1 // Copyright 2011 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 /* 8 Floating-point tangent. 9 */ 10 11 // The original C code, the long comment, and the constants 12 // below were from http://netlib.sandia.gov/cephes/cmath/sin.c, 13 // available from http://www.netlib.org/cephes/cmath.tgz. 14 // The go code is a simplified version of the original C. 15 // 16 // tan.c 17 // 18 // Circular tangent 19 // 20 // SYNOPSIS: 21 // 22 // double x, y, tan(); 23 // y = tan( x ); 24 // 25 // DESCRIPTION: 26 // 27 // Returns the circular tangent of the radian argument x. 28 // 29 // Range reduction is modulo pi/4. A rational function 30 // x + x**3 P(x**2)/Q(x**2) 31 // is employed in the basic interval [0, pi/4]. 32 // 33 // ACCURACY: 34 // Relative error: 35 // arithmetic domain # trials peak rms 36 // DEC +-1.07e9 44000 4.1e-17 1.0e-17 37 // IEEE +-1.07e9 30000 2.9e-16 8.1e-17 38 // 39 // Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss 40 // is not gradual, but jumps suddenly to about 1 part in 10e7. Results may 41 // be meaningless for x > 2**49 = 5.6e14. 42 // [Accuracy loss statement from sin.go comments.] 43 // 44 // Cephes Math Library Release 2.8: June, 2000 45 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier 46 // 47 // The readme file at http://netlib.sandia.gov/cephes/ says: 48 // Some software in this archive may be from the book _Methods and 49 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster 50 // International, 1989) or from the Cephes Mathematical Library, a 51 // commercial product. In either event, it is copyrighted by the author. 52 // What you see here may be used freely but it comes with no support or 53 // guarantee. 54 // 55 // The two known misprints in the book are repaired here in the 56 // source listings for the gamma function and the incomplete beta 57 // integral. 58 // 59 // Stephen L. Moshier 60 // [email protected] 61 62 // tan coefficients 63 var _tanP = [...]float64{ 64 -1.30936939181383777646e4, // 0xc0c992d8d24f3f38 65 1.15351664838587416140e6, // 0x413199eca5fc9ddd 66 -1.79565251976484877988e7, // 0xc1711fead3299176 67 } 68 var _tanQ = [...]float64{ 69 1.00000000000000000000e0, 70 1.36812963470692954678e4, //0x40cab8a5eeb36572 71 -1.32089234440210967447e6, //0xc13427bc582abc96 72 2.50083801823357915839e7, //0x4177d98fc2ead8ef 73 -5.38695755929454629881e7, //0xc189afe03cbe5a31 74 } 75 76 // Tan returns the tangent of the radian argument x. 77 // 78 // Special cases are: 79 // Tan(±0) = ±0 80 // Tan(±Inf) = NaN 81 // Tan(NaN) = NaN 82 func Tan(x float64) float64 { 83 if haveArchTan { 84 return archTan(x) 85 } 86 return tan(x) 87 } 88 89 func tan(x float64) float64 { 90 const ( 91 PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts 92 PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000, 93 PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170, 94 ) 95 // special cases 96 switch { 97 case x == 0 || IsNaN(x): 98 return x // return ±0 || NaN() 99 case IsInf(x, 0): 100 return NaN() 101 } 102 103 // make argument positive but save the sign 104 sign := false 105 if x < 0 { 106 x = -x 107 sign = true 108 } 109 var j uint64 110 var y, z float64 111 if x >= reduceThreshold { 112 j, z = trigReduce(x) 113 } else { 114 j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle 115 y = float64(j) // integer part of x/(Pi/4), as float 116 117 /* map zeros and singularities to origin */ 118 if j&1 == 1 { 119 j++ 120 y++ 121 } 122 123 z = ((x - y*PI4A) - y*PI4B) - y*PI4C 124 } 125 zz := z * z 126 127 if zz > 1e-14 { 128 y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4])) 129 } else { 130 y = z 131 } 132 if j&2 == 2 { 133 y = -1 / y 134 } 135 if sign { 136 y = -y 137 } 138 return y 139 } 140