1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak __cpowl = cpowl 31 32 #include "libm.h" /* __k_clog_rl/__k_atan2l */ 33 /* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */ 34 #include "complex_wrapper.h" 35 #include "longdouble.h" 36 37 #if defined(__sparc) 38 #define HALF(x) ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000 39 #define LAST(x) ((int *) &x)[3] 40 #elif defined(__x86) 41 #define HALF(x) ((int *) &x)[0] = 0 42 #define LAST(x) ((int *) &x)[0] 43 #endif 44 45 /* INDENT OFF */ 46 static const int hiinf = 0x7fff0000; 47 static const long double 48 tiny = 1.0e-4000L, 49 huge = 1.0e4000L, 50 #if defined(__x86) 51 /* 43 significant bits, 21 trailing zeros */ 52 ln2hil = 0.693147180559890330187045037746429443359375L, 53 ln2lol = 5.497923018708371174712471612513436025525412068e-14L, 54 #else /* sparc */ 55 /* 0x3FF962E4 2FEFA39E F35793C7 00000000 */ 56 ln2hil = 0.693147180559945309417231592858066493070671489074L, 57 ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L, 58 #endif 59 invln2 = 1.442695040888963407359924681001892137427e+0000L, 60 one = 1.0L, 61 zero = 0.0L; 62 /* INDENT ON */ 63 64 /* 65 * Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine 66 * compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers. 67 */ 68 static long double sum4fpl(long double ta[], long double *w) 69 { 70 long double t1, t2, t3, t4, w1, w2, t; 71 t1 = ta[0]; t2 = ta[1]; t3 = ta[2]; t4 = ta[3]; 72 /* 73 * Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4| 74 */ 75 if (fabsl(t4) > fabsl(t1)) { 76 t = t1; t1 = t3; t3 = t; 77 t = t2; t2 = t4; t4 = t; 78 } else if (fabsl(t3) > fabsl(t1)) { 79 t = t1; t1 = t3; 80 if (fabsl(t4) > fabsl(t2)) { 81 t3 = t4; t4 = t2; t2 = t; 82 } else { 83 t3 = t2; t2 = t; 84 } 85 } else if (fabsl(t3) > fabsl(t2)) { 86 t = t2; t2 = t3; 87 if (fabsl(t4) > fabsl(t2)) { 88 t3 = t4; t4 = t; 89 } else 90 t3 = t; 91 } 92 /* summing r = t1 + t2 + t3 + t4 to w1 + w2 */ 93 w1 = t3 + t4; 94 w2 = t4 - (w1 - t3); 95 t = t2 + w1; 96 w2 += w1 - (t - t2); 97 w1 = t + w2; 98 w2 += t - w1; 99 t = t1 + w1; 100 w2 += w1 - (t - t1); 101 w1 = t + w2; 102 *w = w2 - (w1 - t); 103 return (w1); 104 } 105 106 ldcomplex 107 cpowl(ldcomplex z, ldcomplex w) { 108 ldcomplex ans; 109 long double x, y, u, v, t, c, s, r; 110 long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2; 111 int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k; 112 113 x = LD_RE(z); 114 y = LD_IM(z); 115 u = LD_RE(w); 116 v = LD_IM(w); 117 hx = HI_XWORD(x); 118 hy = HI_XWORD(y); 119 hu = HI_XWORD(u); 120 hv = HI_XWORD(v); 121 ix = hx & 0x7fffffff; 122 iy = hy & 0x7fffffff; 123 iu = hu & 0x7fffffff; 124 iv = hv & 0x7fffffff; 125 126 j = 0; 127 if (v == zero) { /* z**(real) */ 128 if (u == one) { /* (anything) ** 1 is itself */ 129 LD_RE(ans) = x; 130 LD_IM(ans) = y; 131 } else if (u == zero) { /* (anything) ** 0 is 1 */ 132 LD_RE(ans) = one; 133 LD_IM(ans) = zero; 134 } else if (y == zero) { /* real ** real */ 135 LD_IM(ans) = zero; 136 if (hx < 0 && ix < hiinf && iu < hiinf) { 137 /* -x ** u is exp(i*pi*u)*pow(x,u) */ 138 r = powl(-x, u); 139 sincospil(u, &s, &c); 140 LD_RE(ans) = (c == zero)? c: c * r; 141 LD_IM(ans) = (s == zero)? s: s * r; 142 } else 143 LD_RE(ans) = powl(x, u); 144 } else if (x == zero || ix >= hiinf || iy >= hiinf) { 145 if (isnanl(x) || isnanl(y) || isnanl(u)) 146 LD_RE(ans) = LD_IM(ans) = x + y + u; 147 else { 148 if (x == zero) 149 r = fabsl(y); 150 else 151 r = fabsl(x) + fabsl(y); 152 t = atan2pil(y, x); 153 sincospil(t * u, &s, &c); 154 LD_RE(ans) = (c == zero)? c: c * r; 155 LD_IM(ans) = (s == zero)? s: s * r; 156 } 157 } else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */ 158 if (hx >= 0) { 159 t = (hy >= 0)? 0.25L : -0.25L; 160 sincospil(t * u, &s, &c); 161 } else if ((LAST(u) & 3) == 0) { 162 t = (hy >= 0)? 0.75L : -0.75L; 163 sincospil(t * u, &s, &c); 164 } else { 165 r = (hy >= 0)? u : -u; 166 t = -0.25L * r; 167 w1 = r + t; 168 w2 = t - (w1 - r); 169 sincospil(w1, &t1, &t2); 170 sincospil(w2, &t3, &t4); 171 s = t1 * t4 + t3 * t2; 172 c = t2 * t4 - t1 * t3; 173 } 174 if (ix < 0x3ffe0000) /* |x| < 1/2 */ 175 r = powl(fabsl(x + x), u) * exp2l(-0.5L * u); 176 else if (ix >= 0x3fff0000 || iu < 0x400cfff8) 177 /* |x| >= 1 or |u| < 16383 */ 178 r = powl(fabsl(x), u) * exp2l(0.5L * u); 179 else /* special treatment */ 180 j = 2; 181 if (j == 0) { 182 LD_RE(ans) = (c == zero)? c: c * r; 183 LD_IM(ans) = (s == zero)? s: s * r; 184 } 185 } else 186 j = 1; 187 if (j == 0) 188 return (ans); 189 } 190 if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) { 191 /* 192 * non-zero imag part(s) with inf component(s) yields NaN 193 */ 194 t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v); 195 LD_RE(ans) = LD_IM(ans) = t - t; 196 } else { 197 k = 0; /* no scaling */ 198 if (iu > 0x7ffe0000 || iv > 0x7ffe0000) { 199 u *= 1.52587890625000000000e-05L; 200 v *= 1.52587890625000000000e-05L; 201 k = 1; /* scale u and v by 2**-16 */ 202 } 203 /* 204 * Use similated higher precision arithmetic to compute: 205 * r = u * log(hypot(x, y)) - v * atan2(y, x) 206 * q = u * atan2(y, x) + v * log(hypot(x, y)) 207 */ 208 209 t1 = __k_clog_rl(x, y, &t2); 210 t3 = __k_atan2l(y, x, &t4); 211 x1 = t1; HALF(x1); 212 y1 = t3; HALF(y1); 213 u1 = u; HALF(u1); 214 v1 = v; HALF(v1); 215 x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */ 216 y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */ 217 /* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */ 218 if (j != 2) { 219 b[0] = u1 * y1; 220 b[1] = (u - u1) * y1 + u * y2; 221 if (j == 1) { /* v = 0 */ 222 w1 = b[0] + b[1]; 223 w2 = b[1] - (w1 - b[0]); 224 } else { 225 b[2] = v1 * x1; 226 b[3] = (v - v1) * x1 + v * x2; 227 w1 = sum4fpl(b, &w2); 228 } 229 sincosl(w1, &t1, &t2); 230 sincosl(w2, &t3, &t4); 231 s = t1 * t4 + t3 * t2; 232 c = t2 * t4 - t1 * t3; 233 if (k == 1) /* square j times */ 234 for (i = 0; i < 10; i++) { 235 t1 = s * c; 236 c = (c + s) * (c - s); 237 s = t1 + t1; 238 } 239 } 240 /* compute r = u * (t1, t2) - v * (t3, t4) */ 241 b[0] = u1 * x1; 242 b[1] = (u - u1) * x1 + u * x2; 243 if (j == 1) { /* v = 0 */ 244 w1 = b[0] + b[1]; 245 w2 = b[1] - (w1 - b[0]); 246 } else { 247 b[2] = -v1 * y1; 248 b[3] = (v1 - v) * y1 - v * y2; 249 w1 = sum4fpl(b, &w2); 250 } 251 /* scale back unless w1 is large enough to cause exception */ 252 if (k != 0 && fabsl(w1) < 20000.0L) { 253 w1 *= 65536.0L; w2 *= 65536.0L; 254 } 255 hx = HI_XWORD(w1); 256 ix = hx & 0x7fffffff; 257 /* compute exp(w1 + w2) */ 258 k = 0; 259 if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */ 260 r = one; 261 else if (ix >= 0x400c6760) /* overflow/underflow */ 262 r = (hx < 0)? tiny * tiny : huge * huge; 263 else { /* compute exp(w1 + w2) */ 264 k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L)); 265 t1 = (long double) k; 266 t2 = w1 - t1 * ln2hil; 267 t3 = w2 - t1 * ln2lol; 268 r = expl(t2 + t3); 269 } 270 if (c != zero) c *= r; 271 if (s != zero) s *= r; 272 if (k != 0) { 273 c = scalbnl(c, k); 274 s = scalbnl(s, k); 275 } 276 LD_RE(ans) = c; 277 LD_IM(ans) = s; 278 } 279 return (ans); 280 } 281