cscg22-gearboy

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

k_cos.c (3404B)

      1/* @(#)k_cos.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_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
     16#endif
     17
     18/*
     19 * __kernel_cos( x,  y )
     20 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
     21 * Input x is assumed to be bounded by ~pi/4 in magnitude.
     22 * Input y is the tail of x.
     23 *
     24 * Algorithm
     25 *	1. Since cos(-x) = cos(x), we need only to consider positive x.
     26 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
     27 *	3. cos(x) is approximated by a polynomial of degree 14 on
     28 *	   [0,pi/4]
     29 *		  	                 4            14
     30 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
     31 *	   where the remez error is
     32 *
     33 * 	|              2     4     6     8     10    12     14 |     -58
     34 * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
     35 * 	|    					               |
     36 *
     37 * 	               4     6     8     10    12     14
     38 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
     39 *	       cos(x) = 1 - x*x/2 + r
     40 *	   since cos(x+y) ~ cos(x) - sin(x)*y
     41 *			  ~ cos(x) - x*y,
     42 *	   a correction term is necessary in cos(x) and hence
     43 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
     44 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
     45 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
     46 *	   Then
     47 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
     48 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
     49 *	   magnitude of the latter is at least a quarter of x*x/2,
     50 *	   thus, reducing the rounding error in the subtraction.
     51 */
     52
     53#include "math_libm.h"
     54#include "math_private.h"
     55
     56#ifdef __STDC__
     57static const double
     58#else
     59static double
     60#endif
     61  one = 1.00000000000000000000e+00,     /* 0x3FF00000, 0x00000000 */
     62    C1 = 4.16666666666666019037e-02,    /* 0x3FA55555, 0x5555554C */
     63    C2 = -1.38888888888741095749e-03,   /* 0xBF56C16C, 0x16C15177 */
     64    C3 = 2.48015872894767294178e-05,    /* 0x3EFA01A0, 0x19CB1590 */
     65    C4 = -2.75573143513906633035e-07,   /* 0xBE927E4F, 0x809C52AD */
     66    C5 = 2.08757232129817482790e-09,    /* 0x3E21EE9E, 0xBDB4B1C4 */
     67    C6 = -1.13596475577881948265e-11;   /* 0xBDA8FAE9, 0xBE8838D4 */
     68
     69#ifdef __STDC__
     70double attribute_hidden
     71__kernel_cos(double x, double y)
     72#else
     73double attribute_hidden
     74__kernel_cos(x, y)
     75     double x, y;
     76#endif
     77{
     78    double a, hz, z, r, qx;
     79    int32_t ix;
     80    GET_HIGH_WORD(ix, x);
     81    ix &= 0x7fffffff;           /* ix = |x|'s high word */
     82    if (ix < 0x3e400000) {      /* if x < 2**27 */
     83        if (((int) x) == 0)
     84            return one;         /* generate inexact */
     85    }
     86    z = x * x;
     87    r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
     88    if (ix < 0x3FD33333)        /* if |x| < 0.3 */
     89        return one - (0.5 * z - (z * r - x * y));
     90    else {
     91        if (ix > 0x3fe90000) {  /* x > 0.78125 */
     92            qx = 0.28125;
     93        } else {
     94            INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
     95        }
     96        hz = 0.5 * z - qx;
     97        a = one - qx;
     98        return a - (hz - (z * r - x * y));
     99    }
    100}