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floatformat.c revision 1.6
      1  1.1  mrg /* IEEE floating point support routines, for GDB, the GNU Debugger.
      2  1.6  mrg    Copyright 1991, 1994, 1999, 2000, 2003, 2005, 2006, 2010, 2012, 2015
      3  1.1  mrg    Free Software Foundation, Inc.
      4  1.1  mrg 
      5  1.1  mrg This file is part of GDB.
      6  1.1  mrg 
      7  1.1  mrg This program is free software; you can redistribute it and/or modify
      8  1.1  mrg it under the terms of the GNU General Public License as published by
      9  1.1  mrg the Free Software Foundation; either version 2 of the License, or
     10  1.1  mrg (at your option) any later version.
     11  1.1  mrg 
     12  1.1  mrg This program is distributed in the hope that it will be useful,
     13  1.1  mrg but WITHOUT ANY WARRANTY; without even the implied warranty of
     14  1.1  mrg MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     15  1.1  mrg GNU General Public License for more details.
     16  1.1  mrg 
     17  1.1  mrg You should have received a copy of the GNU General Public License
     18  1.1  mrg along with this program; if not, write to the Free Software
     19  1.1  mrg Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.  */
     20  1.1  mrg 
     21  1.1  mrg /* This is needed to pick up the NAN macro on some systems.  */
     22  1.6  mrg #ifndef _GNU_SOURCE
     23  1.1  mrg #define _GNU_SOURCE
     24  1.6  mrg #endif
     25  1.1  mrg 
     26  1.1  mrg #ifdef HAVE_CONFIG_H
     27  1.1  mrg #include "config.h"
     28  1.1  mrg #endif
     29  1.1  mrg 
     30  1.1  mrg #include <math.h>
     31  1.1  mrg 
     32  1.1  mrg #ifdef HAVE_STRING_H
     33  1.1  mrg #include <string.h>
     34  1.1  mrg #endif
     35  1.1  mrg 
     36  1.1  mrg /* On some platforms, <float.h> provides DBL_QNAN.  */
     37  1.1  mrg #ifdef STDC_HEADERS
     38  1.1  mrg #include <float.h>
     39  1.1  mrg #endif
     40  1.1  mrg 
     41  1.1  mrg #include "ansidecl.h"
     42  1.1  mrg #include "libiberty.h"
     43  1.1  mrg #include "floatformat.h"
     44  1.1  mrg 
     45  1.1  mrg #ifndef INFINITY
     46  1.1  mrg #ifdef HUGE_VAL
     47  1.1  mrg #define INFINITY HUGE_VAL
     48  1.1  mrg #else
     49  1.1  mrg #define INFINITY (1.0 / 0.0)
     50  1.1  mrg #endif
     51  1.1  mrg #endif
     52  1.1  mrg 
     53  1.1  mrg #ifndef NAN
     54  1.1  mrg #ifdef DBL_QNAN
     55  1.1  mrg #define NAN DBL_QNAN
     56  1.1  mrg #else
     57  1.1  mrg #define NAN (0.0 / 0.0)
     58  1.1  mrg #endif
     59  1.1  mrg #endif
     60  1.1  mrg 
     61  1.1  mrg static int mant_bits_set (const struct floatformat *, const unsigned char *);
     62  1.1  mrg static unsigned long get_field (const unsigned char *,
     63  1.1  mrg                                 enum floatformat_byteorders,
     64  1.1  mrg                                 unsigned int,
     65  1.1  mrg                                 unsigned int,
     66  1.1  mrg                                 unsigned int);
     67  1.1  mrg static int floatformat_always_valid (const struct floatformat *fmt,
     68  1.1  mrg                                      const void *from);
     69  1.1  mrg 
     70  1.1  mrg static int
     71  1.1  mrg floatformat_always_valid (const struct floatformat *fmt ATTRIBUTE_UNUSED,
     72  1.1  mrg                           const void *from ATTRIBUTE_UNUSED)
     73  1.1  mrg {
     74  1.1  mrg   return 1;
     75  1.1  mrg }
     76  1.1  mrg 
     77  1.1  mrg /* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not
     78  1.1  mrg    going to bother with trying to muck around with whether it is defined in
     79  1.1  mrg    a system header, what we do if not, etc.  */
     80  1.1  mrg #define FLOATFORMAT_CHAR_BIT 8
     81  1.1  mrg 
     82  1.3  mrg /* floatformats for IEEE half, single and double, big and little endian.  */
     83  1.3  mrg const struct floatformat floatformat_ieee_half_big =
     84  1.3  mrg {
     85  1.3  mrg   floatformat_big, 16, 0, 1, 5, 15, 31, 6, 10,
     86  1.3  mrg   floatformat_intbit_no,
     87  1.3  mrg   "floatformat_ieee_half_big",
     88  1.3  mrg   floatformat_always_valid,
     89  1.3  mrg   NULL
     90  1.3  mrg };
     91  1.3  mrg const struct floatformat floatformat_ieee_half_little =
     92  1.3  mrg {
     93  1.3  mrg   floatformat_little, 16, 0, 1, 5, 15, 31, 6, 10,
     94  1.3  mrg   floatformat_intbit_no,
     95  1.3  mrg   "floatformat_ieee_half_little",
     96  1.3  mrg   floatformat_always_valid,
     97  1.3  mrg   NULL
     98  1.3  mrg };
     99  1.1  mrg const struct floatformat floatformat_ieee_single_big =
    100  1.1  mrg {
    101  1.1  mrg   floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23,
    102  1.1  mrg   floatformat_intbit_no,
    103  1.1  mrg   "floatformat_ieee_single_big",
    104  1.1  mrg   floatformat_always_valid,
    105  1.1  mrg   NULL
    106  1.1  mrg };
    107  1.1  mrg const struct floatformat floatformat_ieee_single_little =
    108  1.1  mrg {
    109  1.1  mrg   floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23,
    110  1.1  mrg   floatformat_intbit_no,
    111  1.1  mrg   "floatformat_ieee_single_little",
    112  1.1  mrg   floatformat_always_valid,
    113  1.1  mrg   NULL
    114  1.1  mrg };
    115  1.1  mrg const struct floatformat floatformat_ieee_double_big =
    116  1.1  mrg {
    117  1.1  mrg   floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52,
    118  1.1  mrg   floatformat_intbit_no,
    119  1.1  mrg   "floatformat_ieee_double_big",
    120  1.1  mrg   floatformat_always_valid,
    121  1.1  mrg   NULL
    122  1.1  mrg };
    123  1.1  mrg const struct floatformat floatformat_ieee_double_little =
    124  1.1  mrg {
    125  1.1  mrg   floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52,
    126  1.1  mrg   floatformat_intbit_no,
    127  1.1  mrg   "floatformat_ieee_double_little",
    128  1.1  mrg   floatformat_always_valid,
    129  1.1  mrg   NULL
    130  1.1  mrg };
    131  1.1  mrg 
    132  1.1  mrg /* floatformat for IEEE double, little endian byte order, with big endian word
    133  1.1  mrg    ordering, as on the ARM.  */
    134  1.1  mrg 
    135  1.1  mrg const struct floatformat floatformat_ieee_double_littlebyte_bigword =
    136  1.1  mrg {
    137  1.1  mrg   floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52,
    138  1.1  mrg   floatformat_intbit_no,
    139  1.1  mrg   "floatformat_ieee_double_littlebyte_bigword",
    140  1.1  mrg   floatformat_always_valid,
    141  1.1  mrg   NULL
    142  1.1  mrg };
    143  1.1  mrg 
    144  1.1  mrg /* floatformat for VAX.  Not quite IEEE, but close enough.  */
    145  1.1  mrg 
    146  1.1  mrg const struct floatformat floatformat_vax_f =
    147  1.1  mrg {
    148  1.1  mrg   floatformat_vax, 32, 0, 1, 8, 129, 0, 9, 23,
    149  1.1  mrg   floatformat_intbit_no,
    150  1.1  mrg   "floatformat_vax_f",
    151  1.1  mrg   floatformat_always_valid,
    152  1.1  mrg   NULL
    153  1.1  mrg };
    154  1.1  mrg const struct floatformat floatformat_vax_d =
    155  1.1  mrg {
    156  1.1  mrg   floatformat_vax, 64, 0, 1, 8, 129, 0, 9, 55,
    157  1.1  mrg   floatformat_intbit_no,
    158  1.1  mrg   "floatformat_vax_d",
    159  1.1  mrg   floatformat_always_valid,
    160  1.1  mrg   NULL
    161  1.1  mrg };
    162  1.1  mrg const struct floatformat floatformat_vax_g =
    163  1.1  mrg {
    164  1.1  mrg   floatformat_vax, 64, 0, 1, 11, 1025, 0, 12, 52,
    165  1.1  mrg   floatformat_intbit_no,
    166  1.1  mrg   "floatformat_vax_g",
    167  1.1  mrg   floatformat_always_valid,
    168  1.1  mrg   NULL
    169  1.1  mrg };
    170  1.1  mrg 
    171  1.1  mrg static int floatformat_i387_ext_is_valid (const struct floatformat *fmt,
    172  1.1  mrg 					  const void *from);
    173  1.1  mrg 
    174  1.1  mrg static int
    175  1.1  mrg floatformat_i387_ext_is_valid (const struct floatformat *fmt, const void *from)
    176  1.1  mrg {
    177  1.1  mrg   /* In the i387 double-extended format, if the exponent is all ones,
    178  1.1  mrg      then the integer bit must be set.  If the exponent is neither 0
    179  1.1  mrg      nor ~0, the intbit must also be set.  Only if the exponent is
    180  1.1  mrg      zero can it be zero, and then it must be zero.  */
    181  1.1  mrg   unsigned long exponent, int_bit;
    182  1.1  mrg   const unsigned char *ufrom = (const unsigned char *) from;
    183  1.1  mrg 
    184  1.1  mrg   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
    185  1.1  mrg 			fmt->exp_start, fmt->exp_len);
    186  1.1  mrg   int_bit = get_field (ufrom, fmt->byteorder, fmt->totalsize,
    187  1.1  mrg 		       fmt->man_start, 1);
    188  1.1  mrg 
    189  1.1  mrg   if ((exponent == 0) != (int_bit == 0))
    190  1.1  mrg     return 0;
    191  1.1  mrg   else
    192  1.1  mrg     return 1;
    193  1.1  mrg }
    194  1.1  mrg 
    195  1.1  mrg const struct floatformat floatformat_i387_ext =
    196  1.1  mrg {
    197  1.1  mrg   floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
    198  1.1  mrg   floatformat_intbit_yes,
    199  1.1  mrg   "floatformat_i387_ext",
    200  1.1  mrg   floatformat_i387_ext_is_valid,
    201  1.1  mrg   NULL
    202  1.1  mrg };
    203  1.1  mrg const struct floatformat floatformat_m68881_ext =
    204  1.1  mrg {
    205  1.1  mrg   /* Note that the bits from 16 to 31 are unused.  */
    206  1.1  mrg   floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64,
    207  1.1  mrg   floatformat_intbit_yes,
    208  1.1  mrg   "floatformat_m68881_ext",
    209  1.1  mrg   floatformat_always_valid,
    210  1.1  mrg   NULL
    211  1.1  mrg };
    212  1.1  mrg const struct floatformat floatformat_i960_ext =
    213  1.1  mrg {
    214  1.1  mrg   /* Note that the bits from 0 to 15 are unused.  */
    215  1.1  mrg   floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64,
    216  1.1  mrg   floatformat_intbit_yes,
    217  1.1  mrg   "floatformat_i960_ext",
    218  1.1  mrg   floatformat_always_valid,
    219  1.1  mrg   NULL
    220  1.1  mrg };
    221  1.1  mrg const struct floatformat floatformat_m88110_ext =
    222  1.1  mrg {
    223  1.1  mrg   floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
    224  1.1  mrg   floatformat_intbit_yes,
    225  1.1  mrg   "floatformat_m88110_ext",
    226  1.1  mrg   floatformat_always_valid,
    227  1.1  mrg   NULL
    228  1.1  mrg };
    229  1.1  mrg const struct floatformat floatformat_m88110_harris_ext =
    230  1.1  mrg {
    231  1.1  mrg   /* Harris uses raw format 128 bytes long, but the number is just an ieee
    232  1.1  mrg      double, and the last 64 bits are wasted. */
    233  1.1  mrg   floatformat_big,128, 0, 1, 11,  0x3ff,  0x7ff, 12, 52,
    234  1.1  mrg   floatformat_intbit_no,
    235  1.1  mrg   "floatformat_m88110_ext_harris",
    236  1.1  mrg   floatformat_always_valid,
    237  1.1  mrg   NULL
    238  1.1  mrg };
    239  1.1  mrg const struct floatformat floatformat_arm_ext_big =
    240  1.1  mrg {
    241  1.1  mrg   /* Bits 1 to 16 are unused.  */
    242  1.1  mrg   floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
    243  1.1  mrg   floatformat_intbit_yes,
    244  1.1  mrg   "floatformat_arm_ext_big",
    245  1.1  mrg   floatformat_always_valid,
    246  1.1  mrg   NULL
    247  1.1  mrg };
    248  1.1  mrg const struct floatformat floatformat_arm_ext_littlebyte_bigword =
    249  1.1  mrg {
    250  1.1  mrg   /* Bits 1 to 16 are unused.  */
    251  1.1  mrg   floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
    252  1.1  mrg   floatformat_intbit_yes,
    253  1.1  mrg   "floatformat_arm_ext_littlebyte_bigword",
    254  1.1  mrg   floatformat_always_valid,
    255  1.1  mrg   NULL
    256  1.1  mrg };
    257  1.1  mrg const struct floatformat floatformat_ia64_spill_big =
    258  1.1  mrg {
    259  1.1  mrg   floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
    260  1.1  mrg   floatformat_intbit_yes,
    261  1.1  mrg   "floatformat_ia64_spill_big",
    262  1.1  mrg   floatformat_always_valid,
    263  1.1  mrg   NULL
    264  1.1  mrg };
    265  1.1  mrg const struct floatformat floatformat_ia64_spill_little =
    266  1.1  mrg {
    267  1.1  mrg   floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
    268  1.1  mrg   floatformat_intbit_yes,
    269  1.1  mrg   "floatformat_ia64_spill_little",
    270  1.1  mrg   floatformat_always_valid,
    271  1.1  mrg   NULL
    272  1.1  mrg };
    273  1.1  mrg const struct floatformat floatformat_ia64_quad_big =
    274  1.1  mrg {
    275  1.1  mrg   floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
    276  1.1  mrg   floatformat_intbit_no,
    277  1.1  mrg   "floatformat_ia64_quad_big",
    278  1.1  mrg   floatformat_always_valid,
    279  1.1  mrg   NULL
    280  1.1  mrg };
    281  1.1  mrg const struct floatformat floatformat_ia64_quad_little =
    282  1.1  mrg {
    283  1.1  mrg   floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
    284  1.1  mrg   floatformat_intbit_no,
    285  1.1  mrg   "floatformat_ia64_quad_little",
    286  1.1  mrg   floatformat_always_valid,
    287  1.1  mrg   NULL
    288  1.1  mrg };
    289  1.1  mrg 
    290  1.1  mrg static int
    291  1.1  mrg floatformat_ibm_long_double_is_valid (const struct floatformat *fmt,
    292  1.1  mrg 				      const void *from)
    293  1.1  mrg {
    294  1.1  mrg   const unsigned char *ufrom = (const unsigned char *) from;
    295  1.1  mrg   const struct floatformat *hfmt = fmt->split_half;
    296  1.1  mrg   long top_exp, bot_exp;
    297  1.1  mrg   int top_nan = 0;
    298  1.1  mrg 
    299  1.1  mrg   top_exp = get_field (ufrom, hfmt->byteorder, hfmt->totalsize,
    300  1.1  mrg 		       hfmt->exp_start, hfmt->exp_len);
    301  1.1  mrg   bot_exp = get_field (ufrom + 8, hfmt->byteorder, hfmt->totalsize,
    302  1.1  mrg 		       hfmt->exp_start, hfmt->exp_len);
    303  1.1  mrg 
    304  1.1  mrg   if ((unsigned long) top_exp == hfmt->exp_nan)
    305  1.1  mrg     top_nan = mant_bits_set (hfmt, ufrom);
    306  1.1  mrg 
    307  1.1  mrg   /* A NaN is valid with any low part.  */
    308  1.1  mrg   if (top_nan)
    309  1.1  mrg     return 1;
    310  1.1  mrg 
    311  1.1  mrg   /* An infinity, zero or denormal requires low part 0 (positive or
    312  1.1  mrg      negative).  */
    313  1.1  mrg   if ((unsigned long) top_exp == hfmt->exp_nan || top_exp == 0)
    314  1.1  mrg     {
    315  1.1  mrg       if (bot_exp != 0)
    316  1.1  mrg 	return 0;
    317  1.1  mrg 
    318  1.1  mrg       return !mant_bits_set (hfmt, ufrom + 8);
    319  1.1  mrg     }
    320  1.1  mrg 
    321  1.1  mrg   /* The top part is now a finite normal value.  The long double value
    322  1.1  mrg      is the sum of the two parts, and the top part must equal the
    323  1.1  mrg      result of rounding the long double value to nearest double.  Thus
    324  1.1  mrg      the bottom part must be <= 0.5ulp of the top part in absolute
    325  1.1  mrg      value, and if it is < 0.5ulp then the long double is definitely
    326  1.1  mrg      valid.  */
    327  1.1  mrg   if (bot_exp < top_exp - 53)
    328  1.1  mrg     return 1;
    329  1.1  mrg   if (bot_exp > top_exp - 53 && bot_exp != 0)
    330  1.1  mrg     return 0;
    331  1.1  mrg   if (bot_exp == 0)
    332  1.1  mrg     {
    333  1.1  mrg       /* The bottom part is 0 or denormal.  Determine which, and if
    334  1.1  mrg 	 denormal the first two set bits.  */
    335  1.1  mrg       int first_bit = -1, second_bit = -1, cur_bit;
    336  1.1  mrg       for (cur_bit = 0; (unsigned int) cur_bit < hfmt->man_len; cur_bit++)
    337  1.1  mrg 	if (get_field (ufrom + 8, hfmt->byteorder, hfmt->totalsize,
    338  1.1  mrg 		       hfmt->man_start + cur_bit, 1))
    339  1.1  mrg 	  {
    340  1.1  mrg 	    if (first_bit == -1)
    341  1.1  mrg 	      first_bit = cur_bit;
    342  1.1  mrg 	    else
    343  1.1  mrg 	      {
    344  1.1  mrg 		second_bit = cur_bit;
    345  1.1  mrg 		break;
    346  1.1  mrg 	      }
    347  1.1  mrg 	  }
    348  1.1  mrg       /* Bottom part 0 is OK.  */
    349  1.1  mrg       if (first_bit == -1)
    350  1.1  mrg 	return 1;
    351  1.1  mrg       /* The real exponent of the bottom part is -first_bit.  */
    352  1.1  mrg       if (-first_bit < top_exp - 53)
    353  1.1  mrg 	return 1;
    354  1.1  mrg       if (-first_bit > top_exp - 53)
    355  1.1  mrg 	return 0;
    356  1.1  mrg       /* The bottom part is at least 0.5ulp of the top part.  For this
    357  1.1  mrg 	 to be OK, the bottom part must be exactly 0.5ulp (i.e. no
    358  1.1  mrg 	 more bits set) and the top part must have last bit 0.  */
    359  1.1  mrg       if (second_bit != -1)
    360  1.1  mrg 	return 0;
    361  1.1  mrg       return !get_field (ufrom, hfmt->byteorder, hfmt->totalsize,
    362  1.1  mrg 			 hfmt->man_start + hfmt->man_len - 1, 1);
    363  1.1  mrg     }
    364  1.1  mrg   else
    365  1.1  mrg     {
    366  1.1  mrg       /* The bottom part is at least 0.5ulp of the top part.  For this
    367  1.1  mrg 	 to be OK, it must be exactly 0.5ulp (i.e. no explicit bits
    368  1.1  mrg 	 set) and the top part must have last bit 0.  */
    369  1.1  mrg       if (get_field (ufrom, hfmt->byteorder, hfmt->totalsize,
    370  1.1  mrg 		     hfmt->man_start + hfmt->man_len - 1, 1))
    371  1.1  mrg 	return 0;
    372  1.1  mrg       return !mant_bits_set (hfmt, ufrom + 8);
    373  1.1  mrg     }
    374  1.1  mrg }
    375  1.1  mrg 
    376  1.5  mrg const struct floatformat floatformat_ibm_long_double_big =
    377  1.1  mrg {
    378  1.1  mrg   floatformat_big, 128, 0, 1, 11, 1023, 2047, 12, 52,
    379  1.1  mrg   floatformat_intbit_no,
    380  1.5  mrg   "floatformat_ibm_long_double_big",
    381  1.1  mrg   floatformat_ibm_long_double_is_valid,
    382  1.1  mrg   &floatformat_ieee_double_big
    383  1.1  mrg };
    384  1.5  mrg 
    385  1.5  mrg const struct floatformat floatformat_ibm_long_double_little =
    386  1.5  mrg {
    387  1.5  mrg   floatformat_little, 128, 0, 1, 11, 1023, 2047, 12, 52,
    388  1.5  mrg   floatformat_intbit_no,
    389  1.5  mrg   "floatformat_ibm_long_double_little",
    390  1.5  mrg   floatformat_ibm_long_double_is_valid,
    391  1.5  mrg   &floatformat_ieee_double_little
    392  1.5  mrg };
    393  1.1  mrg 
    394  1.1  mrg 
    396  1.1  mrg #ifndef min
    397  1.1  mrg #define min(a, b) ((a) < (b) ? (a) : (b))
    398  1.1  mrg #endif
    399  1.1  mrg 
    400  1.1  mrg /* Return 1 if any bits are explicitly set in the mantissa of UFROM,
    401  1.1  mrg    format FMT, 0 otherwise.  */
    402  1.1  mrg static int
    403  1.1  mrg mant_bits_set (const struct floatformat *fmt, const unsigned char *ufrom)
    404  1.1  mrg {
    405  1.1  mrg   unsigned int mant_bits, mant_off;
    406  1.1  mrg   int mant_bits_left;
    407  1.1  mrg 
    408  1.1  mrg   mant_off = fmt->man_start;
    409  1.1  mrg   mant_bits_left = fmt->man_len;
    410  1.1  mrg   while (mant_bits_left > 0)
    411  1.1  mrg     {
    412  1.1  mrg       mant_bits = min (mant_bits_left, 32);
    413  1.1  mrg 
    414  1.1  mrg       if (get_field (ufrom, fmt->byteorder, fmt->totalsize,
    415  1.1  mrg 		     mant_off, mant_bits) != 0)
    416  1.1  mrg 	return 1;
    417  1.1  mrg 
    418  1.1  mrg       mant_off += mant_bits;
    419  1.1  mrg       mant_bits_left -= mant_bits;
    420  1.1  mrg     }
    421  1.1  mrg   return 0;
    422  1.1  mrg }
    423  1.1  mrg 
    424  1.1  mrg /* Extract a field which starts at START and is LEN bits long.  DATA and
    425  1.1  mrg    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
    426  1.1  mrg static unsigned long
    427  1.1  mrg get_field (const unsigned char *data, enum floatformat_byteorders order,
    428  1.1  mrg            unsigned int total_len, unsigned int start, unsigned int len)
    429  1.1  mrg {
    430  1.1  mrg   unsigned long result = 0;
    431  1.1  mrg   unsigned int cur_byte;
    432  1.1  mrg   int lo_bit, hi_bit, cur_bitshift = 0;
    433  1.1  mrg   int nextbyte = (order == floatformat_little) ? 1 : -1;
    434  1.1  mrg 
    435  1.1  mrg   /* Start is in big-endian bit order!  Fix that first.  */
    436  1.1  mrg   start = total_len - (start + len);
    437  1.1  mrg 
    438  1.1  mrg   /* Start at the least significant part of the field.  */
    439  1.1  mrg   if (order == floatformat_little)
    440  1.1  mrg     cur_byte = start / FLOATFORMAT_CHAR_BIT;
    441  1.1  mrg   else
    442  1.1  mrg     cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT;
    443  1.1  mrg 
    444  1.1  mrg   lo_bit = start % FLOATFORMAT_CHAR_BIT;
    445  1.1  mrg   hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT);
    446  1.1  mrg 
    447  1.1  mrg   do
    448  1.1  mrg     {
    449  1.1  mrg       unsigned int shifted = *(data + cur_byte) >> lo_bit;
    450  1.1  mrg       unsigned int bits = hi_bit - lo_bit;
    451  1.1  mrg       unsigned int mask = (1 << bits) - 1;
    452  1.1  mrg       result |= (shifted & mask) << cur_bitshift;
    453  1.1  mrg       len -= bits;
    454  1.1  mrg       cur_bitshift += bits;
    455  1.1  mrg       cur_byte += nextbyte;
    456  1.1  mrg       lo_bit = 0;
    457  1.1  mrg       hi_bit = min (len, FLOATFORMAT_CHAR_BIT);
    458  1.1  mrg     }
    459  1.1  mrg   while (len != 0);
    460  1.1  mrg 
    461  1.1  mrg   return result;
    462  1.1  mrg }
    463  1.1  mrg 
    464  1.1  mrg /* Convert from FMT to a double.
    465  1.1  mrg    FROM is the address of the extended float.
    466  1.1  mrg    Store the double in *TO.  */
    467  1.1  mrg 
    468  1.1  mrg void
    469  1.1  mrg floatformat_to_double (const struct floatformat *fmt,
    470  1.1  mrg                        const void *from, double *to)
    471  1.1  mrg {
    472  1.1  mrg   const unsigned char *ufrom = (const unsigned char *) from;
    473  1.1  mrg   double dto;
    474  1.1  mrg   long exponent;
    475  1.1  mrg   unsigned long mant;
    476  1.1  mrg   unsigned int mant_bits, mant_off;
    477  1.1  mrg   int mant_bits_left;
    478  1.1  mrg 
    479  1.1  mrg   /* Split values are not handled specially, since the top half has
    480  1.1  mrg      the correctly rounded double value (in the only supported case of
    481  1.1  mrg      split values).  */
    482  1.1  mrg 
    483  1.1  mrg   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
    484  1.1  mrg 			fmt->exp_start, fmt->exp_len);
    485  1.1  mrg 
    486  1.1  mrg   /* If the exponent indicates a NaN, we don't have information to
    487  1.1  mrg      decide what to do.  So we handle it like IEEE, except that we
    488  1.1  mrg      don't try to preserve the type of NaN.  FIXME.  */
    489  1.1  mrg   if ((unsigned long) exponent == fmt->exp_nan)
    490  1.1  mrg     {
    491  1.1  mrg       int nan = mant_bits_set (fmt, ufrom);
    492  1.1  mrg 
    493  1.1  mrg       /* On certain systems (such as GNU/Linux), the use of the
    494  1.1  mrg 	 INFINITY macro below may generate a warning that can not be
    495  1.1  mrg 	 silenced due to a bug in GCC (PR preprocessor/11931).  The
    496  1.1  mrg 	 preprocessor fails to recognise the __extension__ keyword in
    497  1.1  mrg 	 conjunction with the GNU/C99 extension for hexadecimal
    498  1.1  mrg 	 floating point constants and will issue a warning when
    499  1.1  mrg 	 compiling with -pedantic.  */
    500  1.1  mrg       if (nan)
    501  1.1  mrg 	dto = NAN;
    502  1.1  mrg       else
    503  1.1  mrg #ifdef __vax__
    504  1.1  mrg 	dto = HUGE_VAL;
    505  1.1  mrg #else
    506  1.1  mrg 	dto = INFINITY;
    507  1.1  mrg #endif
    508  1.1  mrg 
    509  1.1  mrg       if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
    510  1.1  mrg 	dto = -dto;
    511  1.1  mrg 
    512  1.1  mrg       *to = dto;
    513  1.1  mrg 
    514  1.1  mrg       return;
    515  1.1  mrg     }
    516  1.1  mrg 
    517  1.1  mrg   mant_bits_left = fmt->man_len;
    518  1.1  mrg   mant_off = fmt->man_start;
    519  1.1  mrg   dto = 0.0;
    520  1.1  mrg 
    521  1.1  mrg   /* Build the result algebraically.  Might go infinite, underflow, etc;
    522  1.1  mrg      who cares. */
    523  1.3  mrg 
    524  1.3  mrg   /* For denorms use minimum exponent.  */
    525  1.3  mrg   if (exponent == 0)
    526  1.3  mrg     exponent = 1 - fmt->exp_bias;
    527  1.3  mrg   else
    528  1.3  mrg     {
    529  1.3  mrg       exponent -= fmt->exp_bias;
    530  1.3  mrg 
    531  1.3  mrg       /* If this format uses a hidden bit, explicitly add it in now.
    532  1.3  mrg 	 Otherwise, increment the exponent by one to account for the
    533  1.1  mrg 	 integer bit.  */
    534  1.1  mrg 
    535  1.1  mrg       if (fmt->intbit == floatformat_intbit_no)
    536  1.1  mrg 	dto = ldexp (1.0, exponent);
    537  1.1  mrg       else
    538  1.1  mrg 	exponent++;
    539  1.1  mrg     }
    540  1.1  mrg 
    541  1.1  mrg   while (mant_bits_left > 0)
    542  1.1  mrg     {
    543  1.1  mrg       mant_bits = min (mant_bits_left, 32);
    544  1.1  mrg 
    545  1.1  mrg       mant = get_field (ufrom, fmt->byteorder, fmt->totalsize,
    546  1.1  mrg 			 mant_off, mant_bits);
    547  1.3  mrg 
    548  1.3  mrg       dto += ldexp ((double) mant, exponent - mant_bits);
    549  1.1  mrg       exponent -= mant_bits;
    550  1.1  mrg       mant_off += mant_bits;
    551  1.1  mrg       mant_bits_left -= mant_bits;
    552  1.1  mrg     }
    553  1.1  mrg 
    554  1.1  mrg   /* Negate it if negative.  */
    555  1.1  mrg   if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
    556  1.1  mrg     dto = -dto;
    557  1.1  mrg   *to = dto;
    558  1.1  mrg }
    559  1.1  mrg 
    560  1.1  mrg static void put_field (unsigned char *, enum floatformat_byteorders,
    562  1.1  mrg                        unsigned int,
    563  1.1  mrg                        unsigned int,
    564  1.1  mrg                        unsigned int,
    565  1.1  mrg                        unsigned long);
    566  1.1  mrg 
    567  1.1  mrg /* Set a field which starts at START and is LEN bits long.  DATA and
    568  1.1  mrg    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
    569  1.1  mrg static void
    570  1.1  mrg put_field (unsigned char *data, enum floatformat_byteorders order,
    571  1.1  mrg            unsigned int total_len, unsigned int start, unsigned int len,
    572  1.1  mrg            unsigned long stuff_to_put)
    573  1.1  mrg {
    574  1.1  mrg   unsigned int cur_byte;
    575  1.1  mrg   int lo_bit, hi_bit;
    576  1.1  mrg   int nextbyte = (order == floatformat_little) ? 1 : -1;
    577  1.1  mrg 
    578  1.1  mrg   /* Start is in big-endian bit order!  Fix that first.  */
    579  1.1  mrg   start = total_len - (start + len);
    580  1.1  mrg 
    581  1.1  mrg   /* Start at the least significant part of the field.  */
    582  1.1  mrg   if (order == floatformat_little)
    583  1.1  mrg     cur_byte = start / FLOATFORMAT_CHAR_BIT;
    584  1.1  mrg   else
    585  1.1  mrg     cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT;
    586  1.1  mrg 
    587  1.1  mrg   lo_bit = start % FLOATFORMAT_CHAR_BIT;
    588  1.1  mrg   hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT);
    589  1.1  mrg 
    590  1.1  mrg   do
    591  1.1  mrg     {
    592  1.1  mrg       unsigned char *byte_ptr = data + cur_byte;
    593  1.1  mrg       unsigned int bits = hi_bit - lo_bit;
    594  1.1  mrg       unsigned int mask = ((1 << bits) - 1) << lo_bit;
    595  1.1  mrg       *byte_ptr = (*byte_ptr & ~mask) | ((stuff_to_put << lo_bit) & mask);
    596  1.1  mrg       stuff_to_put >>= bits;
    597  1.1  mrg       len -= bits;
    598  1.1  mrg       cur_byte += nextbyte;
    599  1.1  mrg       lo_bit = 0;
    600  1.1  mrg       hi_bit = min (len, FLOATFORMAT_CHAR_BIT);
    601  1.1  mrg     }
    602  1.1  mrg   while (len != 0);
    603  1.1  mrg }
    604  1.1  mrg 
    605  1.1  mrg /* The converse: convert the double *FROM to an extended float
    606  1.1  mrg    and store where TO points.  Neither FROM nor TO have any alignment
    607  1.1  mrg    restrictions.  */
    608  1.1  mrg 
    609  1.1  mrg void
    610  1.1  mrg floatformat_from_double (const struct floatformat *fmt,
    611  1.1  mrg                          const double *from, void *to)
    612  1.1  mrg {
    613  1.1  mrg   double dfrom;
    614  1.1  mrg   int exponent;
    615  1.1  mrg   double mant;
    616  1.1  mrg   unsigned int mant_bits, mant_off;
    617  1.1  mrg   int mant_bits_left;
    618  1.1  mrg   unsigned char *uto = (unsigned char *) to;
    619  1.1  mrg 
    620  1.1  mrg   dfrom = *from;
    621  1.1  mrg   memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT);
    622  1.1  mrg 
    623  1.1  mrg   /* Split values are not handled specially, since a bottom half of
    624  1.1  mrg      zero is correct for any value representable as double (in the
    625  1.1  mrg      only supported case of split values).  */
    626  1.1  mrg 
    627  1.1  mrg   /* If negative, set the sign bit.  */
    628  1.1  mrg   if (dfrom < 0)
    629  1.1  mrg     {
    630  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1);
    631  1.1  mrg       dfrom = -dfrom;
    632  1.1  mrg     }
    633  1.1  mrg 
    634  1.1  mrg   if (dfrom == 0)
    635  1.1  mrg     {
    636  1.1  mrg       /* 0.0.  */
    637  1.1  mrg       return;
    638  1.1  mrg     }
    639  1.1  mrg 
    640  1.1  mrg   if (dfrom != dfrom)
    641  1.1  mrg     {
    642  1.1  mrg       /* NaN.  */
    643  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
    644  1.1  mrg 		 fmt->exp_len, fmt->exp_nan);
    645  1.1  mrg       /* Be sure it's not infinity, but NaN value is irrelevant.  */
    646  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start,
    647  1.1  mrg 		 32, 1);
    648  1.1  mrg       return;
    649  1.1  mrg     }
    650  1.1  mrg 
    651  1.1  mrg   if (dfrom + dfrom == dfrom)
    652  1.1  mrg     {
    653  1.1  mrg       /* This can only happen for an infinite value (or zero, which we
    654  1.1  mrg 	 already handled above).  */
    655  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
    656  1.1  mrg 		 fmt->exp_len, fmt->exp_nan);
    657  1.1  mrg       return;
    658  1.1  mrg     }
    659  1.1  mrg 
    660  1.1  mrg   mant = frexp (dfrom, &exponent);
    661  1.1  mrg   if (exponent + fmt->exp_bias - 1 > 0)
    662  1.1  mrg     put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
    663  1.1  mrg 	       fmt->exp_len, exponent + fmt->exp_bias - 1);
    664  1.1  mrg   else
    665  1.1  mrg     {
    666  1.1  mrg       /* Handle a denormalized number.  FIXME: What should we do for
    667  1.1  mrg 	 non-IEEE formats?  */
    668  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
    669  1.1  mrg 		 fmt->exp_len, 0);
    670  1.1  mrg       mant = ldexp (mant, exponent + fmt->exp_bias - 1);
    671  1.1  mrg     }
    672  1.1  mrg 
    673  1.1  mrg   mant_bits_left = fmt->man_len;
    674  1.1  mrg   mant_off = fmt->man_start;
    675  1.1  mrg   while (mant_bits_left > 0)
    676  1.1  mrg     {
    677  1.1  mrg       unsigned long mant_long;
    678  1.1  mrg       mant_bits = mant_bits_left < 32 ? mant_bits_left : 32;
    679  1.1  mrg 
    680  1.1  mrg       mant *= 4294967296.0;
    681  1.1  mrg       mant_long = (unsigned long)mant;
    682  1.1  mrg       mant -= mant_long;
    683  1.1  mrg 
    684  1.1  mrg       /* If the integer bit is implicit, and we are not creating a
    685  1.1  mrg 	 denormalized number, then we need to discard it.  */
    686  1.1  mrg       if ((unsigned int) mant_bits_left == fmt->man_len
    687  1.1  mrg 	  && fmt->intbit == floatformat_intbit_no
    688  1.1  mrg 	  && exponent + fmt->exp_bias - 1 > 0)
    689  1.1  mrg 	{
    690  1.1  mrg 	  mant_long &= 0x7fffffff;
    691  1.1  mrg 	  mant_bits -= 1;
    692  1.1  mrg 	}
    693  1.1  mrg       else if (mant_bits < 32)
    694  1.1  mrg 	{
    695  1.1  mrg 	  /* The bits we want are in the most significant MANT_BITS bits of
    696  1.1  mrg 	     mant_long.  Move them to the least significant.  */
    697  1.1  mrg 	  mant_long >>= 32 - mant_bits;
    698  1.1  mrg 	}
    699  1.1  mrg 
    700  1.1  mrg       put_field (uto, fmt->byteorder, fmt->totalsize,
    701  1.1  mrg 		 mant_off, mant_bits, mant_long);
    702  1.1  mrg       mant_off += mant_bits;
    703  1.1  mrg       mant_bits_left -= mant_bits;
    704  1.1  mrg     }
    705  1.1  mrg }
    706  1.1  mrg 
    707  1.1  mrg /* Return non-zero iff the data at FROM is a valid number in format FMT.  */
    708  1.1  mrg 
    709  1.1  mrg int
    710  1.1  mrg floatformat_is_valid (const struct floatformat *fmt, const void *from)
    711  1.1  mrg {
    712  1.1  mrg   return fmt->is_valid (fmt, from);
    713  1.1  mrg }
    714  1.1  mrg 
    715  1.1  mrg 
    716  1.1  mrg #ifdef IEEE_DEBUG
    717  1.1  mrg 
    718  1.1  mrg #include <stdio.h>
    719  1.1  mrg 
    720  1.1  mrg /* This is to be run on a host which uses IEEE floating point.  */
    721  1.1  mrg 
    722  1.1  mrg void
    723  1.1  mrg ieee_test (double n)
    724  1.1  mrg {
    725  1.1  mrg   double result;
    726  1.1  mrg 
    727  1.1  mrg   floatformat_to_double (&floatformat_ieee_double_little, &n, &result);
    728  1.1  mrg   if ((n != result && (! isnan (n) || ! isnan (result)))
    729  1.1  mrg       || (n < 0 && result >= 0)
    730  1.1  mrg       || (n >= 0 && result < 0))
    731  1.1  mrg     printf ("Differ(to): %.20g -> %.20g\n", n, result);
    732  1.1  mrg 
    733  1.1  mrg   floatformat_from_double (&floatformat_ieee_double_little, &n, &result);
    734  1.1  mrg   if ((n != result && (! isnan (n) || ! isnan (result)))
    735  1.1  mrg       || (n < 0 && result >= 0)
    736  1.1  mrg       || (n >= 0 && result < 0))
    737  1.1  mrg     printf ("Differ(from): %.20g -> %.20g\n", n, result);
    738  1.1  mrg 
    739  1.1  mrg #if 0
    740  1.1  mrg   {
    741  1.1  mrg     char exten[16];
    742  1.1  mrg 
    743  1.1  mrg     floatformat_from_double (&floatformat_m68881_ext, &n, exten);
    744  1.1  mrg     floatformat_to_double (&floatformat_m68881_ext, exten, &result);
    745  1.1  mrg     if (n != result)
    746  1.1  mrg       printf ("Differ(to+from): %.20g -> %.20g\n", n, result);
    747  1.1  mrg   }
    748  1.1  mrg #endif
    749  1.1  mrg 
    750  1.1  mrg #if IEEE_DEBUG > 1
    751  1.1  mrg   /* This is to be run on a host which uses 68881 format.  */
    752  1.1  mrg   {
    753  1.1  mrg     long double ex = *(long double *)exten;
    754  1.1  mrg     if (ex != n)
    755  1.1  mrg       printf ("Differ(from vs. extended): %.20g\n", n);
    756  1.1  mrg   }
    757  1.1  mrg #endif
    758  1.1  mrg }
    759  1.1  mrg 
    760  1.1  mrg int
    761  1.1  mrg main (void)
    762  1.1  mrg {
    763  1.3  mrg   ieee_test (0.0);
    764  1.1  mrg   ieee_test (0.5);
    765  1.1  mrg   ieee_test (1.1);
    766  1.1  mrg   ieee_test (256.0);
    767  1.1  mrg   ieee_test (0.12345);
    768  1.1  mrg   ieee_test (234235.78907234);
    769  1.1  mrg   ieee_test (-512.0);
    770  1.1  mrg   ieee_test (-0.004321);
    771  1.1  mrg   ieee_test (1.2E-70);
    772  1.1  mrg   ieee_test (1.2E-316);
    773  1.1  mrg   ieee_test (4.9406564584124654E-324);
    774  1.1  mrg   ieee_test (- 4.9406564584124654E-324);
    775  1.1  mrg   ieee_test (- 0.0);
    776  1.1  mrg   ieee_test (- INFINITY);
    777  1.1  mrg   ieee_test (- NAN);
    778  1.1  mrg   ieee_test (INFINITY);
    779  1.1  mrg   ieee_test (NAN);
    780  1.1  mrg   return 0;
    781           }
    782           #endif
    783