github.com/afumu/libc@v0.0.6/musl/src/math/__tandf.c (about)

     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  }