lib/libm/src/s_sinl.c

   1 /*      $OpenBSD: s_sinl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $     */
   2 /*-
   3  * Copyright (c) 2007 Steven G. Kargl
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice unmodified, this list of conditions, and the following
  11  *    disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  26  */
  27
  28 /*
  29  * Compute sin(x) for x where x is reduced to y = x - k * pi / 2.
  30  */
  31
  32 #include <sys/types.h>
  33 #include <machine/ieee.h>
  34 #include <float.h>
  35 #include <math.h>
  36
  37 #include "math_private.h"
  38
  39 #if LDBL_MANT_DIG == 64
  40 #define NX      3
  41 #define PREC    2
  42 #elif LDBL_MANT_DIG == 113
  43 #define NX      5
  44 #define PREC    3
  45 #else
  46 #error "Unsupported long double format"
  47 #endif
  48
  49 static const long double two24 = 1.67772160000000000000e+07L;
  50
  51 long double
  52 sinl(long double x)
  53 {
  54         union {
  55                 long double e;
  56                 struct ieee_ext bits;
  57         } z;
  58         int i, e0, s;
  59         double xd[NX], yd[PREC];
  60         long double hi, lo;
  61
  62         z.e = x;
  63         s = z.bits.ext_sign;
  64         z.bits.ext_sign = 0;
  65
  66         /* If x = +-0 or x is a subnormal number, then sin(x) = x */
  67         if (z.bits.ext_exp == 0)
  68                 return (x);
  69
  70         /* If x = NaN or Inf, then sin(x) = NaN. */
  71         if (z.bits.ext_exp == 32767)
  72                 return ((x - x) / (x - x));
  73
  74         /* Optimize the case where x is already within range. */
  75         if (z.e < M_PI_4) {
  76                 hi = __kernel_sinl(z.e, 0, 0);
  77                 return  (s ? -hi : hi);
  78         }
  79
  80         /* Split z.e into a 24-bit representation. */
  81         e0 = ilogbl(z.e) - 23;
  82         z.e = scalbnl(z.e, -e0);
  83         for (i = 0; i < NX; i++) {
  84                 xd[i] = (double)((int32_t)z.e);
  85                 z.e = (z.e - xd[i]) * two24;
  86         }
  87
  88         /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
  89         e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
  90
  91 #if PREC == 2
  92         hi = (long double)yd[0] + yd[1];
  93         lo = yd[1] - (hi - yd[0]);
  94 #else /* PREC == 3 */
  95         long double t;
  96         t = (long double)yd[2] + yd[1];
  97         hi = t + yd[0];
  98         lo = yd[0] - (hi - t);
  99 #endif
 100
 101         switch (e0 & 3) {
 102         case 0:
 103             hi = __kernel_sinl(hi, lo, 1);
 104             break;
 105         case 1:
 106             hi = __kernel_cosl(hi, lo);
 107             break;
 108         case 2:
 109             hi = - __kernel_sinl(hi, lo, 1);
 110             break;
 111         case 3:
 112             hi = - __kernel_cosl(hi, lo);
 113             break;
 114         }
 115
 116         return (s ? -hi : hi);
 117 }