lib/libm/src/k_sin.c

   1 /* @(#)k_sin.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, 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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
  16 #endif
  17
  18 /* __kernel_sin( x, y, iy)
  19  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
  20  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  21  * Input y is the tail of x.
  22  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
  23  *
  24  * Algorithm
  25  *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
  26  *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
  27  *      3. sin(x) is approximated by a polynomial of degree 13 on
  28  *         [0,pi/4]
  29  *                               3            13
  30  *              sin(x) ~ x + S1*x + ... + S6*x
  31  *         where
  32  *
  33  *      |sin(x)         2     4     6     8     10     12  |     -58
  34  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
  35  *      |  x                                               |
  36  *
  37  *      4. sin(x+y) = sin(x) + sin'(x')*y
  38  *                  ~ sin(x) + (1-x*x/2)*y
  39  *         For better accuracy, let
  40  *                   3      2      2      2      2
  41  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
  42  *         then                   3    2
  43  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
  44  */
  45
  46 #include "math.h"
  47 #include "math_private.h"
  48
  49 static const double
  50 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  51 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
  52 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
  53 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
  54 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
  55 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
  56 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
  57
  58 double
  59 __kernel_sin(double x, double y, int iy)
  60 {
  61         double z,r,v;
  62         int32_t ix;
  63         GET_HIGH_WORD(ix,x);
  64         ix &= 0x7fffffff;                       /* high word of x */
  65         if(ix<0x3e400000)                       /* |x| < 2**-27 */
  66            {if((int)x==0) return x;}            /* generate inexact */
  67         z       =  x*x;
  68         v       =  z*x;
  69         r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
  70         if(iy==0) return x+v*(S1+z*r);
  71         else      return x-((z*(half*y-v*r)-y)-v*S1);
  72 }