1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 
  26 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 /*
  32  * long double sinpil(long double x),
  33  * return long double precision sinl(pi*x).
  34  *
  35  * Algorithm, 10/17/2002, K.C. Ng
  36  * ------------------------------
  37  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
  38  *      1. If y == z, then x is a multiple of pi/4. Return the following values:
  39  *             ---------------------------------------------------
  40  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
  41  *             ---------------------------------------------------
  42  *              000  0.00       +0 ___       +1 ___      +0
  43  *              001  0.25       +\/0.5       +\/0.5      +1
  44  *              010  0.50       +1 ___       +0 ___      +inf
  45  *              011  0.75       +\/0.5       -\/0.5      -1
  46  *              100  1.00       -0 ___       -1 ___      +0
  47  *              101  1.25       -\/0.5       -\/0.5      +1
  48  *              110  1.50       -1 ___       -0 ___      +inf
  49  *              111  1.75       -\/0.5       +\/0.5      -1
  50  *             ---------------------------------------------------
  51  *      2. Otherwise,
  52  *             ---------------------------------------------------
  53  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
  54  *             ---------------------------------------------------
  55  *              000  (y-z)/4     sinpi(t)     cospi(t)    tanpi(t)
  56  *              001  (z+1-y)/4   cospi(t)     sinpi(t)    1/tanpi(t)
  57  *              010  (y-z)/4     cospi(t)    -sinpi(t)   -1/tanpi(t)
  58  *              011  (z+1-y)/4   sinpi(t)    -cospi(t)   -tanpi(t)
  59  *              100  (y-z)/4    -sinpi(t)    -cospi(t)    tanpi(t)
  60  *              101  (z+1-y)/4  -cospi(t)    -sinpi(t)    1/tanpi(t)
  61  *              110  (y-z)/4    -cospi(t)     sinpi(t)   -1/tanpi(t)
  62  *              111  (z+1-y)/4  -sinpi(t)     cospi(t)   -tanpi(t)
  63  *             ---------------------------------------------------
  64  *
  65  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
  66  * This will return a result with error slightly more than one ulp (but less
  67  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
  68  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
  69  * instead.
  70  */
  71 
  72 #include "libm.h"
  73 #include "longdouble.h"
  74 
  75 #define I(q, m)                         ((int *)&(q))[m]
  76 #define U(q, m)                         ((unsigned *)&(q))[m]
  77 #if defined(__LITTLE_ENDIAN) || defined(__x86)
  78 #define LDBL_MOST_SIGNIF_I(ld)          ((I(ld, 2) << 16) | (0xffff & (I(ld, \
  79         1) >> 15)))
  80 #define LDBL_LEAST_SIGNIF_U(ld)         U(ld, 0)
  81 #define PREC                            64
  82 #define PRECM1                          63
  83 #define PRECM2                          62
  84 
  85 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
  86 #else
  87 #define LDBL_MOST_SIGNIF_I(ld)          I(ld, 0)
  88 #define LDBL_LEAST_SIGNIF_U(ld)         U(ld, sizeof (long double) / \
  89         sizeof (int) - 1)
  90 #define PREC                            113
  91 #define PRECM1                          112
  92 #define PRECM2                          111
  93 
  94 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
  95 #endif
  96 
  97 static const long double zero = 0.0L,
  98         quater = 0.25L,
  99         one = 1.0L,
 100         pi = 3.141592653589793238462643383279502884197e+0000L,
 101         sqrth = 0.707106781186547524400844362104849039284835937688474,
 102         tiny = 1.0e-100;
 103 
 104 long double
 105 sinpil(long double x)
 106 {
 107         long double y, z, t;
 108         int hx, n, k;
 109         unsigned lx;
 110 
 111         hx = LDBL_MOST_SIGNIF_I(x);
 112         lx = LDBL_LEAST_SIGNIF_U(x);
 113         k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
 114 
 115         if (k >= PRECM2) {           /* |x| >= 2**(Prec-2) */
 116                 if (k >= 16384) {
 117                         y = x - x;
 118                 } else {
 119                         if (k >= PREC) {
 120                                 y = zero;
 121                         } else if (k == PRECM1) {
 122                                 y = (lx & 1) == 0 ? zero : -zero;
 123                         } else { /* k = Prec - 2 */
 124                                 y = (lx & 1) == 0 ? zero : one;
 125 
 126                                 if ((lx & 2) != 0)
 127                                         y = -y;
 128                         }
 129                 }
 130         } else if (k < -2) {         /* |x| < 0.25 */
 131                 y = __k_sinl(pi * fabsl(x), zero);
 132         } else {
 133                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 134                 y = 4.0L * fabsl(x);
 135 
 136                 if (k < PRECM2) {
 137                         z = y + twoPRECM2;
 138                         n = LDBL_LEAST_SIGNIF_U(z) & 7;     /* 3 LSb of z */
 139                         t = z - twoPRECM2;
 140                         k = 0;
 141 
 142                         if (t == y) {
 143                                 k = 1;
 144                         } else if (t > y) {
 145                                 n -= 1;
 146                                 t = quater + (y - t) * quater;
 147                         } else {
 148                                 t = (y - t) * quater;
 149                         }
 150                 } else {                                /* k = Prec-3 */
 151                         n = LDBL_LEAST_SIGNIF_U(y) & 7;     /* 3 LSb of z */
 152                         k = 1;
 153                 }
 154 
 155                 if (k) {                /* x = N/4 */
 156                         if ((n & 1) != 0)
 157                                 y = sqrth + tiny;
 158                         else
 159                                 y = (n & 2) == 0 ? zero : one;
 160 
 161                         if ((n & 4) != 0)
 162                                 y = -y;
 163                 } else {
 164                         if ((n & 1) != 0)
 165                                 t = quater - t;
 166 
 167                         if (((n + (n & 1)) & 2) == 0)
 168                                 y = __k_sinl(pi * t, zero);
 169                         else
 170                                 y = __k_cosl(pi * t, zero);
 171 
 172                         if ((n & 4) != 0)
 173                                 y = -y;
 174                 }
 175         }
 176 
 177         return (hx >= 0 ? y : -y);
 178 }
 179 
 180 #undef U
 181 #undef LDBL_LEAST_SIGNIF_U
 182 #undef I
 183 #undef LDBL_MOST_SIGNIF_I