src/libm/k_sin.c
author Ryan C. Gordon <icculus@icculus.org>
Fri, 12 Aug 2016 19:59:00 -0400
changeset 10266 c09f06c4e8c8
parent 6044 35448a5ea044
permissions -rw-r--r--
emscripten: send fake mouse events for touches, like other targets do. (This really should be handled at the higher level and not in the individual targets, but this fixes the immediate bug.)

/* @(#)k_sin.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static const char rcsid[] =
    "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
#endif

/* __kernel_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
 *
 * Algorithm
 *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *	3. sin(x) is approximated by a polynomial of degree 13 on
 *	   [0,pi/4]
 *		  	         3            13
 *	   	sin(x) ~ x + S1*x + ... + S6*x
 *	   where
 *
 * 	|sin(x)         2     4     6     8     10     12  |     -58
 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 * 	|  x 					           |
 *
 *	4. sin(x+y) = sin(x) + sin'(x')*y
 *		    ~ sin(x) + (1-x*x/2)*y
 *	   For better accuracy, let
 *		     3      2      2      2      2
 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *	   then                   3    2
 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

#include "math_libm.h"
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
  half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
    S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
    S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
    S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
    S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
    S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
    S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */

#ifdef __STDC__
double attribute_hidden
__kernel_sin(double x, double y, int iy)
#else
double attribute_hidden
__kernel_sin(x, y, iy)
     double x, y;
     int iy;                    /* iy=0 if y is zero */
#endif
{
    double z, r, v;
    int32_t ix;
    GET_HIGH_WORD(ix, x);
    ix &= 0x7fffffff;           /* high word of x */
    if (ix < 0x3e400000) {      /* |x| < 2**-27 */
        if ((int) x == 0)
            return x;
    }                           /* generate inexact */
    z = x * x;
    v = z * x;
    r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
    if (iy == 0)
        return x + v * (S1 + z * r);
    else
        return x - ((z * (half * y - v * r) - y) - v * S1);
}