usr/src/lib/libm/common/complex/cabs.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 #pragma weak __cabs = cabs
  30
  31 #include <math.h>
  32 #include "complex_wrapper.h"
  33
  34 /*
  35  * If C were the only standard we cared about, cabs could just call
  36  * hypot.  Unfortunately, various other standards say that hypot must
  37  * call matherr and/or set errno to ERANGE when the result overflows.
  38  * Since cabs should do neither of these things, we have to either
  39  * make hypot a wrapper on another internal function or duplicate
  40  * the hypot implementation here.  I've chosen to do the latter.
  41  */
  42
  43 static const double
  44         zero = 0.0,
  45         onep1u = 1.00000000000000022204e+00,    /* 0x3ff00000 1 = 1+2**-52 */
  46         twom53 = 1.11022302462515654042e-16,    /* 0x3ca00000 0 = 2**-53 */
  47         twom768 = 6.441148769597133308e-232,    /* 2^-768 */
  48         two768  = 1.552518092300708935e+231;    /* 2^768 */
  49
  50 double
  51 cabs(dcomplex z)
  52 {
  53         double          x, y, xh, yh, w, ax, ay;
  54         int             i, j, nx, ny, ix, iy, iscale = 0;
  55         unsigned        lx, ly;
  56
  57         x = D_RE(z);
  58         y = D_IM(z);
  59
  60         ix = ((int *)&x)[HIWORD] & ~0x80000000;
  61         lx = ((int *)&x)[LOWORD];
  62         iy = ((int *)&y)[HIWORD] & ~0x80000000;
  63         ly = ((int *)&y)[LOWORD];
  64
  65         /* force ax = |x| ~>~ ay = |y| */
  66         if (iy > ix) {
  67                 ax = fabs(y);
  68                 ay = fabs(x);
  69                 i = ix;
  70                 ix = iy;
  71                 iy = i;
  72                 i = lx;
  73                 lx = ly;
  74                 ly = i;
  75         } else {
  76                 ax = fabs(x);
  77                 ay = fabs(y);
  78         }
  79         nx = ix >> 20;
  80         ny = iy >> 20;
  81         j  = nx - ny;
  82
  83         if (nx >= 0x5f3) {
  84                 /* x >= 2^500 (x*x or y*y may overflow) */
  85                 if (nx == 0x7ff) {
  86                         /* inf or NaN, signal of sNaN */
  87                         if (((ix - 0x7ff00000) | lx) == 0)
  88                                 return ((ax == ay)? ay : ax);
  89                         else if (((iy - 0x7ff00000) | ly) == 0)
  90                                 return ((ay == ax)? ax : ay);
  91                         else
  92                                 return (ax * ay);
  93                 } else if (j > 32) {
  94                         /* x >> y */
  95                         if (j <= 53)
  96                                 ay *= twom53;
  97                         ax += ay;
  98                         return (ax);
  99                 }
 100                 ax *= twom768;
 101                 ay *= twom768;
 102                 iscale = 2;
 103                 ix -= 768 << 20;
 104                 iy -= 768 << 20;
 105         } else if (ny < 0x23d) {
 106                 /* y < 2^-450 (x*x or y*y may underflow) */
 107                 if ((ix | lx) == 0)
 108                         return (ay);
 109                 if ((iy | ly) == 0)
 110                         return (ax);
 111                 if (j > 53)             /* x >> y */
 112                         return (ax + ay);
 113                 iscale = 1;
 114                 ax *= two768;
 115                 ay *= two768;
 116                 if (nx == 0) {
 117                         if (ax == zero) /* guard subnormal flush to zero */
 118                                 return (ax);
 119                         ix = ((int *)&ax)[HIWORD];
 120                 } else {
 121                         ix += 768 << 20;
 122                 }
 123                 if (ny == 0) {
 124                         if (ay == zero) /* guard subnormal flush to zero */
 125                                 return (ax * twom768);
 126                         iy = ((int *)&ay)[HIWORD];
 127                 } else {
 128                         iy += 768 << 20;
 129                 }
 130                 j = (ix >> 20) - (iy >> 20);
 131                 if (j > 32) {
 132                         /* x >> y */
 133                         if (j <= 53)
 134                                 ay *= twom53;
 135                         return ((ax + ay) * twom768);
 136                 }
 137         } else if (j > 32) {
 138                 /* x >> y */
 139                 if (j <= 53)
 140                         ay *= twom53;
 141                 return (ax + ay);
 142         }
 143
 144         /*
 145          * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32.
 146          * First check rounding mode by comparing onep1u*onep1u with onep1u
 147          * + twom53.  Make sure the computation is done at run-time.
 148          */
 149         if (((lx | ly) << 5) == 0) {
 150                 ay = ay * ay;
 151                 ax += ay / (ax + sqrt(ax * ax + ay));
 152         } else if (onep1u * onep1u != onep1u + twom53) {
 153                 /* round-to-zero, positive, negative mode */
 154                 /* magic formula with less than an ulp error */
 155                 w = sqrt(ax * ax + ay * ay);
 156                 ax += ay / ((ax + w) / ay);
 157         } else {
 158                 /* round-to-nearest mode */
 159                 w = ax - ay;
 160                 if (w > ay) {
 161                         ((int *)&xh)[HIWORD] = ix;
 162                         ((int *)&xh)[LOWORD] = 0;
 163                         ay = ay * ay + (ax - xh) * (ax + xh);
 164                         ax = sqrt(xh * xh + ay);
 165                 } else {
 166                         ax = ax + ax;
 167                         ((int *)&xh)[HIWORD] = ix + 0x00100000;
 168                         ((int *)&xh)[LOWORD] = 0;
 169                         ((int *)&yh)[HIWORD] = iy;
 170                         ((int *)&yh)[LOWORD] = 0;
 171                         ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
 172                         ax = sqrt(xh * yh + ay);
 173                 }
 174         }
 175         if (iscale > 0) {
 176                 if (iscale == 1)
 177                         ax *= twom768;
 178                 else
 179                         ax *= two768;   /* must generate side effect here */
 180         }
 181         return (ax);
 182 }