fpu/softfloat-parts.c.inc

   1 /*
   2  * QEMU float support
   3  *
   4  * The code in this source file is derived from release 2a of the SoftFloat
   5  * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
   6  * some later contributions) are provided under that license, as detailed below.
   7  * It has subsequently been modified by contributors to the QEMU Project,
   8  * so some portions are provided under:
   9  *  the SoftFloat-2a license
  10  *  the BSD license
  11  *  GPL-v2-or-later
  12  *
  13  * Any future contributions to this file after December 1st 2014 will be
  14  * taken to be licensed under the Softfloat-2a license unless specifically
  15  * indicated otherwise.
  16  */
  17
  18 static void partsN(return_nan)(FloatPartsN *a, float_status *s)
  19 {
  20     switch (a->cls) {
  21     case float_class_snan:
  22         float_raise(float_flag_invalid, s);
  23         if (s->default_nan_mode) {
  24             parts_default_nan(a, s);
  25         } else {
  26             parts_silence_nan(a, s);
  27         }
  28         break;
  29     case float_class_qnan:
  30         if (s->default_nan_mode) {
  31             parts_default_nan(a, s);
  32         }
  33         break;
  34     default:
  35         g_assert_not_reached();
  36     }
  37 }
  38
  39 static FloatPartsN *partsN(pick_nan)(FloatPartsN *a, FloatPartsN *b,
  40                                      float_status *s)
  41 {
  42     if (is_snan(a->cls) || is_snan(b->cls)) {
  43         float_raise(float_flag_invalid, s);
  44     }
  45
  46     if (s->default_nan_mode) {
  47         parts_default_nan(a, s);
  48     } else {
  49         int cmp = frac_cmp(a, b);
  50         if (cmp == 0) {
  51             cmp = a->sign < b->sign;
  52         }
  53
  54         if (pickNaN(a->cls, b->cls, cmp > 0, s)) {
  55             a = b;
  56         }
  57         if (is_snan(a->cls)) {
  58             parts_silence_nan(a, s);
  59         }
  60     }
  61     return a;
  62 }
  63
  64 static FloatPartsN *partsN(pick_nan_muladd)(FloatPartsN *a, FloatPartsN *b,
  65                                             FloatPartsN *c, float_status *s,
  66                                             int ab_mask, int abc_mask)
  67 {
  68     int which;
  69
  70     if (unlikely(abc_mask & float_cmask_snan)) {
  71         float_raise(float_flag_invalid, s);
  72     }
  73
  74     which = pickNaNMulAdd(a->cls, b->cls, c->cls,
  75                           ab_mask == float_cmask_infzero, s);
  76
  77     if (s->default_nan_mode || which == 3) {
  78         /*
  79          * Note that this check is after pickNaNMulAdd so that function
  80          * has an opportunity to set the Invalid flag for infzero.
  81          */
  82         parts_default_nan(a, s);
  83         return a;
  84     }
  85
  86     switch (which) {
  87     case 0:
  88         break;
  89     case 1:
  90         a = b;
  91         break;
  92     case 2:
  93         a = c;
  94         break;
  95     default:
  96         g_assert_not_reached();
  97     }
  98     if (is_snan(a->cls)) {
  99         parts_silence_nan(a, s);
 100     }
 101     return a;
 102 }
 103
 104 /*
 105  * Canonicalize the FloatParts structure.  Determine the class,
 106  * unbias the exponent, and normalize the fraction.
 107  */
 108 static void partsN(canonicalize)(FloatPartsN *p, float_status *status,
 109                                  const FloatFmt *fmt)
 110 {
 111     if (unlikely(p->exp == 0)) {
 112         if (likely(frac_eqz(p))) {
 113             p->cls = float_class_zero;
 114         } else if (status->flush_inputs_to_zero) {
 115             float_raise(float_flag_input_denormal, status);
 116             p->cls = float_class_zero;
 117             frac_clear(p);
 118         } else {
 119             int shift = frac_normalize(p);
 120             p->cls = float_class_normal;
 121             p->exp = fmt->frac_shift - fmt->exp_bias - shift + 1;
 122         }
 123     } else if (likely(p->exp < fmt->exp_max) || fmt->arm_althp) {
 124         p->cls = float_class_normal;
 125         p->exp -= fmt->exp_bias;
 126         frac_shl(p, fmt->frac_shift);
 127         p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
 128     } else if (likely(frac_eqz(p))) {
 129         p->cls = float_class_inf;
 130     } else {
 131         frac_shl(p, fmt->frac_shift);
 132         p->cls = (parts_is_snan_frac(p->frac_hi, status)
 133                   ? float_class_snan : float_class_qnan);
 134     }
 135 }
 136
 137 /*
 138  * Round and uncanonicalize a floating-point number by parts. There
 139  * are FRAC_SHIFT bits that may require rounding at the bottom of the
 140  * fraction; these bits will be removed. The exponent will be biased
 141  * by EXP_BIAS and must be bounded by [EXP_MAX-1, 0].
 142  */
 143 static void partsN(uncanon)(FloatPartsN *p, float_status *s,
 144                             const FloatFmt *fmt)
 145 {
 146     const int exp_max = fmt->exp_max;
 147     const int frac_shift = fmt->frac_shift;
 148     const uint64_t frac_lsb = fmt->frac_lsb;
 149     const uint64_t frac_lsbm1 = fmt->frac_lsbm1;
 150     const uint64_t round_mask = fmt->round_mask;
 151     const uint64_t roundeven_mask = fmt->roundeven_mask;
 152     uint64_t inc;
 153     bool overflow_norm;
 154     int exp, flags = 0;
 155
 156     if (unlikely(p->cls != float_class_normal)) {
 157         switch (p->cls) {
 158         case float_class_zero:
 159             p->exp = 0;
 160             frac_clear(p);
 161             return;
 162         case float_class_inf:
 163             g_assert(!fmt->arm_althp);
 164             p->exp = fmt->exp_max;
 165             frac_clear(p);
 166             return;
 167         case float_class_qnan:
 168         case float_class_snan:
 169             g_assert(!fmt->arm_althp);
 170             p->exp = fmt->exp_max;
 171             frac_shr(p, fmt->frac_shift);
 172             return;
 173         default:
 174             break;
 175         }
 176         g_assert_not_reached();
 177     }
 178
 179     switch (s->float_rounding_mode) {
 180     case float_round_nearest_even:
 181         overflow_norm = false;
 182         inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
 183         break;
 184     case float_round_ties_away:
 185         overflow_norm = false;
 186         inc = frac_lsbm1;
 187         break;
 188     case float_round_to_zero:
 189         overflow_norm = true;
 190         inc = 0;
 191         break;
 192     case float_round_up:
 193         inc = p->sign ? 0 : round_mask;
 194         overflow_norm = p->sign;
 195         break;
 196     case float_round_down:
 197         inc = p->sign ? round_mask : 0;
 198         overflow_norm = !p->sign;
 199         break;
 200     case float_round_to_odd:
 201         overflow_norm = true;
 202         inc = p->frac_lo & frac_lsb ? 0 : round_mask;
 203         break;
 204     default:
 205         g_assert_not_reached();
 206     }
 207
 208     exp = p->exp + fmt->exp_bias;
 209     if (likely(exp > 0)) {
 210         if (p->frac_lo & round_mask) {
 211             flags |= float_flag_inexact;
 212             if (frac_addi(p, p, inc)) {
 213                 frac_shr(p, 1);
 214                 p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
 215                 exp++;
 216             }
 217         }
 218         frac_shr(p, frac_shift);
 219
 220         if (fmt->arm_althp) {
 221             /* ARM Alt HP eschews Inf and NaN for a wider exponent.  */
 222             if (unlikely(exp > exp_max)) {
 223                 /* Overflow.  Return the maximum normal.  */
 224                 flags = float_flag_invalid;
 225                 exp = exp_max;
 226                 frac_allones(p);
 227             }
 228         } else if (unlikely(exp >= exp_max)) {
 229             flags |= float_flag_overflow | float_flag_inexact;
 230             if (overflow_norm) {
 231                 exp = exp_max - 1;
 232                 frac_allones(p);
 233             } else {
 234                 p->cls = float_class_inf;
 235                 exp = exp_max;
 236                 frac_clear(p);
 237             }
 238         }
 239     } else if (s->flush_to_zero) {
 240         flags |= float_flag_output_denormal;
 241         p->cls = float_class_zero;
 242         exp = 0;
 243         frac_clear(p);
 244     } else {
 245         bool is_tiny = s->tininess_before_rounding || exp < 0;
 246
 247         if (!is_tiny) {
 248             FloatPartsN discard;
 249             is_tiny = !frac_addi(&discard, p, inc);
 250         }
 251
 252         frac_shrjam(p, 1 - exp);
 253
 254         if (p->frac_lo & round_mask) {
 255             /* Need to recompute round-to-even/round-to-odd. */
 256             switch (s->float_rounding_mode) {
 257             case float_round_nearest_even:
 258                 inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
 259                        ? frac_lsbm1 : 0);
 260                 break;
 261             case float_round_to_odd:
 262                 inc = p->frac_lo & frac_lsb ? 0 : round_mask;
 263                 break;
 264             default:
 265                 break;
 266             }
 267             flags |= float_flag_inexact;
 268             frac_addi(p, p, inc);
 269         }
 270
 271         exp = (p->frac_hi & DECOMPOSED_IMPLICIT_BIT) != 0;
 272         frac_shr(p, frac_shift);
 273
 274         if (is_tiny && (flags & float_flag_inexact)) {
 275             flags |= float_flag_underflow;
 276         }
 277         if (exp == 0 && frac_eqz(p)) {
 278             p->cls = float_class_zero;
 279         }
 280     }
 281     p->exp = exp;
 282     float_raise(flags, s);
 283 }
 284
 285 /*
 286  * Returns the result of adding or subtracting the values of the
 287  * floating-point values `a' and `b'. The operation is performed
 288  * according to the IEC/IEEE Standard for Binary Floating-Point
 289  * Arithmetic.
 290  */
 291 static FloatPartsN *partsN(addsub)(FloatPartsN *a, FloatPartsN *b,
 292                                    float_status *s, bool subtract)
 293 {
 294     bool b_sign = b->sign ^ subtract;
 295     int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
 296
 297     if (a->sign != b_sign) {
 298         /* Subtraction */
 299         if (likely(ab_mask == float_cmask_normal)) {
 300             if (parts_sub_normal(a, b)) {
 301                 return a;
 302             }
 303             /* Subtract was exact, fall through to set sign. */
 304             ab_mask = float_cmask_zero;
 305         }
 306
 307         if (ab_mask == float_cmask_zero) {
 308             a->sign = s->float_rounding_mode == float_round_down;
 309             return a;
 310         }
 311
 312         if (unlikely(ab_mask & float_cmask_anynan)) {
 313             goto p_nan;
 314         }
 315
 316         if (ab_mask & float_cmask_inf) {
 317             if (a->cls != float_class_inf) {
 318                 /* N - Inf */
 319                 goto return_b;
 320             }
 321             if (b->cls != float_class_inf) {
 322                 /* Inf - N */
 323                 return a;
 324             }
 325             /* Inf - Inf */
 326             float_raise(float_flag_invalid, s);
 327             parts_default_nan(a, s);
 328             return a;
 329         }
 330     } else {
 331         /* Addition */
 332         if (likely(ab_mask == float_cmask_normal)) {
 333             parts_add_normal(a, b);
 334             return a;
 335         }
 336
 337         if (ab_mask == float_cmask_zero) {
 338             return a;
 339         }
 340
 341         if (unlikely(ab_mask & float_cmask_anynan)) {
 342             goto p_nan;
 343         }
 344
 345         if (ab_mask & float_cmask_inf) {
 346             a->cls = float_class_inf;
 347             return a;
 348         }
 349     }
 350
 351     if (b->cls == float_class_zero) {
 352         g_assert(a->cls == float_class_normal);
 353         return a;
 354     }
 355
 356     g_assert(a->cls == float_class_zero);
 357     g_assert(b->cls == float_class_normal);
 358  return_b:
 359     b->sign = b_sign;
 360     return b;
 361
 362  p_nan:
 363     return parts_pick_nan(a, b, s);
 364 }