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Diffstat (limited to 'src/math/atanh.go')
-rw-r--r-- | src/math/atanh.go | 77 |
1 files changed, 77 insertions, 0 deletions
diff --git a/src/math/atanh.go b/src/math/atanh.go new file mode 100644 index 000000000..113d5c103 --- /dev/null +++ b/src/math/atanh.go @@ -0,0 +1,77 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package math + +// The original C code, the long comment, and the constants +// below are from FreeBSD's /usr/src/lib/msun/src/e_atanh.c +// and came with this notice. The go code is a simplified +// version of the original C. +// +// ==================================================== +// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +// +// Developed at SunPro, a Sun Microsystems, Inc. business. +// Permission to use, copy, modify, and distribute this +// software is freely granted, provided that this notice +// is preserved. +// ==================================================== +// +// +// __ieee754_atanh(x) +// Method : +// 1. Reduce x to positive by atanh(-x) = -atanh(x) +// 2. For x>=0.5 +// 1 2x x +// atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) +// 2 1 - x 1 - x +// +// For x<0.5 +// atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) +// +// Special cases: +// atanh(x) is NaN if |x| > 1 with signal; +// atanh(NaN) is that NaN with no signal; +// atanh(+-1) is +-INF with signal. +// + +// Atanh returns the inverse hyperbolic tangent of x. +// +// Special cases are: +// Atanh(1) = +Inf +// Atanh(±0) = ±0 +// Atanh(-1) = -Inf +// Atanh(x) = NaN if x < -1 or x > 1 +// Atanh(NaN) = NaN +func Atanh(x float64) float64 { + const NearZero = 1.0 / (1 << 28) // 2**-28 + // special cases + switch { + case x < -1 || x > 1 || IsNaN(x): + return NaN() + case x == 1: + return Inf(1) + case x == -1: + return Inf(-1) + } + sign := false + if x < 0 { + x = -x + sign = true + } + var temp float64 + switch { + case x < NearZero: + temp = x + case x < 0.5: + temp = x + x + temp = 0.5 * Log1p(temp+temp*x/(1-x)) + default: + temp = 0.5 * Log1p((x+x)/(1-x)) + } + if sign { + temp = -temp + } + return temp +} |