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Source file src/math/acosh.go

Documentation: math

  // 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_acosh.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_acosh(x)
  // Method :
  //	Based on
  //	        acosh(x) = log [ x + sqrt(x*x-1) ]
  //	we have
  //	        acosh(x) := log(x)+ln2,	if x is large; else
  //	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  //	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  //
  // Special cases:
  //	acosh(x) is NaN with signal if x<1.
  //	acosh(NaN) is NaN without signal.
  //
  
  // Acosh returns the inverse hyperbolic cosine of x.
  //
  // Special cases are:
  //	Acosh(+Inf) = +Inf
  //	Acosh(x) = NaN if x < 1
  //	Acosh(NaN) = NaN
  func Acosh(x float64) float64
  
  func acosh(x float64) float64 {
  	const (
  		Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
  		Large = 1 << 28                    // 2**28
  	)
  	// first case is special case
  	switch {
  	case x < 1 || IsNaN(x):
  		return NaN()
  	case x == 1:
  		return 0
  	case x >= Large:
  		return Log(x) + Ln2 // x > 2**28
  	case x > 2:
  		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
  	}
  	t := x - 1
  	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
  }
  

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