src/math/__sin.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12 /* __sin( x, y, iy)
  13  * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
  14  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  15  * Input y is the tail of x.
  16  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
  17  *
  18  * Algorithm
  19  *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
  20  *      2. Callers must return sin(-0) = -0 without calling here since our
  21  *         odd polynomial is not evaluated in a way that preserves -0.
  22  *         Callers may do the optimization sin(x) ~ x for tiny x.
  23  *      3. sin(x) is approximated by a polynomial of degree 13 on
  24  *         [0,pi/4]
  25  *                               3            13
  26  *              sin(x) ~ x + S1*x + ... + S6*x
  27  *         where
  28  *
  29  *      |sin(x)         2     4     6     8     10     12  |     -58
  30  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
  31  *      |  x                                               |
  32  *
  33  *      4. sin(x+y) = sin(x) + sin'(x')*y
  34  *                  ~ sin(x) + (1-x*x/2)*y
  35  *         For better accuracy, let
  36  *                   3      2      2      2      2
  37  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
  38  *         then                   3    2
  39  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
  40  */
  41
  42 #include "libm.h"
  43
  44 static const double
  45 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
  46 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
  47 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
  48 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
  49 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
  50 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
  51
  52 double __sin(double x, double y, int iy)
  53 {
  54         double_t z,r,v,w;
  55
  56         z = x*x;
  57         w = z*z;
  58         r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
  59         v = z*x;
  60         if (iy == 0)
  61                 return x + v*(S1 + z*r);
  62         else
  63                 return x - ((z*(0.5*y - v*r) - y) - v*S1);
  64 }