Home | History | Annotate | Line # | Download | only in ld128
s_sinpil.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_sinpi.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 sinpil(long double x)
     48 {
     49 	long double ai, ar, ax, hi, lo, s;
     50 
     51 	ax = fabsl(x);
     52 
     53 	if (ax < 1) {
     54 		if (ax < 0.25) {
     55 			if (ax < 0x1p-60) {
     56 				if (x == 0)
     57 					return (x);
     58 				hi = (double)x;
     59 				hi *= 0x1p113L;
     60 				lo = x * 0x1p113L - hi;
     61 				s = (pi_lo + pi_hi) * lo + pi_lo * lo +
     62 				    pi_hi * hi;
     63 				return (s * 0x1p-113L);
     64 			}
     65 
     66 			s = __kernel_sinpil(ax);
     67 			return (x < 0 ? -s : s);
     68 		}
     69 
     70 		if (ax < 0.5)
     71 			s = __kernel_cospil(0.5 - ax);
     72 		else if (ax < 0.75)
     73 			s = __kernel_cospil(ax - 0.5);
     74 		else
     75 			s = __kernel_sinpil(1 - ax);
     76 		return (x < 0 ? -s : s);
     77 	}
     78 
     79 	if (ax < 0x1p112) {
     80 		/* Split ax = ai + ar with 0 <= ar < 1. */
     81 		FFLOORL128(ax, ai, ar);
     82 
     83 		if (ar == 0) {
     84 			s = 0;
     85 		} else {
     86 			if (ar < 0.5) {
     87 				if (ar <= 0.25)
     88 					s = __kernel_sinpil(ar);
     89 				else
     90 					s = __kernel_cospil(0.5 - ar);
     91 			} else {
     92 				if (ar < 0.75)
     93 					s = __kernel_cospil(ar - 0.5);
     94 				else
     95 					s = __kernel_sinpil(1 - ar);
     96 			}
     97 
     98 			s = fmodl(ai, 2.L) == 0 ? s : -s;
     99 		}
    100 		return (x < 0 ? -s : s);
    101 	}
    102 
    103 	if (isinf(x) || isnan(x))
    104 		return (vzero / vzero);
    105 
    106 	/*
    107 	 * |x| >= 0x1p112 is always an integer, so return +-0.
    108 	 */
    109 	return (copysignl(0, x));
    110 }
    111