libgo/go/math/tan.go

   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 //      Tan(±0) = ±0
  80 //      Tan(±Inf) = NaN
  81 //      Tan(NaN) = NaN
  82 func Tan(x float64) float64 {
  83         return libc_tan(x)
  84 }
  85
  86 //extern tan
  87 func libc_tan(float64) float64
  88
  89 func tan(x float64) float64 {
  90         const (
  91                 PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
  92                 PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
  93                 PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
  94         )
  95         // special cases
  96         switch {
  97         case x == 0 || IsNaN(x):
  98                 return x // return ±0 || NaN()
  99         case IsInf(x, 0):
 100                 return NaN()
 101         }
 102
 103         // make argument positive but save the sign
 104         sign := false
 105         if x < 0 {
 106                 x = -x
 107                 sign = true
 108         }
 109         var j uint64
 110         var y, z float64
 111         if x >= reduceThreshold {
 112                 j, z = trigReduce(x)
 113         } else {
 114                 j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
 115                 y = float64(j)           // integer part of x/(Pi/4), as float
 116
 117                 /* map zeros and singularities to origin */
 118                 if j&1 == 1 {
 119                         j++
 120                         y++
 121                 }
 122
 123                 z = ((x - y*PI4A) - y*PI4B) - y*PI4C
 124         }
 125         zz := z * z
 126
 127         if zz > 1e-14 {
 128                 y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
 129         } else {
 130                 y = z
 131         }
 132         if j&2 == 2 {
 133                 y = -1 / y
 134         }
 135         if sign {
 136                 y = -y
 137         }
 138         return y
 139 }