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 clog = __clog 30 31 /* INDENT OFF */ 32 /* 33 * dcomplex clog(dcomplex z); 34 * 35 * _________ 36 * / 2 2 -1 y 37 * log(x+iy) = log(\/ x + y ) + i tan (---) 38 * x 39 * 40 * 1 2 2 -1 y 41 * = --- log(x + y ) + i tan (---) 42 * 2 x 43 * 44 * Note that the arctangent ranges from -PI to +PI, thus the imaginary 45 * part of clog is atan2(y,x). 46 * 47 * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)): 48 * clog(-0 + i 0 ) = -inf + i pi 49 * clog( 0 + i 0 ) = -inf + i 0 50 * clog( x + i inf ) = -inf + i pi/2, for finite x 51 * clog( x + i NaN ) = NaN + i NaN with invalid for finite x 52 * clog(-inf + iy )= +inf + i pi, for finite positive-signed y 53 * clog(+inf + iy )= +inf + i 0 , for finite positive-signed y 54 * clog(-inf + i inf)= inf + i 3pi/4 55 * clog(+inf + i inf)= inf + i pi/4 56 * clog(+-inf+ i NaN)= inf + i NaN 57 * clog(NaN + i y )= NaN + i NaN for finite y 58 * clog(NaN + i inf)= inf + i NaN 59 * clog(NaN + i NaN)= NaN + i NaN 60 */ 61 /* INDENT ON */ 62 63 #include "libm_synonyms.h" 64 #include <math.h> /* atan2/fabs/log/log1p */ 65 #include "complex_wrapper.h" 66 #include "libm_protos.h" /* __k_clog_r */ 67 68 69 static const double half = 0.5, one = 1.0; 70 71 dcomplex 72 clog(dcomplex z) { 73 dcomplex ans; 74 double x, y, t, ax, ay, w; 75 int n, ix, iy, hx, hy; 76 unsigned lx, ly; 77 78 x = D_RE(z); 79 y = D_IM(z); 80 hx = HI_WORD(x); 81 lx = LO_WORD(x); 82 hy = HI_WORD(y); 83 ly = LO_WORD(y); 84 ix = hx & 0x7fffffff; 85 iy = hy & 0x7fffffff; 86 ay = fabs(y); 87 ax = fabs(x); 88 D_IM(ans) = carg(z); 89 if (ix < iy || (ix == iy && lx < ly)) { 90 /* swap x and y to force ax >= ay */ 91 t = ax; 92 ax = ay; 93 ay = t; 94 n = ix, ix = iy; 95 iy = n; 96 n = lx, lx = ly; 97 ly = n; 98 } 99 n = (ix - iy) >> 20; 100 if (ix >= 0x7ff00000) { /* x or y is Inf or NaN */ 101 if (ISINF(ix, lx)) 102 D_RE(ans) = ax; 103 else if (ISINF(iy, ly)) 104 D_RE(ans) = ay; 105 else 106 D_RE(ans) = ax * ay; 107 } else if ((iy | ly) == 0) { 108 D_RE(ans) = ((ix | lx) == 0)? -one / ax : log(ax); 109 } else if (((0x3fffffff - ix) ^ (ix - 0x3fe00000)) >= 0) { 110 /* 0.5 <= x < 2 */ 111 if (ix >= 0x3ff00000) { 112 if (((ix - 0x3ff00000) | lx) == 0) 113 D_RE(ans) = half * log1p(ay * ay); 114 else if (n >= 60) 115 D_RE(ans) = log(ax); 116 else 117 D_RE(ans) = half * (log1p(ay * ay + (ax - 118 one) * (ax + one))); 119 } else if (n >= 60) { 120 D_RE(ans) = log(ax); 121 } else { 122 D_RE(ans) = __k_clog_r(ax, ay, &w); 123 } 124 } else if (n >= 30) { 125 D_RE(ans) = log(ax); 126 } else if (ix < 0x5f300000 && iy >= 0x20b00000) { 127 /* 2**-500< y < x < 2**500 */ 128 D_RE(ans) = half * log(ax * ax + ay * ay); 129 } else { 130 t = ay / ax; 131 D_RE(ans) = log(ax) + half * log1p(t * t); 132 } 133 return (ans); 134 } 135