Branch data     Line data    Source code

       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 "cdefs-compat.h"
      18                 :             : //__FBSDID("$FreeBSD: src/lib/msun/src/k_tanf.c,v 1.23 2009/06/03 08:16:34 ed Exp $");
      19                 :             : #endif
      20                 :             : 
      21                 :             : #include <openlibm_math.h>
      22                 :             : 
      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                 :             : #ifndef INLINE_KERNEL_TANDF
      37                 :             : extern
      38                 :             : #endif
      39                 :             : //__inline float
      40                 :             : OLM_DLLEXPORT float
      41                 :           2 : __kernel_tandf(double x, int iy)
      42                 :             : {
      43                 :             :         double z,r,w,s,t,u;
      44                 :             : 
      45                 :           2 :         z       =  x*x;
      46                 :             :         /*
      47                 :             :          * Split up the polynomial into small independent terms to give
      48                 :             :          * opportunities for parallel evaluation.  The chosen splitting is
      49                 :             :          * micro-optimized for Athlons (XP, X64).  It costs 2 multiplications
      50                 :             :          * relative to Horner's method on sequential machines.
      51                 :             :          *
      52                 :             :          * We add the small terms from lowest degree up for efficiency on
      53                 :             :          * non-sequential machines (the lowest degree terms tend to be ready
      54                 :             :          * earlier).  Apart from this, we don't care about order of
      55                 :             :          * operations, and don't need to to care since we have precision to
      56                 :             :          * spare.  However, the chosen splitting is good for accuracy too,
      57                 :             :          * and would give results as accurate as Horner's method if the
      58                 :             :          * small terms were added from highest degree down.
      59                 :             :          */
      60                 :           2 :         r = T[4]+z*T[5];
      61                 :           2 :         t = T[2]+z*T[3];
      62                 :           2 :         w = z*z;
      63                 :           2 :         s = z*x;
      64                 :           2 :         u = T[0]+z*T[1];
      65                 :           2 :         r = (x+s*u)+(s*w)*(t+w*r);
      66         [ +  + ]:           2 :         if(iy==1) return r;
      67                 :           1 :         else return -1.0/r;
      68                 :             : }