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 // moshier@na-net.ornl.gov
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 //
80 // Tan(±0) = ±0
81 // Tan(±Inf) = NaN
82 // Tan(NaN) = NaN
83 func Tan(x float64) float64 {
84 if haveArchTan {
85 return archTan(x)
86 }
87 return tan(x)
88 }
89 90 func tan(x float64) float64 {
91 const (
92 PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts
93 PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000,
94 PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
95 )
96 // special cases
97 switch {
98 case x == 0 || IsNaN(x):
99 return x // return ±0 || NaN()
100 case IsInf(x, 0):
101 return NaN()
102 }
103 104 // make argument positive but save the sign
105 sign := false
106 if x < 0 {
107 x = -x
108 sign = true
109 }
110 var j uint64
111 var y, z float64
112 if x >= reduceThreshold {
113 j, z = trigReduce(x)
114 } else {
115 j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
116 y = float64(j) // integer part of x/(Pi/4), as float
117 118 /* map zeros and singularities to origin */
119 if j&1 == 1 {
120 j++
121 y++
122 }
123 124 z = ((x - y*PI4A) - y*PI4B) - y*PI4C
125 }
126 zz := z * z
127 128 if zz > 1e-14 {
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]))
130 } else {
131 y = z
132 }
133 if j&2 == 2 {
134 y = -1 / y
135 }
136 if sign {
137 y = -y
138 }
139 return y
140 }
141