newlib/libm/ld128/s_cospil.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_cospi.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 cospil(long double x)
  49 {
  50         long double ai, ar, ax, c;
  51
  52         ax = fabsl(x);
  53
  54         if (ax <= 1) {
  55                 if (ax < 0.25) {
  56                         if (ax < 0x1p-60) {
  57                                 if ((int)x == 0)
  58                                         return (1);
  59                         }
  60                         return (__kernel_cospil(ax));
  61                 }
  62
  63                 if (ax < 0.5)
  64                         c = __kernel_sinpil(0.5 - ax);
  65                 else if (ax < 0.75) {
  66                         if (ax == 0.5)
  67                                 return (0);
  68                         c = -__kernel_sinpil(ax - 0.5);
  69                 } else
  70                         c = -__kernel_cospil(1 - ax);
  71                 return (c);
  72         }
  73
  74         if (ax < 0x1p112) {
  75                 /* Split ax = ai + ar with 0 <= ar < 1. */
  76                 FFLOORL128(ax, ai, ar);
  77
  78                 if (ar < 0.5) {
  79                         if (ar < 0.25)
  80                                 c = ar == 0 ? 1 : __kernel_cospil(ar);
  81                         else
  82                                 c = __kernel_sinpil(0.5 - ar);
  83                 } else {
  84                         if (ar < 0.75) {
  85                                 if (ar == 0.5)
  86                                         return (0);
  87                                 c = -__kernel_sinpil(ar - 0.5);
  88                         } else
  89                                 c = -__kernel_cospil(1 - ar);
  90                 }
  91                 return (fmodl(ai, 2.L) == 0 ? c : -c);
  92         }
  93
  94         if (isinf(x) || isnan(x))
  95                 return (vzero / vzero);
  96
  97         /*
  98          * For |x| >= 0x1p113, it is always an even integer, so return 1.
  99          */
 100         if (ax >= 0x1p113)
 101                 return (1);
 102         /*
 103          * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
 104          * or odd integer to return 1 or -1.
 105          */
 106
 107         return (fmodl(ax, 2.L) == 0 ? 1 : -1);
 108 }