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