newlib/libm/ld80/s_cospil.c

   1 /*-
   2  * Copyright (c) 2017 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 #ifdef __i386__
  32 #include <ieeefp.h>
  33 #endif
  34 #include <stdint.h>
  35
  36 #include "../ld/fpmath.h"
  37 #include "math.h"
  38 #include "../ld/math_private.h"
  39
  40 static const double
  41 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
  42 pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
  43
  44 #include "k_cospil.h"
  45 #include "k_sinpil.h"
  46
  47 volatile static const double vzero = 0;
  48
  49 long double
  50 cospil(long double x)
  51 {
  52         long double ax, c;
  53         uint64_t lx, m;
  54         uint32_t j0;
  55         uint16_t hx, ix;
  56
  57         EXTRACT_LDBL80_WORDS(hx, lx, x);
  58         ix = hx & 0x7fff;
  59         INSERT_LDBL80_WORDS(ax, ix, lx);
  60
  61         ENTERI();
  62
  63         if (ix < 0x3fff) {                      /* |x| < 1 */
  64                 if (ix < 0x3ffd) {              /* |x| < 0.25 */
  65                         if (ix < 0x3fdd) {      /* |x| < 0x1p-34 */
  66                                 if ((int)x == 0)
  67                                         RETURNI(1);
  68                         }
  69                         RETURNI(__kernel_cospil(ax));
  70                 }
  71
  72                 if (ix < 0x3ffe)                        /* |x| < 0.5 */
  73                         c = __kernel_sinpil(0.5 - ax);
  74                 else if (lx < 0xc000000000000000ull) {  /* |x| < 0.75 */
  75                         if (ax == 0.5)
  76                                 RETURNI(0);
  77                         c = -__kernel_sinpil(ax - 0.5);
  78                 } else
  79                         c = -__kernel_cospil(1 - ax);
  80                 RETURNI(c);
  81         }
  82
  83         if (ix < 0x403e) {              /* 1 <= |x| < 0x1p63 */
  84                 /* Determine integer part of ax. */
  85                 j0 = ix - 0x3fff + 1;
  86                 if (j0 < 32) {
  87                         lx = (lx >> 32) << 32;
  88                         lx &= ~(((lx << 32)-1) >> j0);
  89                 } else {
  90                         m = (uint64_t)-1 >> (j0 + 1);
  91                         if (lx & m) lx &= ~m;
  92                 }
  93                 INSERT_LDBL80_WORDS(x, ix, lx);
  94
  95                 ax -= x;
  96                 EXTRACT_LDBL80_WORDS(ix, lx, ax);
  97
  98                 if (ix < 0x3ffe) {                      /* |x| < 0.5 */
  99                         if (ix < 0x3ffd)                /* |x| < 0.25 */
 100                                 c = ix == 0 ? 1 : __kernel_cospil(ax);
 101                         else
 102                                 c = __kernel_sinpil(0.5 - ax);
 103
 104                 } else {
 105                         if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
 106                                 if (ax == 0.5)
 107                                         RETURNI(0);
 108                                 c = -__kernel_sinpil(ax - 0.5);
 109                         } else
 110                                 c = -__kernel_cospil(1 - ax);
 111                 }
 112
 113                 if (j0 > 40)
 114                         x -= 0x1p40;
 115                 if (j0 > 30)
 116                         x -= 0x1p30;
 117                 j0 = (uint32_t)x;
 118
 119                 RETURNI(j0 & 1 ? -c : c);
 120         }
 121
 122         if (ix >= 0x7fff)
 123                 RETURNI(vzero / vzero);
 124
 125         /*
 126          * |x| >= 0x1p63 is always an even integer, so return 1.
 127          */
 128         RETURNI(1);
 129 }