mathh

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mathh
Documentation
- Math Functions
  - Usage
  - bessel-j0
  - bessel-j1
  - bessel-jn
  - bessel-jn
  - bessel-y0
  - bessel-y1
  - bessel-yn
  - cosh
  - sinh
  - tanh
  - acosh
  - asinh
  - atanh
  - hypot
  - gamma
  - lgamma
  - erf
  - erfc
  - log10
  - log2
  - log1p
  - log-with-base
  - log/base
  - ldexp
  - scalbn
  - cbrt
  - nextafter
  - fpmod
  - modf
  - modf*
  - frexp
  - signbit
  - copysign
  - fpclassify
  - fpclass
- Notes
- Math Constants (Module)
  - Usage
  - Constants
- Math Constants (Include)
  - Usage
  - Constants
- Miscellaneous Math Functions
  - Usage
  - number->sign
  - log-with-base
  - log/base
  - simple-interest
  - compound-interest
  - fibonacci
  - fibonacci*
  - binomial
  - cross-ratio
  - square
  - cube
  - average
  - least-squares
  - trapezoid
  - factorial
  - factorial-
  - factorial+
  - harmonic
  - big-pi
  - big-sigma
- Miscellaneous Vector Math Functions
  - Usage
  - absolute-magnitude
  - cosine-similarity
  - dot-product
  - cross-product
  - vector-mul
  - vector-sum
  - vector-div
  - vector-dif
  - vector-min
  - vector-max
  - vector-lcm
  - vector-gcd
  - vector<?
  - vector=?
  - vector>?
  - vector<=?
  - vector>=?
  - vector-compare
  - vector-apply
Requirements
Bugs and Limitations
Author
Repository
Version history
License

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 ; fixnum. : P2 ; integer. : N, M, N1, N2 ; float.

Usage

(import "mathh")

bessel-j0

bessel-j1

bessel-jn

bessel-y0

bessel-y1

log-with-base

log/base

log-with-base Bprocedure
log/base Bprocedure: Returns a function for the base B logarithm.

ldexp

ldexp N P2procedure

scalbn

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*

modf Nprocedure
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

Notes

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
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

Math Constants (Module)

Usage

(import mathh-consts)

Constants

These are all float.

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)

Miscellaneous Math Functions

Note that unlike mathh the domain & range are number, not float.

Usage

(import misc-math-utils)

number->sign

number->sign Nprocedure: Returns -1, 0, or +1 to represent the sign of the number N.

log-with-base

log/base

log-with-base Bprocedure
log/base Bprocedure: Returns a function for the base B logarithm.

simple-interest

simple-interest RATE TIME #!optional PRINprocedure

The accumulation function, the principle is assumed 1. Returns the simple interest for the RATE over TIME.

RATE ; number ; interest rate
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1

compound-interest

compound-interest RATE FREQ TIME #!optional PRINprocedure

The accumulation function, the principle is assumed 1. Returns the compound interest for the RATE, applied with FREQ, over TIME.

RATE ; number ; interest rate
FREQ ; number ; compounding frequency
TIME ; number ; time period to cover
PRIN ; number ; principle, default 1

(compound-interest 0.043 4 6 1500)
;=> 1938.84 ;rounded to 2 places

fibonacci

fibonacci Nprocedure: Returns fibonacci of N.

fibonacci*

fibonacci* Nprocedure: Returns an approximate fibonacci of N.

binomial

binomial N1 N2procedure

Returns the Binomial in N1 to N2.

: N1 ; integer ; : N2 ; integer ;

cross-ratio

cross-ratio N1 N2 N3 N4procedure

Returns the Cross-ratio of N1, N2 and N3, N4.

: N1 ; number ; : N2 ; number ; : N3 ; number ; : N4 ; number ;

square

square Nprocedure

cube

cube Nprocedure

average

average N1 N2 ...procedure

average NUMSprocedure

: N1 ; number ; : N1 ; number ;

: NUMS ; (list-of number) ;

least-squares

least-squares PNTSprocedure

Returns b & e such that y ~= b * x + e.

: PNTS ; (list-of (pair number number)) ; list of x,y pairs

trapezoid

trapezoid F N1 N2procedure

Returns a function to calculate the area under F between N1 & N2 using the Trapezoid Rule. The function takes the number of estimations as an argument, larger for a "better" result.

: F ; (number -> number) ; : N1 ; number ; : N2 ; number ;

factorial

factorial-

factorial+

factorial Nprocedure
factorial- N1 FALLprocedure
factorial+ N1 RISEprocedure: : N ; integer ; : FALL : number ; falling factorial : RISE : number ; rising factorial

harmonic

harmonic Nprocedure

Result of Harmonic series expansion to N terms.

: N ; integer ;

big-pi

(big-pi F N1 N2) -> numbersyntax

Product of F in N1 to N2.

: F ; (number -> number) ; : N1 ; number ; : N2 ; number ;

big-sigma

(big-sigma F N1 N2) -> numbersyntax

Sum of F in N1 to N2.

: F ; (number -> number) ; : N1 ; number ; : N2 ; number ;

Miscellaneous Vector Math Functions

Usage

(import misc-vector-math-utils)

absolute-magnitude

absolute-magnitude NUMVECprocedure

NUMVEC: (vector-of number) ; .

cosine-similarity

NUMVEC1: (vector-of number) ; .
NUMVEC2: (vector-of number) ; .

Must be same vector-length.

dot-product

dot-product NUMVEC1 NUMVEC2procedure

NUMVEC1: (vector-of number) ; .
NUMVEC2: (vector-of number) ; .

Must be same vector-length.

cross-product

cross-product NUMVEC1 NUMVEC2procedure

NUMVEC1: (vector-of number) ; .
NUMVEC2: (vector-of number) ; .

Must be same vector-length.

Only defined for a vector-length of (0 1 2), returning a number, and (3 4 8), returning a (vector-of number). All others generate an error.

vector-div NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector-dif NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector-min NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector-max NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector-lcm NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector-gcd NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

NUMVEC#: (vector-of number) ; .

Must be same vector-length.

vector>? NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector<=? NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

vector>=? NUMVEC1 NUMVEC2 #!optional NUMVEC...procedure

NUMVEC#: (vector-of number) ; .

Must be same vector-length.

vector-compare

(vector-compare NUMVEC1 NUMVEC2 -> (vector-of number)procedure

Result is (vector-dif NUMVEC2 NUMVEC1).

NUMVEC1: (vector-of number) ; .
NUMVEC2: (vector-of number) ; .

Must be same vector-length.

vector-apply

vector-apply FUNC VEC1 VEC2 #!optional VEC...procedure

FUNC: (* * !#rest * -> *) ; .
VEC#: vector ; .

Must be same vector-length.

Requirements

test test-utils vector-lib

Bugs and Limitations

The fpclass quiet-nan is only distinguished on Windows.

Author

Kon Lovett John Cowan

Repository

This egg is hosted on the CHICKEN Subversion repository:

https://anonymous@code.call-cc.org/svn/chicken-eggs/release/5/mathh

If you want to check out the source code repository of this egg and you are not familiar with Subversion, see this page.

Version history

4.6.4: Add number->sign. Add test dependency.
4.6.3: Remove vector-apply numeric restriction.
4.6.2: Add vector-mul/div/sum/dif/min/max/lcm/gcd, vector</=/>/<=/>, vector-compare, vector-apply.
4.6.1: Add vector-product & vector-sum. Fix cross-product(3).
4.6.0: Add misc-vector-math-utils.
4.5.1: Fix for include source mathh-constants.scm.
4.5.0: Add log function to misc-math-utils.
4.4.0: Add interest functions to misc-math-utils.
4.3.0: Remove Windows restrictions (C2 era), assume BSD has tgamma.
4.2.3: .
4.2.2: .
4.2.1: .
4.2.0: Add modf*.
4.0.0: CHICKEN 5 release.

License

This code is in the public domain.

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