diff options
Diffstat (limited to 'soft-fp/op-common.h')
| -rw-r--r-- | soft-fp/op-common.h | 1041 |
1 files changed, 782 insertions, 259 deletions
diff --git a/soft-fp/op-common.h b/soft-fp/op-common.h index f30260e..957f71d 100644 --- a/soft-fp/op-common.h +++ b/soft-fp/op-common.h @@ -21,8 +21,8 @@ Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. */ -#define _FP_DECL(wc, X) \ - _FP_I_TYPE X##_c, X##_s, X##_e; \ +#define _FP_DECL(wc, X) \ + _FP_I_TYPE X##_c __attribute__((unused)), X##_s, X##_e; \ _FP_FRAC_DECL_##wc(X) /* @@ -71,6 +71,87 @@ do { \ } \ } while (0) +/* Finish unpacking an fp value in semi-raw mode: the mantissa is + shifted by _FP_WORKBITS but the implicit MSB is not inserted and + other classification is not done. */ +#define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc(X, _FP_WORKBITS) + +/* A semi-raw value has overflowed to infinity. Adjust the mantissa + and exponent appropriately. */ +#define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \ +do { \ + if (FP_ROUNDMODE == FP_RND_NEAREST \ + || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \ + || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \ + { \ + X##_e = _FP_EXPMAX_##fs; \ + _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ + } \ + else \ + { \ + X##_e = _FP_EXPMAX_##fs - 1; \ + FP_SET_EXCEPTION(FP_EX_OVERFLOW); \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \ + } \ +} while (0) + +/* Check for a semi-raw value being a signaling NaN and raise the + invalid exception if so. */ +#define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \ +do { \ + if (X##_e == _FP_EXPMAX_##fs \ + && !_FP_FRAC_ZEROP_##wc(X) \ + && !(_FP_FRAC_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs)) \ + FP_SET_EXCEPTION(FP_EX_INVALID); \ +} while (0) + +/* Choose a NaN result from an operation on two semi-raw NaN + values. */ +#define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \ +do { \ + /* _FP_CHOOSENAN expects raw values, so shift as required. */ \ + _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ + _FP_FRAC_SRL_##wc(Y, _FP_WORKBITS); \ + _FP_CHOOSENAN(fs, wc, R, X, Y, OP); \ + _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \ +} while (0) + +/* Test whether a biased exponent is normal (not zero or maximum). */ +#define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1) + +/* Prepare to pack an fp value in semi-raw mode: the mantissa is + rounded and shifted right, with the rounding possibly increasing + the exponent (including changing a finite value to infinity). */ +#define _FP_PACK_SEMIRAW(fs, wc, X) \ +do { \ + _FP_ROUND(wc, X); \ + if (_FP_FRAC_HIGH_##fs(X) \ + & (_FP_OVERFLOW_##fs >> 1)) \ + { \ + _FP_FRAC_HIGH_##fs(X) &= ~(_FP_OVERFLOW_##fs >> 1); \ + X##_e++; \ + if (X##_e == _FP_EXPMAX_##fs) \ + _FP_OVERFLOW_SEMIRAW(fs, wc, X); \ + } \ + _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ + if (!_FP_EXP_NORMAL(fs, wc, X) && !_FP_FRAC_ZEROP_##wc(X)) \ + { \ + if (X##_e == 0) \ + FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \ + else \ + { \ + if (!_FP_KEEPNANFRACP) \ + { \ + _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \ + X##_s = _FP_NANSIGN_##fs; \ + } \ + else \ + _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \ + } \ + } \ +} while (0) + /* * Before packing the bits back into the native fp result, take care * of such mundane things as rounding and overflow. Also, for some @@ -202,153 +283,433 @@ do { \ -/* - * Main addition routine. The input values should be cooked. - */ - -#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ -do { \ - switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \ - { \ - case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \ - { \ - /* shift the smaller number so that its exponent matches the larger */ \ - _FP_I_TYPE diff = X##_e - Y##_e; \ - \ - if (diff < 0) \ - { \ - diff = -diff; \ - if (diff <= _FP_WFRACBITS_##fs) \ - _FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs); \ - else if (!_FP_FRAC_ZEROP_##wc(X)) \ - _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ - R##_e = Y##_e; \ - } \ - else \ - { \ - if (diff > 0) \ - { \ - if (diff <= _FP_WFRACBITS_##fs) \ - _FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs); \ - else if (!_FP_FRAC_ZEROP_##wc(Y)) \ - _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \ - } \ - R##_e = X##_e; \ - } \ - \ - R##_c = FP_CLS_NORMAL; \ - \ - if (X##_s == Y##_s) \ - { \ - R##_s = X##_s; \ - _FP_FRAC_ADD_##wc(R, X, Y); \ - if (_FP_FRAC_OVERP_##wc(fs, R)) \ - { \ - _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ - R##_e++; \ - } \ - } \ - else \ - { \ - R##_s = X##_s; \ - _FP_FRAC_SUB_##wc(R, X, Y); \ - if (_FP_FRAC_ZEROP_##wc(R)) \ - { \ - /* return an exact zero */ \ - if (FP_ROUNDMODE == FP_RND_MINF) \ - R##_s |= Y##_s; \ - else \ - R##_s &= Y##_s; \ - R##_c = FP_CLS_ZERO; \ - } \ - else \ - { \ - if (_FP_FRAC_NEGP_##wc(R)) \ - { \ - _FP_FRAC_SUB_##wc(R, Y, X); \ - R##_s = Y##_s; \ - } \ - \ - /* renormalize after subtraction */ \ - _FP_FRAC_CLZ_##wc(diff, R); \ - diff -= _FP_WFRACXBITS_##fs; \ - if (diff) \ - { \ - R##_e -= diff; \ - _FP_FRAC_SLL_##wc(R, diff); \ - } \ - } \ - } \ - break; \ - } \ - \ - case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \ - _FP_CHOOSENAN(fs, wc, R, X, Y, OP); \ - break; \ - \ - case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \ - R##_e = X##_e; \ - case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \ - case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \ - case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \ - _FP_FRAC_COPY_##wc(R, X); \ - R##_s = X##_s; \ - R##_c = X##_c; \ - break; \ - \ - case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \ - R##_e = Y##_e; \ - case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \ - case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \ - case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \ - _FP_FRAC_COPY_##wc(R, Y); \ - R##_s = Y##_s; \ - R##_c = Y##_c; \ - break; \ - \ - case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \ - if (X##_s != Y##_s) \ - { \ - /* +INF + -INF => NAN */ \ - _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ - R##_s = _FP_NANSIGN_##fs; \ - R##_c = FP_CLS_NAN; \ - FP_SET_EXCEPTION(FP_EX_INVALID); \ - break; \ - } \ - /* FALLTHRU */ \ - \ - case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \ - case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \ - R##_s = X##_s; \ - R##_c = FP_CLS_INF; \ - break; \ - \ - case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \ - case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \ - R##_s = Y##_s; \ - R##_c = FP_CLS_INF; \ - break; \ - \ - case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \ - /* make sure the sign is correct */ \ - if (FP_ROUNDMODE == FP_RND_MINF) \ - R##_s = X##_s | Y##_s; \ - else \ - R##_s = X##_s & Y##_s; \ - R##_c = FP_CLS_ZERO; \ - break; \ - \ - default: \ - abort(); \ - } \ +/* Addition on semi-raw values. */ +#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ +do { \ + if (X##_s == Y##_s) \ + { \ + /* Addition. */ \ + R##_s = X##_s; \ + int ediff = X##_e - Y##_e; \ + if (ediff > 0) \ + { \ + R##_e = X##_e; \ + if (Y##_e == 0) \ + { \ + /* Y is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_ADD_##wc(R, X, Y); \ + goto add3; \ + } \ + if (X##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto add_done; \ + } \ + goto add1; \ + } \ + } \ + else if (X##_e == _FP_EXPMAX_##fs) \ + { \ + /* X is NaN or Inf, Y is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto add_done; \ + } \ + \ + /* Insert implicit MSB of Y. */ \ + _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \ + \ + add1: \ + /* Shift the mantissa of Y to the right EDIFF steps; \ + remember to account later for the implicit MSB of X. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc(Y)) \ + _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \ + _FP_FRAC_ADD_##wc(R, X, Y); \ + } \ + else if (ediff < 0) \ + { \ + ediff = -ediff; \ + R##_e = Y##_e; \ + if (X##_e == 0) \ + { \ + /* X is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_ADD_##wc(R, Y, X); \ + goto add3; \ + } \ + if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto add_done; \ + } \ + goto add2; \ + } \ + } \ + else if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + /* Y is NaN or Inf, X is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto add_done; \ + } \ + \ + /* Insert implicit MSB of X. */ \ + _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \ + \ + add2: \ + /* Shift the mantissa of X to the right EDIFF steps; \ + remember to account later for the implicit MSB of Y. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc(X)) \ + _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ + _FP_FRAC_ADD_##wc(R, Y, X); \ + } \ + else \ + { \ + /* ediff == 0. */ \ + if (!_FP_EXP_NORMAL(fs, wc, X)) \ + { \ + if (X##_e == 0) \ + { \ + /* X and Y are zero or denormalized. */ \ + R##_e = 0; \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + { \ + if (!_FP_FRAC_ZEROP_##wc(Y)) \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto add_done; \ + } \ + else if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_ADD_##wc(R, X, Y); \ + if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* Normalized result. */ \ + _FP_FRAC_HIGH_##fs(R) \ + &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ + R##_e = 1; \ + } \ + goto add_done; \ + } \ + } \ + else \ + { \ + /* X and Y are NaN or Inf. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + R##_e = _FP_EXPMAX_##fs; \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + _FP_FRAC_COPY_##wc(R, Y); \ + else if (_FP_FRAC_ZEROP_##wc(Y)) \ + _FP_FRAC_COPY_##wc(R, X); \ + else \ + _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \ + goto add_done; \ + } \ + } \ + /* The exponents of X and Y, both normal, are equal. The \ + implicit MSBs will always add to increase the \ + exponent. */ \ + _FP_FRAC_ADD_##wc(R, X, Y); \ + R##_e = X##_e + 1; \ + _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ + if (R##_e == _FP_EXPMAX_##fs) \ + /* Overflow to infinity (depending on rounding mode). */ \ + _FP_OVERFLOW_SEMIRAW(fs, wc, R); \ + goto add_done; \ + } \ + add3: \ + if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* Overflow. */ \ + _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ + R##_e++; \ + _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ + if (R##_e == _FP_EXPMAX_##fs) \ + /* Overflow to infinity (depending on rounding mode). */ \ + _FP_OVERFLOW_SEMIRAW(fs, wc, R); \ + } \ + add_done: ; \ + } \ + else \ + { \ + /* Subtraction. */ \ + int ediff = X##_e - Y##_e; \ + if (ediff > 0) \ + { \ + R##_e = X##_e; \ + R##_s = X##_s; \ + if (Y##_e == 0) \ + { \ + /* Y is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_SUB_##wc(R, X, Y); \ + goto sub3; \ + } \ + if (X##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto sub_done; \ + } \ + goto sub1; \ + } \ + } \ + else if (X##_e == _FP_EXPMAX_##fs) \ + { \ + /* X is NaN or Inf, Y is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_FRAC_COPY_##wc(R, X); \ + goto sub_done; \ + } \ + \ + /* Insert implicit MSB of Y. */ \ + _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \ + \ + sub1: \ + /* Shift the mantissa of Y to the right EDIFF steps; \ + remember to account later for the implicit MSB of X. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc(Y)) \ + _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \ + _FP_FRAC_SUB_##wc(R, X, Y); \ + } \ + else if (ediff < 0) \ + { \ + ediff = -ediff; \ + R##_e = Y##_e; \ + R##_s = Y##_s; \ + if (X##_e == 0) \ + { \ + /* X is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_SUB_##wc(R, Y, X); \ + goto sub3; \ + } \ + if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto sub_done; \ + } \ + goto sub2; \ + } \ + } \ + else if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + /* Y is NaN or Inf, X is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + _FP_FRAC_COPY_##wc(R, Y); \ + goto sub_done; \ + } \ + \ + /* Insert implicit MSB of X. */ \ + _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \ + \ + sub2: \ + /* Shift the mantissa of X to the right EDIFF steps; \ + remember to account later for the implicit MSB of Y. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc(X)) \ + _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ + _FP_FRAC_SUB_##wc(R, Y, X); \ + } \ + else \ + { \ + /* ediff == 0. */ \ + if (!_FP_EXP_NORMAL(fs, wc, X)) \ + { \ + if (X##_e == 0) \ + { \ + /* X and Y are zero or denormalized. */ \ + R##_e = 0; \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + { \ + _FP_FRAC_COPY_##wc(R, Y); \ + if (_FP_FRAC_ZEROP_##wc(Y)) \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + R##_s = Y##_s; \ + } \ + goto sub_done; \ + } \ + else if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc(R, X); \ + R##_s = X##_s; \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_SUB_##wc(R, X, Y); \ + R##_s = X##_s; \ + if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* |X| < |Y|, negate result. */ \ + _FP_FRAC_SUB_##wc(R, Y, X); \ + R##_s = Y##_s; \ + } \ + else if (_FP_FRAC_ZEROP_##wc(R)) \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + goto sub_done; \ + } \ + } \ + else \ + { \ + /* X and Y are NaN or Inf, of opposite signs. */ \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ + _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ + R##_e = _FP_EXPMAX_##fs; \ + if (_FP_FRAC_ZEROP_##wc(X)) \ + { \ + if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + /* Inf - Inf. */ \ + R##_s = _FP_NANSIGN_##fs; \ + _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ + _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \ + FP_SET_EXCEPTION(FP_EX_INVALID); \ + } \ + else \ + { \ + /* Inf - NaN. */ \ + R##_s = Y##_s; \ + _FP_FRAC_COPY_##wc(R, Y); \ + } \ + } \ + else \ + { \ + if (_FP_FRAC_ZEROP_##wc(Y)) \ + { \ + /* NaN - Inf. */ \ + R##_s = X##_s; \ + _FP_FRAC_COPY_##wc(R, X); \ + } \ + else \ + { \ + /* NaN - NaN. */ \ + _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \ + } \ + } \ + goto sub_done; \ + } \ + } \ + /* The exponents of X and Y, both normal, are equal. The \ + implicit MSBs cancel. */ \ + R##_e = X##_e; \ + _FP_FRAC_SUB_##wc(R, X, Y); \ + R##_s = X##_s; \ + if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* |X| < |Y|, negate result. */ \ + _FP_FRAC_SUB_##wc(R, Y, X); \ + R##_s = Y##_s; \ + } \ + else if (_FP_FRAC_ZEROP_##wc(R)) \ + { \ + R##_e = 0; \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + goto sub_done; \ + } \ + goto norm; \ + } \ + sub3: \ + if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ + { \ + int diff; \ + /* Carry into most significant bit of larger one of X and Y, \ + canceling it; renormalize. */ \ + _FP_FRAC_HIGH_##fs(R) &= _FP_IMPLBIT_SH_##fs - 1; \ + norm: \ + _FP_FRAC_CLZ_##wc(diff, R); \ + diff -= _FP_WFRACXBITS_##fs; \ + _FP_FRAC_SLL_##wc(R, diff); \ + if (R##_e <= diff) \ + { \ + /* R is denormalized. */ \ + diff = diff - R##_e + 1; \ + _FP_FRAC_SRS_##wc(R, diff, _FP_WFRACBITS_##fs); \ + R##_e = 0; \ + } \ + else \ + { \ + R##_e -= diff; \ + _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ + } \ + } \ + sub_done: ; \ + } \ } while (0) #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+') -#define _FP_SUB(fs, wc, R, X, Y) \ - do { \ - if (Y##_c != FP_CLS_NAN) Y##_s ^= 1; \ - _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \ +#define _FP_SUB(fs, wc, R, X, Y) \ + do { \ + if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) Y##_s ^= 1; \ + _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \ } while (0) @@ -537,20 +898,20 @@ do { \ /* Simplification for strict equality. */ -#define _FP_CMP_EQ(fs, wc, ret, X, Y) \ - do { \ - /* NANs are unordered */ \ - if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \ - || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \ - { \ - ret = 1; \ - } \ - else \ - { \ - ret = !(X##_e == Y##_e \ - && _FP_FRAC_EQ_##wc(X, Y) \ - && (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \ - } \ +#define _FP_CMP_EQ(fs, wc, ret, X, Y) \ + do { \ + /* NANs are unordered */ \ + if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \ + || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \ + { \ + ret = 1; \ + } \ + else \ + { \ + ret = !(X##_e == Y##_e \ + && _FP_FRAC_EQ_##wc(X, Y) \ + && (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc(X)))); \ + } \ } while (0) /* Version to test unordered. */ @@ -616,115 +977,277 @@ do { \ } while (0) /* - * Convert from FP to integer + * Convert from FP to integer. Input is raw. */ /* RSIGNED can have following values: * 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus - * the result is either 0 or (2^rsize)-1 depending on the sign in such case. - * 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is - * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending - * on the sign in such case. + * the result is either 0 or (2^rsize)-1 depending on the sign in such + * case. + * 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, + * NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 + * depending on the sign in such case. * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is - * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending - * on the sign in such case. + * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 + * depending on the sign in such case. */ -#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \ - do { \ - switch (X##_c) \ - { \ - case FP_CLS_NORMAL: \ - if (X##_e < 0) \ - { \ - FP_SET_EXCEPTION(FP_EX_INEXACT); \ - case FP_CLS_ZERO: \ - r = 0; \ - } \ - else if (X##_e >= rsize - (rsigned > 0 || X##_s) \ - || (!rsigned && X##_s)) \ - { /* overflow */ \ - case FP_CLS_NAN: \ - case FP_CLS_INF: \ - if (rsigned) \ - { \ - r = 1; \ - r <<= rsize - 1; \ - r -= 1 - X##_s; \ - } else { \ - r = 0; \ - if (X##_s) \ - r = ~r; \ - } \ - FP_SET_EXCEPTION(FP_EX_INVALID); \ - } \ - else \ - { \ - if (_FP_W_TYPE_SIZE*wc < rsize) \ - { \ - _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ - r <<= X##_e - _FP_WFRACBITS_##fs; \ - } \ - else \ - { \ - if (X##_e >= _FP_WFRACBITS_##fs) \ - _FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1)); \ - else if (X##_e < _FP_WFRACBITS_##fs - 1) \ - { \ - _FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2), \ - _FP_WFRACBITS_##fs); \ - if (_FP_FRAC_LOW_##wc(X) & 1) \ - FP_SET_EXCEPTION(FP_EX_INEXACT); \ - _FP_FRAC_SRL_##wc(X, 1); \ - } \ - _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ - } \ - if (rsigned && X##_s) \ - r = -r; \ - } \ - break; \ - } \ - } while (0) - -#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \ - do { \ - if (r) \ - { \ - unsigned rtype ur_; \ - X##_c = FP_CLS_NORMAL; \ - \ - if ((X##_s = (r < 0))) \ - r = -r; \ - \ - ur_ = (unsigned rtype) r; \ - if (rsize <= _FP_W_TYPE_SIZE) \ - __FP_CLZ(X##_e, ur_); \ - else \ - __FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \ - (_FP_W_TYPE)ur_); \ - if (rsize < _FP_W_TYPE_SIZE) \ - X##_e -= (_FP_W_TYPE_SIZE - rsize); \ - X##_e = rsize - X##_e - 1; \ +#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \ +do { \ + if (X##_e < _FP_EXPBIAS_##fs) \ + { \ + r = 0; \ + if (X##_e == 0) \ + { \ + if (!_FP_FRAC_ZEROP_##wc(X)) \ + { \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + } \ + } \ + else \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + } \ + else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \ + || (!rsigned && X##_s)) \ + { \ + /* Overflow or converting to the most negative integer. */ \ + if (rsigned) \ + { \ + r = 1; \ + r <<= rsize - 1; \ + r -= 1 - X##_s; \ + } else { \ + r = 0; \ + if (X##_s) \ + r = ~r; \ + } \ \ - if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e) \ - __FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\ - _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \ - if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0) \ - _FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1)); \ - } \ - else \ - { \ - X##_c = FP_CLS_ZERO, X##_s = 0; \ - } \ + if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \ + { \ + /* Possibly converting to most negative integer; check the \ + mantissa. */ \ + int inexact = 0; \ + (void)((_FP_FRACBITS_##fs > rsize) \ + ? ({ _FP_FRAC_SRST_##wc(X, inexact, \ + _FP_FRACBITS_##fs - rsize, \ + _FP_FRACBITS_##fs); 0; }) \ + : 0); \ + if (!_FP_FRAC_ZEROP_##wc(X)) \ + FP_SET_EXCEPTION(FP_EX_INVALID); \ + else if (inexact) \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + } \ + else \ + FP_SET_EXCEPTION(FP_EX_INVALID); \ + } \ + else \ + { \ + _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \ + if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \ + { \ + _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ + r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \ + } \ + else \ + { \ + int inexact; \ + _FP_FRAC_SRST_##wc(X, inexact, \ + (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \ + - X##_e), \ + _FP_FRACBITS_##fs); \ + if (inexact) \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ + } \ + if (rsigned && X##_s) \ + r = -r; \ + } \ +} while (0) + +/* Convert integer to fp. Output is raw. RTYPE is unsigned even if + input is signed. */ +#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \ + do { \ + if (r) \ + { \ + rtype ur_; \ + \ + if ((X##_s = (r < 0))) \ + r = -(rtype)r; \ + \ + ur_ = (rtype) r; \ + (void)((rsize <= _FP_W_TYPE_SIZE) \ + ? ({ \ + int lz_; \ + __FP_CLZ(lz_, (_FP_W_TYPE)ur_); \ + X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \ + }) \ + : ((rsize <= 2 * _FP_W_TYPE_SIZE) \ + ? ({ \ + int lz_; \ + __FP_CLZ_2(lz_, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \ + (_FP_W_TYPE)ur_); \ + X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \ + - lz_); \ + }) \ + : (abort(), 0))); \ + \ + if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \ + && X##_e >= _FP_EXPMAX_##fs) \ + { \ + /* Exponent too big; overflow to infinity. (May also \ + happen after rounding below.) */ \ + _FP_OVERFLOW_SEMIRAW(fs, wc, X); \ + goto pack_semiraw; \ + } \ + \ + if (rsize <= _FP_FRACBITS_##fs \ + || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \ + { \ + /* Exactly representable; shift left. */ \ + _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \ + _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \ + + _FP_FRACBITS_##fs - 1 - X##_e)); \ + } \ + else \ + { \ + /* More bits in integer than in floating type; need to \ + round. */ \ + if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \ + ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \ + - _FP_WFRACBITS_##fs + 1)) \ + | ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \ + - _FP_WFRACBITS_##fs + 1))) \ + != 0)); \ + _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \ + if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \ + _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \ + + _FP_WFRACBITS_##fs - 1 - X##_e)); \ + _FP_FRAC_HIGH_##fs(X) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ + pack_semiraw: \ + _FP_PACK_SEMIRAW(fs, wc, X); \ + } \ + } \ + else \ + { \ + X##_s = 0; \ + X##_e = 0; \ + _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ + } \ } while (0) -#define FP_CONV(dfs,sfs,dwc,swc,D,S) \ - do { \ - _FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S); \ - D##_e = S##_e; \ - D##_c = S##_c; \ - D##_s = S##_s; \ - } while (0) +/* Extend from a narrower floating-point format to a wider one. Input + and output are raw. */ +#define FP_EXTEND(dfs,sfs,dwc,swc,D,S) \ +do { \ + if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \ + || (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \ + < _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \ + || _FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \ + abort(); \ + D##_s = S##_s; \ + _FP_FRAC_COPY_##dwc##_##swc(D, S); \ + if (_FP_EXP_NORMAL(sfs, swc, S)) \ + { \ + D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ + _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \ + } \ + else \ + { \ + if (S##_e == 0) \ + { \ + if (_FP_FRAC_ZEROP_##swc(S)) \ + D##_e = 0; \ + else \ + { \ + int _lz; \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + _FP_FRAC_CLZ_##swc(_lz, S); \ + _FP_FRAC_SLL_##dwc(D, \ + _lz + _FP_FRACBITS_##dfs \ + - _FP_FRACTBITS_##sfs); \ + D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \ + + _FP_FRACXBITS_##sfs - _lz); \ + } \ + } \ + else \ + { \ + D##_e = _FP_EXPMAX_##dfs; \ + if (!_FP_FRAC_ZEROP_##swc(S)) \ + { \ + if (!(_FP_FRAC_HIGH_RAW_##sfs(S) & _FP_QNANBIT_##sfs)) \ + FP_SET_EXCEPTION(FP_EX_INVALID); \ + _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \ + - _FP_FRACBITS_##sfs)); \ + } \ + } \ + } \ +} while (0) + +/* Truncate from a wider floating-point format to a narrower one. + Input and output are semi-raw. */ +#define FP_TRUNC(dfs,sfs,dwc,swc,D,S) \ +do { \ + if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \ + || _FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \ + abort(); \ + D##_s = S##_s; \ + if (_FP_EXP_NORMAL(sfs, swc, S)) \ + { \ + D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ + if (D##_e >= _FP_EXPMAX_##dfs) \ + _FP_OVERFLOW_SEMIRAW(dfs, dwc, D); \ + else \ + { \ + if (D##_e <= 0) \ + { \ + if (D##_e <= 1 - _FP_FRACBITS_##dfs) \ + _FP_FRAC_SET_##swc(S, _FP_ZEROFRAC_##swc); \ + else \ + { \ + _FP_FRAC_HIGH_##sfs(S) |= _FP_IMPLBIT_SH_##sfs; \ + _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs + 1 - D##_e), \ + _FP_WFRACBITS_##sfs); \ + } \ + D##_e = 0; \ + } \ + else \ + _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs), \ + _FP_WFRACBITS_##sfs); \ + _FP_FRAC_COPY_##dwc##_##swc(D, S); \ + } \ + } \ + else \ + { \ + if (S##_e == 0) \ + { \ + D##_e = 0; \ + _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \ + if (!_FP_FRAC_ZEROP_##swc(S)) \ + { \ + FP_SET_EXCEPTION(FP_EX_DENORM); \ + FP_SET_EXCEPTION(FP_EX_INEXACT); \ + } \ + } \ + else \ + { \ + D##_e = _FP_EXPMAX_##dfs; \ + if (_FP_FRAC_ZEROP_##swc(S)) \ + _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \ + else \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW(sfs, swc, S); \ + _FP_FRAC_SRL_##swc(S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs)); \ + _FP_FRAC_COPY_##dwc##_##swc(D, S); \ + _FP_FRAC_HIGH_##dfs(D) |= _FP_QNANBIT_SH_##dfs; \ + } \ + } \ + } \ +} while (0) /* * Helper primitives. |