraic
Square root sqrt 2e-17 2e-16
Long integer square root lsqrt 1 1
Cube root cbrt 2e-17 2e-16
Evaluate polynomial polevl
Evaluate Chebyshev series chbevl
Round to nearest integer value round
Truncate upward to integer ceil
Truncate downward to integer floor
Extract exponent frexp
Add integer to exponent ldexp
Absolute value fabs
Rational arithmetic euclid
Roots of a polynomial polrt
Reversion of power series revers
IEEE 854 arithmetic ieee
Polynomial arithmetic (polyn.c):
Add polynomials poladd
Subtract polynomials polsub
Multiply polynomials polmul
Divide polynomials poldiv
Substitute polynomial variable polsbt
Evaluate polynomial poleva
Set all coefficients to zero polclr
Copy coefficients polmov
Display coefficients polprt
Note, polyr.c contains routines corresponding to
the above for polynomials with rational coefficients.
Power series manipulations (polmisc.c):
Square root of a polynomial polsqt
Arctangent polatn
Sine polsin
Reversion of power series revers
Exponential and Trigonometric
Arc cosine acos 3e-17 3e-16
Arc hyperbolic cosine acosh 4e-17 5e-16
Arc hyperbolic sine asinh 5e-17 4e-16
Arc hyperbolic tangent atanh 3e-17 2e-16
Arcsine asin 6e-17 5e-16
Arctangent atan 4e-17 3e-16
Quadrant correct arctangent atan2 4e-17 4e-16
Cosine cos 3e-17 2e-16
Cosine of arg in degrees cosdg 4e-17 2e-16
Exponential, base e exp 3e-17 2e-16
Exponential, base 2 exp2 2e-17 2e-16
Exponential, base 10 exp10 3e-17 2e-16
Hyperbolic cosine cosh 3e-17 3e-16
Hyperbolic sine sinh 4e-17 3e-16
Hyperbolic tangent tanh 3e-17 3e-16
Logarithm, base e log 2e-17 2e-16
Logarithm, base 2 log2 2e-16
Logarithm, base 10 log10 3e-17 2e-16
Power pow 1e-15 2e-14
Integer Power powi 9e-14
Sine sin 3e-17 2e-16
Sine of arg in degrees sindg 4e-17 2e-16
Tangent tan 4e-17 3e-16
Tangent of arg in degrees tandg 3e-17 3e-16
Exponential integral
Exponential integral expn 2e-16 2e-15
Hyperbolic cosine integral shichi 9e-17 8e-16
Hyperbolic sine integral shichi 9e-17 7e-16
Cosine integral sici 8e-17A 7e-16
Sine integral sici 4e-17A 4e-16
Gamma
Beta beta 8e-15 8e-14
Factorial fac 2e-17 2e-15
Gamma gamma 1e-16 1e-15
Logarithm of gamma function lgam 5e-17 5e-16
Incomplete beta integral incbet 4e-14 4e-13
Inverse beta integral incbi 3e-13 8e-13
Incomplete gamma integral igam 5e-15 4e-14
Complemented gamma integral igamc 3e-15 1e-12
Inverse gamma integral igami 9e-16 1e-14
Psi (digamma) function psi 2e-16 1e-15
Reciprocal Gamma rgamma 1e-16 1e-15
Error function
Error function erf 5e-17 4e-16
Complemented error function erfc 5e-16 6e-14
Dawson's integral dawsn 7e-16 7e-16
Fresnel integral (C) fresnl 2e-16 2e-15
Fresnel integral (S) fresnl 2e-16 2e-15
Bessel
Airy (Ai) airy 6e-16A 2e-15A
Airy (Ai') airy 6e-16A 5e-15A
Airy (Bi) airy 6e-16A 4e-15A
Airy (Bi') airy 6e-16A 5e-15A
Bessel, order 0 j0 4e-17A 4e-16A
Bessel, order 1 j1 4e-17A 3e-16A
Bessel, order n jn 7e-17A 2e-15A
Bessel, noninteger order jv 5e-15A
Bessel, second kind, order 0 y0 7e-17A 1e-15A
Bessel, second kind, order 1 y1 9e-17A 1e-15A
Bessel, second kind, order n yn 3e-16A 3e-15A
Bessel, noninteger order yv see struve.c
Modified Bessel, order 0 i0 8e-17 6e-16
Exponentially scaled i0 i0e 8e-17 5e-16
Modified Bessel, order 1 i1 1e-16 2e-15
Exponentially scaled i1 i1e 1e-16 2e-15
Modified Bessel, nonint. order iv 3e-15 2e-14
Mod. Bessel, 3rd kind, order 0 k0 1e-16 1e-15
Exponentially scaled k0 k0e 1e-16 1e-15
Mod. Bessel, 3rd kind, order 1 k1 9e-17 1e-15
Exponentially scaled k1 k1e 9e-17 8e-16
Mod. Bessel, 3rd kind, order n kn 1e-9 2e-8
Hypergeometric
Confluent hypergeometric hyperg 1e-15 2e-14
Gauss hypergeometric function hyp2f1 4e-11 9e-8
2F0 hyp2f0f see hyperg.c
1F2 onef2f see struve.c
3F0 threef0f see struve.c
Elliptic
Complete elliptic integral (E) ellpe 3e-17 2e-16
Incomplete elliptic integral (E) ellie 2e-16 2e-15
Complete elliptic integral (K) ellpk 4e-17 3e-16
Incomplete elliptic integral (K) ellik 9e-17 6e-16
Jacobian elliptic function (sn) ellpj 5e-16A 4e-15A
Jacobian elliptic function (cn) ellpj 4e-15A
Jacobian elliptic function (dn) ellpj 1e-12A
Jacobian elliptic function (phi) ellpj 9e-16
Probability
Binomial distribution bdtr 4e-14 4e-13
Complemented binomial bdtrc 4e-14 4e-13
Inverse binomial bdtri 3e-13 8e-13
Chi square distribution chdtr 5e-15 3e-14
Complemented Chi square chdtrc 3e-15 2e-14
Inverse Chi square chdtri 9e-16 6e-15
F distribution fdtr 4e-14 4e-13
Complemented F fdtrc 4e-14 4e-13
Inverse F distribution fdtri 3e-13 8e-13
Gamma distribution gdtr 5e-15 3e-14
Complemented gamma gdtrc 3e-15 2e-14
Negative binomial distribution nbdtr 4e-14 4e-13
Complemented negative binomial nbdtrc 4e-14 4e-13
Normal distribution ndtr 2e-15 3e-14
Inverse normal distribution ndtri 1e-16 7e-16
Poisson distribution pdtr 3e-15 2e-14
Complemented Poisson pdtrc 5e-15 3e-14
Inverse Poisson distribution pdtri 3e-15 5e-14
Student's t distribution stdtr 2e-15 2e-14
Miscellaneous
Dilogarithm spence 3e-16 4e-15
Riemann Zeta function zetac 1e-16 1e-15
Two argument zeta function zeta
Struve function struve
Matrix
Fast Fourier transform fftr
Simultaneous linear equations simq
Simultaneous linear equations gels (symmetric coefficient matrix)
Matrix inversion minv
Matrix multiply mmmpy
Matrix times vector mvmpy
Matrix transpose mtransp
Eigenvectors (symmetric matrix) eigens
Levenberg-Marquardt nonlinear equations lmdif
Numerical Integration
Simpson's rule simpsn
Runge-Kutta runge - see de118
Adams-Bashforth adams - see de118
Complex Arithmetic
Complex addition cadd 1e-17 1e-16
Subtraction csub 1e-17 1e-16
Multiplication cmul 2e-17 2e-16
Division cdiv 5e-17 4e-16
Absolute value cabs 3e-17 3e-16
Square root csqrt 3e-17 3e-16
Complex Exponential and Trigonometric
Exponential cexp 4e-17 3e-16
Logarithm clog 9e-17 5e-16A
Cosine ccos 5e-17 4e-16
Arc cosine cacos 2e-15 2e-14
Sine csin 5e-17 4e-16
Arc sine casin 2e-15 2e-14
Tangent ctan 7e-17 7e-16
Arc tangent catan 1e-16 2e-15
Cotangent ccot 7e-17 9e-16
Applications
Minimax rational approximations to functions remes
Digital elliptic filters ellf
Numerical integration of the Moon and planets de118
IEEE compliance test for printf(), scanf() ieetst
Long Double Precision Functions
Function Name Accuracy
-------- ---- --------
Arc hyperbolic cosine acoshl 2e-19
Arc cosine acosl 1e-19
Arc hyperbolic sine asinhl 2e-19
Arcsine asinl 3e-19
Arc hyperbolic tangent atanhl 1e-19
Arctangent atanl 1e-19
Quadrant correct arctangent atan2l 2e-19
Cube root cbrtl 7e-20
Truncate upward to integer ceill
Hyperbolic cosine coshl 1e-19
Cosine cosl 1e-19
Cotangent cotl 2e-19
Exponential, base e expl 1e-19
Exponential, base 2 exp2l 9e-20
Exponential, base 10 exp10l 1e-19
Absolute value fabsl
Truncate downward to integer floorl
Extract exponent frexpl
Add integer to exponent ldexpl
Logarithm, base e logl 9e-20
Logarithm, base 2 log2l 1e-19
Logarithm, base 10 log10l 9e-20
Integer Power powil 4e-17
Power powl 3e-18
Hyperbolic sine sinhl 2e-19
Sine sinl 1e-19
Square root sqrtl 8e-20
Hyperbolic tangent tanhl 1e-19
Tangent tanl 2e-19
Single Precision Routines
Function Name Accuracy
-------- ---- --------
Arithmetic
Truncate upward to integer ceilf
Truncate downward to integer floorf
Extract exponent frexpf
Add integer to exponent ldexpf
Absolute value fabsf
Square root sqrtf 9e-8
Cube root cbrtf 8e-8
Polynomials and Power Series
Polynomial arithmetic (polynf.c):
Add polynomials poladdf
Subtract polynomials polsubf
Multiply polynomials polmulf
Divide polynomials poldivf
Substitute polynomial variable polsbtf
Evaluate polynomial polevaf
Set all coefficients to zero polclrf
Copy coefficients polmovf
Display coefficients polprtf
Note, polyr.c contains routines corresponding to
the above for polynomials with rational coefficients.
Evaluate polynomial polevlf (coefficients in reverse order)
Evaluate Chebyshev series chbevlf (coefficients in reverse order)
Exponential and Trigonometric
Arc cosine acosf 1e-7
Arc hyperbolic cosine acoshf 2e-7
Arc hyperbolic sine asinhf 2e-7
Arc hyperbolic tangent atanhf 1e-7
Arcsine asinf 3e-7
Arctangent atanf 2e-7
Quadrant correct arctangent atan2f 2e-7
Cosine cosf 1e-7
Cosine of arg in degrees cosdgf 1e-7
Cotangent cotf 3e-7
Cotangent of arg in degrees cotdgf 2e-7
Exponential, base e expf 2e-7
Exponential, base 2 exp2f 2e-7
Exponential, base 10 exp10f 1e-7
Hyperbolic cosine coshf 2e-7
Hyperbolic sine sinhf 1e-7
Hyperbolic tangent tanhf 1e-7
Logarithm, base e logf 8e-8
Logarithm, base 2 log2f 1e-7
Logarithm, base 10 log10f 1e-7
Power powf 1e-6
Integer Power powif 1e-6
Sine sinf 1e-7
Sine of arg in degrees sindgf 1e-7
Tangent tanf 3e-7
Tangent of arg in degrees tandgf 2e-7
Exponential integral
Exponential integral expnf 6e-7
Hyperbolic cosine integral shichif 4e-7A
Hyperbolic sine integral shichif 4e-7
Cosine integral sicif 2e-7A
Sine integral sicif 4e-7A
Gamma
Beta betaf 4e-5
Factorial facf 6e-8
Gamma gammaf 6e-7
Logarithm of gamma function lgamf 7e-7(A)
Incomplete beta integral incbetf 2e-4
Inverse beta integral incbif 3e-4
Incomplete gamma integral igamf 8e-6
Complemented gamma integral igamcf 8e-6
Inverse gamma integral igamif 1e-5
Psi (digamma) function psif 8e-7
Reciprocal Gamma rgammaf 9e-7
Error function
Error function erff 2e-7
Complemented error function erfcf 4e-6
Dawson's integral dawsnf 4e-7
Fresnel integral (C) fresnlf 1e-6
Fresnel integral (S) fresnlf 1e-6
Bessel
Airy (Ai) airyf 1e-5A
Airy (Ai') airyf 9e-6A
Airy (Bi) airyf 2e-6A
Airy (Bi') airyf 2e-6A
Bessel, order 0 j0f 2e-7A
Bessel, order 1 j1f 2e-7A
Bessel, order n jnf 4e-7A
Bessel, noninteger order jvf 2e-6A
Bessel, second kind, order 0 y0f 2e-7A
Bessel, second kind, order 1 y1f 2e-7A
Bessel, second kind, order n ynf 2e-6A
Bessel, second kind, order v yvf see struvef.c
Modified Bessel, order 0 i0f 4e-7
Exponentially scaled i0 i0ef 4e-7
Modified Bessel, order 1 i1f 2e-6
Exponentially scaled i1 i1ef 2e-6
Modified Bessel, nonint. order ivf 9e-6
Mod. Bessel, 3rd kind, order 0 k0f 8e-7
Exponentially scaled k0 k0ef 8e-7
Mod. Bessel, 3rd kind, order 1 k1f 5e-7
Exponentially scaled k1 k1ef 5e-7
Mod. Bessel, 3rd kind, order n knf 2e-4A
Hypergeometric
Confluent hypergeometric 1F1 hypergf 1e-5
Gauss hypergeometric function hyp2f1f 2e-3
2F0 hyp2f0f see hypergf.c
1F2 onef2f see struvef.c
3F0 threef0f see struvef.c
Elliptic
Complete elliptic integral (E) ellpef 1e-7
Incomplete elliptic integral (E) ellief 5e-7
Complete elliptic integral (K) ellpkf 1e-7
Incomplete elliptic integral (K) ellikf 3e-7
Jacobian elliptic function (sn) ellpjf 2e-6A
Jacobian elliptic function (cn) ellpjf 2e-6A
Jacobian elliptic function (dn) ellpjf 1e-3A
Jacobian elliptic function (phi) ellpjf 4e-7
Probability
Binomial distribution bdtrf 7e-5
Complemented binomial bdtrcf 6e-5
Inverse binomial bdtrif 4e-5
Chi square distribution chdtrf 3e-5
Complemented Chi square chdtrcf 3e-5
Inverse Chi square chdtrif 2e-5
F distribution fdtrf 2e-5
Complemented F fdtrcf 7e-5
Inverse F distribution fdtrif 4e-5A
Gamma distribution gdtrf 6e-5
Complemented gamma gdtrcf 9e-5
Negative binomial distribution nbdtrf 2e-4
Complemented negative binomial nbdtrcf 1e-4
Normal distribution ndtrf 2e-5
Inverse normal distribution ndtrif 4e-7
Poisson distribution pdtrf 7e-5
Complemented Poisson pdtrcf 8e-5
Inverse Poisson distribution pdtrif 9e-6
Student's t distribution stdtrf 2e-5
Miscellaneous
Dilogarithm spencef 4e-7
Riemann Zeta function zetacf 6e-7
Two argument zeta function zetaf 7e-7
Struve function struvef 9e-5
Complex Arithmetic
Complex addition caddf 6e-8
Subtraction csubf 6e-8
Multiplication cmulf 1e-7
Division cdivf 2e-7
Absolute value cabsf 1e-7
Square root csqrtf 2e-7
Complex Exponential and Trigonometric
Exponential cexpf 1e-7
Logarithm clogf 3e-7A
Cosine ccosf 2e-7
Arc cosine cacosf 9e-6
Sine csinf 2e-7
Arc sine casinf 1e-5
Tangent ctanf 3e-7
Arc tangent catanf 2e-6
Cotangent ccotf 4e-7
QLIB Extended Precision Mathematical Library
q100asm.bat Create 100-decimal Q type library (for IBM PC MSDOS)
q100asm.rsp
qlibasm.bat 43-decimal Q type library (for IBM PC MSDOS)
qlibasm.rsp
qlib.lib Q type library, 43 decimal
qlib100.lib Q type library, 100 decimal
qlib120.lib Q type library, 120 decimal
Function calling arguments:
NQ is the number of 16-bit short integers in a number (see qhead.h)
short x[NQ], x1[NQ], ... are inputs
short y[NQ], y1[NQ], ... are outputs
mconf.h Machine configuration file
mtherr.c Common error handling routine
qacosh.c Arc hyperbolic cosine
qacosh( x, y );
qairy.c Airy functions
qairy( x, Ai, Ai', Bi, Bi' );
Also see source program for auxiliary functions.
qasin.c Arc sine
qasin( x, y );
qasinh.c Arc hyperbolic sine
qasinh( x, y );
qatanh.c Arc hyperbolic tangent
qatanh( x, y );
qatn.c Arc tangent
qatn( x, y );
qatn2( x1, x2, y ); y = radian angle whose tangent is x2/x1
qbeta.c Beta function
qbeta( x, y );
qcbrt.c Cube root
qcbrt( x, y );
qcmplx.c Complex variable functions:
qcabs absolute value qcabs( y );
qcadd add
qcsub subtract qcsub( a, b, y ); y = b - a
qcmul multiply
qcdiv divide qcdiv( d, n, y ); y = n/d
qcmov move
qcneg negate qcneg( y );
qcexp exponential function
qclog logarithm
qcsin sine
qccos cosine
qcasin arcsine
qcacos arccosine
qcsqrt square root
qctan tangent
qccot cotangent
qcatan arctangent
qcos.c Cosine
qcosm1( x, y ); y = cos(x) - 1
qcosh.c Hyperbolic cosine
qctst1.c Universal function test program for complex variables
qdawsn.c Dawson's integral
qellie.c Incomplete elliptic integral (E)
qellik.c Incomplete elliptic integral (K)
qellpe.c Complete elliptic integral (E)
qellpj.c Jacobian elliptic functions sn, cn, dn, phi
qellpj( u, m, sn, cn, dn, phi ); sn = sn(u|m), etc.
qellpk.c Complete elliptic integral (K)
qerf.c Error integral
qerfc.c Complementary error integral
qeuclid.c Q type rational arithmetic:
qradd add fractions
qrsub subtract fractions
qrmul multiply fractions
qrdiv divide fractions
qreuclid reduce to lowest terms
qexp.c Exponential function
qexp10.c Base 10 exponential function
qexp2.c Base 2 exponential function
qexp21.c 2**x - 1
qexpn.c Exponential integral
qf68k.a Q type arithmetic for 68000 OS-9
qf68k.asm Q type arithmetic for 68000 (Definicon assembler)
qf68k.s Q type arithmetic for 68000 (System V Unix)
qfac.c Factorial
qfresf.c Fresnel integral S(x)
Fresnel integral C(x)
qgamma.c Gamma function
log Gamma function
qhead.asm Q type configuration file for assembly language
qhead.h Q type configuration file for C language
qhy2f1.c Gauss hypergeometric function
qhyp.c Confluent hypergeometric function
qigam.c Incomplete gamma integral
qigami.c Functional inverse of incomplete gamma integral
qin.c Bessel function In
qincb.c Incomplete beta integral
qincbi.c Functional inverse of incomplete beta integral
qine.c Exponentially weighted In
qjn.c Bessel function Jv (noninteger order)
qhank Hankel's asymptotic expansion
qjypn.c Auxiliary Bessel functions
qjyqn.c
qkn.c modified Bessel function Kn
qkne.c Exponentially weighted Kn
qlog.c Natural logarithm
qlog1.c log(1+x)
qlog10.c Common logarithm
qndtr.c Gaussian distribution function
qndtri.c Functional inverse of Gaussian distribution function
qpolyr.c Q type polynomial arithmetic, rational coefficients:
poleva Evaluate polynomial a(t) at t = x.
polprt Print the coefficients of a to D digits.
polclr Set a identically equal to zero, up to a[na].
polmov Set b = a.
poladd c = b + a, nc = max(na,nb)
polsub c = b - a, nc = max(na,nb)
polmul c = b * a, nc = na+nb
poldiv c = b / a, nc = MAXPOL
qpow.c Power function, also
qpowi raise to integer power
qprob.c Various probability integrals:
qbdtr binomial distribution
qbdtrc complemented binomial distribution
qbdtri inverse of binomial distribution
qchdtr chi-square distribution
qchdti inverse of chi-square distribution
qfdtr F distribution
qfdtrc complemented F distribution
qfdtri inverse of F distribution
qgdtr gamma distribution
qgdtrc complemented gamma distribution
qnbdtr negative binomial distribution
qnbdtc complemented negative binomial
qpdtr Poisson distribution
qpdtrc complemented Poisson distribution
qpdtri inverse of Poisson distribution
qpsi.c psi function
qshici.c hyperbolic sine integral
hyperbolic cosine integral
qsici.c sine integral
cosine integral
qsimq.c solve simultaneous equations
qsin.c sine
qsinmx3(x,y); y = sin(x) - x
qsindg.c sine of arg in degrees
qsinh.obj hyperbolic sine
qspenc.c Spence's integral (dilogarithm)
qsqrt.c square root
qsqrta.c strictly rounded square root
qstudt.c Student's t distribution function
qtan.c tangent
qtanh.c hyperbolic tangent
qtst1.c Universal function test program
qyn.c Bessel function Yn (integer order), also
qyaux0 auxiliary functions
qyaux1
qymod modulus
qyphase phase
qzetac.c Riemann zeta function
Arithmetic routines
qflt.c Main Q type arithmetic package:
asctoq decimal ASCII string to Q type
dtoq DEC double precision to Q type
etoq IEEE double precision to Q type
ltoq long integer to Q type
qabs absolute value
qadd add
qclear set to zero
qcmp compare
qdiv divide
qifrac long integer part plus q type fraction
qinfin set to infinity, leaving its sign alone
qmov b = a
qmul multiply
qmuli multiply by small integer
qneg negate
qnrmlz adjust exponent and mantissa
qsub subtract
qtoasc Q type to decimal ASCII string
qtod convert Q type to DEC double precision
qtoe convert Q type to IEEE double precision
qflta.c Q type arithmetic, C language loops, strict rounding
qfltb.c Q type arithmetic, C language faster loops
mulr.asm Q type multiply, IBM PC assembly language
divn.asm Q type IBM PC divide routine
subm.asm Q type assembly language add, subtract for MSDOS
qfltd.asm Q type arithmetic for 68020 (Definicon assembler)
qconst.c Q type common constants
qc120.c 120 decimal version of qconst.c
mul128.a Fast multiply algorithm (for OS-9 68000)
mul128ts.c Test program for above
mul32.a
mul64.a
qfloor.c Q type floor(), also
qround() round to integer
Applications
calc100.doc Documentation for 100 digit calculator program
qcalc.c Command interpreter for calculator program
qcalc.h Include file for command interpreter
qcalc120.exe 120 decimal calculator program
qcalcasm.bat Make calculator program
qcalclin.bat
qccalc.mak Make complex variable calculator program
qparanoi.c Paranoia arithmetic test for Q type arithmetic
notes Paranoia documentation
qparanoi.mak Paranoia makefile
etst.c Arithmetic demo program
etstasm.bat
etstlink.bat
dentst.c frexp(), ldexp() tester
qstirling.c Find coefficients for Stirling's formula
qbernum.c Generates Bernoulli numbers
qbernum.lst
qbernuma.bat
Calculator programs for qcalc
euler.tak Euler's constant
gamcof.tak Bernoulli numbers for gamma function
gamma.tak Gamma function
lgamnum.doc Stirling's formula
lgamnum.tak
zeta.tak zeta function
ctest.tak exercise complex variable calculator
A: absolute error; others are relative error (i.e., % of reading)
Copyright 1984 - 1992 by Stephen L. Moshier
Release 1.0: July, 1984
Release 1.1: March, 1985
Release 1.2: May, 1986
Release 2.0: April, 1987
Release 2.1: March, 1989
Release 2.2: July, 1992
