common/complex/cpowf.c

	cpowf.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 cpowf = __cpowf

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

extern void sincospi(double, double *, double *);
extern void sincospif(float, float *, float *);
extern double atan2pi(double, double);
extern float atan2pif(float, float);

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

static const double
    dpi = 3.1415926535897931160E0,  /* Hex 2^ 1 * 1.921FB54442D18 */
    dhalf = 0.5,
    dsqrt2 = 1.41421356237309514547,    /* 3FF6A09E 667F3BCD */
    dinvpi = 0.3183098861837906715377675;

static const float one = 1.0F, zero = 0.0F;

#define hiinf   0x7f800000

fcomplex
cpowf(fcomplex z, fcomplex w) {
    fcomplex    ans;
    float       x, y, u, v, t, c, s;
    double      dx, dy, du, dv, dt, dc, ds, dp, dq, dr;
    int     ix, iy, hx, hy, hv, hu, iu, iv, j;

    x = F_RE(z);
    y = F_IM(z);
    u = F_RE(w);
    v = F_IM(w);
    hx = THE_WORD(x);
    hy = THE_WORD(y);
    hu = THE_WORD(u);
    hv = THE_WORD(v);
    ix = hx & 0x7fffffff;
    iy = hy & 0x7fffffff;
    iu = hu & 0x7fffffff;
    iv = hv & 0x7fffffff;

    j = 0;
    if (iv == 0) {      /* z**(real) */
        if (hu == 0x3f800000) { /* (anything) ** 1  is itself */
            F_RE(ans) = x;
            F_IM(ans) = y;
        } else if (iu == 0) {   /* (anything) ** 0  is 1 */
            F_RE(ans) = one;
            F_IM(ans) = zero;
        } else if (iy == 0) {   /* (real)**(real) */
            F_IM(ans) = zero;
            if (hx < 0 && ix < hiinf && iu < hiinf) {
                /* -x ** u  is exp(i*pi*u)*pow(x,u) */
                t = powf(-x, u);
                sincospif(u, &s, &c);
                F_RE(ans) = (c == zero)? c: c * t;
                F_IM(ans) = (s == zero)? s: s * t;
            } else {
                F_RE(ans) = powf(x, u);
            }
        } else if (ix == 0 || ix >= hiinf || iy >= hiinf) {
            if (ix > hiinf || iy > hiinf || iu > hiinf) {
                F_RE(ans) = F_IM(ans) = x + y + u;
            } else {
                v = fabsf(y);
                if (ix != 0)
                    v += fabsf(x);
                t = atan2pif(y, x);
                sincospif(t * u, &s, &c);
                F_RE(ans) = (c == zero)? c: c * v;
                F_IM(ans) = (s == zero)? s: s * v;
            }
        } else if (ix == iy) {  /* if |x| == |y| */
#if defined(__i386) && !defined(__amd64)
            int rp = __swapRP(fp_extended);
#endif
            dx = (double)x;
            du = (double)u;
            dt = (hx >= 0)? 0.25 : 0.75;
            if (hy < 0)
                dt = -dt;
            dr = pow(dsqrt2 * dx, du);
            sincospi(dt * du, &ds, &dc);
            F_RE(ans) = (float)(dr * dc);
            F_IM(ans) = (float)(dr * ds);
#if defined(__i386) && !defined(__amd64)
            if (rp != fp_extended)
                (void) __swapRP(rp);
#endif
        } else {
            j = 1;
        }
        if (j == 0)
            return (ans);
    }
    if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
        /*
         * non-zero imaginery part(s) with inf component(s) yields NaN
         */
        t = fabsf(x) + fabsf(y) + fabsf(u) + fabsf(v);
        F_RE(ans) = F_IM(ans) = t - t;
    } else {
#if defined(__i386) && !defined(__amd64)
        int rp = __swapRP(fp_extended);
#endif
        /* INDENT OFF */
        /*
         * r = u*log(hypot(x,y))-v*atan2(y,x),
         * q = u*atan2(y,x)+v*log(hypot(x,y))
         * or
         * r = u*log(hypot(x,y))-v*pi*atan2pi(y,x),
         * q/pi = u*atan2pi(y,x)+v*log(hypot(x,y))/pi
         * ans = exp(r)*(cospi(q/pi)  + i sinpi(q/pi))
         */
        /* INDENT ON */
        dx = (double)x;
        dy = (double)y;
        du = (double)u;
        dv = (double)v;
        if (ix > 0x3f000000 && ix < 0x40000000) /* .5 < |x| < 2 */
            dt = dhalf * log1p((dx - 1.0) * (dx + 1.0) + dy * dy);
        else if (iy > 0x3f000000 && iy < 0x40000000) /* .5 < |y| < 2 */
            dt = dhalf * log1p((dy - 1.0) * (dy + 1.0) + dx * dx);
        else
            dt = dhalf * log(dx * dx + dy * dy);
        dp = atan2pi(dy, dx);
        if (iv == 0) {  /* dv = 0 */
            dr = exp(du * dt);
            dq = du * dp;
        } else {
            dr = exp(du * dt - dv * dp * dpi);
            dq = du * dp + dv * dt * dinvpi;
        }
        sincospi(dq, &ds, &dc);
        F_RE(ans) = (float)(dr * dc);
        F_IM(ans) = (float)(dr * ds);
#if defined(__i386) && !defined(__amd64)
        if (rp != fp_extended)
            (void) __swapRP(rp);
#endif
    }
    return (ans);
}