CSL: Chicken Scientific Library

NOTE: This egg is still very much a work in progress.

This is a Chicken Scheme egg for the GNU Scientific Library (GSL), providing both low-level bindings and a more idiomatic API, as well as some generic functions for convenience.

For GSL function/variable reference, see the official gsl documentation. In this document I’ll only point out functions that have been added, omitted, or whose names have changed.

• If a function or constant is not listed, you can safely assume the name and parameters are the same as in gsl but with the prefix dropped and underscores changed to dashes.
• Functions prefixed with ! are provided despite there being an equal (or better) built-in alternative (this might be opinionated, and is open to discussion).
• Because of the way GSL’s representation of complex numbers is wrapped, GSL functions that work on complex numbers in GSL should work on both complex and real numbers in CSL.

Mathematical Functions

(import (csl math double))
;; equivalently: (import csl.math.double)

GSL prefix: gsl_ (except constants, all of which were changed)

Mathematical Constants

CSL	GSL
e	M_E
log2e	M_LOG2E
sqrt2	M_SQRT2
sqrt1/2	M_SQRT1_2
sqrt3	M_SQRT3
pi	M_PI
pi/2	M_PI_2
pi/4	M_PI_4
sqrtpi	M_SQRTPI
2/sqrtpi	M_2_SQRTPI
1/pi	M_1_PI
2/pi	M_2_PI
ln10	M_LN10
ln2	M_LN2
lnpi	M_LNPI
euler	M_EULER

Infinities and Not-a-number

Constants

CSL	GSL
+inf	GSL_POSINF
-inf	GSL_NAN
nan	GSL_NAN

Functions

CSL NAME	GSL
!nan?	gsl_isnan
!infinite?	gsl_isinf
!finite?	gsl_finite

Elementary Functions

CSL	GSL
log1+	gsl_log1p
exp-1	gsl_expm1
hypot2	gsl_hypot

Modified

[procedure] (frexp x)

Splits the number x into its normalized fraction (double) f and exponent e, such that (= x (* f (expt 2 e))) and (and (<= 0.5 f) (< f 1)). Returns f and e as multiple values.

Modification reason: ‘Out parameters’ are messy in compiled chicken, unavailable in interpreted chicken, and un-idiomatic in both.

Added

[procedure] (hypot a b [c])

Computes the value of (sqrt (expt a 2) (expt b 2)) or (sqrt (expt a 2) (expt b 2) (expt c 2)) as needed, using hypot2 or hypot3, respectively.

Addition reason: In scheme, optional parameters are more convenient than multiple functions.

[procedure] (cosh x)
[procedure] (sinh x)
[procedure] (tanh x)

Compute the hyperbolic sine, cosine, and tangent of x, respectively. These come from math.h.

Addition reason: GSL provides the inverse of these, but does not provide its own versions of these with the assumption that the user will utilize the math.h versions, but Chicken doesn’t provide these either, so it’s convenient to provide provide these as well.

Small integer powers

CSL	GSL
expt-int	gsl_pow_int
expt2	gsl_pow_2
expt3	gsl_pow_3
expt4	gsl_pow_4
expt5	gsl_pow_5
expt6	gsl_pow_6
expt7	gsl_pow_7
expt8	gsl_pow_8
expt9	gsl_pow_9

Testing the sign of numbers

CSL	GSL
sign	GSL_SIGN

Testing for odd and even numbers

CSL	GSL
!odd?	GSL_IS_ODD
!even?	GSL_IS_EVEN

Maximum and minimum functions

CSL	GSL
!max-dbl	GSL_MAX_DBL
!min-dbl	GSL_MIN_DBL
!max-int	GSL_MAX_INT
!min-int	GSL_MIN_INT
!max-ldbl	GSL_MAX_LDBL
!min-ldbl	GSL_MIN_LDBL

Modified

[procedure] (!max . args)
[procedure] (!min . args)

Get the maximum and minimum argument, respectively. Wrap GSL_MAX and GSL_MIN.

Modification reason: accept multiple args.

Complex Numbers

(import (csl math complex))
;; equivalently: (import csl.math.complex)

GSL prefix: gsl_complex_

Representation of complex numbers

CSL	GSL
!make-rectangular	gsl_complex_rect
!make-polar	gsl_complex_polar
!angle	gsl_complex_arg
!magnitude	gsl_complex_abs
magnitude-squared	gsl_complex_abs2
log-magnitude	gsl_logabs
!negative	gsl_complex_negative
!sqrt	gsl_complex_sqrt
!expt	gsl_complex_pow
!exp	gsl_complex_exp
!log10	gsl_complex_log10
!log	gsl_complex_log
!sin	gsl_complex_sin
!asin	gsl_complex_asin
!cos	gsl_complex_cos
!acos	gsl_complex_acos
!tan	gsl_complex_tan
!atan	gsl_complex_atan

Modified

[procedure] (!+ . args)
[procedure] (!- . args)
[procedure] (!* . args)
[procedure] (!/ . args)

Add, subtract, multiply, and divide numbers, based on gsl_complex_add, gsl_complex_sub, gsl_complex_mul, and gsl_complex_div, respectively, but accept an arbitrary number of arguments.

Modification reason: accept multiple args.

Polynomials

(import (csl poly))
;; equivalently: (import csl.poly)

GSL prefix: gsl_

Polynomial evaluation

Omitted

Function	Reason
gsl_poly_eval	Functionality is covered by gsl_complex_poly_complex_eval
gsl_poly_complex_eval	See above

Modified

[procedure] (poly-eval c z)

Wraps gsl_complex_poly_complex_eval. Evaluates a polynomial with complex or real coefficients given by list c for the complex or real variable x.

Modification reason: Handles either complex or real doubles. Working with pointers to C arrays isn’t available in interpreted scheme.

[procedure] (poly-eval-derivs c x [num-derivs])

Evaluates a polynomial and its derivatives, returning a list of the results.

Modification reason: Working with pointers to C arrays isn’t available in interpreted scheme.

Added

[procedure] (poly-eval* c z)

Similar to poly-eval, but implemented purely in scheme - should be able to handle all numerical types supported by Chicken Scheme, including exact numbers and bignums.

Addition reason: support more numerical types.

[procedure] (poly-eval-derivs* c z)

Similar to poly-eval-derivs, but implemented purely in scheme - should be able to handle all numerical types supported by Chicken Scheme, including complex numbers, exact numbers, and bignums.

Addition reason: support more numerical types

Divided Difference Representation of Polynomials

Modified

[procedure] (poly-dd-init xa ya)

Computes a divided-difference representation of the interpolating polynomial for the points (x, y) stored in the lists xa and ya of equal size.

Modification reason: Pointers to arrays and out paramaters aren’t easy to work with in interpreted scheme.

[procedure] (poly-dd-eval dd xa x)

Evaluates the polynomial stored in divided-difference form in the lists dd and xa of equal length at point x.

Modification reason: Pointers to arrays aren’t easy to work with in interpreted scheme.

[procedure] (poly-dd-taylor xp dd xa)

Converts the divided-difference representation of a polynomial to a Taylor expansion. The divided-difference representation is supplied in the lists dd and xa of equal size. On output the Taylor coefficients of the polynomial expanded about the point xp are returned as an array.

Quadratic Equations

Omitted

Function	Reason
gsl_poly_solve_quadratic	Functionality is covered by gsl_poly_complex_solve_quadratic

Modified

[procedure] (solve-quadratic a b c)

Wraps gsl_poly_complex_solve_quadratic. Returns two roots, or one root and #f, as multiple values.

Modification reason: Out parameters and C pointers.

Added

[procedure] (solve-quadratic* a b c)

Like solve-quadratic, but implemented purely in scheme - should be able to handle all numerical types supported by Chicken Scheme, including complex numbers, exact numbers, and bignums.

Addition reason: support more numerical types.

Cubic Equations

Omitted

Function	Reason
gsl_poly_solve_cubic	Functionality is covered by gsl_poly_complex_solve_cubic

Modified

[procedure] (solve-cubic a b c)

Wraps gsl_poly_complex_solve_cubic. Returns three roots as multiple values.

Modification reason: Out parameters and C pointers.

Added

example [procedure] (solve-cubic* a b c)

Like solve-cubic, but implemented purely in scheme - should be able to handle all numerical types supported by Chicken Scheme, including complex numbers, exact numbers, and bignums.

Addition reason: support more numerical types.

General Polynomial Equations

Modified

[procedure] (poly-solve a)

Wraps gsl_poly_complex_solve. Computes the roots of the general polynomial whose coefficients are given by the list a. The coefficient of the highest order term must be non-zero.

Modification reason: Out parameters and C pointers.

Special Functions

Vectors and Matrices