A common lisp CFFI wrapper for the SciPy version of Cephes special functions.
For many years Cephes was considered the gold standard in cross-platform mathematical libraries, superior to the libm distributions of the time (early 1990's). Since then C99 and later ANSI C specifications have closed the gap, but there are still certain special and statistical functions available in Cephes that are not in the standard C libraries.
The SciPy version differs from standard Cephes in that it has some additional functions, improvements in accuracy, and is better documented. Only double-float versions are provided.
The ASDF file will automatically build the shared library as part of the load operation. If you need to build on a system other than MS Windows or UNIX, you will need to modify the make file to account for the linker command to create a shared library.
As delivered, the Makefile is set-up to work on MS Windows or UNIX, and you can build it manually like so:
cd scipy-cephes && makeIf you build this on another platform, please drop a note into a Cephes repository issue with the build instructions so we can update the Makefile and system definition.
The init.lisp file, where CFFI loads the library, should work out of
the box if libmd on the path somewhere, regardless of platform. If
in doubt, place a copy in the same directory as this README.
If you know your way around special functions, the table below should
suffice to get started. For a more complete description, see the doc
strings in cephes.lisp. Finally, the C source code itself, referenced
in cephes.lisp, is thorough and complete from a mathematical perspective.
You can also use the scipy.special online documentation.
There is no overlap between the wrapped Cephes functions and the
Common Lisp numerical tower. All functions are in the cephes
package.
Exported functions are:
| function | description |
|---|---|
| airy | Airy function |
| bdtr | Binomial distribution |
| bdtrc | Complement of binomial distribution |
| bdtri | Inverse binomial distribution |
| besselpoly | Weighted integral of the Bessel function of the first kind |
| beta | Beta function |
| lbeta | Natural log of beta |
| btdtr | incomplete beta integral |
| cbrt | cube root |
| chdtr | Chi-square distribution |
| chdtrc | Complemented Chi-square distribution |
| chdtri | Inverse of complemented Chi-square distribution |
| dawsn | Dawson's Integral |
| ellik | Incomplete elliptic integral of the first kind |
| ellie | Incomplete elliptic integral of the second kind |
| ellpk | Complete elliptic integral of the first kind |
| ellpe | Complete elliptic integral of the second kind |
| jacobian-elliptic | jacobian Elliptic Functions |
| exp2 | Base 2 exponential function |
| exp10 | Base 10 exponential function (Common antilogarithm) |
| expn | Exponential integral |
| fdtr | F distribution |
| fdtrc | Complemented F distribution |
| fdtri | Inverse of F distribution |
| fresnl | Fresnel integral |
| gamma | Gamma function |
| log-gamma | Natural logarithm of Gamma function |
| gdtr | Gamma distribution function |
| gdtrc | Complemented Gamma distribution function |
| gdtri | Inverse Gamma distribution function (?) - not documented in src |
| hyp2f1 | Gauss hypergeometric function |
| hyperg | Confluent hypergeometric function |
| i0 | Modified Bessel function of order zero |
| i0e | Modified Bessel function of order zero, exponentially scaled |
| i1 | Modified Bessel function of order one |
| i1e | Modified Bessel function of order one, exponentially scaled |
| igam | Regularized lower incomplete gamma function |
| igamc | Regularized upper incomplete gamma function |
| igami | Inverse of the lower incomplete gamma function |
| igamci | Inverse of the upper incomplete gamma function |
| incbet | Incomplete beta integral |
| incbi | Inverse of incomplete beta integral |
| iv | Modified Bessel function of noninteger order |
| j0 | Bessel function of order zero |
| y0 | Bessel function of the second kind, order zero |
| j1 | Bessel function of order one |
| y1 | Bessel function of second kind of order one |
| jv | Bessel function of noninteger order |
| k0 | Modified Bessel function, third kind, order zero |
| k0e | Modified Bessel function, third kind, order zero, exponentially scaled |
| k1 | Modified Bessel function of the third kind of order one |
| k1e | Modified Bessel function of the third kind of order one, exponentially scaled |
| kn | Modified Bessel function, third kind, integer order |
| nbdtr | Negative binomial distribution |
| nbdtrc | Complemented negative binomial distribution |
| nbdtri | Inverse complemented negative binomial distribution |
| ndtr | Normal distribution function |
| log-ndtr | Log of the normal distribution function |
| erf | Error function |
| erfc | Complementary error function |
| erfinv | Inverse of the error function |
| erfcinv | Inverse of the complementary error function |
| ndtri | Inverse of Normal distribution function |
| pdtr | Poisson distribution |
| pdtrc | Complemented poisson distribution |
| pdtri | Inverse Poisson distribution |
| poch | Pochhammer symbol (a)_m = gamma(a + m) / gamma(a) |
| psi | Psi (digamma) function |
| rgamma | Reciprocal Gamma function |
| shichi | Hyperbolic sine and cosine integrals |
| sici | Sine and cosine integrals |
| sindg | Circular sine of angle in degrees |
| cosdg | Circular cosine of angle in degrees |
| sinpi | Compute sin(pi * x) |
| cospi | Compute cos(pi * x) |
| spence | Dilogarithm |
| stdtr | Student's t distribution |
| stdtri | Functional inverse of Student's t distribution |
| yv | Bessel function of noninteger order |
| tandg | Circular tangent of angle in degrees |
| cotdg | Circular cotangent of argument in degrees |
| log1p | log(1 + x) |
| log1pmx | log(1 + x) - x |
| expm1 | exp(x) - 1 |
| cosm1 | cos(x) - 1 |
| lgam1p | lgam(x + 1) |
| yn | Bessel function of second kind of integer order |
| zeta | Riemann zeta function of two arguments |
| zetac | Riemann zeta function |
| owens-t | Owen's T-Function |
When contributing to this repository, please first discuss major changes to the existing code you wish to make via a github issue. Minor changes and major additions are welcome. Please write good commit messages.
CEPHES.CL is available under the Microsoft Public License.