modules/fdlibm/src/k_tanf.cpp

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