usr/src/lib/libm/common/Q/powl.c

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