newlib/libm/ld80/s_sinpil.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_sinpi.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 union IEEEl2bits
  41 pi_hi_u = LD80C(0xc90fdaa200000000,   1, 3.14159265346825122833e+00L),
  42 pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L);
  43 #define pi_hi   (pi_hi_u.e)
  44 #define pi_lo   (pi_lo_u.e)
  45
  46 #include "k_cospil.h"
  47 #include "k_sinpil.h"
  48
  49 volatile static const double vzero = 0;
  50
  51 long double
  52 sinpil(long double x)
  53 {
  54         long double ax, hi, lo, s;
  55         uint64_t lx, m;
  56         uint32_t j0;
  57         uint16_t hx, ix;
  58
  59         EXTRACT_LDBL80_WORDS(hx, lx, x);
  60         ix = hx & 0x7fff;
  61         INSERT_LDBL80_WORDS(ax, ix, lx);
  62
  63         ENTERI();
  64
  65         if (ix < 0x3fff) {                      /* |x| < 1 */
  66                 if (ix < 0x3ffd) {              /* |x| < 0.25 */
  67                         if (ix < 0x3fdd) {      /* |x| < 0x1p-34 */
  68                                 if (x == 0)
  69                                         RETURNI(x);
  70                                 INSERT_LDBL80_WORDS(hi, hx,
  71                                     lx & 0xffffffff00000000ull);
  72                                 hi *= 0x1p63L;
  73                                 lo = x * 0x1p63L - hi;
  74                                 s = (pi_lo + pi_hi) * lo + pi_lo * hi +
  75                                     pi_hi * hi;
  76                                 RETURNI(s * 0x1p-63L);
  77                         }
  78                         s = __kernel_sinpil(ax);
  79                         RETURNI((hx & 0x8000) ? -s : s);
  80                 }
  81
  82                 if (ix < 0x3ffe)                        /* |x| < 0.5 */
  83                         s = __kernel_cospil(0.5 - ax);
  84                 else if (lx < 0xc000000000000000ull)    /* |x| < 0.75 */
  85                         s = __kernel_cospil(ax - 0.5);
  86                 else
  87                         s = __kernel_sinpil(1 - ax);
  88                 RETURNI((hx & 0x8000) ? -s : s);
  89         }
  90
  91         if (ix < 0x403e) {              /* 1 <= |x| < 0x1p63 */
  92                 /* Determine integer part of ax. */
  93                 j0 = ix - 0x3fff + 1;
  94                 if (j0 < 32) {
  95                         lx = (lx >> 32) << 32;
  96                         lx &= ~(((lx << 32)-1) >> j0);
  97                 } else {
  98                         m = (uint64_t)-1 >> (j0 + 1);
  99                         if (lx & m) lx &= ~m;
 100                 }
 101                 INSERT_LDBL80_WORDS(x, ix, lx);
 102
 103                 ax -= x;
 104                 EXTRACT_LDBL80_WORDS(ix, lx, ax);
 105
 106                 if (ix == 0) {
 107                         s = 0;
 108                 } else {
 109                         if (ix < 0x3ffe) {              /* |x| < 0.5 */
 110                                 if (ix < 0x3ffd)        /* |x| < 0.25 */
 111                                         s = __kernel_sinpil(ax);
 112                                 else
 113                                         s = __kernel_cospil(0.5 - ax);
 114                         } else {
 115                                                         /* |x| < 0.75 */
 116                                 if (lx < 0xc000000000000000ull)
 117                                         s = __kernel_cospil(ax - 0.5);
 118                                 else
 119                                         s = __kernel_sinpil(1 - ax);
 120                         }
 121
 122                         if (j0 > 40)
 123                                 x -= 0x1p40;
 124                         if (j0 > 30)
 125                                 x -= 0x1p30;
 126                         j0 = (uint32_t)x;
 127                         if (j0 & 1) s = -s;
 128                 }
 129                 RETURNI((hx & 0x8000) ? -s : s);
 130         }
 131
 132         /* x = +-inf or nan. */
 133         if (ix >= 0x7fff)
 134                 RETURNI(vzero / vzero);
 135
 136         /*
 137          * |x| >= 0x1p63 is always an integer, so return +-0.
 138          */
 139         RETURNI(copysignl(0, x));
 140 }