hyperbolic

nimony/lib/std/math/hyperbolic.nim

Native (libc-free) implementations of expm1, sinh, cosh, tanh, arcsinh, arccosh and arctanh. The hyperbolic formulas and range handling follow Rust compiler-builtins/libm's corresponding f32/f64 routines; expm1 is adapted from FreeBSD/SunPro fdlibm s_expm1.c. Rust sources: library/compiler-builtins/libm/src/math/{expm1,expm1f,sinh,sinhf,cosh,coshf,tanh,tanhf,asinh,asinhf,acosh,acoshf,atanh,atanhf,k_expo2,k_expo2f}.rs. Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Copyright (c) 2018 Jorge Aparicio (Rust compiler-builtins/libm code). Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. Selected instead of math/cmath by std/math when nimNativeIo is defined.

func expm1(x: float64): float64
Exponential, base e, of x-1 (f64)
Calculates the exponential of x and subtract 1, that is, e raised to the power x minus 1 (where e is the base of the natural system of logarithms, approximately 2.71828). The result is accurate even for small values of x, where using exp(x)-1 would lose many significant digits.
func expm1(x: float32): float32
Exponential, base e, of x-1 (f32)
Calculates the exponential of x and subtract 1, that is, e raised to the power x minus 1 (where e is the base of the natural system of logarithms, approximately 2.71828). The result is accurate even for small values of x, where using exp(x)-1 would lose many significant digits.
func k_expo2(x: float64): float64
Compute exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5exp(x/2)exp(x/2)
func k_expo2f(x: float32): float32
Compute expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5fexpf(x/2)expf(x/2)
func sinh(x: float32): float32
The hyperbolic sine of x (f32).
func sinh(x: float64): float64
The hyperbolic sine of x (f64).
func cosh(x: float32): float32
Hyperbolic cosine (f32)
Computes the hyperbolic cosine of the argument x. Is defined as (exp(x) + exp(-x))/2 Angles are specified in radians.
func cosh(x: float64): float64
Hyperbolic cosine (f64)
Computes the hyperbolic cosine of the argument x. Is defined as (exp(x) + exp(-x))/2 Angles are specified in radians.
func tanh(x: float32): float32
The hyperbolic tangent of x (f32).
x is specified in radians.
func tanh(x: float64): float64
The hyperbolic tangent of x (f64).
x is specified in radians.
func arcsinh(x: float32): float32
Inverse hyperbolic sine (f32)
Calculates the inverse hyperbolic sine of x. Is defined as sgn(x)*log(|x|+sqrt(x*x+1)).
func arcsinh(x: float64): float64
Inverse hyperbolic sine (f64)
Calculates the inverse hyperbolic sine of x. Is defined as sgn(x)*log(|x|+sqrt(x*x+1)).
func arccosh(x: float32): float32
Inverse hyperbolic cosine (f32)
Calculates the inverse hyperbolic cosine of x. Is defined as log(x + sqrt(x*x-1)). x must be a number greater than or equal to 1.
func arccosh(x: float64): float64
Inverse hyperbolic cosine (f64)
Calculates the inverse hyperbolic cosine of x. Is defined as log(x + sqrt(x*x-1)). x must be a number greater than or equal to 1.
func arctanh(x: float32): float32
Inverse hyperbolic tangent (f32)
Calculates the inverse hyperbolic tangent of x. Is defined as log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2.
func arctanh(x: float64): float64
Inverse hyperbolic tangent (f64)
Calculates the inverse hyperbolic tangent of x. Is defined as log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2.