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+/*
+ * 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 2006 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak cpow = __cpow
+
+/* INDENT OFF */
+/*
+ * dcomplex cpow(dcomplex z);
+ *
+ * z**w analytically equivalent to
+ *
+ * cpow(z,w) = cexp(w clog(z))
+ *
+ * Let z = x+iy, w = u+iv.
+ * Since
+ * _________
+ * / 2 2 -1 y
+ * log(x+iy) = log(\/ x + y ) + i tan (---)
+ * x
+ *
+ * 1 2 2 -1 y
+ * = --- log(x + y ) + i tan (---)
+ * 2 x
+ * u 2 2 -1 y
+ * (u+iv)* log(x+iy) = --- log(x + y ) - v tan (---) + (1)
+ * 2 x
+ *
+ * v 2 2 -1 y
+ * i * [ --- log(x + y ) + u tan (---) ] (2)
+ * 2 x
+ *
+ * = r + i q
+ *
+ * Therefore,
+ * w r+iq r
+ * z = e = e (cos(q)+i*sin(q))
+ * _______
+ * / 2 2
+ * r \/ x + y -v*atan2(y,x)
+ * Here e can be expressed as: u * e
+ *
+ * Special cases (in the order of appearance):
+ * 1. (anything) ** 0 is 1
+ * 2. (anything) ** 1 is itself
+ * 3. When v = 0, y = 0:
+ * If x is finite and negative, and u is finite, then
+ * x ** u = exp(u*pi i) * pow(|x|, u);
+ * otherwise,
+ * x ** u = pow(x, u);
+ * 4. When v = 0, x = 0 or |x| = |y| or x is inf or y is inf:
+ * (x + y i) ** u = r * exp(q i)
+ * where
+ * r = hypot(x,y) ** u
+ * q = u * atan2pi(y, x)
+ *
+ * 5. otherwise, z**w is NAN if any x, y, u, v is a Nan or inf
+ *
+ * Note: many results of special cases are obtained in terms of
+ * polar coordinate. In the conversion from polar to rectangle:
+ * r exp(q i) = r * cos(q) + r * sin(q) i,
+ * we regard r * 0 is 0 except when r is a NaN.
+ */
+/* INDENT ON */
+
+#include "libm.h" /* atan2/exp/fabs/hypot/log/pow/scalbn */
+ /* atan2pi/exp2/sincos/sincospi/__k_clog_r/__k_atan2 */
+#include "complex_wrapper.h"
+
+extern void sincospi(double, double *, double *);
+
+static const double
+ huge = 1e300,
+ tiny = 1e-300,
+ invln2 = 1.44269504088896338700e+00,
+ ln2hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ ln2lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ one = 1.0,
+ zero = 0.0;
+
+static const int hiinf = 0x7ff00000;
+extern double atan2pi(double, double);
+
+/*
+ * Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fp subroutine
+ * compute t[0] + t[1] + t[2] + t[3] into two double fp numbers.
+ */
+static double
+sum4fp(double ta[], double *w) {
+ double t1, t2, t3, t4, w1, w2, t;
+ t1 = ta[0]; t2 = ta[1]; t3 = ta[2]; t4 = ta[3];
+ /*
+ * Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4|
+ */
+ if (fabs(t4) > fabs(t1)) {
+ t = t1; t1 = t3; t3 = t;
+ t = t2; t2 = t4; t4 = t;
+ } else if (fabs(t3) > fabs(t1)) {
+ t = t1; t1 = t3;
+ if (fabs(t4) > fabs(t2)) {
+ t3 = t4; t4 = t2; t2 = t;
+ } else {
+ t3 = t2; t2 = t;
+ }
+ } else if (fabs(t3) > fabs(t2)) {
+ t = t2; t2 = t3;
+ if (fabs(t4) > fabs(t2)) {
+ t3 = t4; t4 = t;
+ } else
+ t3 = t;
+ }
+ /* summing r = t1 + t2 + t3 + t4 to w1 + w2 */
+ w1 = t3 + t4;
+ w2 = t4 - (w1 - t3);
+ t = t2 + w1;
+ w2 += w1 - (t - t2);
+ w1 = t + w2;
+ w2 += t - w1;
+ t = t1 + w1;
+ w2 += w1 - (t - t1);
+ w1 = t + w2;
+ *w = w2 - (w1 - t);
+ return (w1);
+}
+
+dcomplex
+cpow(dcomplex z, dcomplex w) {
+ dcomplex ans;
+ double x, y, u, v, t, c, s, r, x2, y2;
+ double b[4], t1, t2, t3, t4, w1, w2, u1, v1, x1, y1;
+ int ix, iy, hx, lx, hy, ly, hv, hu, iu, iv, lu, lv;
+ int i, j, k;
+
+ x = D_RE(z);
+ y = D_IM(z);
+ u = D_RE(w);
+ v = D_IM(w);
+ hx = ((int *) &x)[HIWORD];
+ lx = ((int *) &x)[LOWORD];
+ hy = ((int *) &y)[HIWORD];
+ ly = ((int *) &y)[LOWORD];
+ hu = ((int *) &u)[HIWORD];
+ lu = ((int *) &u)[LOWORD];
+ hv = ((int *) &v)[HIWORD];
+ lv = ((int *) &v)[LOWORD];
+ ix = hx & 0x7fffffff;
+ iy = hy & 0x7fffffff;
+ iu = hu & 0x7fffffff;
+ iv = hv & 0x7fffffff;
+
+ j = 0;
+ if ((iv | lv) == 0) { /* z**(real) */
+ if (((hu - 0x3ff00000) | lu) == 0) { /* z ** 1 = z */
+ D_RE(ans) = x;
+ D_IM(ans) = y;
+ } else if ((iu | lu) == 0) { /* z ** 0 = 1 */
+ D_RE(ans) = one;
+ D_IM(ans) = zero;
+ } else if ((iy | ly) == 0) { /* (real)**(real) */
+ D_IM(ans) = zero;
+ if (hx < 0 && ix < hiinf && iu < hiinf) {
+ /* -x ** u is exp(i*pi*u)*pow(x,u) */
+ r = pow(-x, u);
+ sincospi(u, &s, &c);
+ D_RE(ans) = (c == zero)? c: c * r;
+ D_IM(ans) = (s == zero)? s: s * r;
+ } else
+ D_RE(ans) = pow(x, u);
+ } else if (((ix | lx) == 0) || ix >= hiinf || iy >= hiinf) {
+ if (isnan(x) || isnan(y) || isnan(u))
+ D_RE(ans) = D_IM(ans) = x + y + u;
+ else {
+ if ((ix | lx) == 0)
+ r = fabs(y);
+ else
+ r = fabs(x) + fabs(y);
+ t = atan2pi(y, x);
+ sincospi(t * u, &s, &c);
+ D_RE(ans) = (c == zero)? c: c * r;
+ D_IM(ans) = (s == zero)? s: s * r;
+ }
+ } else if (((ix - iy) | (lx - ly)) == 0) { /* |x| = |y| */
+ if (hx >= 0) {
+ t = (hy >= 0)? 0.25 : -0.25;
+ sincospi(t * u, &s, &c);
+ } else if ((lu & 3) == 0) {
+ t = (hy >= 0)? 0.75 : -0.75;
+ sincospi(t * u, &s, &c);
+ } else {
+ r = (hy >= 0)? u : -u;
+ t = -0.25 * r;
+ w1 = r + t;
+ w2 = t - (w1 - r);
+ sincospi(w1, &t1, &t2);
+ sincospi(w2, &t3, &t4);
+ s = t1 * t4 + t3 * t2;
+ c = t2 * t4 - t1 * t3;
+ }
+ if (ix < 0x3fe00000) /* |x| < 1/2 */
+ r = pow(fabs(x + x), u) * exp2(-0.5 * u);
+ else if (ix >= 0x3ff00000 || iu < 0x408ff800)
+ /* |x| >= 1 or |u| < 1023 */
+ r = pow(fabs(x), u) * exp2(0.5 * u);
+ else /* special treatment */
+ j = 2;
+ if (j == 0) {
+ D_RE(ans) = (c == zero)? c: c * r;
+ D_IM(ans) = (s == zero)? s: s * r;
+ }
+ } else
+ j = 1;
+ if (j == 0)
+ return (ans);
+ }
+ if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
+ /*
+ * non-zero imag part(s) with inf component(s) yields NaN
+ */
+ t = fabs(x) + fabs(y) + fabs(u) + fabs(v);
+ D_RE(ans) = D_IM(ans) = t - t;
+ } else {
+ k = 0; /* no scaling */
+ if (iu > 0x7f000000 || iv > 0x7f000000) {
+ u *= .0009765625; /* scale 2**-10 to avoid overflow */
+ v *= .0009765625;
+ k = 1; /* scale by 2**-10 */
+ }
+ /*
+ * Use similated higher precision arithmetic to compute:
+ * r = u * log(hypot(x, y)) - v * atan2(y, x)
+ * q = u * atan2(y, x) + v * log(hypot(x, y))
+ */
+ t1 = __k_clog_r(x, y, &t2);
+ t3 = __k_atan2(y, x, &t4);
+ x1 = t1;
+ y1 = t3;
+ u1 = u;
+ v1 = v;
+ ((int *) &u1)[LOWORD] &= 0xf8000000;
+ ((int *) &v1)[LOWORD] &= 0xf8000000;
+ ((int *) &x1)[LOWORD] &= 0xf8000000;
+ ((int *) &y1)[LOWORD] &= 0xf8000000;
+ x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
+ y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
+ /* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
+ if (j != 2) {
+ b[0] = u1 * y1;
+ b[1] = (u - u1) * y1 + u * y2;
+ if (j == 1) { /* v = 0 */
+ w1 = b[0] + b[1];
+ w2 = b[1] - (w1 - b[0]);
+ } else {
+ b[2] = v1 * x1;
+ b[3] = (v - v1) * x1 + v * x2;
+ w1 = sum4fp(b, &w2);
+ }
+ sincos(w1, &t1, &t2);
+ sincos(w2, &t3, &t4);
+ s = t1 * t4 + t3 * t2;
+ c = t2 * t4 - t1 * t3;
+ if (k == 1)
+ /*
+ * square (cos(q) + i sin(q)) k times to get
+ * (cos(2^k * q + i sin(2^k * q)
+ */
+ for (i = 0; i < 10; i++) {
+ t1 = s * c;
+ c = (c + s) * (c - s);
+ s = t1 + t1;
+ }
+ }
+ /* compute r = u * (t1, t2) - v * (t3, t4) */
+ b[0] = u1 * x1;
+ b[1] = (u - u1) * x1 + u * x2;
+ if (j == 1) { /* v = 0 */
+ w1 = b[0] + b[1];
+ w2 = b[1] - (w1 - b[0]);
+ } else {
+ b[2] = -v1 * y1;
+ b[3] = (v1 - v) * y1 - v * y2;
+ w1 = sum4fp(b, &w2);
+ }
+ /* check over/underflow for exp(w1 + w2) */
+ if (k && fabs(w1) < 1000.0) {
+ w1 *= 1024; w2 *= 1024; k = 0;
+ }
+ hx = ((int *) &w1)[HIWORD];
+ lx = ((int *) &w1)[LOWORD];
+ ix = hx & 0x7fffffff;
+ /* compute exp(w1 + w2) */
+ if (ix < 0x3c900000) /* exp(tiny < 2**-54) = 1 */
+ r = one;
+ else if (ix >= 0x40880000) /* overflow/underflow */
+ r = (hx < 0)? tiny * tiny : huge * huge;
+ else { /* compute exp(w1 + w2) */
+ k = (int) (invln2 * w1 + ((hx >= 0)? 0.5 : -0.5));
+ t1 = (double) k;
+ t2 = w1 - t1 * ln2hi;
+ t3 = w2 - t1 * ln2lo;
+ r = exp(t2 + t3);
+ }
+ if (c != zero) c *= r;
+ if (s != zero) s *= r;
+ if (k != 0) {
+ c = scalbn(c, k);
+ s = scalbn(s, k);
+ }
+ D_RE(ans) = c;
+ D_IM(ans) = s;
+ }
+ return (ans);
+}