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 "libm_synonyms.h" 32 #include <math.h> 33 #include "complex_wrapper.h" 34 35 /* 36 * If C were the only standard we cared about, cabs could just call 37 * hypot. Unfortunately, various other standards say that hypot must 38 * call matherr and/or set errno to ERANGE when the result overflows. 39 * Since cabs should do neither of these things, we have to either 40 * make hypot a wrapper on another internal function or duplicate 41 * the hypot implementation here. I've chosen to do the latter. 42 */ 43 44 static const double 45 zero = 0.0, 46 onep1u = 1.00000000000000022204e+00, /* 0x3ff00000 1 = 1+2**-52 */ 47 twom53 = 1.11022302462515654042e-16, /* 0x3ca00000 0 = 2**-53 */ 48 twom768 = 6.441148769597133308e-232, /* 2^-768 */ 49 two768 = 1.552518092300708935e+231; /* 2^768 */ 50 51 double 52 cabs(dcomplex z) 53 { 54 double x, y, xh, yh, w, ax, ay; 55 int i, j, nx, ny, ix, iy, iscale = 0; 56 unsigned lx, ly; 57 58 x = D_RE(z); 59 y = D_IM(z); 60 61 ix = ((int *)&x)[HIWORD] & ~0x80000000; 62 lx = ((int *)&x)[LOWORD]; 63 iy = ((int *)&y)[HIWORD] & ~0x80000000; 64 ly = ((int *)&y)[LOWORD]; 65 66 /* force ax = |x| ~>~ ay = |y| */ 67 if (iy > ix) { 68 ax = fabs(y); 69 ay = fabs(x); 70 i = ix; 71 ix = iy; 72 iy = i; 73 i = lx; 74 lx = ly; 75 ly = i; 76 } else { 77 ax = fabs(x); 78 ay = fabs(y); 79 } 80 nx = ix >> 20; 81 ny = iy >> 20; 82 j = nx - ny; 83 84 if (nx >= 0x5f3) { 85 /* x >= 2^500 (x*x or y*y may overflow) */ 86 if (nx == 0x7ff) { 87 /* inf or NaN, signal of sNaN */ 88 if (((ix - 0x7ff00000) | lx) == 0) 89 return ((ax == ay)? ay : ax); 90 else if (((iy - 0x7ff00000) | ly) == 0) 91 return ((ay == ax)? ax : ay); 92 else 93 return (ax * ay); 94 } else if (j > 32) { 95 /* x >> y */ 96 if (j <= 53) 97 ay *= twom53; 98 ax += ay; 99 return (ax); 100 } 101 ax *= twom768; 102 ay *= twom768; 103 iscale = 2; 104 ix -= 768 << 20; 105 iy -= 768 << 20; 106 } else if (ny < 0x23d) { 107 /* y < 2^-450 (x*x or y*y may underflow) */ 108 if ((ix | lx) == 0) 109 return (ay); 110 if ((iy | ly) == 0) 111 return (ax); 112 if (j > 53) /* x >> y */ 113 return (ax + ay); 114 iscale = 1; 115 ax *= two768; 116 ay *= two768; 117 if (nx == 0) { 118 if (ax == zero) /* guard subnormal flush to zero */ 119 return (ax); 120 ix = ((int *)&ax)[HIWORD]; 121 } else { 122 ix += 768 << 20; 123 } 124 if (ny == 0) { 125 if (ay == zero) /* guard subnormal flush to zero */ 126 return (ax * twom768); 127 iy = ((int *)&ay)[HIWORD]; 128 } else { 129 iy += 768 << 20; 130 } 131 j = (ix >> 20) - (iy >> 20); 132 if (j > 32) { 133 /* x >> y */ 134 if (j <= 53) 135 ay *= twom53; 136 return ((ax + ay) * twom768); 137 } 138 } else if (j > 32) { 139 /* x >> y */ 140 if (j <= 53) 141 ay *= twom53; 142 return (ax + ay); 143 } 144 145 /* 146 * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32. 147 * First check rounding mode by comparing onep1u*onep1u with onep1u 148 * + twom53. Make sure the computation is done at run-time. 149 */ 150 if (((lx | ly) << 5) == 0) { 151 ay = ay * ay; 152 ax += ay / (ax + sqrt(ax * ax + ay)); 153 } else if (onep1u * onep1u != onep1u + twom53) { 154 /* round-to-zero, positive, negative mode */ 155 /* magic formula with less than an ulp error */ 156 w = sqrt(ax * ax + ay * ay); 157 ax += ay / ((ax + w) / ay); 158 } else { 159 /* round-to-nearest mode */ 160 w = ax - ay; 161 if (w > ay) { 162 ((int *)&xh)[HIWORD] = ix; 163 ((int *)&xh)[LOWORD] = 0; 164 ay = ay * ay + (ax - xh) * (ax + xh); 165 ax = sqrt(xh * xh + ay); 166 } else { 167 ax = ax + ax; 168 ((int *)&xh)[HIWORD] = ix + 0x00100000; 169 ((int *)&xh)[LOWORD] = 0; 170 ((int *)&yh)[HIWORD] = iy; 171 ((int *)&yh)[LOWORD] = 0; 172 ay = w * w + ((ax - xh) * yh + (ay - yh) * ax); 173 ax = sqrt(xh * yh + ay); 174 } 175 } 176 if (iscale > 0) { 177 if (iscale == 1) 178 ax *= twom768; 179 else 180 ax *= two768; /* must generate side effect here */ 181 } 182 return (ax); 183 } 184