usr/src/lib/libm/common/LD/sinpil.c

   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 /* long double sinpil(long double x),
  31  * return long double precision sinl(pi*x).
  32  *
  33  * Algorithm, 10/17/2002, K.C. Ng
  34  * ------------------------------
  35  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
  36  *      1. If y == z, then x is a multiple of pi/4. Return the following values:
  37  *             ---------------------------------------------------
  38  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
  39  *             ---------------------------------------------------
  40  *              000  0.00       +0 ___       +1 ___      +0
  41  *              001  0.25       +\/0.5       +\/0.5      +1
  42  *              010  0.50       +1 ___       +0 ___      +inf
  43  *              011  0.75       +\/0.5       -\/0.5      -1
  44  *              100  1.00       -0 ___       -1 ___      +0
  45  *              101  1.25       -\/0.5       -\/0.5      +1
  46  *              110  1.50       -1 ___       -0 ___      +inf
  47  *              111  1.75       -\/0.5       +\/0.5      -1
  48  *             ---------------------------------------------------
  49  *      2. Otherwise,
  50  *             ---------------------------------------------------
  51  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
  52  *             ---------------------------------------------------
  53  *              000  (y-z)/4     sinpi(t)     cospi(t)    tanpi(t)
  54  *              001  (z+1-y)/4   cospi(t)     sinpi(t)    1/tanpi(t)
  55  *              010  (y-z)/4     cospi(t)    -sinpi(t)   -1/tanpi(t)
  56  *              011  (z+1-y)/4   sinpi(t)    -cospi(t)   -tanpi(t)
  57  *              100  (y-z)/4    -sinpi(t)    -cospi(t)    tanpi(t)
  58  *              101  (z+1-y)/4  -cospi(t)    -sinpi(t)    1/tanpi(t)
  59  *              110  (y-z)/4    -cospi(t)     sinpi(t)   -1/tanpi(t)
  60  *              111  (z+1-y)/4  -sinpi(t)     cospi(t)   -tanpi(t)
  61  *             ---------------------------------------------------
  62  *
  63  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
  64  * This will return a result with error slightly more than one ulp (but less
  65  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
  66  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
  67  * instead.
  68  */
  69
  70 #include "libm.h"
  71 #include "longdouble.h"
  72
  73 #include <sys/isa_defs.h>
  74
  75 #define I(q, m) ((int *) &(q))[m]
  76 #define U(q, m) ((unsigned *) &(q))[m]
  77 #if defined(__i386) || defined(__amd64)
  78 #define LDBL_MOST_SIGNIF_I(ld)  ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
  79 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
  80 #define PREC    64
  81 #define PRECM1  63
  82 #define PRECM2  62
  83 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
  84 #else
  85 #define LDBL_MOST_SIGNIF_I(ld)  I(ld, 0)
  86 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
  87 #define PREC    113
  88 #define PRECM1  112
  89 #define PRECM2  111
  90 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
  91 #endif
  92
  93 static const long double
  94 zero    = 0.0L,
  95 quater  = 0.25L,
  96 one     = 1.0L,
  97 pi      = 3.141592653589793238462643383279502884197e+0000L,
  98 sqrth   = 0.707106781186547524400844362104849039284835937688474,
  99 tiny    = 1.0e-100;
 100
 101 long double
 102 sinpil(long double x) {
 103         long double y, z, t;
 104         int hx, n, k;
 105         unsigned lx;
 106
 107         hx = LDBL_MOST_SIGNIF_I(x);
 108         lx = LDBL_LEAST_SIGNIF_U(x);
 109         k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
 110         if (k >= PRECM2) {              /* |x| >= 2**(Prec-2) */
 111                 if (k >= 16384)
 112                         y = x - x;
 113                 else {
 114                         if (k >= PREC)
 115                                 y = zero;
 116                         else if (k == PRECM1)
 117                                 y = (lx & 1) == 0 ? zero: -zero;
 118                         else {  /* k = Prec - 2 */
 119                                 y = (lx & 1) == 0 ? zero : one;
 120                                 if ((lx & 2) != 0)
 121                                         y = -y;
 122                         }
 123                 }
 124         }
 125         else if (k < -2)        /* |x| < 0.25 */
 126                 y = __k_sinl(pi * fabsl(x), zero);
 127         else {
 128                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 129                 y = 4.0L * fabsl(x);
 130                 if (k < PRECM2) {
 131                         z = y + twoPRECM2;
 132                         n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
 133                         t = z - twoPRECM2;
 134                         k = 0;
 135                         if (t == y)
 136                                 k = 1;
 137                         else if (t > y) {
 138                                 n -= 1;
 139                                 t = quater + (y - t) * quater;
 140                         }
 141                         else
 142                                 t = (y - t) * quater;
 143                 }
 144                 else {  /* k = Prec-3 */
 145                         n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
 146                         k = 1;
 147                 }
 148                 if (k) {        /* x = N/4 */
 149                         if ((n & 1) != 0)
 150                                 y = sqrth + tiny;
 151                         else
 152                                 y = (n & 2) == 0 ? zero : one;
 153                         if ((n & 4) != 0)
 154                                 y = -y;
 155                 }
 156                 else {
 157                         if ((n & 1) != 0)
 158                                 t = quater - t;
 159                         if (((n + (n & 1)) & 2) == 0)
 160                                 y = __k_sinl(pi * t, zero);
 161                         else
 162                                 y = __k_cosl(pi * t, zero);
 163                         if ((n & 4) != 0)
 164                                 y = -y;
 165                 }
 166         }
 167         return hx >= 0 ? y : -y;
 168 }
 169 #undef U
 170 #undef LDBL_LEAST_SIGNIF_U
 171 #undef I
 172 #undef LDBL_MOST_SIGNIF_I