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      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 #include <stdint.h>
     32 
     33 #include "math.h"
     34 #include "math_private.h"
     35 
     36 static const double
     37 pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
     38 pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
     39 
     40 #include "k_cospil.h"
     41 #include "k_sinpil.h"
     42 
     43 static volatile const double vzero = 0;
     44 
     45 long double
     46 cospil(long double x)
     47 {
     48 	long double ax, c;
     49 	uint64_t lx;
     50 	uint32_t j0;
     51 	uint16_t hx, ix;
     52 
     53 	EXTRACT_LDBL80_WORDS(hx, lx, x);
     54 	ix = hx & 0x7fff;
     55 	INSERT_LDBL80_WORDS(ax, ix, lx);
     56 
     57 	ENTERI();
     58 
     59 	if (ix < 0x3fff) {			/* |x| < 1 */
     60 		if (ix < 0x3ffd) {		/* |x| < 0.25 */
     61 			if (ix < 0x3fdd) {	/* |x| < 0x1p-34 */
     62 				if ((int)x == 0)
     63 					RETURNI(1);
     64 			}
     65 			RETURNI(__kernel_cospil(ax));
     66 		}
     67 
     68 		if (ix < 0x3ffe)			/* |x| < 0.5 */
     69 			c = __kernel_sinpil(0.5 - ax);
     70 		else if (lx < 0xc000000000000000ull) {	/* |x| < 0.75 */
     71 			if (ax == 0.5)
     72 				RETURNI(0);
     73 			c = -__kernel_sinpil(ax - 0.5);
     74 		} else
     75 			c = -__kernel_cospil(1 - ax);
     76 		RETURNI(c);
     77 	}
     78 
     79 	if (ix < 0x403e) {			/* 1 <= |x| < 0x1p63 */
     80 		FFLOORL80(x, j0, ix, lx);	/* Integer part of ax. */
     81 		ax -= x;
     82 		EXTRACT_LDBL80_WORDS(ix, lx, ax);
     83 
     84 		if (ix < 0x3ffe) {			/* |x| < 0.5 */
     85 			if (ix < 0x3ffd)		/* |x| < 0.25 */
     86 				c = ix == 0 ? 1 : __kernel_cospil(ax);
     87 			else
     88 				c = __kernel_sinpil(0.5 - ax);
     89 
     90 		} else {
     91 			if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
     92 				if (ax == 0.5)
     93 					RETURNI(0);
     94 				c = -__kernel_sinpil(ax - 0.5);
     95 			} else
     96 				c = -__kernel_cospil(1 - ax);
     97 		}
     98 
     99 		if (j0 > 40)
    100 			x -= 0x1p40;
    101 		if (j0 > 30)
    102 			x -= 0x1p30;
    103 		j0 = (uint32_t)x;
    104 
    105 		RETURNI(j0 & 1 ? -c : c);
    106 	}
    107 
    108 	if (ix >= 0x7fff)
    109 		RETURNI(vzero / vzero);
    110 
    111 	/*
    112 	 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
    113 	 * or odd integer to return t = +1 or -1.
    114 	 * For |x| >= 0x1p64, it is always an even integer, so t = 1.
    115 	 */
    116 	RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1));
    117 }
    118