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 #if defined(ELFOBJ) 31 #pragma weak powl = __powl 32 #endif 33 34 #include "libm.h" 35 #include "xpg6.h" /* __xpg6 */ 36 #define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int 37 38 #if defined(__sparc) 39 #define i0 0 40 #define i1 1 41 #define i2 2 42 #define i3 3 43 44 static const long double zero = 0.0L, one = 1.0L, two = 2.0L; 45 46 extern const long double _TBL_logl_hi[], _TBL_logl_lo[]; 47 48 static const long double 49 two113 = 10384593717069655257060992658440192.0L, 50 ln2hi = 6.931471805599453094172319547495844850203e-0001L, 51 ln2lo = 1.667085920830552208890449330400379754169e-0025L, 52 A2 = 6.666666666666666666666666666666091393804e-0001L, 53 A3 = 4.000000000000000000000000407167070220671e-0001L, 54 A4 = 2.857142857142857142730077490612903681164e-0001L, 55 A5 = 2.222222222222242577702836920812882605099e-0001L, 56 A6 = 1.818181816435493395985912667105885828356e-0001L, 57 A7 = 1.538537835211839751112067512805496931725e-0001L, 58 B1 = 6.666666666666666666666666666666666667787e-0001L, 59 B2 = 3.999999999999999999999999999999848524411e-0001L, 60 B3 = 2.857142857142857142857142865084581075070e-0001L, 61 B4 = 2.222222222222222222222010781800643808497e-0001L, 62 B5 = 1.818181818181818185051442171337036403674e-0001L, 63 B6 = 1.538461538461508363540720286292008207673e-0001L, 64 B7 = 1.333333333506731842033180638329317108428e-0001L, 65 B8 = 1.176469984587418890634302788283946761670e-0001L, 66 B9 = 1.053794891561452331722969901564862497132e-0001L; 67 68 static long double 69 logl_x(long double x, long double *w) { 70 long double f, f1, v, s, z, qn, h, t; 71 int *px = (int *) &x; 72 int *pz = (int *) &z; 73 int i, j, ix, n; 74 75 n = 0; 76 ix = px[i0]; 77 if (ix > 0x3ffef03f && ix < 0x3fff0820) { /* 65/63 > x > 63/65 */ 78 f = x - one; 79 z = f * f; 80 if (((ix - 0x3fff0000) | px[i1] | px[i2] | px[i3]) == 0) { 81 *w = zero; 82 return (zero); /* log(1)= +0 */ 83 } 84 qn = one / (two + f); 85 s = f * qn; /* |s|<2**-6 */ 86 v = s * s; 87 h = (long double) (2.0 * (double) s); 88 f1 = (long double) ((double) f); 89 t = ((two * (f - h) - h * f1) - h * (f - f1)) * qn + 90 s * (v * (B1 + v * (B2 + v * (B3 + v * (B4 + 91 v * (B5 + v * (B6 + v * (B7 + v * (B8 + v * B9))))))))); 92 s = (long double) ((double) (h + t)); 93 *w = t - (s - h); 94 return (s); 95 } 96 if (ix < 0x00010000) { /* subnormal x */ 97 x *= two113; 98 n = -113; 99 ix = px[i0]; 100 } 101 /* LARGE_N */ 102 n += ((ix + 0x200) >> 16) - 0x3fff; 103 ix = (ix & 0x0000ffff) | 0x3fff0000; /* scale x to [1,2] */ 104 px[i0] = ix; 105 i = ix + 0x200; 106 pz[i0] = i & 0xfffffc00; 107 pz[i1] = pz[i2] = pz[i3] = 0; 108 qn = one / (x + z); 109 f = x - z; 110 s = f * qn; 111 f1 = (long double) ((double) f); 112 h = (long double) (2.0 * (double) s); 113 t = qn * ((two * (f - z * h) - h * f1) - h * (f - f1)); 114 j = (i >> 10) & 0x3f; 115 v = s * s; 116 qn = (long double) n; 117 t += qn * ln2lo + _TBL_logl_lo[j]; 118 t += s * (v * (A2 + v * (A3 + v * (A4 + v * (A5 + v * (A6 + 119 v * A7)))))); 120 v = qn * ln2hi + _TBL_logl_hi[j]; 121 s = h + v; 122 t += (h - (s - v)); 123 z = (long double) ((double) (s + t)); 124 *w = t - (z - s); 125 return (z); 126 } 127 128 extern const long double _TBL_expl_hi[], _TBL_expl_lo[]; 129 static const long double 130 invln2_32 = 4.616624130844682903551758979206054839765e+1L, 131 ln2_32hi = 2.166084939249829091928849858592451515688e-2L, 132 ln2_32lo = 5.209643502595475652782654157501186731779e-27L, 133 ln2_64 = 1.083042469624914545964425189778400898568e-2L; 134 135 long double 136 powl(long double x, long double y) { 137 long double z, ax; 138 long double y1, y2, w1, w2; 139 int sbx, sby, j, k, yisint, m; 140 int hx, lx, hy, ly, ahx, ahy; 141 int *pz = (int *) &z; 142 int *px = (int *) &x; 143 int *py = (int *) &y; 144 145 hx = px[i0]; 146 lx = px[i1] | px[i2] | px[i3]; 147 hy = py[i0]; 148 ly = py[i1] | py[i2] | py[i3]; 149 ahx = hx & ~0x80000000; 150 ahy = hy & ~0x80000000; 151 152 if ((ahy | ly) == 0) 153 return (one); /* x**+-0 = 1 */ 154 else if (hx == 0x3fff0000 && lx == 0 && 155 (__xpg6 & _C99SUSv3_pow) != 0) 156 return (one); /* C99: 1**anything = 1 */ 157 else if (ahx > 0x7fff0000 || (ahx == 0x7fff0000 && lx != 0) || 158 ahy > 0x7fff0000 || (ahy == 0x7fff0000 && ly != 0)) 159 return (x + y); /* +-NaN return x+y */ 160 /* includes Sun: 1**NaN = NaN */ 161 sbx = (unsigned) hx >> 31; 162 sby = (unsigned) hy >> 31; 163 ax = fabsl(x); 164 /* 165 * determine if y is an odd int when x < 0 166 * yisint = 0 ... y is not an integer 167 * yisint = 1 ... y is an odd int 168 * yisint = 2 ... y is an even int 169 */ 170 yisint = 0; 171 if (sbx) { 172 if (ahy >= 0x40700000) /* if |y|>=2**113 */ 173 yisint = 2; /* even integer y */ 174 else if (ahy >= 0x3fff0000) { 175 k = (ahy >> 16) - 0x3fff; /* exponent */ 176 if (k > 80) { 177 j = ((unsigned) py[i3]) >> (112 - k); 178 if ((j << (112 - k)) == py[i3]) 179 yisint = 2 - (j & 1); 180 } else if (k > 48) { 181 j = ((unsigned) py[i2]) >> (80 - k); 182 if ((j << (80 - k)) == py[i2]) 183 yisint = 2 - (j & 1); 184 } else if (k > 16) { 185 j = ((unsigned) py[i1]) >> (48 - k); 186 if ((j << (48 - k)) == py[i1]) 187 yisint = 2 - (j & 1); 188 } else if (ly == 0) { 189 j = ahy >> (16 - k); 190 if ((j << (16 - k)) == ahy) 191 yisint = 2 - (j & 1); 192 } 193 } 194 } 195 196 /* special value of y */ 197 if (ly == 0) { 198 if (ahy == 0x7fff0000) { /* y is +-inf */ 199 if (((ahx - 0x3fff0000) | lx) == 0) { 200 if ((__xpg6 & _C99SUSv3_pow) != 0) 201 return (one); 202 /* C99: (-1)**+-inf = 1 */ 203 else 204 return (y - y); 205 /* Sun: (+-1)**+-inf = NaN */ 206 } else if (ahx >= 0x3fff0000) 207 /* (|x|>1)**+,-inf = inf,0 */ 208 return (sby == 0 ? y : zero); 209 else /* (|x|<1)**-,+inf = inf,0 */ 210 return (sby != 0 ? -y : zero); 211 } else if (ahy == 0x3fff0000) { /* y is +-1 */ 212 if (sby != 0) 213 return (one / x); 214 else 215 return (x); 216 } else if (hy == 0x40000000) /* y is 2 */ 217 return (x * x); 218 else if (hy == 0x3ffe0000) { /* y is 0.5 */ 219 if (!((ahx | lx) == 0 || ((ahx - 0x7fff0000) | lx) == 220 0)) 221 return (sqrtl(x)); 222 } 223 } 224 225 /* special value of x */ 226 if (lx == 0) { 227 if (ahx == 0x7fff0000 || ahx == 0 || ahx == 0x3fff0000) { 228 /* x is +-0,+-inf,+-1 */ 229 z = ax; 230 if (sby == 1) 231 z = one / z; /* z = 1/|x| if y is negative */ 232 if (sbx == 1) { 233 if (ahx == 0x3fff0000 && yisint == 0) 234 z = zero / zero; 235 /* (-1)**non-int is NaN */ 236 else if (yisint == 1) 237 z = -z; /* (x<0)**odd = -(|x|**odd) */ 238 } 239 return (z); 240 } 241 } 242 243 /* (x<0)**(non-int) is NaN */ 244 if (sbx == 1 && yisint == 0) 245 return (zero / zero); /* should be volatile */ 246 247 /* Now ax is finite, y is finite */ 248 /* first compute log(ax) = w1+w2, with 53 bits w1 */ 249 w1 = logl_x(ax, &w2); 250 251 /* split up y into y1+y2 and compute (y1+y2)*(w1+w2) */ 252 if (ly == 0 || ahy >= 0x43fe0000) { 253 y1 = y * w1; 254 y2 = y * w2; 255 } else { 256 y1 = (long double) ((double) y); 257 y2 = (y - y1) * w1 + y * w2; 258 y1 *= w1; 259 } 260 z = y1 + y2; 261 j = pz[i0]; 262 if ((unsigned) j >= 0xffff0000) { /* NaN or -inf */ 263 if (sbx == 1 && yisint == 1) 264 return (one / z); 265 else 266 return (-one / z); 267 } else if ((j & ~0x80000000) < 0x3fc30000) { /* |x|<2^-60 */ 268 if (sbx == 1 && yisint == 1) 269 return (-one - z); 270 else 271 return (one + z); 272 } else if (j > 0) { 273 if (j > 0x400d0000) { 274 if (sbx == 1 && yisint == 1) 275 return (scalbnl(-one, 20000)); 276 else 277 return (scalbnl(one, 20000)); 278 } 279 k = (int) (invln2_32 * (z + ln2_64)); 280 } else { 281 if ((unsigned) j > 0xc00d0000) { 282 if (sbx == 1 && yisint == 1) 283 return (scalbnl(-one, -20000)); 284 else 285 return (scalbnl(one, -20000)); 286 } 287 k = (int) (invln2_32 * (z - ln2_64)); 288 } 289 j = k & 0x1f; 290 m = k >> 5; 291 { 292 /* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */ 293 long double 294 t1 = 1.666666666666666666666666666660876387437e-1L, 295 t2 = -2.777777777777777777777707812093173478756e-3L, 296 t3 = 6.613756613756613482074280932874221202424e-5L, 297 t4 = -1.653439153392139954169609822742235851120e-6L, 298 t5 = 4.175314851769539751387852116610973796053e-8L; 299 long double t = (long double) k; 300 301 w1 = (y2 - (t * ln2_32hi - y1)) - t * ln2_32lo; 302 t = w1 * w1; 303 w2 = (w1 - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) - 304 two; 305 z = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (w1 + w1)) / w2 - 306 _TBL_expl_lo[j]); 307 } 308 j = m + (pz[i0] >> 16); 309 if (j && (unsigned) j < 0x7fff) 310 pz[i0] += m << 16; 311 else 312 z = scalbnl(z, m); 313 314 if (sbx == 1 && yisint == 1) 315 z = -z; /* (-ve)**(odd int) */ 316 return (z); 317 } 318 #else 319 #error Unsupported Architecture 320 #endif /* defined(__sparc) */ 321