README.md (66447B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # Special Functions 22 23 > Standard library base special math functions. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var special = require( '@stdlib/math/base/special' ); 31 ``` 32 33 #### special 34 35 Standard library base special math functions. 36 37 ```javascript 38 var fcns = special; 39 // returns {...} 40 ``` 41 42 ### Exponential & Logarithmic Functions 43 44 <!-- <toc pattern="+(*log*|ln|exp*|*pow*)" ignore="logit" > --> 45 46 <div class="namespace-toc"> 47 48 - <span class="signature">[`exp( x )`][@stdlib/math/base/special/exp]</span><span class="delimiter">: </span><span class="description">natural exponential function.</span> 49 - <span class="signature">[`exp10( x )`][@stdlib/math/base/special/exp10]</span><span class="delimiter">: </span><span class="description">base `10` exponential function.</span> 50 - <span class="signature">[`exp2( x )`][@stdlib/math/base/special/exp2]</span><span class="delimiter">: </span><span class="description">base `2` exponential function.</span> 51 - <span class="signature">[`expit( x )`][@stdlib/math/base/special/expit]</span><span class="delimiter">: </span><span class="description">compute the standard logistic function.</span> 52 - <span class="signature">[`expm1( x )`][@stdlib/math/base/special/expm1]</span><span class="delimiter">: </span><span class="description">compute `exp(x) - 1`.</span> 53 - <span class="signature">[`expm1rel( x )`][@stdlib/math/base/special/expm1rel]</span><span class="delimiter">: </span><span class="description">compute the relative error exponential.</span> 54 - <span class="signature">[`ln( x )`][@stdlib/math/base/special/ln]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm.</span> 55 - <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> 56 - <span class="signature">[`log10( x )`][@stdlib/math/base/special/log10]</span><span class="delimiter">: </span><span class="description">evaluate the common logarithm.</span> 57 - <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> 58 - <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> 59 - <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> 60 - <span class="signature">[`log2( x )`][@stdlib/math/base/special/log2]</span><span class="delimiter">: </span><span class="description">evaluate the binary logarithm.</span> 61 - <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> 62 - <span class="signature">[`pow( base, exponent )`][@stdlib/math/base/special/pow]</span><span class="delimiter">: </span><span class="description">exponential function.</span> 63 - <span class="signature">[`powm1( b, x )`][@stdlib/math/base/special/powm1]</span><span class="delimiter">: </span><span class="description">evaluate `bˣ - 1`.</span> 64 - <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> 65 - <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> 66 67 </div> 68 69 <!-- </toc> --> 70 71 ### Trigonometric Functions 72 73 <!-- <toc pattern="*+(sin|cos|tan)*" ignore="+(kernel-sin|kernel-cos|kernel-tan)"> --> 74 75 <div class="namespace-toc"> 76 77 - <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> 78 - <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> 79 - <span class="signature">[`acovercos( x )`][@stdlib/math/base/special/acovercos]</span><span class="delimiter">: </span><span class="description">compute the inverse coversed cosine.</span> 80 - <span class="signature">[`acoversin( x )`][@stdlib/math/base/special/acoversin]</span><span class="delimiter">: </span><span class="description">compute the inverse coversed sine.</span> 81 - <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> 82 - <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> 83 - <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> 84 - <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> 85 - <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> 86 - <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> 87 - <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> 88 - <span class="signature">[`avercos( x )`][@stdlib/math/base/special/avercos]</span><span class="delimiter">: </span><span class="description">compute the inverse versed cosine.</span> 89 - <span class="signature">[`aversin( x )`][@stdlib/math/base/special/aversin]</span><span class="delimiter">: </span><span class="description">compute the inverse versed sine.</span> 90 - <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> 91 - <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> 92 - <span class="signature">[`cosm1( x )`][@stdlib/math/base/special/cosm1]</span><span class="delimiter">: </span><span class="description">compute `cos(x) - 1`.</span> 93 - <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> 94 - <span class="signature">[`covercos( x )`][@stdlib/math/base/special/covercos]</span><span class="delimiter">: </span><span class="description">compute the coversed cosine.</span> 95 - <span class="signature">[`coversin( x )`][@stdlib/math/base/special/coversin]</span><span class="delimiter">: </span><span class="description">compute the coversed sine.</span> 96 - <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> 97 - <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> 98 - <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> 99 - <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> 100 - <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> 101 - <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> 102 - <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> 103 - <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> 104 - <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> 105 - <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> 106 - <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> 107 - <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> 108 - <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> 109 - <span class="signature">[`vercos( x )`][@stdlib/math/base/special/vercos]</span><span class="delimiter">: </span><span class="description">compute the versed cosine.</span> 110 - <span class="signature">[`versin( x )`][@stdlib/math/base/special/versin]</span><span class="delimiter">: </span><span class="description">compute the versed sine.</span> 111 112 </div> 113 114 <!-- </toc> --> 115 116 ### Bessel Functions 117 118 <!-- <toc pattern="*bessel*" > --> 119 120 <div class="namespace-toc"> 121 122 - <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> 123 - <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> 124 - <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> 125 - <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> 126 127 </div> 128 129 <!-- </toc> --> 130 131 ### Absolute Value and Rounding Functions 132 133 <!-- <toc pattern="*+(abs|ceil|floor|clamp|trunc|round|signum)*" > --> 134 135 <div class="namespace-toc"> 136 137 - <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> 138 - <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> 139 - <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> 140 - <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> 141 - <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> 142 - <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> 143 - <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> 144 - <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> 145 - <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> 146 - <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> 147 - <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> 148 - <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> 149 - <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> 150 - <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> 151 - <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> 152 - <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> 153 - <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> 154 - <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> 155 - <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> 156 - <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> 157 - <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> 158 - <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> 159 - <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> 160 - <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> 161 - <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> 162 - <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> 163 - <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> 164 - <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> 165 - <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> 166 - <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> 167 - <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> 168 - <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> 169 - <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> 170 - <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> 171 - <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> 172 - <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> 173 - <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> 174 - <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> 175 - <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> 176 - <span class="signature">[`signum( x )`][@stdlib/math/base/special/signum]</span><span class="delimiter">: </span><span class="description">signum function.</span> 177 - <span class="signature">[`signumf( x )`][@stdlib/math/base/special/signumf]</span><span class="delimiter">: </span><span class="description">signum function.</span> 178 - <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> 179 - <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> 180 - <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> 181 - <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> 182 - <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> 183 - <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> 184 - <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> 185 186 </div> 187 188 <!-- </toc> --> 189 190 ### Other Special Functions 191 192 <!-- <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*" > --> 193 194 <div class="namespace-toc"> 195 196 - <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> 197 - <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> 198 - <span class="signature">[`bernoulli( n )`][@stdlib/math/base/special/bernoulli]</span><span class="delimiter">: </span><span class="description">compute the nth Bernoulli number.</span> 199 - <span class="signature">[`beta( x, y )`][@stdlib/math/base/special/beta]</span><span class="delimiter">: </span><span class="description">beta function.</span> 200 - <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> 201 - <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> 202 - <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> 203 - <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> 204 - <span class="signature">[`binomcoef( n, k )`][@stdlib/math/base/special/binomcoef]</span><span class="delimiter">: </span><span class="description">compute the binomial coefficient.</span> 205 - <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> 206 - <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> 207 - <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> 208 - <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> 209 - <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> 210 - <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> 211 - <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> 212 - <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> 213 - <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> 214 - <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> 215 - <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> 216 - <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> 217 - <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> 218 - <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> 219 - <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> 220 - <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> 221 - <span class="signature">[`digamma( x )`][@stdlib/math/base/special/digamma]</span><span class="delimiter">: </span><span class="description">digamma function.</span> 222 - <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> 223 - <span class="signature">[`eta( s )`][@stdlib/math/base/special/dirichlet-eta]</span><span class="delimiter">: </span><span class="description">dirichlet eta function.</span> 224 - <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> 225 - <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> 226 - <span class="signature">[`erf( x )`][@stdlib/math/base/special/erf]</span><span class="delimiter">: </span><span class="description">error function.</span> 227 - <span class="signature">[`erfc( x )`][@stdlib/math/base/special/erfc]</span><span class="delimiter">: </span><span class="description">complementary error function.</span> 228 - <span class="signature">[`erfcinv( x )`][@stdlib/math/base/special/erfcinv]</span><span class="delimiter">: </span><span class="description">inverse complementary error function.</span> 229 - <span class="signature">[`erfinv( x )`][@stdlib/math/base/special/erfinv]</span><span class="delimiter">: </span><span class="description">inverse error function.</span> 230 - <span class="signature">[`factorial( x )`][@stdlib/math/base/special/factorial]</span><span class="delimiter">: </span><span class="description">factorial function.</span> 231 - <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> 232 - <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> 233 - <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> 234 - <span class="signature">[`fibonacci( n )`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</span> 235 - <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> 236 - <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> 237 - <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> 238 - <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> 239 - <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> 240 - <span class="signature">[`gamma( x )`][@stdlib/math/base/special/gamma]</span><span class="delimiter">: </span><span class="description">gamma function.</span> 241 - <span class="signature">[`gamma1pm1( x )`][@stdlib/math/base/special/gamma1pm1]</span><span class="delimiter">: </span><span class="description">compute `gamma(x+1) - 1`.</span> 242 - <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> 243 - <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> 244 - <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> 245 - <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> 246 - <span class="signature">[`heaviside( x[, continuity] )`][@stdlib/math/base/special/heaviside]</span><span class="delimiter">: </span><span class="description">evaluate the Heaviside function.</span> 247 - <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> 248 - <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> 249 - <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> 250 - <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> 251 - <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> 252 - <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> 253 - <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> 254 - <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> 255 - <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> 256 - <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> 257 - <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> 258 - <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> 259 - <span class="signature">[`lucas( n )`][@stdlib/math/base/special/lucas]</span><span class="delimiter">: </span><span class="description">compute the nth Lucas number.</span> 260 - <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> 261 - <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> 262 - <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> 263 - <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> 264 - <span class="signature">[`negafibonacci( n )`][@stdlib/math/base/special/negafibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth negaFibonacci number.</span> 265 - <span class="signature">[`negalucas( n )`][@stdlib/math/base/special/negalucas]</span><span class="delimiter">: </span><span class="description">compute the nth negaLucas number.</span> 266 - <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> 267 - <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> 268 - <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> 269 - <span class="signature">[`polygamma( n, x )`][@stdlib/math/base/special/polygamma]</span><span class="delimiter">: </span><span class="description">polygamma function.</span> 270 - <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> 271 - <span class="signature">[`ramp( x )`][@stdlib/math/base/special/ramp]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span> 272 - <span class="signature">[`rampf( x )`][@stdlib/math/base/special/rampf]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span> 273 - <span class="signature">[`zeta( s )`][@stdlib/math/base/special/riemann-zeta]</span><span class="delimiter">: </span><span class="description">riemann zeta function.</span> 274 - <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> 275 - <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> 276 - <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> 277 - <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> 278 - <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> 279 - <span class="signature">[`sqrt1pm1( x )`][@stdlib/math/base/special/sqrt1pm1]</span><span class="delimiter">: </span><span class="description">compute `sqrt( 1 + x ) - 1`.</span> 280 - <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> 281 - <span class="signature">[`tribonacci( n )`][@stdlib/math/base/special/tribonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Tribonacci number.</span> 282 - <span class="signature">[`trigamma( x )`][@stdlib/math/base/special/trigamma]</span><span class="delimiter">: </span><span class="description">trigamma function.</span> 283 - <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> 284 - <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> 285 - <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> 286 287 </div> 288 289 <!-- </toc> --> 290 291 Fast algorithms of various special functions, which trade accuracy for increased speed, are available in the following sub-namespace: 292 293 <!-- <toc pattern="*fast*" > --> 294 295 <div class="namespace-toc"> 296 297 - <span class="signature">[`fast`][@stdlib/math/base/special/fast]</span><span class="delimiter">: </span><span class="description">standard library fast math special functions.</span> 298 299 </div> 300 301 <!-- </toc> --> 302 303 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. 304 305 <!-- <toc pattern="+(gammaDeltaRatio|gammaLanczosSum|gammaLanczosSumExpGScaled|rempio2|kernel-*)" > --> 306 307 <div class="namespace-toc"> 308 309 - <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> 310 - <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> 311 - <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> 312 - <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> 313 - <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> 314 - <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> 315 316 </div> 317 318 <!-- </toc> --> 319 320 </section> 321 322 <!-- /.usage --> 323 324 <section class="examples"> 325 326 ## Examples 327 328 <!-- TODO: better examples --> 329 330 <!-- eslint no-undef: "error" --> 331 332 ```javascript 333 var objectKeys = require( '@stdlib/utils/keys' ); 334 var special = require( '@stdlib/math/base/special' ); 335 336 console.log( objectKeys( special ) ); 337 ``` 338 339 </section> 340 341 <!-- /.examples --> 342 343 <section class="links"> 344 345 <!-- <toc-links> --> 346 347 [@stdlib/math/base/special/kernel-betainc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-betainc 348 349 [@stdlib/math/base/special/kernel-betaincinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-betaincinv 350 351 [@stdlib/math/base/special/kernel-cos]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-cos 352 353 [@stdlib/math/base/special/kernel-sin]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-sin 354 355 [@stdlib/math/base/special/kernel-tan]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/kernel-tan 356 357 [@stdlib/math/base/special/rempio2]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/rempio2 358 359 [@stdlib/math/base/special/fast]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/fast 360 361 [@stdlib/math/base/special/acot]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/acot 362 363 [@stdlib/math/base/special/acoth]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/acoth 364 365 [@stdlib/math/base/special/bernoulli]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/bernoulli 366 367 [@stdlib/math/base/special/beta]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/beta 368 369 [@stdlib/math/base/special/betainc]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betainc 370 371 [@stdlib/math/base/special/betaincinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betaincinv 372 373 [@stdlib/math/base/special/betaln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/betaln 374 375 [@stdlib/math/base/special/binet]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binet 376 377 [@stdlib/math/base/special/binomcoef]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binomcoef 378 379 [@stdlib/math/base/special/binomcoefln]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/binomcoefln 380 381 [@stdlib/math/base/special/boxcox]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox 382 383 [@stdlib/math/base/special/boxcox1p]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox1p 384 385 [@stdlib/math/base/special/boxcox1pinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcox1pinv 386 387 [@stdlib/math/base/special/boxcoxinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/boxcoxinv 388 389 [@stdlib/math/base/special/cbrt]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cbrt 390 391 [@stdlib/math/base/special/cbrtf]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cbrtf 392 393 [@stdlib/math/base/special/ccis]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/ccis 394 395 [@stdlib/math/base/special/cexp]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cexp 396 397 [@stdlib/math/base/special/cflipsign]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cflipsign 398 399 [@stdlib/math/base/special/cinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cinv 400 401 [@stdlib/math/base/special/copysign]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/copysign 402 403 [@stdlib/math/base/special/cphase]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cphase 404 405 [@stdlib/math/base/special/cpolar]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cpolar 406 407 [@stdlib/math/base/special/deg2rad]: 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