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

Special Functions

Standard library base special math functions.

Usage

var special = require( '@stdlib/math/base/special' );

special

Standard library base special math functions.

var fcns = special;
// returns {...}

Exponential & Logarithmic Functions

• exp( x ): natural exponential function.
• exp10( x ): base 10 exponential function.
• exp2( x ): base 2 exponential function.
• expit( x ): compute the standard logistic function.
• expm1( x ): compute exp(x) - 1.
• expm1rel( x ): compute the relative error exponential.
• ln( x ): evaluate the natural logarithm.
• log( x, b ): compute the base b logarithm.
• log10( x ): evaluate the common logarithm.
• log1mexp( x ): evaluates the natural logarithm of 1-exp(-|x|).
• log1p( x ): evaluate the natural logarithm of 1+x.
• log1pexp( x ): evaluates the natural logarithm of 1+exp(x).
• log2( x ): evaluate the binary logarithm.
• logaddexp( x, y ): evaluates the natural logarithm of exp(x) + exp(y).
• pow( base, exponent ): exponential function.
• powm1( b, x ): evaluate bˣ - 1.
• xlog1py( x, y ): compute x * ln(y+1) so that the result is 0 if x = 0.
• xlogy( x, y ): compute x * ln(y) so that the result is 0 if x = 0.

Trigonometric Functions

• acos( x ): compute the arccosine of a number.
• acosh( x ): compute the hyperbolic arccosine of a 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 number.
• asinh( x ): compute the hyperbolic arcsine of a number.
• atan( x ): compute the arctangent of a 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).
• atanh( x ): compute the hyperbolic arctangent of a number.
• avercos( x ): compute the inverse versed cosine.
• aversin( x ): compute the inverse versed sine.
• cos( x ): compute the cosine of a number.
• cosh( x ): compute the hyperbolic cosine of a number.
• cosm1( x ): compute cos(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( [out,] x ): simultaneously compute the sine and cosine of a number.
• sincospi( [out,] x ): simultaneously compute the sine and cosine of a number times π.
• sinh( x ): compute the hyperbolic sine of a number.
• sinpi( x ): compute the sine of a number times π.
• tan( x ): evaluate the tangent of a number.
• tanh( x ): compute the hyperbolic tangent of a 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( re, im ): compute an absolute value of a complex number.
• cabs2( re, im ): compute the squared absolute value of a complex number.
• cceil( [out,] re, im ): round a complex number toward positive infinity.
• cceiln( [out,] re, im, n ): round a complex number to the nearest multiple of 10^n toward 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( [out,] re, im ): round a complex number toward negative infinity.
• cfloorn( [out,] re, im, n ): round a complex number to the nearest multiple of 10^n toward 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( [out,] re, im ): round a complex number to the nearest integer.
• croundn( [out,] re, im, n ): round a complex number to the nearest multiple of 10^n.
• csignum( [out,] re, im ): evaluate the signum function of a complex 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 numeric value 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[, ...args]]] ): return the maximum absolute value.
• minabs( [x[, y[, ...args]]] ): return the minimum absolute value.
• minmaxabs( [out,] 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 numeric value to the nearest multiple of 10^n.
• roundsd( x, n[, b] ): round a numeric value to the nearest number with n significant 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 with n significant figures.

Other Special Functions

• acot( x ): compute the inverse cotangent of a number.
• acoth( x ): compute the inverse hyperbolic cotangent 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 of 1+x.
• boxcox1pinv( y, lambda ): compute the inverse of a one-parameter Box-Cox transformation for 1+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( [out,] re, im ): compute the cis function of a complex number.
• cexp( [out,] re, im ): compute the exponential function of a complex number.
• cflipsign( [out,] re, im, y ): return a complex number with the same magnitude as z and the sign of y*z.
• cinv( [out,] re1, im1 ): compute the inverse of a complex number.
• copysign( x, y ): return a double-precision floating-point number with the magnitude of x and the sign of y.
• cphase( re, im ): compute the argument of a complex number in radians.
• cpolar( [out,] re, im ): compute the absolute value and phase of a complex 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.
• 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.
• erfinv( x ): inverse error function.
• factorial( x ): 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 of x and the sign of x*y.
• fresnel( [out,] 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( [out,] x ): split a double-precision floating-point number into a normalized fraction and an integer power of two.
• gamma( x ): gamma function.
• gamma1pm1( x ): compute gamma(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.
• 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.
• imul( a, b ): perform C-like multiplication of two signed 32-bit integers.
• imuldw( [out,] a, b ): compute the double word product of two signed 32-bit integers.
• 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[, ...args]]] ): return the maximum value.
• min( [x[, y[, ...args]]] ): return the minimum value.
• minmax( [out,] x[, y[, ...args]] ): return the minimum and maximum values.
• modf( [out,] 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 between x and y.
• pdifff( x, y ): return the positive difference between x and y.
• polygamma( n, x ): polygamma function.
• rad2deg( x ): convert an angle from radians to degrees.
• ramp( x ): evaluate the ramp function.
• rampf( x ): evaluate the ramp function.
• 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.
• sici( [out,] 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 ): compute sqrt( 1 + x ) - 1.
• sqrtf( x ): compute the principal square root of a single-precision floating-point number.
• tribonacci( n ): compute the nth Tribonacci number.
• trigamma( x ): trigamma function.
• uimul( a, b ): perform C-like multiplication of two unsigned 32-bit integers.
• uimuldw( [out,] a, b ): compute the double word product of two unsigned 32-bit integers.
• 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: standard library 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 number on [-π/4, π/4].
• kernelSin( x, y ): compute the sine of a number on [-π/4, π/4].
• kernelTan( x, y, k ): compute the tangent of a number on [-π/4, π/4].
• rempio2( x, y ): compute x - nπ/2 = r.

Examples

var objectKeys = require( '@stdlib/utils/keys' );
var special = require( '@stdlib/math/base/special' );

console.log( objectKeys( special ) );