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mathh
- mathh
- Documentation
- Notes
- Bugs and Limitations
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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) => realgamma
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
make-log/base
[procedure] (make-log/base N) => (provedure (real) real)Returns a procedure of one argument, the logarithm function for the base N.
ldexp
scalbn
[procedure] (ldexp N P2) => real[procedure] (scalbn N P2) => real
cbrt
[procedure] (cbrt N) => realnextafter
[procedure] (nextafter N M) => realReturns the next N in the direction of M.
fpmod
[procedure] (fpmod N M) => realReturns 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) => booleanReturns #t when negative, #f otherwise.
copysign
[procedure] (copysign N M) => realReturns N with same sign as M.
fpclassify
[procedure] (fpclassify N) => symbolReturns a symbol denoting the floating-point kind of N.
- infinite
- nan
- normal
- subnormal
- zero
- unclassified
fpclass
[procedure] (fpclass N) => symbolReturns 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
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)
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]) => flonumN fixnum limit.
fpzero?
[procedure] (fpzero? N) => booleanfppositive?
[procedure] (fppositive? N) => booleanfpcardinal?
[procedure] (fpcardinal? N) => booleanfpnegative?
[procedure] (fpnegative? N) => booleanfpeven?
[procedure] (fpeven? N) => booleanfpodd?
[procedure] (fpodd? N) => booleanfpclosed-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) => booleanN, 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) => flonumfpsub1
[procedure] (fpsub1 N) => flonumfpmodulo
[procedure] (fpmodulo N1 N2) => flonumfpquotient
[procedure] (fpquotient N1 N2) => flonumfpremainder
[procedure] (fpremainder N1 N2) => flonumfpfraction
[procedure] (fpfraction N) => flonumfptruncate/precision
[procedure] (fptruncate/precision N [P 4]) => flonumfpround/precision
[procedure] (fpround/precision N [P 4]) => flonumfpceiling/precision
[procedure] (fpceiling/precision N [P 4]) => flonumfpfloor/precision
[procedure] (fpfloor/precision N [P 4]) => flonumfp~=
[procedure] (fp~= N1 N2 [EPS flonum-epsilon]) => flonumCompare floating-point values N1 and N2 within some flonum epsilon EPS.
fp~<=
[procedure] (fp~<= N) => booleanfp~>=
[procedure] (fp~>= N) => booleanfpsqr
[procedure] (fpsqr N) => flonumfpcub
[procedure] (fpcub N) => flonumfpdegree->radian
[procedure] (fpdegree->radian N) => flonumfpradian->degree
[procedure] (fpradian->degree N) => flonumfpdistance
[procedure] (fpdistance X1 Y1 X2 Y2) => flonumPythagorean distance between the points X1 Y1 and X2 Y2.
fpdistance*
[procedure] (fpdistance* X1 Y1 X2 Y2) => flonumPythagorean 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]) => flonumReturns factor for P decimal digits precision.
Fixnum Utilities
Usage
(require-extension fx-utils)
N N1 ... X1 ... Y1 ... below are fixnum.
fxrandom
[procedure] (fxrandom [N]) => fixnumN fixnum limit.
fxzero?
[procedure] (fxzero? N) => booleanfxpositive?
[procedure] (fxpositive? N) => booleanfxcardinal?
[procedure] (fxcardinal? N) => booleanfxnegative?
[procedure] (fxnegative? N) => booleanfxclosed-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) => booleanN, 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) => fixnumfxsub1
[procedure] (fxsub1 N) => fixnumfxabs
[procedure] (fxabs N) => fixnumfxsqr
[procedure] (fxsqr N) => fixnumfxcub
[procedure] (fxcub N) => fixnumfxpow2log2
[procedure] (fxpow2log2 N) => fixnumReturns fixnum 2^N.
fxdistance
[procedure] (fxdistance X1 Y1 X2 Y2) => fixnumPythagorean distance between the points X1 Y1 and X2 Y2.
fxdistance*
[procedure] (fxdistance* X1 Y1 X2 Y2) => fixnumPythagorean 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 (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 does not provide library calls lgamma, gamma, acosh, asinh, atanh, log2, log1p, erf, erfc, scalbn, cbrt & signbit.
Usable log2, log1p, erf, erfc, scalbn & signbit are supplied.
- 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
Version history
- 3.1.1 ; Fix fpodd?. Add fx-utils.scm. Extend fp-utils.scm.
- 3.2.0 ; Added module for mathh-constants.scm. Added fp-utils.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.