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  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak sinpil = __sinpil
  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 "libm_synonyms.h"
  74 #include "longdouble.h"
  75 
  76 #include <sys/isa_defs.h>
  77 
  78 #define I(q, m) ((int *) &(q))[m]
  79 #define U(q, m) ((unsigned *) &(q))[m]
  80 #if defined(__i386) || defined(__amd64)
  81 #define LDBL_MOST_SIGNIF_I(ld)  ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
  82 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
  83 #define PREC    64
  84 #define PRECM1  63
  85 #define PRECM2  62
  86 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
  87 #else
  88 #define LDBL_MOST_SIGNIF_I(ld)  I(ld, 0)
  89 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
  90 #define PREC    113
  91 #define PRECM1  112
  92 #define PRECM2  111
  93 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
  94 #endif
  95 
  96 static const long double
  97 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         long double y, z, t;
 107         int hx, n, k;
 108         unsigned lx;
 109 
 110         hx = LDBL_MOST_SIGNIF_I(x);
 111         lx = LDBL_LEAST_SIGNIF_U(x);
 112         k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
 113         if (k >= PRECM2) {           /* |x| >= 2**(Prec-2) */
 114                 if (k >= 16384)
 115                         y = x - x;
 116                 else {
 117                         if (k >= PREC)
 118                                 y = zero;
 119                         else if (k == PRECM1)
 120                                 y = (lx & 1) == 0 ? zero: -zero;
 121                         else {  /* k = Prec - 2 */
 122                                 y = (lx & 1) == 0 ? zero : one;
 123                                 if ((lx & 2) != 0)
 124                                         y = -y;
 125                         }
 126                 }
 127         }
 128         else if (k < -2)     /* |x| < 0.25 */
 129                 y = __k_sinl(pi * fabsl(x), zero);
 130         else {
 131                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 132                 y = 4.0L * fabsl(x);
 133                 if (k < PRECM2) {
 134                         z = y + twoPRECM2;
 135                         n = LDBL_LEAST_SIGNIF_U(z) & 7;     /* 3 LSb of z */
 136                         t = z - twoPRECM2;
 137                         k = 0;
 138                         if (t == y)
 139                                 k = 1;
 140                         else if (t > y) {
 141                                 n -= 1;
 142                                 t = quater + (y - t) * quater;
 143                         }
 144                         else
 145                                 t = (y - t) * quater;
 146                 }
 147                 else {  /* k = Prec-3 */
 148                         n = LDBL_LEAST_SIGNIF_U(y) & 7;     /* 3 LSb of z */
 149                         k = 1;
 150                 }
 151                 if (k) {        /* x = N/4 */
 152                         if ((n & 1) != 0)
 153                                 y = sqrth + tiny;
 154                         else
 155                                 y = (n & 2) == 0 ? zero : one;
 156                         if ((n & 4) != 0)
 157                                 y = -y;
 158                 }
 159                 else {
 160                         if ((n & 1) != 0)
 161                                 t = quater - t;
 162                         if (((n + (n & 1)) & 2) == 0)
 163                                 y = __k_sinl(pi * t, zero);
 164                         else
 165                                 y = __k_cosl(pi * t, zero);
 166                         if ((n & 4) != 0)
 167                                 y = -y;
 168                 }
 169         }
 170         return hx >= 0 ? y : -y;
 171 }
 172 #undef U
 173 #undef LDBL_LEAST_SIGNIF_U
 174 #undef I
 175 #undef LDBL_MOST_SIGNIF_I