src/math/__tandf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   4  * Optimized by Bruce D. Evans.
   5  */
   6 /*
   7  * ====================================================
   8  * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
   9  *
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include "libm.h"
  17
  18 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
  19 static const double T[] = {
  20   0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
  21   0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
  22   0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
  23   0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
  24   0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
  25   0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
  26 };
  27
  28 float __tandf(double x, int odd)
  29 {
  30         double_t z,r,w,s,t,u;
  31
  32         z = x*x;
  33         /*
  34          * Split up the polynomial into small independent terms to give
  35          * opportunities for parallel evaluation.  The chosen splitting is
  36          * micro-optimized for Athlons (XP, X64).  It costs 2 multiplications
  37          * relative to Horner's method on sequential machines.
  38          *
  39          * We add the small terms from lowest degree up for efficiency on
  40          * non-sequential machines (the lowest degree terms tend to be ready
  41          * earlier).  Apart from this, we don't care about order of
  42          * operations, and don't need to to care since we have precision to
  43          * spare.  However, the chosen splitting is good for accuracy too,
  44          * and would give results as accurate as Horner's method if the
  45          * small terms were added from highest degree down.
  46          */
  47         r = T[4] + z*T[5];
  48         t = T[2] + z*T[3];
  49         w = z*z;
  50         s = z*x;
  51         u = T[0] + z*T[1];
  52         r = (x + s*u) + (s*w)*(t + w*r);
  53         return odd ? -1.0/r : r;
  54 }