common/complex/catanf.c

	catanf.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak catanf = __catanf

#include "libm.h"
#include "complex_wrapper.h"

#if defined(__i386) && !defined(__amd64)
extern int __swapRP(int);
#endif

static const float
    pi_2 = 1.570796326794896558e+00F,
    zero = 0.0F,
    half = 0.5F,
    two = 2.0F,
    one = 1.0F;

fcomplex
catanf(fcomplex z) {
    fcomplex    ans;
    float       x, y, ax, ay, t;
    double      dx, dy, dt;
    int     hx, hy, ix, iy;

    x = F_RE(z);
    y = F_IM(z);
    ax = fabsf(x);
    ay = fabsf(y);
    hx = THE_WORD(x);
    hy = THE_WORD(y);
    ix = hx & 0x7fffffff;
    iy = hy & 0x7fffffff;

    if (ix >= 0x7f800000) {     /* x is inf or NaN */
        if (ix == 0x7f800000) {
            F_RE(ans) = pi_2;
            F_IM(ans) = zero;
        } else {
            F_RE(ans) = x * x;
            if (iy == 0 || iy == 0x7f800000)
                F_IM(ans) = zero;
            else
                F_IM(ans) = (fabsf(y) - ay) / (fabsf(y) - ay);
        }
    } else if (iy >= 0x7f800000) {  /* y is inf or NaN */
        if (iy == 0x7f800000) {
            F_RE(ans) = pi_2;
            F_IM(ans) = zero;
        } else {
            F_RE(ans) = (fabsf(x) - ax) / (fabsf(x) - ax);
            F_IM(ans) = y * y;
        }
    } else if (ix == 0) {
        /* INDENT OFF */
        /*
         * x = 0
         *      1                            1
         * A = --- * atan2(2x, 1-x*x-y*y) = --- atan2(0,1-|y|)
         *      2                            2
         *
         *     1     [ (y+1)*(y+1) ]   1          2      1         2y
         * B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
         *     4     [ (y-1)*(y-1) ]   2         y-1     2         1-y
         */
        /* INDENT ON */
        t = one - ay;
        if (iy == 0x3f800000) {
            /* y=1: catan(0,1)=(0,+inf) with 1/0 signal */
            F_IM(ans) = ay / ax;
            F_RE(ans) = zero;
        } else if (iy > 0x3f800000) {   /* y>1 */
            F_IM(ans) = half * log1pf(two / (-t));
            F_RE(ans) = pi_2;
        } else {        /* y<1 */
            F_IM(ans) = half * log1pf((ay + ay) / t);
            F_RE(ans) = zero;
        }
    } else {
        /* INDENT OFF */
        /*
         * use double precision x,y
         *      1
         * A = --- * atan2(2x, 1-x*x-y*y)
         *      2
         *
         *     1     [ x*x+(y+1)*(y+1) ]   1               4y
         * B = - log [ --------------- ] = - log (1+ -----------------)
         *     4     [ x*x+(y-1)*(y-1) ]   4         x*x + (y-1)*(y-1)
         */
        /* INDENT ON */
#if defined(__i386) && !defined(__amd64)
        int rp = __swapRP(fp_extended);
#endif
        dx = (double)ax;
        dy = (double)ay;
        F_RE(ans) = (float)(0.5 * atan2(dx + dx,
            1.0 - dx * dx - dy * dy));
        dt = dy - 1.0;
        F_IM(ans) = (float)(0.25 * log1p(4.0 * dy /
            (dx * dx + dt * dt)));
#if defined(__i386) && !defined(__amd64)
        if (rp != fp_extended)
            (void) __swapRP(rp);
#endif
    }
    if (hx < 0)
        F_RE(ans) = -F_RE(ans);
    if (hy < 0)
        F_IM(ans) = -F_IM(ans);
    return (ans);
}