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mathh

Documentation

Provides access to ISO C math functions in <math.h> that are not defined by the Chicken core. Please refer to your documentation for <math.h> for a description of the various calls.

Math Functions

O, P2 are integer.

N, N1, N2, M are real.

Usage

(use "mathh")

bessel-j0

bessel-j1

bessel-jn

bessel-jn

bessel-y0

bessel-y1

bessel-yn

bessel-j0 Nprocedure

bessel-j1 Nprocedure

bessel-jn O Nprocedure

bessel-y0 Nprocedure

bessel-y1 Nprocedure

bessel-yn O Nprocedure

cosh

sinh

tanh

acosh

asinh

atanh

cosh Nprocedure

sinh Nprocedure

tanh Nprocedure

acosh Nprocedure

asinh Nprocedure

atanh Nprocedure

hypot

hypot N1 N2procedure

gamma

lgamma

gamma Nprocedure

lgamma Nprocedure

erf

erfc

erf Nprocedure

erfc Nprocedure

log10

log2

log1p

log10 Nprocedure

log2 Nprocedure

log1p Nprocedure

log-with-base

log-with-base Nprocedure

Returns a monadic function, the logarithm of base N.

ldexp

scalbn

ldexp N P2procedure

scalbn N P2procedure

cbrt

cbrt Nprocedure

nextafter

nextafter N Mprocedure

Returns the next N in the direction of M.

fpmod

fpmod N Mprocedure

Returns the modulus of N for M.

modf

modf Nprocedure

Returns two values, the integral and fractional components of N.

frexp

frexp Nprocedure

Returns two values, the fraction and the exponent components of N.

signbit

signbit Nprocedure

Returns #t when negative, #f otherwise.

copysign

copysign N Mprocedure

Returns N with same sign as M.

fpclassify

fpclassify Nprocedure

Returns a symbol denoting the floating-point kind of N.

infinite

nan

normal

subnormal

zero

unclassified

fpclass

fpclass Nprocedure

Returns a symbol denoting the floating-point kind of N.

positive-infinite

negative-infinite

quiet-nan

signaling-nan

positive-normal

negative-normal

positive-subnormal

negative-subnormal

positive-zero

negative-zero

unclassified

Flonum Utilities

Usage

(require-extension fp-utils)

N N1 ... X1 ... Y1 ... below are flonum.

P is the precision in decimal digits, an integer.

fprandom

fprandom #!optional Nprocedure

Returns flonum in [0 -1).

N

fixnum or flonum limit.

fpzero?

fpzero? Nprocedure

fppositive?

fppositive? Nprocedure

Note that -0.0 is not positive, due to (fl<? -0.0 0.0).

fpcardinal?

fpcardinal? Nprocedure

Note that -0.0 is not cardinal, due to (fl<? -0.0 0.0).

fpnegative?

fpnegative? Nprocedure

Note that -0.0 is not negative, due to (fl<? -0.0 0.0).

fpeven?

fpeven? Nprocedure

fpodd?

fpodd? Nprocedure

fpclosed-right?

fpclosedr?

fpclosed-right? L N Hprocedure

fpclosedr? L N Hprocedure

Returns N in (L .. H].

N, L & H are flonum low & high limits.

fpclosed?

Returns N in [L .. H].

fpclosed? L N Hprocedure

N, L & H are flonum low & high limits.

fpclosed-left?

fpclosedl?

Returns N in [L .. H).

fpclosed-left? L N Hprocedure

fpclosedl? L N Hprocedure

N, L & H are flonum low & high limits.

fpadd1

fpadd1 Nprocedure

fpsub1

fpsub1 Nprocedure

fpmodulo

fpmodulo N1 N2procedure

fpquotient

fpquotient N1 N2procedure

fpremainder

fpremainder N1 N2procedure

fpfraction

fpfraction Nprocedure

fptruncate/precision

(fptruncate/precision N [P 4]) -> flonumprocedure

fpround/precision

(fpround/precision N [P 4]) -> flonumprocedure

fpceiling/precision

(fpceiling/precision N [P 4]) -> flonumprocedure

fpfloor/precision

(fpfloor/precision N [P 4]) -> flonumprocedure

fp~=

(fp~= N1 N2 [EPS flonum-epsilon]) -> flonumprocedure

Compare floating-point values N1 and N2 within some flonum epsilon EPS.

fp~<=

fp~<= Nprocedure

fp~>=

fp~>= Nprocedure

fpsqr

fpsqr Nprocedure

fpcub

fpcub Nprocedure

fpdegree->radian

fpdegree->radian Nprocedure

fpradian->degree

fpradian->degree Nprocedure

fpdistance

fpdistance X1 Y1 X2 Y2procedure

Pythagorean distance between the points X1 Y1 and X2 Y2.

fpdistance*

fpdistance* X1 Y1 X2 Y2procedure

Pythagorean distance, inaccurate but useful for relative comparisons.

fpmax-and-min

fpmax-and-min N ...procedure

Returns the maximum & minimum values for the flonums N ....

fpprecision-factor

(fpprecision-factor P [BASE 10.0]) -> flonumprocedure

Returns factor for P decimal digits precision.

Fixnum Utilities

Usage

(require-extension fx-utils)

N N1 ... X1 ... Y1 ... below are fixnum.

fxrandom

fxrandom #!optional Nprocedure

N fixnum limit.

fxzero?

fxzero? Nprocedure

fxpositive?

fxpositive? Nprocedure

fxcardinal?

fxcardinal? Nprocedure

fxnegative?

fxnegative? Nprocedure

fxclosed-right?

fxclosedr?

fxclosed-right? L N Hprocedure

fxclosedr? L N Hprocedure

Returns N in (L .. H].

N, L & H are fixnum low & high limits.

fxclosed?

Returns N in [L .. H].

fxclosed? L N Hprocedure

N, L & H are fixnum low & high limits.

fxclosed-left?

fxclosedl?

Returns N in [L .. H).

fxclosed-left? L N Hprocedure

fxclosedl? L N Hprocedure

N, L & H are fixnum low & high limits.

fxadd1

fxadd1 Nprocedure

fxsub1

fxsub1 Nprocedure

fxabs

fxabs Nprocedure

fxsqr

fxsqr Nprocedure

fxcub

fxcub Nprocedure

fxlog2

fxlog2 Nprocedure

Returns index of highest bit set, so N is treated as unsigned.

fxpow2log2

fxpow2log2 Nprocedure

Returns fixnum 2^N.

fxdistance

fxdistance X1 Y1 X2 Y2procedure

Pythagorean distance between the points X1 Y1 and X2 Y2.

fxdistance*

fxdistance* X1 Y1 X2 Y2procedure

Pythagorean distance, inaccurate but useful for relative comparisons.

fxmax-and-min

fxmax-and-min N ...procedure

Returns the maximum & minimum values for the fixnums N ....

Math Constants (Module)

Usage

(require-extension mathh-consts)

Constants

These are all flonum.

e

e

1/e

1/e

e^2

e^2

e^pi/4

e^(pi/4)

log2e

log2(e)

log10e

log10(e)

ln2

log(2)

ln3

ln(3)

lnpi

ln(pi)

ln10

log(10)

1/ln2

1/ln(2)

1/ln10

1/ln(10)

pi

pi

pi/2

pi/2

pi/4

pi/4

1/pi

1/pi

2/pi

2/pi

2/sqrtpi

2/sqrt(pi)

sqrtpi

sqrt(pi)

pi^2

pi^2

degree

pi/180

sqrt2

sqrt(2)

1/sqrt2

1/sqrt(2)

sqrt3

sqrt(3)

sqrt5

sqrt(5)

sqrt10

sqrt(10)

cubert2

cubert(2)

cubert3

cubert(3)

4thrt2

fourthrt(2)

gamma1/2

gamma(1/2)

gamma1/3

gamma(1/3)

gamma2/3

gamma(2/3)

phi

phi

lnphi

ln(phi)

1/lnphi

1/ln(phi)

euler

euler

e^euler

e^euler

sin1

sin(1)

cos1

cos(1)

zeta3

theta(3)

Math Constants (Include)

Common constants, using 'define-constant'. As such they must be textually included.

Usage

(include "mathh-constants")

Constants

E

e

1/E

1/e

E^2

e^2

E^PI/4

e^(pi/4)

LOG2E

log2(e)

LOG10E

log10(e)

LN2

log(2)

LN3

ln(3)

LNPI

ln(pi)

LN10

log(10)

1/LN2

1/ln(2)

1/LN10

1/ln(10)

PI

pi

PI/2

pi/2

PI/4

pi/4

1/PI

1/pi

2/PI

2/pi

2/SQRTPI

2/sqrt(pi)

SQRTPI

sqrt(pi)

PI^2

pi^2

DEGREE

pi/180

SQRT2

sqrt(2)

1/SQRT2

1/sqrt(2)

SQRT3

sqrt(3)

SQRT5

sqrt(5)

SQRT10

sqrt(10)

CUBERT2

cubert(2)

CUBERT3

cubert(3)

4THRT2

fourthrt(2)

GAMMA1/2

gamma(1/2)

GAMMA1/3

gamma(1/3)

GAMMA2/3

gamma(2/3)

PHI

phi

LNPHI

ln(phi)

1/LNPHI

1/ln(phi)

EULER

euler

E^EULER

e^euler

SIN1

sin(1)

COS1

cos(1)

ZETA3

theta(3)

Notes

• The C library call gamma is deprecated in favor of tgamma but not available yet on some platforms, so we use gamma where necessary.
• Some library calls that are not supplied by the platform have rough implementations supplied. See Bugs and Limitations.
• The general naming convention is to use the C library call name as the Scheme name. But there are exceptions:

fmod

fpmod - fp-utils fpmodulo - should be in Chicken library?

j0

bessel-j0 (Prefixed to distinguish the names from common variables)

j1

bessel-j1

jn

bessel-jn

y0

bessel-y0

y1

bessel-y1

yn

bessel-yn

Bugs and Limitations

• CHICKEN_INCLUDE_PATH must at least state the value of the (repository-path) to include mathh-constants.scm. Suggest using the module mathh-consts.
• The types integer & real refer to the Chicken "core" concept of a number. Support for the full numeric tower is not provided.
• Windows library calls lgamma, gamma, acosh, asinh, atanh, cbrt & signbit are not provided.
• FreeBSD does not provide the library call log2. A usable log2 is supplied.
• The fpclass quiet-nan is only distinguished on Windows.
• fx-utils.scm & fp-utils.scm belong in own eggs.

Author

Kon Lovett John Cowan

Version history

3.4.2

Fix foreign-declare use. Fix fpzero?, fppositive?, fpnegative?, fpcardinal? again.

3.4.1

Remove unneeded dependency.

3.4.0 ; Fix fppositive?, fpnegative?, fpcardinal?, fpeven?, fpodd?.

3.3.3 ; Remove Windows log2, log1p, erf, erfc, scalbn.

3.3.2 ;

3.3.1 ;

3.3.0 ; Add log-with-base. Deprecate make-log/base. Fix fprandom sign preservation.

3.2.4 ; Add fxlog2, fix fxpow2log2.

3.2.3 ; Fix 4THRT2, 1/LNPHI, extend 1/SQRT2.

3.2.2 ; Remove inline generation for mathh.

3.2.1 ; Add types. Fix signbit & fpclass.

3.2.0 ; Fix fpodd?. Add fx-utils.scm. Extend fp-utils.scm.

3.1.0 ; Added module for mathh-constants.scm.

3.0.0 ; Moved copy of mathh-constants.scm to (chicken-home). Ticket #1327

2.2.6 ; better argvector chicken test

2.2.5 ; argvector chicken support

2.2.4 ;

2.2.3 ; Fix for ticket #630

2.2.2 ; mathh-constants.scm copied to Chicken Repository. Produces shared+static object files.

2.2.1

Better no-install support.

2.2.0

Added acosh, asinh, atanh, erf & erfc. Includes <sunmath.h> on Sun platform for log2.

2.1.0

Added signbit, copysign, nextafter & cbrt.

2.0.0

Chicken 4 release. fpclass and fpclassify are now part of the mathh extension.

License

This code is in the public domain.