Source file src/pkg/math/acosh.go

     1	// Copyright 2010 The Go Authors. All rights reserved.
     2	// Use of this source code is governed by a BSD-style
     3	// license that can be found in the LICENSE file.
     4	
     5	package math
     6	
     7	// The original C code, the long comment, and the constants
     8	// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
     9	// and came with this notice.  The go code is a simplified
    10	// version of the original C.
    11	//
    12	// ====================================================
    13	// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
    14	//
    15	// Developed at SunPro, a Sun Microsystems, Inc. business.
    16	// Permission to use, copy, modify, and distribute this
    17	// software is freely granted, provided that this notice
    18	// is preserved.
    19	// ====================================================
    20	//
    21	//
    22	// __ieee754_acosh(x)
    23	// Method :
    24	//	Based on
    25	//	        acosh(x) = log [ x + sqrt(x*x-1) ]
    26	//	we have
    27	//	        acosh(x) := log(x)+ln2,	if x is large; else
    28	//	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
    29	//	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
    30	//
    31	// Special cases:
    32	//	acosh(x) is NaN with signal if x<1.
    33	//	acosh(NaN) is NaN without signal.
    34	//
    35	
    36	// Acosh(x) calculates the inverse hyperbolic cosine of x.
    37	//
    38	// Special cases are:
    39	//	Acosh(+Inf) = +Inf
    40	//	Acosh(x) = NaN if x < 1
    41	//	Acosh(NaN) = NaN
    42	func Acosh(x float64) float64 {
    43		const (
    44			Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
    45			Large = 1 << 28                    // 2**28
    46		)
    47		// first case is special case
    48		switch {
    49		case x < 1 || IsNaN(x):
    50			return NaN()
    51		case x == 1:
    52			return 0
    53		case x >= Large:
    54			return Log(x) + Ln2 // x > 2**28
    55		case x > 2:
    56			return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
    57		}
    58		t := x - 1
    59		return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
    60	}