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.
8 Floating-point tangent.
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.
22 // double x, y, tan();
27 // Returns the circular tangent of the radian argument x.
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].
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
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.]
44 // Cephes Math Library Release 2.8: June, 2000
45 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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
55 // The two known misprints in the book are repaired here in the
56 // source listings for the gamma function and the incomplete beta
60 // moshier@na-net.ornl.gov
63 var _tanP
= [...]float64{
64 -1.30936939181383777646E4
, // 0xc0c992d8d24f3f38
65 1.15351664838587416140E6
, // 0x413199eca5fc9ddd
66 -1.79565251976484877988E7
, // 0xc1711fead3299176
68 var _tanQ
= [...]float64{
69 1.00000000000000000000E0
,
70 1.36812963470692954678E4
, //0x40cab8a5eeb36572
71 -1.32089234440210967447E6
, //0xc13427bc582abc96
72 2.50083801823357915839E7
, //0x4177d98fc2ead8ef
73 -5.38695755929454629881E7
, //0xc189afe03cbe5a31
76 // Tan returns the tangent of x.
84 func libc_tan(float64) float64
86 func Tan(x
float64) float64 {
90 func tan(x
float64) float64 {
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 M4PI
= 1.273239544735162542821171882678754627704620361328125 // 4/pi
99 case x
== 0 ||
IsNaN(x
):
100 return x
// return ±0 || NaN()
105 // make argument positive but save the sign
112 j
:= int64(x
* M4PI
) // integer part of x/(Pi/4), as integer for tests on the phase angle
113 y
:= float64(j
) // integer part of x/(Pi/4), as float
115 /* map zeros and singularities to origin */
121 z
:= ((x
- y
*PI4A
) - y
*PI4B
) - y
*PI4C
125 y
= z
+ z
*(zz
*(((_tanP
[0]*zz
)+_tanP
[1])*zz
+_tanP
[2])/((((zz
+_tanQ
[1])*zz
+_tanQ
[2])*zz
+_tanQ
[3])*zz
+_tanQ
[4]))