usr/src/lib/libm/common/C/__rem_pio2.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  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28
  29 /*
  30  * __rem_pio2(x, y) passes back a better-than-double-precision
  31  * approximation to x mod pi/2 in y[0]+y[1] and returns an integer
  32  * congruent mod 8 to the integer part of x/(pi/2).
  33  *
  34  * This implementation tacitly assumes that x is finite and at
  35  * least about pi/4 in magnitude.
  36  */
  37
  38 #include "libm.h"
  39
  40 extern const int _TBL_ipio2_inf[];
  41
  42 /* INDENT OFF */
  43 /*
  44  * invpio2:  53 bits of 2/pi
  45  * pio2_1:   first  33 bit of pi/2
  46  * pio2_1t:  pi/2 - pio2_1
  47  * pio2_2:   second 33 bit of pi/2
  48  * pio2_2t:  pi/2 - pio2_2
  49  * pio2_3:   third  33 bit of pi/2
  50  * pio2_3t:  pi/2 - pio2_3
  51  */
  52 static const double
  53         half    = 0.5,
  54         invpio2 = 0.636619772367581343075535,   /* 2^ -1  * 1.45F306DC9C883 */
  55         pio2_1  = 1.570796326734125614166,      /* 2^  0  * 1.921FB54400000 */
  56         pio2_1t = 6.077100506506192601475e-11,  /* 2^-34  * 1.0B4611A626331 */
  57         pio2_2  = 6.077100506303965976596e-11,  /* 2^-34  * 1.0B4611A600000 */
  58         pio2_2t = 2.022266248795950732400e-21,  /* 2^-69  * 1.3198A2E037073 */
  59         pio2_3  = 2.022266248711166455796e-21,  /* 2^-69  * 1.3198A2E000000 */
  60         pio2_3t = 8.478427660368899643959e-32;  /* 2^-104 * 1.B839A252049C1 */
  61 /* INDENT ON */
  62
  63 int
  64 __rem_pio2(double x, double *y) {
  65         double  w, t, r, fn;
  66         double  tx[3];
  67         int     e0, i, j, nx, n, ix, hx, lx;
  68
  69         hx = ((int *)&x)[HIWORD];
  70         ix = hx & 0x7fffffff;
  71
  72         if (ix < 0x4002d97c) {
  73                 /* |x| < 3pi/4, special case with n=1 */
  74                 t = fabs(x) - pio2_1;
  75                 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
  76                         y[0] = t - pio2_1t;
  77                         y[1] = (t - y[0]) - pio2_1t;
  78                 } else {                /* near pi/2, use 33+33+53 bit pi */
  79                         t -= pio2_2;
  80                         y[0] = t - pio2_2t;
  81                         y[1] = (t - y[0]) - pio2_2t;
  82                 }
  83                 if (hx < 0) {
  84                         y[0] = -y[0];
  85                         y[1] = -y[1];
  86                         return (-1);
  87                 }
  88                 return (1);
  89         }
  90
  91         if (ix <= 0x413921fb) {
  92                 /* |x| <= 2^19 pi */
  93                 t = fabs(x);
  94                 n = (int)(t * invpio2 + half);
  95                 fn = (double)n;
  96                 r = t - fn * pio2_1;
  97                 j = ix >> 20;
  98                 w = fn * pio2_1t;       /* 1st round good to 85 bit */
  99                 y[0] = r - w;
 100                 i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
 101                 if (i > 16) {   /* 2nd iteration (rare) */
 102                         /* 2nd round good to 118 bit */
 103                         if (i < 35) {
 104                                 t = r;  /* r-fn*pio2_2 may not be exact */
 105                                 w = fn * pio2_2;
 106                                 r = t - w;
 107                                 w = fn * pio2_2t - ((t - r) - w);
 108                                 y[0] = r - w;
 109                         } else {
 110                                 r -= fn * pio2_2;
 111                                 w = fn * pio2_2t;
 112                                 y[0] = r - w;
 113                                 i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
 114                                 if (i > 49) {
 115                                         /* 3rd iteration (extremely rare) */
 116                                         if (i < 68) {
 117                                                 t = r;
 118                                                 w = fn * pio2_3;
 119                                                 r = t - w;
 120                                                 w = fn * pio2_3t -
 121                                                     ((t - r) - w);
 122                                                 y[0] = r - w;
 123                                         } else {
 124                                                 /*
 125                                                  * 3rd round good to 151 bits;
 126                                                  * covered all possible cases
 127                                                  */
 128                                                 r -= fn * pio2_3;
 129                                                 w = fn * pio2_3t;
 130                                                 y[0] = r - w;
 131                                         }
 132                                 }
 133                         }
 134                 }
 135                 y[1] = (r - y[0]) - w;
 136                 if (hx < 0) {
 137                         y[0] = -y[0];
 138                         y[1] = -y[1];
 139                         return (-n);
 140                 }
 141                 return (n);
 142         }
 143
 144         e0 = (ix >> 20) - 1046; /* e0 = ilogb(x)-23; */
 145
 146         /* break x into three 24 bit pieces */
 147         lx = ((int *)&x)[LOWORD];
 148         i = (lx & 0x1f) << 19;
 149         tx[2] = (double)i;
 150         j = (lx >> 5) & 0xffffff;
 151         tx[1] = (double)j;
 152         tx[0] = (double)((((ix & 0xfffff) | 0x100000) << 3) |
 153             ((unsigned)lx >> 29));
 154         nx = 3;
 155         if (i == 0) {
 156                 /* skip zero term */
 157                 nx--;
 158                 if (j == 0)
 159                         nx--;
 160         }
 161         n = __rem_pio2m(tx, y, e0, nx, 2, _TBL_ipio2_inf);
 162         if (hx < 0) {
 163                 y[0] = -y[0];
 164                 y[1] = -y[1];
 165                 return (-n);
 166         }
 167         return (n);
 168 }