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time-to-botec/js/node_modules/@stdlib/math/base/special/README.md

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feat: add the node modules Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00
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# Special Functions
> Standard library base special math functions.
<section class="usage">
## Usage
```javascript
var special = require( '@stdlib/math/base/special' );
```
#### special
Standard library base special math functions.
```javascript
var fcns = special;
// returns {...}
```
### Exponential & Logarithmic Functions
<!-- <toc pattern="+(*log*|ln|exp*|*pow*)" ignore="logit" > -->
<div class="namespace-toc">
- <span class="signature">[`exp( x )`][@stdlib/math/base/special/exp]</span><span class="delimiter">: </span><span class="description">natural exponential function.</span>
- <span class="signature">[`exp10( x )`][@stdlib/math/base/special/exp10]</span><span class="delimiter">: </span><span class="description">base `10` exponential function.</span>
- <span class="signature">[`exp2( x )`][@stdlib/math/base/special/exp2]</span><span class="delimiter">: </span><span class="description">base `2` exponential function.</span>
- <span class="signature">[`expit( x )`][@stdlib/math/base/special/expit]</span><span class="delimiter">: </span><span class="description">compute the standard logistic function.</span>
- <span class="signature">[`expm1( x )`][@stdlib/math/base/special/expm1]</span><span class="delimiter">: </span><span class="description">compute `exp(x) - 1`.</span>
- <span class="signature">[`expm1rel( x )`][@stdlib/math/base/special/expm1rel]</span><span class="delimiter">: </span><span class="description">compute the relative error exponential.</span>
- <span class="signature">[`ln( x )`][@stdlib/math/base/special/ln]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm.</span>
- <span class="signature">[`log( x, b )`][@stdlib/math/base/special/log]</span><span class="delimiter">: </span><span class="description">compute the base `b` logarithm.</span>
- <span class="signature">[`log10( x )`][@stdlib/math/base/special/log10]</span><span class="delimiter">: </span><span class="description">evaluate the common logarithm.</span>
- <span class="signature">[`log1mexp( x )`][@stdlib/math/base/special/log1mexp]</span><span class="delimiter">: </span><span class="description">evaluates the natural logarithm of `1-exp(-|x|)`.</span>
- <span class="signature">[`log1p( x )`][@stdlib/math/base/special/log1p]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of `1+x`.</span>
- <span class="signature">[`log1pexp( x )`][@stdlib/math/base/special/log1pexp]</span><span class="delimiter">: </span><span class="description">evaluates the natural logarithm of `1+exp(x)`.</span>
- <span class="signature">[`log2( x )`][@stdlib/math/base/special/log2]</span><span class="delimiter">: </span><span class="description">evaluate the binary logarithm.</span>
- <span class="signature">[`logaddexp( x, y )`][@stdlib/math/base/special/logaddexp]</span><span class="delimiter">: </span><span class="description">evaluates the natural logarithm of `exp(x) + exp(y)`.</span>
- <span class="signature">[`pow( base, exponent )`][@stdlib/math/base/special/pow]</span><span class="delimiter">: </span><span class="description">exponential function.</span>
- <span class="signature">[`powm1( b, x )`][@stdlib/math/base/special/powm1]</span><span class="delimiter">: </span><span class="description">evaluate `bˣ - 1`.</span>
- <span class="signature">[`xlog1py( x, y )`][@stdlib/math/base/special/xlog1py]</span><span class="delimiter">: </span><span class="description">compute `x * ln(y+1)` so that the result is `0` if `x = 0`.</span>
- <span class="signature">[`xlogy( x, y )`][@stdlib/math/base/special/xlogy]</span><span class="delimiter">: </span><span class="description">compute `x * ln(y)` so that the result is `0` if `x = 0`.</span>
</div>
<!-- </toc> -->
### Trigonometric Functions
<!-- <toc pattern="*+(sin|cos|tan)*" ignore="+(kernel-sin|kernel-cos|kernel-tan)"> -->
<div class="namespace-toc">
- <span class="signature">[`acos( x )`][@stdlib/math/base/special/acos]</span><span class="delimiter">: </span><span class="description">compute the arccosine of a number.</span>
- <span class="signature">[`acosh( x )`][@stdlib/math/base/special/acosh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic arccosine of a number.</span>
- <span class="signature">[`acovercos( x )`][@stdlib/math/base/special/acovercos]</span><span class="delimiter">: </span><span class="description">compute the inverse coversed cosine.</span>
- <span class="signature">[`acoversin( x )`][@stdlib/math/base/special/acoversin]</span><span class="delimiter">: </span><span class="description">compute the inverse coversed sine.</span>
- <span class="signature">[`ahavercos( x )`][@stdlib/math/base/special/ahavercos]</span><span class="delimiter">: </span><span class="description">compute the inverse half-value versed cosine.</span>
- <span class="signature">[`ahaversin( x )`][@stdlib/math/base/special/ahaversin]</span><span class="delimiter">: </span><span class="description">compute the inverse half-value versed sine.</span>
- <span class="signature">[`asin( x )`][@stdlib/math/base/special/asin]</span><span class="delimiter">: </span><span class="description">compute the arcsine of a number.</span>
- <span class="signature">[`asinh( x )`][@stdlib/math/base/special/asinh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic arcsine of a number.</span>
- <span class="signature">[`atan( x )`][@stdlib/math/base/special/atan]</span><span class="delimiter">: </span><span class="description">compute the arctangent of a number.</span>
- <span class="signature">[`atan2( y, x )`][@stdlib/math/base/special/atan2]</span><span class="delimiter">: </span><span class="description">compute the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.</span>
- <span class="signature">[`atanh( x )`][@stdlib/math/base/special/atanh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic arctangent of a number.</span>
- <span class="signature">[`avercos( x )`][@stdlib/math/base/special/avercos]</span><span class="delimiter">: </span><span class="description">compute the inverse versed cosine.</span>
- <span class="signature">[`aversin( x )`][@stdlib/math/base/special/aversin]</span><span class="delimiter">: </span><span class="description">compute the inverse versed sine.</span>
- <span class="signature">[`cos( x )`][@stdlib/math/base/special/cos]</span><span class="delimiter">: </span><span class="description">compute the cosine of a number.</span>
- <span class="signature">[`cosh( x )`][@stdlib/math/base/special/cosh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic cosine of a number.</span>
- <span class="signature">[`cosm1( x )`][@stdlib/math/base/special/cosm1]</span><span class="delimiter">: </span><span class="description">compute `cos(x) - 1`.</span>
- <span class="signature">[`cospi( x )`][@stdlib/math/base/special/cospi]</span><span class="delimiter">: </span><span class="description">compute the cosine of a number times π.</span>
- <span class="signature">[`covercos( x )`][@stdlib/math/base/special/covercos]</span><span class="delimiter">: </span><span class="description">compute the coversed cosine.</span>
- <span class="signature">[`coversin( x )`][@stdlib/math/base/special/coversin]</span><span class="delimiter">: </span><span class="description">compute the coversed sine.</span>
- <span class="signature">[`hacovercos( x )`][@stdlib/math/base/special/hacovercos]</span><span class="delimiter">: </span><span class="description">compute the half-value coversed cosine.</span>
- <span class="signature">[`hacoversin( x )`][@stdlib/math/base/special/hacoversin]</span><span class="delimiter">: </span><span class="description">compute the half-value coversed sine.</span>
- <span class="signature">[`havercos( x )`][@stdlib/math/base/special/havercos]</span><span class="delimiter">: </span><span class="description">compute the half-value versed cosine.</span>
- <span class="signature">[`haversin( x )`][@stdlib/math/base/special/haversin]</span><span class="delimiter">: </span><span class="description">compute the half-value versed sine.</span>
- <span class="signature">[`risingFactorial( x, n )`][@stdlib/math/base/special/rising-factorial]</span><span class="delimiter">: </span><span class="description">compute the rising factorial.</span>
- <span class="signature">[`sin( x )`][@stdlib/math/base/special/sin]</span><span class="delimiter">: </span><span class="description">compute the sine of a number.</span>
- <span class="signature">[`sinc( x )`][@stdlib/math/base/special/sinc]</span><span class="delimiter">: </span><span class="description">compute the cardinal sine of a number.</span>
- <span class="signature">[`sincos( [out,] x )`][@stdlib/math/base/special/sincos]</span><span class="delimiter">: </span><span class="description">simultaneously compute the sine and cosine of a number.</span>
- <span class="signature">[`sincospi( [out,] x )`][@stdlib/math/base/special/sincospi]</span><span class="delimiter">: </span><span class="description">simultaneously compute the sine and cosine of a number times π.</span>
- <span class="signature">[`sinh( x )`][@stdlib/math/base/special/sinh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic sine of a number.</span>
- <span class="signature">[`sinpi( x )`][@stdlib/math/base/special/sinpi]</span><span class="delimiter">: </span><span class="description">compute the sine of a number times π.</span>
- <span class="signature">[`tan( x )`][@stdlib/math/base/special/tan]</span><span class="delimiter">: </span><span class="description">evaluate the tangent of a number.</span>
- <span class="signature">[`tanh( x )`][@stdlib/math/base/special/tanh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic tangent of a number.</span>
- <span class="signature">[`vercos( x )`][@stdlib/math/base/special/vercos]</span><span class="delimiter">: </span><span class="description">compute the versed cosine.</span>
- <span class="signature">[`versin( x )`][@stdlib/math/base/special/versin]</span><span class="delimiter">: </span><span class="description">compute the versed sine.</span>
</div>
<!-- </toc> -->
### Bessel Functions
<!-- <toc pattern="*bessel*" > -->
<div class="namespace-toc">
- <span class="signature">[`besselj0( x )`][@stdlib/math/base/special/besselj0]</span><span class="delimiter">: </span><span class="description">compute the Bessel function of the first kind of order zero.</span>
- <span class="signature">[`besselj1( x )`][@stdlib/math/base/special/besselj1]</span><span class="delimiter">: </span><span class="description">compute the Bessel function of the first kind of order one.</span>
- <span class="signature">[`bessely0( x )`][@stdlib/math/base/special/bessely0]</span><span class="delimiter">: </span><span class="description">compute the Bessel function of the second kind of order zero.</span>
- <span class="signature">[`bessely1( x )`][@stdlib/math/base/special/bessely1]</span><span class="delimiter">: </span><span class="description">compute the Bessel function of the second kind of order one.</span>
</div>
<!-- </toc> -->
### Absolute Value and Rounding Functions
<!-- <toc pattern="*+(abs|ceil|floor|clamp|trunc|round|signum)*" > -->
<div class="namespace-toc">
- <span class="signature">[`abs( x )`][@stdlib/math/base/special/abs]</span><span class="delimiter">: </span><span class="description">compute the absolute value of a double-precision floating-point number.</span>
- <span class="signature">[`abs2( x )`][@stdlib/math/base/special/abs2]</span><span class="delimiter">: </span><span class="description">compute the squared absolute value of a double-precision floating-point number.</span>
- <span class="signature">[`abs2f( x )`][@stdlib/math/base/special/abs2f]</span><span class="delimiter">: </span><span class="description">compute the squared absolute value of a single-precision floating-point number.</span>
- <span class="signature">[`absf( x )`][@stdlib/math/base/special/absf]</span><span class="delimiter">: </span><span class="description">compute the absolute value of a single-precision floating-point number.</span>
- <span class="signature">[`cabs( re, im )`][@stdlib/math/base/special/cabs]</span><span class="delimiter">: </span><span class="description">compute an absolute value of a complex number.</span>
- <span class="signature">[`cabs2( re, im )`][@stdlib/math/base/special/cabs2]</span><span class="delimiter">: </span><span class="description">compute the squared absolute value of a complex number.</span>
- <span class="signature">[`cceil( [out,] re, im )`][@stdlib/math/base/special/cceil]</span><span class="delimiter">: </span><span class="description">round a complex number toward positive infinity.</span>
- <span class="signature">[`cceiln( [out,] re, im, n )`][@stdlib/math/base/special/cceiln]</span><span class="delimiter">: </span><span class="description">round a complex number to the nearest multiple of `10^n` toward positive infinity.</span>
- <span class="signature">[`ceil( x )`][@stdlib/math/base/special/ceil]</span><span class="delimiter">: </span><span class="description">round a double-precision floating-point number toward positive infinity.</span>
- <span class="signature">[`ceil10( x )`][@stdlib/math/base/special/ceil10]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of 10 toward positive infinity.</span>
- <span class="signature">[`ceil2( x )`][@stdlib/math/base/special/ceil2]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of two toward positive infinity.</span>
- <span class="signature">[`ceilb( x, n, b )`][@stdlib/math/base/special/ceilb]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of b^n toward positive infinity.</span>
- <span class="signature">[`ceilf( x )`][@stdlib/math/base/special/ceilf]</span><span class="delimiter">: </span><span class="description">round a single-precision floating-point number toward positive infinity.</span>
- <span class="signature">[`ceiln( x, n )`][@stdlib/math/base/special/ceiln]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of 10^n toward positive infinity.</span>
- <span class="signature">[`ceilsd( x, n[, b] )`][@stdlib/math/base/special/ceilsd]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest number toward positive infinity with N significant figures.</span>
- <span class="signature">[`cfloor( [out,] re, im )`][@stdlib/math/base/special/cfloor]</span><span class="delimiter">: </span><span class="description">round a complex number toward negative infinity.</span>
- <span class="signature">[`cfloorn( [out,] re, im, n )`][@stdlib/math/base/special/cfloorn]</span><span class="delimiter">: </span><span class="description">round a complex number to the nearest multiple of `10^n` toward negative infinity.</span>
- <span class="signature">[`clamp( v, min, max )`][@stdlib/math/base/special/clamp]</span><span class="delimiter">: </span><span class="description">restrict a double-precision floating-point number to a specified range.</span>
- <span class="signature">[`clampf( v, min, max )`][@stdlib/math/base/special/clampf]</span><span class="delimiter">: </span><span class="description">restrict a single-precision floating-point number to a specified range.</span>
- <span class="signature">[`cround( [out,] re, im )`][@stdlib/math/base/special/cround]</span><span class="delimiter">: </span><span class="description">round a complex number to the nearest integer.</span>
- <span class="signature">[`croundn( [out,] re, im, n )`][@stdlib/math/base/special/croundn]</span><span class="delimiter">: </span><span class="description">round a complex number to the nearest multiple of `10^n`.</span>
- <span class="signature">[`csignum( [out,] re, im )`][@stdlib/math/base/special/csignum]</span><span class="delimiter">: </span><span class="description">evaluate the signum function of a complex number.</span>
- <span class="signature">[`floor( x )`][@stdlib/math/base/special/floor]</span><span class="delimiter">: </span><span class="description">round a double-precision floating-point number toward negative infinity.</span>
- <span class="signature">[`floor10( x )`][@stdlib/math/base/special/floor10]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of 10 toward negative infinity.</span>
- <span class="signature">[`floor2( x )`][@stdlib/math/base/special/floor2]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of two toward negative infinity.</span>
- <span class="signature">[`floorb( x, n, b )`][@stdlib/math/base/special/floorb]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of b^n toward negative infinity.</span>
- <span class="signature">[`floorf( x )`][@stdlib/math/base/special/floorf]</span><span class="delimiter">: </span><span class="description">round a single-precision floating-point numeric value toward negative infinity.</span>
- <span class="signature">[`floorn( x, n )`][@stdlib/math/base/special/floorn]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of 10^n toward negative infinity.</span>
- <span class="signature">[`floorsd( x, n[, b] )`][@stdlib/math/base/special/floorsd]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest number toward negative infinity with N significant figures.</span>
- <span class="signature">[`labs( x )`][@stdlib/math/base/special/labs]</span><span class="delimiter">: </span><span class="description">compute an absolute value of a signed 32-bit integer.</span>
- <span class="signature">[`maxabs( [x[, y[, ...args]]] )`][@stdlib/math/base/special/maxabs]</span><span class="delimiter">: </span><span class="description">return the maximum absolute value.</span>
- <span class="signature">[`minabs( [x[, y[, ...args]]] )`][@stdlib/math/base/special/minabs]</span><span class="delimiter">: </span><span class="description">return the minimum absolute value.</span>
- <span class="signature">[`minmaxabs( [out,] x[, y[, ...args]] )`][@stdlib/math/base/special/minmaxabs]</span><span class="delimiter">: </span><span class="description">return the minimum and maximum absolute values.</span>
- <span class="signature">[`round( x )`][@stdlib/math/base/special/round]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest integer.</span>
- <span class="signature">[`round10( x )`][@stdlib/math/base/special/round10]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of 10 on a linear scale.</span>
- <span class="signature">[`round2( x )`][@stdlib/math/base/special/round2]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of two on a linear scale.</span>
- <span class="signature">[`roundb( x, n, b )`][@stdlib/math/base/special/roundb]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of b^n on a linear scale.</span>
- <span class="signature">[`roundn( x, n )`][@stdlib/math/base/special/roundn]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of 10^n.</span>
- <span class="signature">[`roundsd( x, n[, b] )`][@stdlib/math/base/special/roundsd]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest number with `n` significant figures.</span>
- <span class="signature">[`signum( x )`][@stdlib/math/base/special/signum]</span><span class="delimiter">: </span><span class="description">signum function.</span>
- <span class="signature">[`signumf( x )`][@stdlib/math/base/special/signumf]</span><span class="delimiter">: </span><span class="description">signum function.</span>
- <span class="signature">[`trunc( x )`][@stdlib/math/base/special/trunc]</span><span class="delimiter">: </span><span class="description">round a double-precision floating-point number toward zero.</span>
- <span class="signature">[`trunc10( x )`][@stdlib/math/base/special/trunc10]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of 10 toward zero.</span>
- <span class="signature">[`trunc2( x )`][@stdlib/math/base/special/trunc2]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest power of two toward zero.</span>
- <span class="signature">[`truncb( x, n, b )`][@stdlib/math/base/special/truncb]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of b^n toward zero.</span>
- <span class="signature">[`truncf( x )`][@stdlib/math/base/special/truncf]</span><span class="delimiter">: </span><span class="description">round a single-precision floating-point number toward zero.</span>
- <span class="signature">[`truncn( x, n )`][@stdlib/math/base/special/truncn]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest multiple of 10^n toward zero.</span>
- <span class="signature">[`truncsd( x, n[, b] )`][@stdlib/math/base/special/truncsd]</span><span class="delimiter">: </span><span class="description">round a numeric value to the nearest number toward zero with `n` significant figures.</span>
</div>
<!-- </toc> -->
### Other Special Functions
<!-- <toc ignore="*bessel*" ignore="*+(sin|cos|tan)*" ignore="+(*log*|ln|exp*|*pow*)" ignore="*+(abs|ceil|floor|clamp|trunc|round|signum)*" ignore="+(gamma-delta-ratio|gamma-lanczos-sum*|rempio2|kernel-*)" ignore="*fast*" > -->
<div class="namespace-toc">
- <span class="signature">[`acot( x )`][@stdlib/math/base/special/acot]</span><span class="delimiter">: </span><span class="description">compute the inverse cotangent of a number.</span>
- <span class="signature">[`acoth( x )`][@stdlib/math/base/special/acoth]</span><span class="delimiter">: </span><span class="description">compute the inverse hyperbolic cotangent of a number.</span>
- <span class="signature">[`bernoulli( n )`][@stdlib/math/base/special/bernoulli]</span><span class="delimiter">: </span><span class="description">compute the nth Bernoulli number.</span>
- <span class="signature">[`beta( x, y )`][@stdlib/math/base/special/beta]</span><span class="delimiter">: </span><span class="description">beta function.</span>
- <span class="signature">[`betainc( x, a, b[, regularized[, upper]] )`][@stdlib/math/base/special/betainc]</span><span class="delimiter">: </span><span class="description">incomplete beta function.</span>
- <span class="signature">[`betaincinv( p, a, b[, upper] )`][@stdlib/math/base/special/betaincinv]</span><span class="delimiter">: </span><span class="description">inverse of the incomplete beta function.</span>
- <span class="signature">[`betaln( x, y )`][@stdlib/math/base/special/betaln]</span><span class="delimiter">: </span><span class="description">natural logarithm of the beta function.</span>
- <span class="signature">[`binet( x )`][@stdlib/math/base/special/binet]</span><span class="delimiter">: </span><span class="description">evaluate Binet's formula extended to real numbers.</span>
- <span class="signature">[`binomcoef( n, k )`][@stdlib/math/base/special/binomcoef]</span><span class="delimiter">: </span><span class="description">compute the binomial coefficient.</span>
- <span class="signature">[`binomcoefln( n, k )`][@stdlib/math/base/special/binomcoefln]</span><span class="delimiter">: </span><span class="description">compute the natural logarithm of the binomial coefficient.</span>
- <span class="signature">[`boxcox( x, lambda )`][@stdlib/math/base/special/boxcox]</span><span class="delimiter">: </span><span class="description">compute a one-parameter Box-Cox transformation.</span>
- <span class="signature">[`boxcox1p( x, lambda )`][@stdlib/math/base/special/boxcox1p]</span><span class="delimiter">: </span><span class="description">compute a one-parameter Box-Cox transformation of `1+x`.</span>
- <span class="signature">[`boxcox1pinv( y, lambda )`][@stdlib/math/base/special/boxcox1pinv]</span><span class="delimiter">: </span><span class="description">compute the inverse of a one-parameter Box-Cox transformation for `1+x`.</span>
- <span class="signature">[`boxcoxinv( y, lambda )`][@stdlib/math/base/special/boxcoxinv]</span><span class="delimiter">: </span><span class="description">compute the inverse of a one-parameter Box-Cox transformation.</span>
- <span class="signature">[`cbrt( x )`][@stdlib/math/base/special/cbrt]</span><span class="delimiter">: </span><span class="description">compute the cube root of a double-precision floating-point number.</span>
- <span class="signature">[`cbrtf( x )`][@stdlib/math/base/special/cbrtf]</span><span class="delimiter">: </span><span class="description">compute the cube root of a single-precision floating-point number.</span>
- <span class="signature">[`ccis( [out,] re, im )`][@stdlib/math/base/special/ccis]</span><span class="delimiter">: </span><span class="description">compute the cis function of a complex number.</span>
- <span class="signature">[`cexp( [out,] re, im )`][@stdlib/math/base/special/cexp]</span><span class="delimiter">: </span><span class="description">compute the exponential function of a complex number.</span>
- <span class="signature">[`cflipsign( [out,] re, im, y )`][@stdlib/math/base/special/cflipsign]</span><span class="delimiter">: </span><span class="description">return a complex number with the same magnitude as `z` and the sign of `y*z`.</span>
- <span class="signature">[`cinv( [out,] re1, im1 )`][@stdlib/math/base/special/cinv]</span><span class="delimiter">: </span><span class="description">compute the inverse of a complex number.</span>
- <span class="signature">[`copysign( x, y )`][@stdlib/math/base/special/copysign]</span><span class="delimiter">: </span><span class="description">return a double-precision floating-point number with the magnitude of `x` and the sign of `y`.</span>
- <span class="signature">[`cphase( re, im )`][@stdlib/math/base/special/cphase]</span><span class="delimiter">: </span><span class="description">compute the argument of a complex number in radians.</span>
- <span class="signature">[`cpolar( [out,] re, im )`][@stdlib/math/base/special/cpolar]</span><span class="delimiter">: </span><span class="description">compute the absolute value and phase of a complex number.</span>
- <span class="signature">[`deg2rad( x )`][@stdlib/math/base/special/deg2rad]</span><span class="delimiter">: </span><span class="description">convert an angle from degrees to radians.</span>
- <span class="signature">[`deg2radf( x )`][@stdlib/math/base/special/deg2radf]</span><span class="delimiter">: </span><span class="description">convert an angle from degrees to radians (single-precision).</span>
- <span class="signature">[`digamma( x )`][@stdlib/math/base/special/digamma]</span><span class="delimiter">: </span><span class="description">digamma function.</span>
- <span class="signature">[`diracDelta( x )`][@stdlib/math/base/special/dirac-delta]</span><span class="delimiter">: </span><span class="description">evaluate the Dirac delta function.</span>
- <span class="signature">[`eta( s )`][@stdlib/math/base/special/dirichlet-eta]</span><span class="delimiter">: </span><span class="description">dirichlet eta function.</span>
- <span class="signature">[`ellipe( m )`][@stdlib/math/base/special/ellipe]</span><span class="delimiter">: </span><span class="description">compute the complete elliptic integral of the second kind.</span>
- <span class="signature">[`ellipk( m )`][@stdlib/math/base/special/ellipk]</span><span class="delimiter">: </span><span class="description">compute the complete elliptic integral of the first kind.</span>
- <span class="signature">[`erf( x )`][@stdlib/math/base/special/erf]</span><span class="delimiter">: </span><span class="description">error function.</span>
- <span class="signature">[`erfc( x )`][@stdlib/math/base/special/erfc]</span><span class="delimiter">: </span><span class="description">complementary error function.</span>
- <span class="signature">[`erfcinv( x )`][@stdlib/math/base/special/erfcinv]</span><span class="delimiter">: </span><span class="description">inverse complementary error function.</span>
- <span class="signature">[`erfinv( x )`][@stdlib/math/base/special/erfinv]</span><span class="delimiter">: </span><span class="description">inverse error function.</span>
- <span class="signature">[`factorial( x )`][@stdlib/math/base/special/factorial]</span><span class="delimiter">: </span><span class="description">factorial function.</span>
- <span class="signature">[`factorialln( x )`][@stdlib/math/base/special/factorialln]</span><span class="delimiter">: </span><span class="description">natural logarithm of the factorial function.</span>
- <span class="signature">[`fallingFactorial( x, n )`][@stdlib/math/base/special/falling-factorial]</span><span class="delimiter">: </span><span class="description">compute the falling factorial.</span>
- <span class="signature">[`fibonacciIndex( F )`][@stdlib/math/base/special/fibonacci-index]</span><span class="delimiter">: </span><span class="description">compute the Fibonacci number index.</span>
- <span class="signature">[`fibonacci( n )`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span>
- <span class="signature">[`flipsign( x, y )`][@stdlib/math/base/special/flipsign]</span><span class="delimiter">: </span><span class="description">return a double-precision floating-point number with the magnitude of `x` and the sign of `x*y`.</span>
- <span class="signature">[`fresnel( [out,] x )`][@stdlib/math/base/special/fresnel]</span><span class="delimiter">: </span><span class="description">compute the Fresnel integrals S(x) and C(x).</span>
- <span class="signature">[`fresnelc( x )`][@stdlib/math/base/special/fresnelc]</span><span class="delimiter">: </span><span class="description">compute the Fresnel integral C(x).</span>
- <span class="signature">[`fresnels( x )`][@stdlib/math/base/special/fresnels]</span><span class="delimiter">: </span><span class="description">compute the Fresnel integral S(x).</span>
- <span class="signature">[`frexp( [out,] x )`][@stdlib/math/base/special/frexp]</span><span class="delimiter">: </span><span class="description">split a double-precision floating-point number into a normalized fraction and an integer power of two.</span>
- <span class="signature">[`gamma( x )`][@stdlib/math/base/special/gamma]</span><span class="delimiter">: </span><span class="description">gamma function.</span>
- <span class="signature">[`gamma1pm1( x )`][@stdlib/math/base/special/gamma1pm1]</span><span class="delimiter">: </span><span class="description">compute `gamma(x+1) - 1`.</span>
- <span class="signature">[`gammainc( x, s[, regularized[, upper ]] )`][@stdlib/math/base/special/gammainc]</span><span class="delimiter">: </span><span class="description">incomplete gamma function.</span>
- <span class="signature">[`gammaincinv( p, s[, upper ] )`][@stdlib/math/base/special/gammaincinv]</span><span class="delimiter">: </span><span class="description">inverse of incomplete gamma function.</span>
- <span class="signature">[`gammaln( x )`][@stdlib/math/base/special/gammaln]</span><span class="delimiter">: </span><span class="description">natural logarithm of the gamma function.</span>
- <span class="signature">[`gcd( a, b )`][@stdlib/math/base/special/gcd]</span><span class="delimiter">: </span><span class="description">compute the greatest common divisor (gcd).</span>
- <span class="signature">[`heaviside( x[, continuity] )`][@stdlib/math/base/special/heaviside]</span><span class="delimiter">: </span><span class="description">evaluate the Heaviside function.</span>
- <span class="signature">[`hypot( x, y )`][@stdlib/math/base/special/hypot]</span><span class="delimiter">: </span><span class="description">compute the hypotenuse avoiding overflow and underflow.</span>
- <span class="signature">[`hypotf( x, y )`][@stdlib/math/base/special/hypotf]</span><span class="delimiter">: </span><span class="description">compute the hypotenuse avoiding overflow and underflow (single-precision).</span>
- <span class="signature">[`identity( x )`][@stdlib/math/base/special/identity]</span><span class="delimiter">: </span><span class="description">evaluate the identity function of a double-precision floating-point number.</span>
- <span class="signature">[`identityf( x )`][@stdlib/math/base/special/identityf]</span><span class="delimiter">: </span><span class="description">evaluate the identity function of a single-precision floating-point number.</span>
- <span class="signature">[`imul( a, b )`][@stdlib/math/base/special/imul]</span><span class="delimiter">: </span><span class="description">perform C-like multiplication of two signed 32-bit integers.</span>
- <span class="signature">[`imuldw( [out,] a, b )`][@stdlib/math/base/special/imuldw]</span><span class="delimiter">: </span><span class="description">compute the double word product of two signed 32-bit integers.</span>
- <span class="signature">[`inv( x )`][@stdlib/math/base/special/inv]</span><span class="delimiter">: </span><span class="description">compute the multiplicative inverse of a double-precision floating-point number.</span>
- <span class="signature">[`invf( x )`][@stdlib/math/base/special/invf]</span><span class="delimiter">: </span><span class="description">compute the multiplicative inverse of a single-precision floating-point number.</span>
- <span class="signature">[`kroneckerDelta( i, j )`][@stdlib/math/base/special/kronecker-delta]</span><span class="delimiter">: </span><span class="description">evaluate the Kronecker delta.</span>
- <span class="signature">[`kroneckerDeltaf( i, j )`][@stdlib/math/base/special/kronecker-deltaf]</span><span class="delimiter">: </span><span class="description">evaluate the Kronecker delta (single-precision).</span>
- <span class="signature">[`lcm( a, b )`][@stdlib/math/base/special/lcm]</span><span class="delimiter">: </span><span class="description">compute the least common multiple (lcm).</span>
- <span class="signature">[`ldexp( frac, exp )`][@stdlib/math/base/special/ldexp]</span><span class="delimiter">: </span><span class="description">multiply a double-precision floating-point number by an integer power of two.</span>
- <span class="signature">[`lucas( n )`][@stdlib/math/base/special/lucas]</span><span class="delimiter">: </span><span class="description">compute the nth Lucas number.</span>
- <span class="signature">[`max( [x[, y[, ...args]]] )`][@stdlib/math/base/special/max]</span><span class="delimiter">: </span><span class="description">return the maximum value.</span>
- <span class="signature">[`min( [x[, y[, ...args]]] )`][@stdlib/math/base/special/min]</span><span class="delimiter">: </span><span class="description">return the minimum value.</span>
- <span class="signature">[`minmax( [out,] x[, y[, ...args]] )`][@stdlib/math/base/special/minmax]</span><span class="delimiter">: </span><span class="description">return the minimum and maximum values.</span>
- <span class="signature">[`modf( [out,] x )`][@stdlib/math/base/special/modf]</span><span class="delimiter">: </span><span class="description">decompose a double-precision floating-point number into integral and fractional parts.</span>
- <span class="signature">[`negafibonacci( n )`][@stdlib/math/base/special/negafibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth negaFibonacci number.</span>
- <span class="signature">[`negalucas( n )`][@stdlib/math/base/special/negalucas]</span><span class="delimiter">: </span><span class="description">compute the nth negaLucas number.</span>
- <span class="signature">[`nonfibonacci( n )`][@stdlib/math/base/special/nonfibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth non-Fibonacci number.</span>
- <span class="signature">[`pdiff( x, y )`][@stdlib/math/base/special/pdiff]</span><span class="delimiter">: </span><span class="description">return the positive difference between `x` and `y`.</span>
- <span class="signature">[`pdifff( x, y )`][@stdlib/math/base/special/pdifff]</span><span class="delimiter">: </span><span class="description">return the positive difference between `x` and `y`.</span>
- <span class="signature">[`polygamma( n, x )`][@stdlib/math/base/special/polygamma]</span><span class="delimiter">: </span><span class="description">polygamma function.</span>
- <span class="signature">[`rad2deg( x )`][@stdlib/math/base/special/rad2deg]</span><span class="delimiter">: </span><span class="description">convert an angle from radians to degrees.</span>
- <span class="signature">[`ramp( x )`][@stdlib/math/base/special/ramp]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span>
- <span class="signature">[`rampf( x )`][@stdlib/math/base/special/rampf]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span>
- <span class="signature">[`zeta( s )`][@stdlib/math/base/special/riemann-zeta]</span><span class="delimiter">: </span><span class="description">riemann zeta function.</span>
- <span class="signature">[`rsqrt( x )`][@stdlib/math/base/special/rsqrt]</span><span class="delimiter">: </span><span class="description">compute the reciprocal of the principal square root of a double-precision floating-point number.</span>
- <span class="signature">[`rsqrtf( x )`][@stdlib/math/base/special/rsqrtf]</span><span class="delimiter">: </span><span class="description">compute the reciprocal of the principal square root of a single-precision floating-point number.</span>
- <span class="signature">[`sici( [out,] x )`][@stdlib/math/base/special/sici]</span><span class="delimiter">: </span><span class="description">compute the sine and cosine integrals.</span>
- <span class="signature">[`spence( x )`][@stdlib/math/base/special/spence]</span><span class="delimiter">: </span><span class="description">spence’s function, also known as the dilogarithm.</span>
- <span class="signature">[`sqrt( x )`][@stdlib/math/base/special/sqrt]</span><span class="delimiter">: </span><span class="description">compute the principal square root of a double-precision floating-point number.</span>
- <span class="signature">[`sqrt1pm1( x )`][@stdlib/math/base/special/sqrt1pm1]</span><span class="delimiter">: </span><span class="description">compute `sqrt( 1 + x ) - 1`.</span>
- <span class="signature">[`sqrtf( x )`][@stdlib/math/base/special/sqrtf]</span><span class="delimiter">: </span><span class="description">compute the principal square root of a single-precision floating-point number.</span>
- <span class="signature">[`tribonacci( n )`][@stdlib/math/base/special/tribonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Tribonacci number.</span>
- <span class="signature">[`trigamma( x )`][@stdlib/math/base/special/trigamma]</span><span class="delimiter">: </span><span class="description">trigamma function.</span>
- <span class="signature">[`uimul( a, b )`][@stdlib/math/base/special/uimul]</span><span class="delimiter">: </span><span class="description">perform C-like multiplication of two unsigned 32-bit integers.</span>
- <span class="signature">[`uimuldw( [out,] a, b )`][@stdlib/math/base/special/uimuldw]</span><span class="delimiter">: </span><span class="description">compute the double word product of two unsigned 32-bit integers.</span>
- <span class="signature">[`wrap( v, min, max )`][@stdlib/math/base/special/wrap]</span><span class="delimiter">: </span><span class="description">wrap a value on the half-open interval `[min,max)`.</span>
</div>
<!-- </toc> -->
Fast algorithms of various special functions, which trade accuracy for increased speed, are available in the following sub-namespace:
<!-- <toc pattern="*fast*" > -->
<div class="namespace-toc">
- <span class="signature">[`fast`][@stdlib/math/base/special/fast]</span><span class="delimiter">: </span><span class="description">standard library fast math special functions.</span>
</div>
<!-- </toc> -->
Finally, the namespace exports the following kernel functions, which are mainly used internally. Beware that they may only be applicable for input values inside a certain number range and/or may not work as expected if not all arguments satisfy the parameter requirements.
<!-- <toc pattern="+(gammaDeltaRatio|gammaLanczosSum|gammaLanczosSumExpGScaled|rempio2|kernel-*)" > -->
<div class="namespace-toc">
- <span class="signature">[`kernelBetainc( x, a, b, regularized, upper )`][@stdlib/math/base/special/kernel-betainc]</span><span class="delimiter">: </span><span class="description">incomplete beta function and its first derivative.</span>
- <span class="signature">[`kernelBetaincinv( a, b, p, q )`][@stdlib/math/base/special/kernel-betaincinv]</span><span class="delimiter">: </span><span class="description">inverse of the lower incomplete beta function.</span>
- <span class="signature">[`kernelCos( x, y )`][@stdlib/math/base/special/kernel-cos]</span><span class="delimiter">: </span><span class="description">compute the cosine of a number on `[-π/4, π/4]`.</span>
- <span class="signature">[`kernelSin( x, y )`][@stdlib/math/base/special/kernel-sin]</span><span class="delimiter">: </span><span class="description">compute the sine of a number on `[-π/4, π/4]`.</span>
- <span class="signature">[`kernelTan( x, y, k )`][@stdlib/math/base/special/kernel-tan]</span><span class="delimiter">: </span><span class="description">compute the tangent of a number on `[-π/4, π/4]`.</span>
- <span class="signature">[`rempio2( x, y )`][@stdlib/math/base/special/rempio2]</span><span class="delimiter">: </span><span class="description">compute `x - nπ/2 = r`.</span>
</div>
<!-- </toc> -->
</section>
<!-- /.usage -->
<section class="examples">
## Examples
<!-- TODO: better examples -->
<!-- eslint no-undef: "error" -->
```javascript
var objectKeys = require( '@stdlib/utils/keys' );
var special = require( '@stdlib/math/base/special' );
console.log( objectKeys( special ) );
```
</section>
<!-- /.examples -->
<section class="links">
<!-- <toc-links> -->
[@stdlib/math/base/special/kernel-betainc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-betainc
[@stdlib/math/base/special/kernel-betaincinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-betaincinv
[@stdlib/math/base/special/kernel-cos]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-cos
[@stdlib/math/base/special/kernel-sin]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-sin
[@stdlib/math/base/special/kernel-tan]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-tan
[@stdlib/math/base/special/rempio2]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/rempio2
[@stdlib/math/base/special/fast]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fast
[@stdlib/math/base/special/acot]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/acot
[@stdlib/math/base/special/acoth]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/acoth
[@stdlib/math/base/special/bernoulli]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/bernoulli
[@stdlib/math/base/special/beta]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/beta
[@stdlib/math/base/special/betainc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betainc
[@stdlib/math/base/special/betaincinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betaincinv
[@stdlib/math/base/special/betaln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betaln
[@stdlib/math/base/special/binet]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binet
[@stdlib/math/base/special/binomcoef]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binomcoef
[@stdlib/math/base/special/binomcoefln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binomcoefln
[@stdlib/math/base/special/boxcox]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox
[@stdlib/math/base/special/boxcox1p]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox1p
[@stdlib/math/base/special/boxcox1pinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox1pinv
[@stdlib/math/base/special/boxcoxinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcoxinv
[@stdlib/math/base/special/cbrt]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cbrt
[@stdlib/math/base/special/cbrtf]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cbrtf
[@stdlib/math/base/special/ccis]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/ccis
[@stdlib/math/base/special/cexp]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cexp
[@stdlib/math/base/special/cflipsign]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cflipsign
[@stdlib/math/base/special/cinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cinv
[@stdlib/math/base/special/copysign]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/copysign
[@stdlib/math/base/special/cphase]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cphase
[@stdlib/math/base/special/cpolar]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cpolar
[@stdlib/math/base/special/deg2rad]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/deg2rad
[@stdlib/math/base/special/deg2radf]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/deg2radf
[@stdlib/math/base/special/digamma]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/digamma
[@stdlib/math/base/special/dirac-delta]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/dirac-delta
[@stdlib/math/base/special/dirichlet-eta]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/dirichlet-eta
[@stdlib/math/base/special/ellipe]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/ellipe
[@stdlib/math/base/special/ellipk]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/ellipk
[@stdlib/math/base/special/erf]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/erf
[@stdlib/math/base/special/erfc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/erfc
[@stdlib/math/base/special/erfcinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/erfcinv
[@stdlib/math/base/special/erfinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/erfinv
[@stdlib/math/base/special/factorial]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/factorial
[@stdlib/math/base/special/factorialln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/factorialln
[@stdlib/math/base/special/falling-factorial]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/falling-factorial
[@stdlib/math/base/special/fibonacci-index]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fibonacci-index
[@stdlib/math/base/special/fibonacci]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fibonacci
[@stdlib/math/base/special/flipsign]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/flipsign
[@stdlib/math/base/special/fresnel]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fresnel
[@stdlib/math/base/special/fresnelc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fresnelc
[@stdlib/math/base/special/fresnels]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fresnels
[@stdlib/math/base/special/frexp]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/frexp
[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gamma
[@stdlib/math/base/special/gamma1pm1]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gamma1pm1
[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gammainc
[@stdlib/math/base/special/gammaincinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gammaincinv
[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gammaln
[@stdlib/math/base/special/gcd]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/gcd
[@stdlib/math/base/special/heaviside]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/heaviside
[@stdlib/math/base/special/hypot]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/hypot
[@stdlib/math/base/special/hypotf]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/hypotf
[@stdlib/math/base/special/identity]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/identity
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<!-- </toc-links> -->
</section>
<!-- /.links -->
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