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1 // Copyright 2011 The Go Authors. All rights reserved.
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2 // Use of this source code is governed by a BSD-style
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3 // license that can be found in the LICENSE file.
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4
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5 package math
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6
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7 /*
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8 Floating-point tangent.
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9 */
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10
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11 // The original C code, the long comment, and the constants
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12 // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
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13 // available from http://www.netlib.org/cephes/cmath.tgz.
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14 // The go code is a simplified version of the original C.
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15 //
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16 // tan.c
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17 //
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18 // Circular tangent
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19 //
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20 // SYNOPSIS:
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21 //
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22 // double x, y, tan();
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23 // y = tan( x );
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24 //
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25 // DESCRIPTION:
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26 //
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27 // Returns the circular tangent of the radian argument x.
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28 //
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29 // Range reduction is modulo pi/4. A rational function
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30 // x + x**3 P(x**2)/Q(x**2)
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31 // is employed in the basic interval [0, pi/4].
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32 //
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33 // ACCURACY:
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34 // Relative error:
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35 // arithmetic domain # trials peak rms
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36 // DEC +-1.07e9 44000 4.1e-17 1.0e-17
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37 // IEEE +-1.07e9 30000 2.9e-16 8.1e-17
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38 //
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39 // Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss
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40 // is not gradual, but jumps suddenly to about 1 part in 10e7. Results may
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41 // be meaningless for x > 2**49 = 5.6e14.
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42 // [Accuracy loss statement from sin.go comments.]
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43 //
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44 // Cephes Math Library Release 2.8: June, 2000
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45 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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46 //
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47 // The readme file at http://netlib.sandia.gov/cephes/ says:
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48 // Some software in this archive may be from the book _Methods and
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49 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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50 // International, 1989) or from the Cephes Mathematical Library, a
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51 // commercial product. In either event, it is copyrighted by the author.
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52 // What you see here may be used freely but it comes with no support or
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53 // guarantee.
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54 //
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55 // The two known misprints in the book are repaired here in the
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56 // source listings for the gamma function and the incomplete beta
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57 // integral.
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58 //
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59 // Stephen L. Moshier
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60 // moshier@na-net.ornl.gov
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61
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62 // tan coefficients
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63 var _tanP = [...]float64{
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64 -1.30936939181383777646e4, // 0xc0c992d8d24f3f38
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65 1.15351664838587416140e6, // 0x413199eca5fc9ddd
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66 -1.79565251976484877988e7, // 0xc1711fead3299176
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111
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67 }
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68 var _tanQ = [...]float64{
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145
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69 1.00000000000000000000e0,
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70 1.36812963470692954678e4, //0x40cab8a5eeb36572
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71 -1.32089234440210967447e6, //0xc13427bc582abc96
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72 2.50083801823357915839e7, //0x4177d98fc2ead8ef
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73 -5.38695755929454629881e7, //0xc189afe03cbe5a31
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111
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74 }
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75
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76 // Tan returns the tangent of the radian argument x.
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77 //
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78 // Special cases are:
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79 // Tan(±0) = ±0
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80 // Tan(±Inf) = NaN
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81 // Tan(NaN) = NaN
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82
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83 //extern tan
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84 func libc_tan(float64) float64
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85
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86 func Tan(x float64) float64 {
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87 return libc_tan(x)
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88 }
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89
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90 func tan(x float64) float64 {
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91 const (
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145
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92 PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts
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93 PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000,
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94 PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
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111
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95 )
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96 // special cases
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97 switch {
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98 case x == 0 || IsNaN(x):
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99 return x // return ±0 || NaN()
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100 case IsInf(x, 0):
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101 return NaN()
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102 }
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103
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104 // make argument positive but save the sign
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105 sign := false
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106 if x < 0 {
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107 x = -x
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108 sign = true
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109 }
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145
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110 var j uint64
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111 var y, z float64
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112 if x >= reduceThreshold {
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113 j, z = trigReduce(x)
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114 } else {
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115 j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
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116 y = float64(j) // integer part of x/(Pi/4), as float
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111
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117
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145
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118 /* map zeros and singularities to origin */
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119 if j&1 == 1 {
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120 j++
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121 y++
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122 }
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123
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124 z = ((x - y*PI4A) - y*PI4B) - y*PI4C
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111
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125 }
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126 zz := z * z
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127
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128 if zz > 1e-14 {
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129 y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
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130 } else {
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131 y = z
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132 }
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133 if j&2 == 2 {
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134 y = -1 / y
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135 }
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136 if sign {
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137 y = -y
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138 }
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139 return y
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140 }
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