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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 "math.h"
     32 #include "math_private.h"
     33 
     34 /*
     35  * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
     36  */
     37 static const long double
     38 pi_hi = 3.14159265358979322702026593105983920e+00L,
     39 pi_lo = 1.14423774522196636802434264184180742e-17L;
     40 
     41 #include "k_cospil.h"
     42 #include "k_sinpil.h"
     43 
     44 static volatile const double vzero = 0;
     45 
     46 long double
     47 cospil(long double x)
     48 {
     49 	long double ai, ar, ax, c;
     50 
     51 	ax = fabsl(x);
     52 
     53 	if (ax <= 1) {
     54 		if (ax < 0.25) {
     55 			if (ax < 0x1p-60) {
     56 				if ((int)x == 0)
     57 					return (1);
     58 			}
     59 			return (__kernel_cospil(ax));
     60 		}
     61 
     62 		if (ax < 0.5)
     63 			c = __kernel_sinpil(0.5 - ax);
     64 		else if (ax < 0.75) {
     65 			if (ax == 0.5)
     66 				return (0);
     67 			c = -__kernel_sinpil(ax - 0.5);
     68 		} else
     69 			c = -__kernel_cospil(1 - ax);
     70 		return (c);
     71 	}
     72 
     73 	if (ax < 0x1p112) {
     74 		/* Split ax = ai + ar with 0 <= ar < 1. */
     75 		FFLOORL128(ax, ai, ar);
     76 
     77 		if (ar < 0.5) {
     78 			if (ar < 0.25)
     79 				c = ar == 0 ? 1 : __kernel_cospil(ar);
     80 			else
     81 				c = __kernel_sinpil(0.5 - ar);
     82 		} else {
     83 			if (ar < 0.75) {
     84 				if (ar == 0.5)
     85 					return (0);
     86 				c = -__kernel_sinpil(ar - 0.5);
     87 			} else
     88 				c = -__kernel_cospil(1 - ar);
     89 		}
     90 		return (fmodl(ai, 2.L) == 0 ? c : -c);
     91 	}
     92 
     93 	if (isinf(x) || isnan(x))
     94 		return (vzero / vzero);
     95 
     96 	/*
     97 	 * For |x| >= 0x1p113, it is always an even integer, so return 1.
     98 	 */
     99 	if (ax >= 0x1p113)
    100 		return (1);
    101 	/*
    102 	 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
    103 	 * or odd integer to return 1 or -1.
    104 	 */
    105 
    106 	return (fmodl(ax, 2.L) == 0 ? 1 : -1);
    107 }
    108