Special Functions
Base (i.e., lower-level) special math functions.
Usage
var special = require( '@stdlib/math/base/special' );
special
Namespace for "base" (i.e., lower-level) special math functions.
var fcns = special;
// returns {...}
Exponential & Logarithmic Functions
exp( x ): natural exponential function.exp10( x ): base10exponential function.exp2( x ): base2exponential function.expit( x ): compute the standard logistic function.expm1( x ): computeexp(x) - 1.expm1rel( x ): compute the relative error exponential.kernelLog1p( f ): computelog(1+f) - ffor1+fin~[sqrt(2)/2, sqrt(2)].ln( x ): evaluate the natural logarithm of a double-precision floating-point number.log( x, b ): compute the baseblogarithm of a double-precision floating-point number.log10( x ): evaluate the common logarithm.log1mexp( x ): evaluates the natural logarithm of1-exp(-|x|).log1p( x ): evaluate the natural logarithm of1+x.log1pexp( x ): evaluates the natural logarithm of1+exp(x).log1pmx( x ): evaluateln(1+x) - x.log2( x ): evaluate the binary logarithm.logaddexp( x, y ): evaluates the natural logarithm ofexp(x) + exp(y).pow( base, exponent ): exponential function.powm1( b, x ): evaluatebˣ - 1.xlog1py( x, y ): computex * ln(y+1)so that the result is0ifx = 0.xlogy( x, y ): computex * ln(y)so that the result is0ifx = 0.
Trigonometric Functions
acos( x ): compute the arccosine of a double-precision floating-point number.acosd( x ): compute the arccosine in degrees of a double-precision floating-point number.acosf( x ): compute the arccosine of a single-precision floating-point number.acosh( x ): compute the hyperbolic arccosine of a double-precision floating-point number.acovercos( x ): compute the inverse coversed cosine.acoversin( x ): compute the inverse coversed sine.ahavercos( x ): compute the inverse half-value versed cosine.ahaversin( x ): compute the inverse half-value versed sine.asin( x ): compute the arcsine of a double-precision floating-point number.asind( x ): compute the arcsine (in degrees) of a double-precision floating-point number.asindf( x ): compute the arcsine (in degrees) of a single-precision floating-point number.asinf( x ): compute the arcsine of a single-precision floating-point number.asinh( x ): compute the hyperbolic arcsine of a double-precision floating-point number.atan( x ): compute the arctangent of a double-precision floating-point number.atan2( y, x ): compute the angle in the plane (in radians) between the positive x-axis and the ray from(0,0)to the point(x,y).atand( x ): compute the arctangent in degrees of a double-precision floating-point number.atanf( x ): compute the arctangent of a single-precision floating-point number.atanh( x ): compute the hyperbolic arctangent of a double-precision floating-point number.avercos( x ): compute the inverse versed cosine.aversin( x ): compute the inverse versed sine.cos( x ): compute the cosine of a number.cosd( x ): computes the cosine of an angle measured in degrees.cosh( x ): compute the hyperbolic cosine of a double-precision floating-point number.cosm1( x ): computecos(x) - 1.cospi( x ): compute the cosine of a number times π.covercos( x ): compute the coversed cosine.coversin( x ): compute the coversed sine.hacovercos( x ): compute the half-value coversed cosine.hacoversin( x ): compute the half-value coversed sine.havercos( x ): compute the half-value versed cosine.haversin( x ): compute the half-value versed sine.risingFactorial( x, n ): compute the rising factorial.sin( x ): compute the sine of a number.sinc( x ): compute the cardinal sine of a number.sincos( x ): simultaneously compute the sine and cosine of a number.sincospi(): simultaneously compute the sine and cosine of a number times π.sinh( x ): compute the hyperbolic sine of a double-precision floating-point number.sinpi( x ): compute the sine of a number times π.tan( x ): evaluate the tangent of a number.tand( x ): computes the tangent of an angle measured in degrees.tanh( x ): compute the hyperbolic tangent of a double-precision floating-point number.vercos( x ): compute the versed cosine.versin( x ): compute the versed sine.
Bessel Functions
besselj0( x ): compute the Bessel function of the first kind of order zero.besselj1( x ): compute the Bessel function of the first kind of order one.bessely0( x ): compute the Bessel function of the second kind of order zero.bessely1( x ): compute the Bessel function of the second kind of order one.
Absolute Value and Rounding Functions
abs( x ): compute the absolute value of a double-precision floating-point number.abs2( x ): compute the squared absolute value of a double-precision floating-point number.abs2f( x ): compute the squared absolute value of a single-precision floating-point number.absf( x ): compute the absolute value of a single-precision floating-point number.cabs( z ): compute the absolute value of a double-precision complex floating-point number.cabs2( z ): compute the squared absolute value of a double-precision complex floating-point number.cabs2f( z ): compute the squared absolute value of a single-precision complex floating-point number.cabsf( z ): compute the absolute value of a single-precision complex floating-point number.cceil( z ): round a double-precision complex floating-point number toward positive infinity.cceilf( z ): round a single-precision complex floating-point number toward positive infinity.cceiln( z, n ): round each component of a double-precision complex floating-point number to the nearest multiple of10^ntoward positive infinity.ceil( x ): round a double-precision floating-point number toward positive infinity.ceil10( x ): round a numeric value to the nearest power of 10 toward positive infinity.ceil2( x ): round a numeric value to the nearest power of two toward positive infinity.ceilb( x, n, b ): round a numeric value to the nearest multiple of b^n toward positive infinity.ceilf( x ): round a single-precision floating-point number toward positive infinity.ceiln( x, n ): round a numeric value to the nearest multiple of 10^n toward positive infinity.ceilsd( x, n, b ): round a numeric value to the nearest number toward positive infinity with N significant figures.cfloor( z ): round a double-precision complex floating-point number toward negative infinity.cfloorn( z, n ): round each component of a double-precision complex floating-point number to the nearest multiple of10^ntoward negative infinity.clamp( v, min, max ): restrict a double-precision floating-point number to a specified range.clampf( v, min, max ): restrict a single-precision floating-point number to a specified range.cround( z ): round each component of a double-precision complex floating-point number to the nearest integer.croundn( z, n ): round each component of a double-precision complex floating-point number to the nearest multiple of10^n.csignum( z ): evaluate the signum function of a double-precision complex floating-point number.floor( x ): round a double-precision floating-point number toward negative infinity.floor10( x ): round a numeric value to the nearest power of 10 toward negative infinity.floor2( x ): round a numeric value to the nearest power of two toward negative infinity.floorb( x, n, b ): round a numeric value to the nearest multiple of b^n toward negative infinity.floorf( x ): round a single-precision floating-point numeric value toward negative infinity.floorn( x, n ): round a double-precision floating-point number to the nearest multiple of 10^n toward negative infinity.floorsd( x, n, b ): round a numeric value to the nearest number toward negative infinity with N significant figures.labs( x ): compute an absolute value of a signed 32-bit integer.maxabs( x, y ): return the maximum absolute value.maxabsn( [x[, y[, ...args]]] ): return the maximum absolute value.minabs( x, y ): return the minimum absolute value.minabsn( [x[, y[, ...args]]] ): return the minimum absolute value.minmaxabs( x, y ): return the minimum and maximum absolute values.minmaxabsn( [x[, y[, ...args]]] ): return the minimum and maximum absolute values.round( x ): round a numeric value to the nearest integer.round10( x ): round a numeric value to the nearest power of 10 on a linear scale.round2( x ): round a numeric value to the nearest power of two on a linear scale.roundb( x, n, b ): round a numeric value to the nearest multiple of b^n on a linear scale.roundn( x, n ): round a double-precision floating-point number to the nearest multiple of 10^n.roundsd( x, n[, b] ): round a numeric value to the nearest number withnsignificant figures.signum( x ): signum function.signumf( x ): signum function.trunc( x ): round a double-precision floating-point number toward zero.trunc10( x ): round a numeric value to the nearest power of 10 toward zero.trunc2( x ): round a numeric value to the nearest power of two toward zero.truncb( x, n, b ): round a numeric value to the nearest multiple of b^n toward zero.truncf( x ): round a single-precision floating-point number toward zero.truncn( x, n ): round a numeric value to the nearest multiple of 10^n toward zero.truncsd( x, n, b ): round a numeric value to the nearest number toward zero withnsignificant figures.
Other Special Functions
acot( x ): compute the inverse cotangent of a double-precision floating-point number.acotd( x ): compute the arccotangent in degrees of a double-precision floating-point number.acotf( x ): compute the inverse cotangent of a single-precision floating-point number.acoth( x ): compute the inverse hyperbolic cotangent of a double-precision floating-point number.acsc( x ): compute the arccosecant of a number.acscd( x ): compute the arccosecant in degrees of a double-precision floating-point number.acscdf( x ): compute the arccosecant (in degrees) of a single-precision floating-point number.acscf( x ): compute the arccosecant of a single-precision floating-point number.acsch( x ): compute the hyperbolic arccosecant of a number.asec( x ): compute the inverse (arc) secant of a number.asecd( x ): compute the arcsecant (in degrees) of a double-precision floating-point number.asecdf( x ): compute the arcsecant (in degrees) of a single-precision floating-point number.asecf( x ): compute the inverse (arc) secant of a single-precision floating-point number.asech( x ): compute the hyperbolic arcsecant of a number.bernoulli( n ): compute the nth Bernoulli number.beta( x, y ): beta function.betainc( x, a, b[, regularized[, upper]] ): incomplete beta function.betaincinv( p, a, b[, upper] ): inverse of the incomplete beta function.betaln( x, y ): natural logarithm of the beta function.binet( x ): evaluate Binet's formula extended to real numbers.binomcoef( n, k ): compute the binomial coefficient.binomcoefln( n, k ): compute the natural logarithm of the binomial coefficient.boxcox( x, lambda ): compute a one-parameter Box-Cox transformation.boxcox1p( x, lambda ): compute a one-parameter Box-Cox transformation of1+x.boxcox1pinv( y, lambda ): compute the inverse of a one-parameter Box-Cox transformation for1+x.boxcoxinv( y, lambda ): compute the inverse of a one-parameter Box-Cox transformation.cbrt( x ): compute the cube root of a double-precision floating-point number.cbrtf( x ): compute the cube root of a single-precision floating-point number.ccis( z ): evaluate the cis function for a double-precision complex floating-point number.cexp( z ): evaluate the exponential function for a double-precision complex floating-point number.cflipsign( z, y ): return a double-precision complex floating-point number with the same magnitude aszand the sign ofy*z.cflipsignf( z, y ): return a single-precision complex floating-point number with the same magnitude aszand the sign ofy*z.cidentity( z ): evaluate the identity function of a double-precision complex floating-point number.cidentityf( z ): evaluate the identity function of a single-precision complex floating-point number.cinv( z ): compute the inverse of a double-precision complex floating-point number.copysign( x, y ): return a double-precision floating-point number with the magnitude ofxand the sign ofy.copysignf( x, y ): return a single-precision floating-point number with the magnitude ofxand the sign ofy.cot( x ): evaluate the cotangent of a number.cotd( x ): compute the cotangent of an angle measured in degrees.coth( x ): compute the hyperbolic cotangent of a number.cphase( z ): compute the argument of a double-precision complex floating-point number in radians.cpolar( z ): compute the absolute value and phase of a double-precision complex floating-point number.csc( x ): evaluate the cosecant of a number.cscd( x ): compute the cosecant of a degree.csch( x ): compute the hyperbolic cosecant of a number.deg2rad( x ): convert an angle from degrees to radians.deg2radf( x ): convert an angle from degrees to radians (single-precision).digamma( x ): digamma function.diracDelta( x ): evaluate the Dirac delta function.eta( s ): dirichlet eta function.ellipe( m ): compute the complete elliptic integral of the second kind.ellipj( u, m ): compute the Jacobi elliptic functions sn, cn, and dn.ellipk( m ): compute the complete elliptic integral of the first kind.erf( x ): error function.erfc( x ): complementary error function.erfcinv( x ): inverse complementary error function.erfcx( x ): scaled complementary error function.erfinv( x ): inverse error function.factorial( x ): factorial function.factorial2( n ): double factorial function.factorialln( x ): natural logarithm of the factorial function.fallingFactorial( x, n ): compute the falling factorial.fibonacciIndex( F ): compute the Fibonacci number index.fibonacci( n ): compute the nth Fibonacci number.flipsign( x, y ): return a double-precision floating-point number with the magnitude ofxand the sign ofx*y.flipsignf( x, y ): return a single-precision floating-point number with the magnitude ofxand the sign ofx*y.fresnel( x ): compute the Fresnel integrals S(x) and C(x).fresnelc( x ): compute the Fresnel integral C(x).fresnels( x ): compute the Fresnel integral S(x).frexp( x ): split a double-precision floating-point number into a normalized fraction and an integer power of two.gamma( x ): gamma function.gamma1pm1( x ): computegamma(x+1) - 1.gammainc( x, s[, regularized[, upper ]] ): incomplete gamma function.gammaincinv( p, s[, upper ] ): inverse of incomplete gamma function.gammaln( x ): natural logarithm of the gamma function.gammasgn( x ): sign of the gamma function.gcd( a, b ): compute the greatest common divisor (gcd).heaviside( x[, continuity] ): evaluate the Heaviside function.hypot( x, y ): compute the hypotenuse avoiding overflow and underflow.hypotf( x, y ): compute the hypotenuse avoiding overflow and underflow (single-precision).identity( x ): evaluate the identity function of a double-precision floating-point number.identityf( x ): evaluate the identity function of a single-precision floating-point number.inv( x ): compute the multiplicative inverse of a double-precision floating-point number.invf( x ): compute the multiplicative inverse of a single-precision floating-point number.kroneckerDelta( i, j ): evaluate the Kronecker delta.kroneckerDeltaf( i, j ): evaluate the Kronecker delta (single-precision).lcm( a, b ): compute the least common multiple (lcm).ldexp( frac, exp ): multiply a double-precision floating-point number by an integer power of two.lucas( n ): compute the nth Lucas number.max( x, y ): return the maximum value.maxn( [x[, y[, ...args]]] ): return the maximum value.min( x, y ): return the minimum value.minmax( x, y ): return the minimum and maximum values.minmaxn( [x[, y[, ...args]]] ): return the minimum and maximum values.minn( [x[, y[, ...args]]] ): return the minimum value.modf( x ): decompose a double-precision floating-point number into integral and fractional parts.negafibonacci( n ): compute the nth negaFibonacci number.negalucas( n ): compute the nth negaLucas number.nonfibonacci( n ): compute the nth non-Fibonacci number.pdiff( x, y ): return the positive difference betweenxandy.pdifff( x, y ): return the positive difference betweenxandy.polygamma( n, x ): polygamma function.rad2deg( x ): convert an angle from radians to degrees.rad2degf( x ): convert an angle from radians to degrees (single-precision).ramp( x ): evaluate the ramp function.rampf( x ): evaluate the ramp function.rcbrt( x ): compute the reciprocal of the principal cube root of a double-precision floating-point number.rcbrtf( x ): compute the reciprocal of the principal cube root of a single-precision floating-point number.zeta( s ): riemann zeta function.rsqrt( x ): compute the reciprocal of the principal square root of a double-precision floating-point number.rsqrtf( x ): compute the reciprocal of the principal square root of a single-precision floating-point number.secd( x ): compute the secant of an angle measured in degrees.sici( x ): compute the sine and cosine integrals.spence( x ): spence's function, also known as the dilogarithm.sqrt( x ): compute the principal square root of a double-precision floating-point number.sqrt1pm1( x ): computesqrt( 1 + x ) - 1.sqrtf( x ): compute the principal square root of a single-precision floating-point number.sqrtpi( x ): compute the principal square root of the product of π and a positive number.tribonacci( n ): compute the nth Tribonacci number.trigamma( x ): trigamma function.wrap( v, min, max ): wrap a value on the half-open interval[min,max).
Fast algorithms of various special functions, which trade accuracy for increased speed, are available in the following sub-namespace:
fast: fast math special functions.
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.
kernelBetainc( x, a, b, regularized, upper ): incomplete beta function and its first derivative.kernelBetaincinv( a, b, p, q ): inverse of the lower incomplete beta function.kernelCos( x, y ): compute the cosine of a double-precision floating-point number on[-π/4, π/4].kernelSin( x, y ): compute the sine of a double-precision floating-point number on[-π/4, π/4].kernelTan( x, y, k ): compute the tangent of a double-precision floating-point number on[-π/4, π/4].rempio2( x, y ): computex - nπ/2 = r.
Examples
var objectKeys = require( '@stdlib/utils/keys' );
var special = require( '@stdlib/math/base/special' );
console.log( objectKeys( special ) );