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      1 /* k_tanf.c -- float version of k_tan.c
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 #endif
     19 
     20 #include "math.h"
     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 }
     66