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s_cospil.c revision 1.1 
      1 /*-
      2  * Copyright (c) 2017, 2023 Steven G. Kargl
      3  * All rights reserved.
      4  *
      5  * Redistribution and use in source and binary forms, with or without
      6  * modification, are permitted provided that the following conditions
      7  * are met:
      8  * 1. Redistributions of source code must retain the above copyright
      9  *    notice unmodified, this list of conditions, and the following
     10  *    disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  *
     15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
     16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
     17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
     19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
     20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
     21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
     22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
     24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     25  */
     26 
     27 /*
     28  * See ../src/s_cospi.c for implementation details.
     29  */
     30 
     31 #ifdef __i386__
     32 #include <ieeefp.h>
     33 #endif
     34 #include <stdint.h>
     35 
     36 #include "math.h"
     37 #include "math_private.h"
     38 
     39 static const double
     40 pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
     41 pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
     42 
     43 #include "k_cospil.h"
     44 #include "k_sinpil.h"
     45 
     46 static volatile const double vzero = 0;
     47 
     48 long double
     49 cospil(long double x)
     50 {
     51 	long double ax, c;
     52 	uint64_t lx;
     53 	uint32_t j0;
     54 	uint16_t hx, ix;
     55 
     56 	EXTRACT_LDBL80_WORDS(hx, lx, x);
     57 	ix = hx & 0x7fff;
     58 	INSERT_LDBL80_WORDS(ax, ix, lx);
     59 
     60 	ENTERI();
     61 
     62 	if (ix < 0x3fff) {			/* |x| < 1 */
     63 		if (ix < 0x3ffd) {		/* |x| < 0.25 */
     64 			if (ix < 0x3fdd) {	/* |x| < 0x1p-34 */
     65 				if ((int)x == 0)
     66 					RETURNI(1);
     67 			}
     68 			RETURNI(__kernel_cospil(ax));
     69 		}
     70 
     71 		if (ix < 0x3ffe)			/* |x| < 0.5 */
     72 			c = __kernel_sinpil(0.5 - ax);
     73 		else if (lx < 0xc000000000000000ull) {	/* |x| < 0.75 */
     74 			if (ax == 0.5)
     75 				RETURNI(0);
     76 			c = -__kernel_sinpil(ax - 0.5);
     77 		} else
     78 			c = -__kernel_cospil(1 - ax);
     79 		RETURNI(c);
     80 	}
     81 
     82 	if (ix < 0x403e) {			/* 1 <= |x| < 0x1p63 */
     83 		FFLOORL80(x, j0, ix, lx);	/* Integer part of ax. */
     84 		ax -= x;
     85 		EXTRACT_LDBL80_WORDS(ix, lx, ax);
     86 
     87 		if (ix < 0x3ffe) {			/* |x| < 0.5 */
     88 			if (ix < 0x3ffd)		/* |x| < 0.25 */
     89 				c = ix == 0 ? 1 : __kernel_cospil(ax);
     90 			else
     91 				c = __kernel_sinpil(0.5 - ax);
     92 
     93 		} else {
     94 			if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
     95 				if (ax == 0.5)
     96 					RETURNI(0);
     97 				c = -__kernel_sinpil(ax - 0.5);
     98 			} else
     99 				c = -__kernel_cospil(1 - ax);
    100 		}
    101 
    102 		if (j0 > 40)
    103 			x -= 0x1p40;
    104 		if (j0 > 30)
    105 			x -= 0x1p30;
    106 		j0 = (uint32_t)x;
    107 
    108 		RETURNI(j0 & 1 ? -c : c);
    109 	}
    110 
    111 	if (ix >= 0x7fff)
    112 		RETURNI(vzero / vzero);
    113 
    114 	/*
    115 	 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
    116 	 * or odd integer to return t = +1 or -1.
    117 	 * For |x| >= 0x1p64, it is always an even integer, so t = 1.
    118 	 */
    119 	RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1));
    120 }
    121