cscg22-gearboy

CSCG 2022 Challenge 'Gearboy'
git clone https://git.sinitax.com/sinitax/cscg22-gearboy
Log | Files | Refs | sfeed.txt

k_sin.c (2815B)

      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#if defined(LIBM_SCCS) && !defined(lint)
     14static const char rcsid[] =
     15    "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc 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_libm.h"
     47#include "math_private.h"
     48
     49#ifdef __STDC__
     50static const double
     51#else
     52static double
     53#endif
     54  half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
     55    S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
     56    S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
     57    S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
     58    S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
     59    S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
     60    S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */
     61
     62#ifdef __STDC__
     63double attribute_hidden
     64__kernel_sin(double x, double y, int iy)
     65#else
     66double attribute_hidden
     67__kernel_sin(x, y, iy)
     68     double x, y;
     69     int iy;                    /* iy=0 if y is zero */
     70#endif
     71{
     72    double z, r, v;
     73    int32_t ix;
     74    GET_HIGH_WORD(ix, x);
     75    ix &= 0x7fffffff;           /* high word of x */
     76    if (ix < 0x3e400000) {      /* |x| < 2**-27 */
     77        if ((int) x == 0)
     78            return x;
     79    }                           /* generate inexact */
     80    z = x * x;
     81    v = z * x;
     82    r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
     83    if (iy == 0)
     84        return x + v * (S1 + z * r);
     85    else
     86        return x - ((z * (half * y - v * r) - y) - v * S1);
     87}