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This is an egg for CHICKEN 4, the unsupported old release. You're almost certainly looking for the CHICKEN 5 version of this egg, if it exists.

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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

[procedure] (bessel-j0 N) -> real
[procedure] (bessel-j1 N) -> real
[procedure] (bessel-jn O N) -> real
[procedure] (bessel-y0 N) -> real
[procedure] (bessel-y1 N) -> real
[procedure] (bessel-yn O N) -> real

cosh

sinh

tanh

acosh

asinh

atanh

[procedure] (cosh N) -> real
[procedure] (sinh N) -> real
[procedure] (tanh N) -> real
[procedure] (acosh N) -> real
[procedure] (asinh N) -> real
[procedure] (atanh N) -> real

hypot

[procedure] (hypot N1 N2) -> real

gamma

lgamma

[procedure] (gamma N) -> real
[procedure] (lgamma N) -> real

erf

erfc

[procedure] (erf N) -> real
[procedure] (erfc N) -> real

log10

log2

log1p

[procedure] (log10 N) -> real
[procedure] (log2 N) -> real
[procedure] (log1p N) -> real

log-with-base

[procedure] (log-with-base N) -> (procedure (real) real)

Returns a monadic function, the logarithm of base N.

ldexp

scalbn

[procedure] (ldexp N P2) -> real
[procedure] (scalbn N P2) -> real

cbrt

[procedure] (cbrt N) -> real

nextafter

[procedure] (nextafter N M) -> real

Returns the next N in the direction of M.

fpmod

[procedure] (fpmod N M) -> real

Returns the modulus of N for M.

modf

[procedure] (modf N) -> (values real integer)

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

frexp

[procedure] (frexp N) -> (values real real)

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

signbit

[procedure] (signbit N) -> boolean

Returns #t when negative, #f otherwise.

copysign

[procedure] (copysign N M) -> real

Returns N with same sign as M.

fpclassify

[procedure] (fpclassify N) -> symbol

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

infinite

nan

normal

subnormal

zero

unclassified

fpclass

[procedure] (fpclass N) -> symbol

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

[procedure] (fprandom [N]) -> flonum

Returns flonum in [0 -1).

N

fixnum or flonum limit.

fpzero?

[procedure] (fpzero? N) -> boolean

fppositive?

[procedure] (fppositive? N) -> boolean

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

fpcardinal?

[procedure] (fpcardinal? N) -> boolean

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

fpnegative?

[procedure] (fpnegative? N) -> boolean

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

fpeven?

[procedure] (fpeven? N) -> boolean

fpodd?

[procedure] (fpodd? N) -> boolean

fpclosed-right?

fpclosedr?

[procedure] (fpclosed-right? L N H) -> boolean
[procedure] (fpclosedr? L N H) -> boolean

Returns N in (L .. H].

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

fpclosed?

Returns N in [L .. H].

[procedure] (fpclosed? L N H) -> boolean

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

fpclosed-left?

fpclosedl?

Returns N in [L .. H).

[procedure] (fpclosed-left? L N H) -> boolean
[procedure] (fpclosedl? L N H) -> boolean

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

fpadd1

[procedure] (fpadd1 N) -> flonum

fpsub1

[procedure] (fpsub1 N) -> flonum

fpmodulo

[procedure] (fpmodulo N1 N2) -> flonum

fpquotient

[procedure] (fpquotient N1 N2) -> flonum

fpremainder

[procedure] (fpremainder N1 N2) -> flonum

fpfraction

[procedure] (fpfraction N) -> flonum

fptruncate/precision

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

fpround/precision

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

fpceiling/precision

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

fpfloor/precision

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

fp~=

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

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

fp~<=

[procedure] (fp~<= N) -> boolean

fp~>=

[procedure] (fp~>= N) -> boolean

fpsqr

[procedure] (fpsqr N) -> flonum

fpcub

[procedure] (fpcub N) -> flonum

fpdegree->radian

[procedure] (fpdegree->radian N) -> flonum

fpradian->degree

[procedure] (fpradian->degree N) -> flonum

fpdistance

[procedure] (fpdistance X1 Y1 X2 Y2) -> flonum

Pythagorean distance between the points X1 Y1 and X2 Y2.

fpdistance*

[procedure] (fpdistance* X1 Y1 X2 Y2) -> flonum

Pythagorean distance, inaccurate but useful for relative comparisons.

fpmax-and-min

[procedure] (fpmax-and-min N ...) -> (values flonum flonum)

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

fpprecision-factor

[procedure] (fpprecision-factor P [BASE 10.0]) -> flonum

Returns factor for P decimal digits precision.

Fixnum Utilities

Usage

(require-extension fx-utils)

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

fxrandom

[procedure] (fxrandom [N]) -> fixnum

N fixnum limit.

fxzero?

[procedure] (fxzero? N) -> boolean

fxpositive?

[procedure] (fxpositive? N) -> boolean

fxcardinal?

[procedure] (fxcardinal? N) -> boolean

fxnegative?

[procedure] (fxnegative? N) -> boolean

fxclosed-right?

fxclosedr?

[procedure] (fxclosed-right? L N H) -> boolean
[procedure] (fxclosedr? L N H) -> boolean

Returns N in (L .. H].

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

fxclosed?

Returns N in [L .. H].

[procedure] (fxclosed? L N H) -> boolean

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

fxclosed-left?

fxclosedl?

Returns N in [L .. H).

[procedure] (fxclosed-left? L N H) -> boolean
[procedure] (fxclosedl? L N H) -> boolean

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

fxadd1

[procedure] (fxadd1 N) -> fixnum

fxsub1

[procedure] (fxsub1 N) -> fixnum

fxabs

[procedure] (fxabs N) -> fixnum

fxsqr

[procedure] (fxsqr N) -> fixnum

fxcub

[procedure] (fxcub N) -> fixnum

fxlog2

[procedure] (fxlog2 N) -> fixnum

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

fxpow2log2

[procedure] (fxpow2log2 N) -> fixnum

Returns fixnum 2^N.

fxdistance

[procedure] (fxdistance X1 Y1 X2 Y2) -> fixnum

Pythagorean distance between the points X1 Y1 and X2 Y2.

fxdistance*

[procedure] (fxdistance* X1 Y1 X2 Y2) -> fixnum

Pythagorean distance, inaccurate but useful for relative comparisons.

fxmax-and-min

[procedure] (fxmax-and-min N ...) -> (values fixnum fixnum)

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.