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 <math.h> /* atan2/fabs/log/log1p */ 64 #include "complex_wrapper.h" 65 #include "libm_protos.h" /* __k_clog_r */ 66 67 68 static const double half = 0.5, one = 1.0; 69 70 dcomplex 71 __clog(dcomplex z) { 72 dcomplex ans; 73 double x, y, t, ax, ay, w; 74 int n, ix, iy, hx, hy; 75 unsigned lx, ly; 76 77 x = D_RE(z); 78 y = D_IM(z); 79 hx = HI_WORD(x); 80 lx = LO_WORD(x); 81 hy = HI_WORD(y); 82 ly = LO_WORD(y); 83 ix = hx & 0x7fffffff; 84 iy = hy & 0x7fffffff; 85 ay = fabs(y); 86 ax = fabs(x); 87 D_IM(ans) = carg(z); 88 if (ix < iy || (ix == iy && lx < ly)) { 89 /* swap x and y to force ax >= ay */ 90 t = ax; 91 ax = ay; 92 ay = t; 93 n = ix, ix = iy; 94 iy = n; 95 n = lx, lx = ly; 96 ly = n; 97 } 98 n = (ix - iy) >> 20; 99 if (ix >= 0x7ff00000) { /* x or y is Inf or NaN */ 100 if (ISINF(ix, lx)) 101 D_RE(ans) = ax; 102 else if (ISINF(iy, ly)) 103 D_RE(ans) = ay; 104 else 105 D_RE(ans) = ax * ay; 106 } else if ((iy | ly) == 0) { 107 D_RE(ans) = ((ix | lx) == 0)? -one / ax : log(ax); 108 } else if (((0x3fffffff - ix) ^ (ix - 0x3fe00000)) >= 0) { 109 /* 0.5 <= x < 2 */ 110 if (ix >= 0x3ff00000) { 111 if (((ix - 0x3ff00000) | lx) == 0) 112 D_RE(ans) = half * log1p(ay * ay); 113 else if (n >= 60) 114 D_RE(ans) = log(ax); 115 else 116 D_RE(ans) = half * (log1p(ay * ay + (ax - 117 one) * (ax + one))); 118 } else if (n >= 60) { 119 D_RE(ans) = log(ax); 120 } else { 121 D_RE(ans) = __k_clog_r(ax, ay, &w); 122 } 123 } else if (n >= 30) { 124 D_RE(ans) = log(ax); 125 } else if (ix < 0x5f300000 && iy >= 0x20b00000) { 126 /* 2**-500< y < x < 2**500 */ 127 D_RE(ans) = half * log(ax * ax + ay * ay); 128 } else { 129 t = ay / ax; 130 D_RE(ans) = log(ax) + half * log1p(t * t); 131 } 132 return (ans); 133 } 134