src/libm/k_sin.c
author Ryan C. Gordon <icculus@icculus.org>
Tue, 26 May 2015 21:19:23 -0400
changeset 9649 d7762e30ba24
parent 6044 35448a5ea044
child 11683 48bcba563d9c
permissions -rw-r--r--
Stack hint should look for 0, not -1, and not care about environment variables.
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/* @(#)k_sin.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#if defined(LIBM_SCCS) && !defined(lint)
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static const char rcsid[] =
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    "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
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#endif
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/* __kernel_sin( x, y, iy)
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 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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 * Input y is the tail of x.
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 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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 *
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 * Algorithm
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 *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
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 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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 *	3. sin(x) is approximated by a polynomial of degree 13 on
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 *	   [0,pi/4]
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 *		  	         3            13
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 *	   	sin(x) ~ x + S1*x + ... + S6*x
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 *	   where
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 *
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 * 	|sin(x)         2     4     6     8     10     12  |     -58
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 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
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 * 	|  x 					           |
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 *
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 *	4. sin(x+y) = sin(x) + sin'(x')*y
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 *		    ~ sin(x) + (1-x*x/2)*y
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 *	   For better accuracy, let
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 *		     3      2      2      2      2
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 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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 *	   then                   3    2
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 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
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 */
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#include "math_libm.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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  half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
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    S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
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    S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
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    S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
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    S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
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    S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
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    S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */
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#ifdef __STDC__
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double attribute_hidden
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__kernel_sin(double x, double y, int iy)
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#else
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double attribute_hidden
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__kernel_sin(x, y, iy)
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     double x, y;
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     int iy;                    /* iy=0 if y is zero */
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#endif
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{
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    double z, r, v;
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    int32_t ix;
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    GET_HIGH_WORD(ix, x);
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    ix &= 0x7fffffff;           /* high word of x */
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    if (ix < 0x3e400000) {      /* |x| < 2**-27 */
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        if ((int) x == 0)
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            return x;
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    }                           /* generate inexact */
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    z = x * x;
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    v = z * x;
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    r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
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    if (iy == 0)
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        return x + v * (S1 + z * r);
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    else
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        return x - ((z * (half * y - v * r) - y) - v * S1);
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}