compiler/mlib/k_tanf.c

   1 /* k_tanf.c -- float version of k_tan.c
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  * Optimized by Bruce D. Evans.
   4  */
   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 #ifndef INLINE_KERNEL_TANDF
  17 #ifndef lint
  18 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_tanf.c,v 1.20 2005/11/28 11:46:20 bde Exp $";
  19 #endif
  20 #endif
  21
  22 #include "math.h"
  23 #include "math_private.h"
  24
  25 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
  26 static const double
  27 T[] =  {
  28   0x15554d3418c99f.0p-54,       /* 0.333331395030791399758 */
  29   0x1112fd38999f72.0p-55,       /* 0.133392002712976742718 */
  30   0x1b54c91d865afe.0p-57,       /* 0.0533812378445670393523 */
  31   0x191df3908c33ce.0p-58,       /* 0.0245283181166547278873 */
  32   0x185dadfcecf44e.0p-61,       /* 0.00297435743359967304927 */
  33   0x1362b9bf971bcd.0p-59,       /* 0.00946564784943673166728 */
  34 };
  35
  36 #ifdef INLINE_KERNEL_TANDF
  37 static __inline
  38 #endif
  39 float
  40 __kernel_tandf(double x, int iy)
  41 {
  42         double z,r,w,s,t,u;
  43
  44         z       =  x*x;
  45         /*
  46          * Split up the polynomial into small independent terms to give
  47          * opportunities for parallel evaluation.  The chosen splitting is
  48          * micro-optimized for Athlons (XP, X64).  It costs 2 multiplications
  49          * relative to Horner's method on sequential machines.
  50          *
  51          * We add the small terms from lowest degree up for efficiency on
  52          * non-sequential machines (the lowest degree terms tend to be ready
  53          * earlier).  Apart from this, we don't care about order of
  54          * operations, and don't need to to care since we have precision to
  55          * spare.  However, the chosen splitting is good for accuracy too,
  56          * and would give results as accurate as Horner's method if the
  57          * small terms were added from highest degree down.
  58      */
  59         r = T[4]+z*T[5];
  60         t = T[2]+z*T[3];
  61         w = z*z;
  62         s = z*x;
  63         u = T[0]+z*T[1];
  64         r = (x+s*u)+(s*w)*(t+w*r);
  65         if(iy==1) return r;
  66         else return -1.0/r;
  67 }