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 cmplx 6 7 import "math" 8 9 // The original C code, the long comment, and the constants 10 // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c. 11 // The go code is a simplified version of the original C. 12 // 13 // Cephes Math Library Release 2.8: June, 2000 14 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier 15 // 16 // The readme file at http://netlib.sandia.gov/cephes/ says: 17 // Some software in this archive may be from the book _Methods and 18 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster 19 // International, 1989) or from the Cephes Mathematical Library, a 20 // commercial product. In either event, it is copyrighted by the author. 21 // What you see here may be used freely but it comes with no support or 22 // guarantee. 23 // 24 // The two known misprints in the book are repaired here in the 25 // source listings for the gamma function and the incomplete beta 26 // integral. 27 // 28 // Stephen L. Moshier 29 // moshier (a] na-net.ornl.gov 30 31 // Complex circular sine 32 // 33 // DESCRIPTION: 34 // 35 // If 36 // z = x + iy, 37 // 38 // then 39 // 40 // w = sin x cosh y + i cos x sinh y. 41 // 42 // csin(z) = -i csinh(iz). 43 // 44 // ACCURACY: 45 // 46 // Relative error: 47 // arithmetic domain # trials peak rms 48 // DEC -10,+10 8400 5.3e-17 1.3e-17 49 // IEEE -10,+10 30000 3.8e-16 1.0e-16 50 // Also tested by csin(casin(z)) = z. 51 52 // Sin returns the sine of x. 53 func Sin(x complex128) complex128 { 54 s, c := math.Sincos(real(x)) 55 sh, ch := sinhcosh(imag(x)) 56 return complex(s*ch, c*sh) 57 } 58 59 // Complex hyperbolic sine 60 // 61 // DESCRIPTION: 62 // 63 // csinh z = (cexp(z) - cexp(-z))/2 64 // = sinh x * cos y + i cosh x * sin y . 65 // 66 // ACCURACY: 67 // 68 // Relative error: 69 // arithmetic domain # trials peak rms 70 // IEEE -10,+10 30000 3.1e-16 8.2e-17 71 72 // Sinh returns the hyperbolic sine of x. 73 func Sinh(x complex128) complex128 { 74 s, c := math.Sincos(imag(x)) 75 sh, ch := sinhcosh(real(x)) 76 return complex(c*sh, s*ch) 77 } 78 79 // Complex circular cosine 80 // 81 // DESCRIPTION: 82 // 83 // If 84 // z = x + iy, 85 // 86 // then 87 // 88 // w = cos x cosh y - i sin x sinh y. 89 // 90 // ACCURACY: 91 // 92 // Relative error: 93 // arithmetic domain # trials peak rms 94 // DEC -10,+10 8400 4.5e-17 1.3e-17 95 // IEEE -10,+10 30000 3.8e-16 1.0e-16 96 97 // Cos returns the cosine of x. 98 func Cos(x complex128) complex128 { 99 s, c := math.Sincos(real(x)) 100 sh, ch := sinhcosh(imag(x)) 101 return complex(c*ch, -s*sh) 102 } 103 104 // Complex hyperbolic cosine 105 // 106 // DESCRIPTION: 107 // 108 // ccosh(z) = cosh x cos y + i sinh x sin y . 109 // 110 // ACCURACY: 111 // 112 // Relative error: 113 // arithmetic domain # trials peak rms 114 // IEEE -10,+10 30000 2.9e-16 8.1e-17 115 116 // Cosh returns the hyperbolic cosine of x. 117 func Cosh(x complex128) complex128 { 118 s, c := math.Sincos(imag(x)) 119 sh, ch := sinhcosh(real(x)) 120 return complex(c*ch, s*sh) 121 } 122 123 // calculate sinh and cosh 124 func sinhcosh(x float64) (sh, ch float64) { 125 if math.Abs(x) <= 0.5 { 126 return math.Sinh(x), math.Cosh(x) 127 } 128 e := math.Exp(x) 129 ei := 0.5 / e 130 e *= 0.5 131 return e - ei, e + ei 132 } 133
