125c28e83SPiotr Jasiukajtis /*
225c28e83SPiotr Jasiukajtis * CDDL HEADER START
325c28e83SPiotr Jasiukajtis *
425c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the
525c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License").
625c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License.
725c28e83SPiotr Jasiukajtis *
825c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
925c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
1025c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions
1125c28e83SPiotr Jasiukajtis * and limitations under the License.
1225c28e83SPiotr Jasiukajtis *
1325c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
1425c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
1525c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
1625c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
1725c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
1825c28e83SPiotr Jasiukajtis *
1925c28e83SPiotr Jasiukajtis * CDDL HEADER END
2025c28e83SPiotr Jasiukajtis */
2125c28e83SPiotr Jasiukajtis /*
2225c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
2325c28e83SPiotr Jasiukajtis */
2425c28e83SPiotr Jasiukajtis /*
2525c28e83SPiotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
2625c28e83SPiotr Jasiukajtis * Use is subject to license terms.
2725c28e83SPiotr Jasiukajtis */
2825c28e83SPiotr Jasiukajtis
2925c28e83SPiotr Jasiukajtis #pragma weak clog = __clog
3025c28e83SPiotr Jasiukajtis
3125c28e83SPiotr Jasiukajtis /* INDENT OFF */
3225c28e83SPiotr Jasiukajtis /*
3325c28e83SPiotr Jasiukajtis * dcomplex clog(dcomplex z);
3425c28e83SPiotr Jasiukajtis *
3525c28e83SPiotr Jasiukajtis * _________
3625c28e83SPiotr Jasiukajtis * / 2 2 -1 y
3725c28e83SPiotr Jasiukajtis * log(x+iy) = log(\/ x + y ) + i tan (---)
3825c28e83SPiotr Jasiukajtis * x
3925c28e83SPiotr Jasiukajtis *
4025c28e83SPiotr Jasiukajtis * 1 2 2 -1 y
4125c28e83SPiotr Jasiukajtis * = --- log(x + y ) + i tan (---)
4225c28e83SPiotr Jasiukajtis * 2 x
4325c28e83SPiotr Jasiukajtis *
4425c28e83SPiotr Jasiukajtis * Note that the arctangent ranges from -PI to +PI, thus the imaginary
4525c28e83SPiotr Jasiukajtis * part of clog is atan2(y,x).
4625c28e83SPiotr Jasiukajtis *
4725c28e83SPiotr Jasiukajtis * EXCEPTION CASES (conform to ISO/IEC 9899:1999(E)):
4825c28e83SPiotr Jasiukajtis * clog(-0 + i 0 ) = -inf + i pi
4925c28e83SPiotr Jasiukajtis * clog( 0 + i 0 ) = -inf + i 0
5025c28e83SPiotr Jasiukajtis * clog( x + i inf ) = -inf + i pi/2, for finite x
5125c28e83SPiotr Jasiukajtis * clog( x + i NaN ) = NaN + i NaN with invalid for finite x
5225c28e83SPiotr Jasiukajtis * clog(-inf + iy )= +inf + i pi, for finite positive-signed y
5325c28e83SPiotr Jasiukajtis * clog(+inf + iy )= +inf + i 0 , for finite positive-signed y
5425c28e83SPiotr Jasiukajtis * clog(-inf + i inf)= inf + i 3pi/4
5525c28e83SPiotr Jasiukajtis * clog(+inf + i inf)= inf + i pi/4
5625c28e83SPiotr Jasiukajtis * clog(+-inf+ i NaN)= inf + i NaN
5725c28e83SPiotr Jasiukajtis * clog(NaN + i y )= NaN + i NaN for finite y
5825c28e83SPiotr Jasiukajtis * clog(NaN + i inf)= inf + i NaN
5925c28e83SPiotr Jasiukajtis * clog(NaN + i NaN)= NaN + i NaN
6025c28e83SPiotr Jasiukajtis */
6125c28e83SPiotr Jasiukajtis /* INDENT ON */
6225c28e83SPiotr Jasiukajtis
6325c28e83SPiotr Jasiukajtis #include <math.h> /* atan2/fabs/log/log1p */
6425c28e83SPiotr Jasiukajtis #include "complex_wrapper.h"
6525c28e83SPiotr Jasiukajtis #include "libm_protos.h" /* __k_clog_r */
6625c28e83SPiotr Jasiukajtis
6725c28e83SPiotr Jasiukajtis
6825c28e83SPiotr Jasiukajtis static const double half = 0.5, one = 1.0;
6925c28e83SPiotr Jasiukajtis
7025c28e83SPiotr Jasiukajtis dcomplex
__clog(dcomplex z)71*ddc0e0b5SRichard Lowe __clog(dcomplex z) {
7225c28e83SPiotr Jasiukajtis dcomplex ans;
7325c28e83SPiotr Jasiukajtis double x, y, t, ax, ay, w;
7425c28e83SPiotr Jasiukajtis int n, ix, iy, hx, hy;
7525c28e83SPiotr Jasiukajtis unsigned lx, ly;
7625c28e83SPiotr Jasiukajtis
7725c28e83SPiotr Jasiukajtis x = D_RE(z);
7825c28e83SPiotr Jasiukajtis y = D_IM(z);
7925c28e83SPiotr Jasiukajtis hx = HI_WORD(x);
8025c28e83SPiotr Jasiukajtis lx = LO_WORD(x);
8125c28e83SPiotr Jasiukajtis hy = HI_WORD(y);
8225c28e83SPiotr Jasiukajtis ly = LO_WORD(y);
8325c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff;
8425c28e83SPiotr Jasiukajtis iy = hy & 0x7fffffff;
8525c28e83SPiotr Jasiukajtis ay = fabs(y);
8625c28e83SPiotr Jasiukajtis ax = fabs(x);
8725c28e83SPiotr Jasiukajtis D_IM(ans) = carg(z);
8825c28e83SPiotr Jasiukajtis if (ix < iy || (ix == iy && lx < ly)) {
8925c28e83SPiotr Jasiukajtis /* swap x and y to force ax >= ay */
9025c28e83SPiotr Jasiukajtis t = ax;
9125c28e83SPiotr Jasiukajtis ax = ay;
9225c28e83SPiotr Jasiukajtis ay = t;
9325c28e83SPiotr Jasiukajtis n = ix, ix = iy;
9425c28e83SPiotr Jasiukajtis iy = n;
9525c28e83SPiotr Jasiukajtis n = lx, lx = ly;
9625c28e83SPiotr Jasiukajtis ly = n;
9725c28e83SPiotr Jasiukajtis }
9825c28e83SPiotr Jasiukajtis n = (ix - iy) >> 20;
9925c28e83SPiotr Jasiukajtis if (ix >= 0x7ff00000) { /* x or y is Inf or NaN */
10025c28e83SPiotr Jasiukajtis if (ISINF(ix, lx))
10125c28e83SPiotr Jasiukajtis D_RE(ans) = ax;
10225c28e83SPiotr Jasiukajtis else if (ISINF(iy, ly))
10325c28e83SPiotr Jasiukajtis D_RE(ans) = ay;
10425c28e83SPiotr Jasiukajtis else
10525c28e83SPiotr Jasiukajtis D_RE(ans) = ax * ay;
10625c28e83SPiotr Jasiukajtis } else if ((iy | ly) == 0) {
10725c28e83SPiotr Jasiukajtis D_RE(ans) = ((ix | lx) == 0)? -one / ax : log(ax);
10825c28e83SPiotr Jasiukajtis } else if (((0x3fffffff - ix) ^ (ix - 0x3fe00000)) >= 0) {
10925c28e83SPiotr Jasiukajtis /* 0.5 <= x < 2 */
11025c28e83SPiotr Jasiukajtis if (ix >= 0x3ff00000) {
11125c28e83SPiotr Jasiukajtis if (((ix - 0x3ff00000) | lx) == 0)
11225c28e83SPiotr Jasiukajtis D_RE(ans) = half * log1p(ay * ay);
11325c28e83SPiotr Jasiukajtis else if (n >= 60)
11425c28e83SPiotr Jasiukajtis D_RE(ans) = log(ax);
11525c28e83SPiotr Jasiukajtis else
11625c28e83SPiotr Jasiukajtis D_RE(ans) = half * (log1p(ay * ay + (ax -
11725c28e83SPiotr Jasiukajtis one) * (ax + one)));
11825c28e83SPiotr Jasiukajtis } else if (n >= 60) {
11925c28e83SPiotr Jasiukajtis D_RE(ans) = log(ax);
12025c28e83SPiotr Jasiukajtis } else {
12125c28e83SPiotr Jasiukajtis D_RE(ans) = __k_clog_r(ax, ay, &w);
12225c28e83SPiotr Jasiukajtis }
12325c28e83SPiotr Jasiukajtis } else if (n >= 30) {
12425c28e83SPiotr Jasiukajtis D_RE(ans) = log(ax);
12525c28e83SPiotr Jasiukajtis } else if (ix < 0x5f300000 && iy >= 0x20b00000) {
12625c28e83SPiotr Jasiukajtis /* 2**-500< y < x < 2**500 */
12725c28e83SPiotr Jasiukajtis D_RE(ans) = half * log(ax * ax + ay * ay);
12825c28e83SPiotr Jasiukajtis } else {
12925c28e83SPiotr Jasiukajtis t = ay / ax;
13025c28e83SPiotr Jasiukajtis D_RE(ans) = log(ax) + half * log1p(t * t);
13125c28e83SPiotr Jasiukajtis }
13225c28e83SPiotr Jasiukajtis return (ans);
13325c28e83SPiotr Jasiukajtis }
134