newlib/libm/ld128/s_sinpil.c

   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 "../ld/fpmath.h"
  32 #include "math.h"
  33 #include "../ld/math_private.h"
  34
  35 /*
  36  * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
  37  */
  38 static const long double
  39 pi_hi = 3.14159265358979322702026593105983920e+00L,
  40 pi_lo = 1.14423774522196636802434264184180742e-17L;
  41
  42 #include "k_cospil.h"
  43 #include "k_sinpil.h"
  44
  45 volatile static const double vzero = 0;
  46
  47 long double
  48 sinpil(long double x)
  49 {
  50         long double ai, ar, ax, hi, lo, s, xhi, xlo;
  51
  52         ax = fabsl(x);
  53
  54         if (ax < 1) {
  55                 if (ax < 0.25) {
  56                         if (ax < 0x1p-60) {
  57                                 if (x == 0)
  58                                         return (x);
  59                                 hi = (double)x;
  60                                 hi *= 0x1p113L;
  61                                 lo = x * 0x1p113L - hi;
  62                                 s = (pi_lo + pi_hi) * lo + pi_lo * lo +
  63                                     pi_hi * hi;
  64                                 return (s * 0x1p-113L);
  65                         }
  66
  67                         s = __kernel_sinpil(ax);
  68                         return (x < 0 ? -s : s);
  69                 }
  70
  71                 if (ax < 0.5)
  72                         s = __kernel_cospil(0.5 - ax);
  73                 else if (ax < 0.75)
  74                         s = __kernel_cospil(ax - 0.5);
  75                 else
  76                         s = __kernel_sinpil(1 - ax);
  77                 return (x < 0 ? -s : s);
  78         }
  79
  80         if (ax < 0x1p112) {
  81                 /* Split ax = ai + ar with 0 <= ar < 1. */
  82                 FFLOORL128(ax, ai, ar);
  83
  84                 if (ar == 0) {
  85                         s = 0;
  86                 } else {
  87                         if (ar < 0.5) {
  88                                 if (ar <= 0.25)
  89                                         s = __kernel_sinpil(ar);
  90                                 else
  91                                         s = __kernel_cospil(0.5 - ar);
  92                         } else {
  93                                 if (ar < 0.75)
  94                                         s = __kernel_cospil(ar - 0.5);
  95                                 else
  96                                         s = __kernel_sinpil(1 - ar);
  97                         }
  98
  99                         s = fmodl(ai, 2.L) == 0 ? s : -s;
 100                 }
 101                 return (x < 0 ? -s : s);
 102         }
 103
 104         if (isinf(x) || isnan(x))
 105                 return (vzero / vzero);
 106
 107         /*
 108          * |x| >= 0x1p112 is always an integer, so return +-0.
 109          */
 110         return (copysignl(0, x));
 111 }