diff options
Diffstat (limited to 'usr/src/lib/libm/common/complex/cpowl.c')
-rw-r--r-- | usr/src/lib/libm/common/complex/cpowl.c | 280 |
1 files changed, 280 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/complex/cpowl.c b/usr/src/lib/libm/common/complex/cpowl.c new file mode 100644 index 0000000000..091155d452 --- /dev/null +++ b/usr/src/lib/libm/common/complex/cpowl.c @@ -0,0 +1,280 @@ +/* + * 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 cpowl = __cpowl + +#include "libm.h" /* __k_clog_rl/__k_atan2l */ +/* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */ +#include "complex_wrapper.h" +#include "longdouble.h" + +#if defined(__sparc) +#define HALF(x) ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000 +#define LAST(x) ((int *) &x)[3] +#elif defined(__x86) +#define HALF(x) ((int *) &x)[0] = 0 +#define LAST(x) ((int *) &x)[0] +#endif + +/* INDENT OFF */ +static const int hiinf = 0x7fff0000; +static const long double + tiny = 1.0e-4000L, + huge = 1.0e4000L, +#if defined(__x86) + /* 43 significant bits, 21 trailing zeros */ + ln2hil = 0.693147180559890330187045037746429443359375L, + ln2lol = 5.497923018708371174712471612513436025525412068e-14L, +#else /* sparc */ + /* 0x3FF962E4 2FEFA39E F35793C7 00000000 */ + ln2hil = 0.693147180559945309417231592858066493070671489074L, + ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L, +#endif + invln2 = 1.442695040888963407359924681001892137427e+0000L, + one = 1.0L, + zero = 0.0L; +/* INDENT ON */ + +/* + * Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine + * compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers. + */ +static long double sum4fpl(long double ta[], long double *w) +{ + long 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 (fabsl(t4) > fabsl(t1)) { + t = t1; t1 = t3; t3 = t; + t = t2; t2 = t4; t4 = t; + } else if (fabsl(t3) > fabsl(t1)) { + t = t1; t1 = t3; + if (fabsl(t4) > fabsl(t2)) { + t3 = t4; t4 = t2; t2 = t; + } else { + t3 = t2; t2 = t; + } + } else if (fabsl(t3) > fabsl(t2)) { + t = t2; t2 = t3; + if (fabsl(t4) > fabsl(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); +} + +ldcomplex +cpowl(ldcomplex z, ldcomplex w) { + ldcomplex ans; + long double x, y, u, v, t, c, s, r; + long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2; + int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k; + + x = LD_RE(z); + y = LD_IM(z); + u = LD_RE(w); + v = LD_IM(w); + hx = HI_XWORD(x); + hy = HI_XWORD(y); + hu = HI_XWORD(u); + hv = HI_XWORD(v); + ix = hx & 0x7fffffff; + iy = hy & 0x7fffffff; + iu = hu & 0x7fffffff; + iv = hv & 0x7fffffff; + + j = 0; + if (v == zero) { /* z**(real) */ + if (u == one) { /* (anything) ** 1 is itself */ + LD_RE(ans) = x; + LD_IM(ans) = y; + } else if (u == zero) { /* (anything) ** 0 is 1 */ + LD_RE(ans) = one; + LD_IM(ans) = zero; + } else if (y == zero) { /* real ** real */ + LD_IM(ans) = zero; + if (hx < 0 && ix < hiinf && iu < hiinf) { + /* -x ** u is exp(i*pi*u)*pow(x,u) */ + r = powl(-x, u); + sincospil(u, &s, &c); + LD_RE(ans) = (c == zero)? c: c * r; + LD_IM(ans) = (s == zero)? s: s * r; + } else + LD_RE(ans) = powl(x, u); + } else if (x == zero || ix >= hiinf || iy >= hiinf) { + if (isnanl(x) || isnanl(y) || isnanl(u)) + LD_RE(ans) = LD_IM(ans) = x + y + u; + else { + if (x == zero) + r = fabsl(y); + else + r = fabsl(x) + fabsl(y); + t = atan2pil(y, x); + sincospil(t * u, &s, &c); + LD_RE(ans) = (c == zero)? c: c * r; + LD_IM(ans) = (s == zero)? s: s * r; + } + } else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */ + if (hx >= 0) { + t = (hy >= 0)? 0.25L : -0.25L; + sincospil(t * u, &s, &c); + } else if ((LAST(u) & 3) == 0) { + t = (hy >= 0)? 0.75L : -0.75L; + sincospil(t * u, &s, &c); + } else { + r = (hy >= 0)? u : -u; + t = -0.25L * r; + w1 = r + t; + w2 = t - (w1 - r); + sincospil(w1, &t1, &t2); + sincospil(w2, &t3, &t4); + s = t1 * t4 + t3 * t2; + c = t2 * t4 - t1 * t3; + } + if (ix < 0x3ffe0000) /* |x| < 1/2 */ + r = powl(fabsl(x + x), u) * exp2l(-0.5L * u); + else if (ix >= 0x3fff0000 || iu < 0x400cfff8) + /* |x| >= 1 or |u| < 16383 */ + r = powl(fabsl(x), u) * exp2l(0.5L * u); + else /* special treatment */ + j = 2; + if (j == 0) { + LD_RE(ans) = (c == zero)? c: c * r; + LD_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 = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v); + LD_RE(ans) = LD_IM(ans) = t - t; + } else { + k = 0; /* no scaling */ + if (iu > 0x7ffe0000 || iv > 0x7ffe0000) { + u *= 1.52587890625000000000e-05L; + v *= 1.52587890625000000000e-05L; + k = 1; /* scale u and v by 2**-16 */ + } + /* + * 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_rl(x, y, &t2); + t3 = __k_atan2l(y, x, &t4); + x1 = t1; HALF(x1); + y1 = t3; HALF(y1); + u1 = u; HALF(u1); + v1 = v; HALF(v1); + 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 = sum4fpl(b, &w2); + } + sincosl(w1, &t1, &t2); + sincosl(w2, &t3, &t4); + s = t1 * t4 + t3 * t2; + c = t2 * t4 - t1 * t3; + if (k == 1) /* square j times */ + 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 = sum4fpl(b, &w2); + } + /* scale back unless w1 is large enough to cause exception */ + if (k != 0 && fabsl(w1) < 20000.0L) { + w1 *= 65536.0L; w2 *= 65536.0L; + } + hx = HI_XWORD(w1); + ix = hx & 0x7fffffff; + /* compute exp(w1 + w2) */ + k = 0; + if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */ + r = one; + else if (ix >= 0x400c6760) /* overflow/underflow */ + r = (hx < 0)? tiny * tiny : huge * huge; + else { /* compute exp(w1 + w2) */ + k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L)); + t1 = (long double) k; + t2 = w1 - t1 * ln2hil; + t3 = w2 - t1 * ln2lol; + r = expl(t2 + t3); + } + if (c != zero) c *= r; + if (s != zero) s *= r; + if (k != 0) { + c = scalbnl(c, k); + s = scalbnl(s, k); + } + LD_RE(ans) = c; + LD_IM(ans) = s; + } + return (ans); +} |