libgo/go/math/atan.go

   1 // Copyright 2009 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 arctangent.
   9 */
  10
  11 // The original C code, the long comment, and the constants below were
  12 // from http://netlib.sandia.gov/cephes/cmath/atan.c, available from
  13 // http://www.netlib.org/cephes/cmath.tgz.
  14 // The go code is a version of the original C.
  15 //
  16 // atan.c
  17 // Inverse circular tangent (arctangent)
  18 //
  19 // SYNOPSIS:
  20 // double x, y, atan();
  21 // y = atan( x );
  22 //
  23 // DESCRIPTION:
  24 // Returns radian angle between -pi/2 and +pi/2 whose tangent is x.
  25 //
  26 // Range reduction is from three intervals into the interval from zero to 0.66.
  27 // The approximant uses a rational function of degree 4/5 of the form
  28 // x + x**3 P(x)/Q(x).
  29 //
  30 // ACCURACY:
  31 //                      Relative error:
  32 // arithmetic   domain    # trials  peak     rms
  33 //    DEC       -10, 10   50000     2.4e-17  8.3e-18
  34 //    IEEE      -10, 10   10^6      1.8e-16  5.0e-17
  35 //
  36 // Cephes Math Library Release 2.8:  June, 2000
  37 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
  38 //
  39 // The readme file at http://netlib.sandia.gov/cephes/ says:
  40 //    Some software in this archive may be from the book _Methods and
  41 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
  42 // International, 1989) or from the Cephes Mathematical Library, a
  43 // commercial product. In either event, it is copyrighted by the author.
  44 // What you see here may be used freely but it comes with no support or
  45 // guarantee.
  46 //
  47 //   The two known misprints in the book are repaired here in the
  48 // source listings for the gamma function and the incomplete beta
  49 // integral.
  50 //
  51 //   Stephen L. Moshier
  52 //   moshier@na-net.ornl.gov
  53
  54 // xatan evaluates a series valid in the range [0, 0.66].
  55 func xatan(x float64) float64 {
  56         const (
  57                 P0 = -8.750608600031904122785e-01
  58                 P1 = -1.615753718733365076637e+01
  59                 P2 = -7.500855792314704667340e+01
  60                 P3 = -1.228866684490136173410e+02
  61                 P4 = -6.485021904942025371773e+01
  62                 Q0 = +2.485846490142306297962e+01
  63                 Q1 = +1.650270098316988542046e+02
  64                 Q2 = +4.328810604912902668951e+02
  65                 Q3 = +4.853903996359136964868e+02
  66                 Q4 = +1.945506571482613964425e+02
  67         )
  68         z := x * x
  69         z = z * ((((P0*z+P1)*z+P2)*z+P3)*z + P4) / (((((z+Q0)*z+Q1)*z+Q2)*z+Q3)*z + Q4)
  70         z = x*z + x
  71         return z
  72 }
  73
  74 // satan reduces its argument (known to be positive)
  75 // to the range [0, 0.66] and calls xatan.
  76 func satan(x float64) float64 {
  77         const (
  78                 Morebits = 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits
  79                 Tan3pio8 = 2.41421356237309504880      // tan(3*pi/8)
  80         )
  81         if x <= 0.66 {
  82                 return xatan(x)
  83         }
  84         if x > Tan3pio8 {
  85                 return Pi/2 - xatan(1/x) + Morebits
  86         }
  87         return Pi/4 + xatan((x-1)/(x+1)) + 0.5*Morebits
  88 }
  89
  90 // Atan returns the arctangent of x.
  91 //
  92 // Special cases are:
  93 //      Atan(±0) = ±0
  94 //      Atan(±Inf) = ±Pi/2
  95
  96 //extern atan
  97 func libc_atan(float64) float64
  98
  99 func Atan(x float64) float64 {
 100         return libc_atan(x)
 101 }
 102
 103 func atan(x float64) float64 {
 104         if x == 0 {
 105                 return x
 106         }
 107         if x > 0 {
 108                 return satan(x)
 109         }
 110         return -satan(-x)
 111 }