libm/k_sin.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* __kernel_sin( x, y, iy)
  13  * kernel sin function on [-pi/4, pi/4], 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. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
  21  *      3. sin(x) is approximated by a polynomial of degree 13 on
  22  *         [0,pi/4]
  23  *                               3            13
  24  *              sin(x) ~ x + S1*x + ... + S6*x
  25  *         where
  26  *
  27  *      |sin(x)         2     4     6     8     10     12  |     -58
  28  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
  29  *      |  x                                               |
  30  *
  31  *      4. sin(x+y) = sin(x) + sin'(x')*y
  32  *                  ~ sin(x) + (1-x*x/2)*y
  33  *         For better accuracy, let
  34  *                   3      2      2      2      2
  35  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
  36  *         then                   3    2
  37  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
  38  */
  39
  40 #include "math.h"
  41 #include "math_private.h"
  42
  43 static const double
  44 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  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 __kernel_sin(double x, double y, int iy)
  53 {
  54         double z,r,v;
  55         int32_t ix;
  56         GET_HIGH_WORD(ix,x);
  57         ix &= 0x7fffffff;                       /* high word of x */
  58         if(ix<0x3e400000)                       /* |x| < 2**-27 */
  59            {if((int)x==0) return x;}            /* generate inexact */
  60         z       =  x*x;
  61         v       =  z*x;
  62         r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
  63         if(iy==0) return x+v*(S1+z*r);
  64         else      return x-((z*(half*y-v*r)-y)-v*S1);
  65 }