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 } 183