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Source file src/math/tan.go

Documentation: math

```     1  // Copyright 2011 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
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
67  }
68  var _tanQ = [...]float64{
69  	1.00000000000000000000e0,
70  	1.36812963470692954678e4,  //0x40cab8a5eeb36572
71  	-1.32089234440210967447e6, //0xc13427bc582abc96
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
84  func tan(x float64) float64 {
85  	const (
86  		PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
87  		PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
88  		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
89  	)
90  	// special cases
91  	switch {
92  	case x == 0 || IsNaN(x):
93  		return x // return ±0 || NaN()
94  	case IsInf(x, 0):
95  		return NaN()
96  	}
97
98  	// make argument positive but save the sign
99  	sign := false
100  	if x < 0 {
101  		x = -x
102  		sign = true
103  	}
104  	var j uint64
105  	var y, z float64
106  	if x >= reduceThreshold {
107  		j, z = trigReduce(x)
108  	} else {
109  		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
110  		y = float64(j)           // integer part of x/(Pi/4), as float
111
112  		/* map zeros and singularities to origin */
113  		if j&1 == 1 {
114  			j++
115  			y++
116  		}
117
118  		z = ((x - y*PI4A) - y*PI4B) - y*PI4C
119  	}
120  	zz := z * z
121
122  	if zz > 1e-14 {
123  		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
124  	} else {
125  		y = z
126  	}
127  	if j&2 == 2 {
128  		y = -1 / y
129  	}
130  	if sign {
131  		y = -y
132  	}
133  	return y
134  }
135
```

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