| /* Software floating-point emulation. Common operations. |
| Copyright (C) 1997-2014 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Richard Henderson (rth@cygnus.com), |
| Jakub Jelinek (jj@ultra.linux.cz), |
| David S. Miller (davem@redhat.com) and |
| Peter Maydell (pmaydell@chiark.greenend.org.uk). |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| In addition to the permissions in the GNU Lesser General Public |
| License, the Free Software Foundation gives you unlimited |
| permission to link the compiled version of this file into |
| combinations with other programs, and to distribute those |
| combinations without any restriction coming from the use of this |
| file. (The Lesser General Public License restrictions do apply in |
| other respects; for example, they cover modification of the file, |
| and distribution when not linked into a combine executable.) |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #define _FP_DECL(wc, X) \ |
| _FP_I_TYPE X##_c __attribute__ ((unused)); \ |
| _FP_I_TYPE X##_s __attribute__ ((unused)); \ |
| _FP_I_TYPE X##_e __attribute__ ((unused)); \ |
| _FP_FRAC_DECL_##wc (X) |
| |
| /* Test whether the qNaN bit denotes a signaling NaN. */ |
| #define _FP_FRAC_SNANP(fs, X) \ |
| ((_FP_QNANNEGATEDP) \ |
| ? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \ |
| : !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs)) |
| #define _FP_FRAC_SNANP_SEMIRAW(fs, X) \ |
| ((_FP_QNANNEGATEDP) \ |
| ? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \ |
| : !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs)) |
| |
| /* Finish truly unpacking a native fp value by classifying the kind |
| of fp value and normalizing both the exponent and the fraction. */ |
| |
| #define _FP_UNPACK_CANONICAL(fs, wc, X) \ |
| do \ |
| { \ |
| switch (X##_e) \ |
| { \ |
| default: \ |
| _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ |
| _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ |
| X##_e -= _FP_EXPBIAS_##fs; \ |
| X##_c = FP_CLS_NORMAL; \ |
| break; \ |
| \ |
| case 0: \ |
| if (_FP_FRAC_ZEROP_##wc (X)) \ |
| X##_c = FP_CLS_ZERO; \ |
| else if (FP_DENORM_ZERO) \ |
| { \ |
| X##_c = FP_CLS_ZERO; \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| } \ |
| else \ |
| { \ |
| /* A denormalized number. */ \ |
| _FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \ |
| _FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \ |
| X); \ |
| _FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \ |
| _FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \ |
| + _FP_WORKBITS)); \ |
| X##_e -= (_FP_EXPBIAS_##fs - 1 \ |
| + _FP_UNPACK_CANONICAL_shift); \ |
| X##_c = FP_CLS_NORMAL; \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| } \ |
| break; \ |
| \ |
| case _FP_EXPMAX_##fs: \ |
| if (_FP_FRAC_ZEROP_##wc (X)) \ |
| X##_c = FP_CLS_INF; \ |
| else \ |
| { \ |
| X##_c = FP_CLS_NAN; \ |
| /* Check for signaling NaN. */ \ |
| if (_FP_FRAC_SNANP (fs, X)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID \ |
| | FP_EX_INVALID_SNAN); \ |
| } \ |
| break; \ |
| } \ |
| } \ |
| 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) |
| |
| /* Check whether a raw or semi-raw input value should be flushed to |
| zero, and flush it to zero if so. */ |
| #define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \ |
| do \ |
| { \ |
| if (FP_DENORM_ZERO \ |
| && X##_e == 0 \ |
| && !_FP_FRAC_ZEROP_##wc (X)) \ |
| { \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| } \ |
| } \ |
| while (0) |
| |
| /* 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_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ |
| } \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ |
| } \ |
| 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_SNANP_SEMIRAW (fs, X)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \ |
| } \ |
| 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) |
| |
| /* Make the fractional part a quiet NaN, preserving the payload |
| if possible, otherwise make it the canonical quiet NaN and set |
| the sign bit accordingly. */ |
| #define _FP_SETQNAN(fs, wc, X) \ |
| do \ |
| { \ |
| if (_FP_QNANNEGATEDP) \ |
| { \ |
| _FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \ |
| if (_FP_FRAC_ZEROP_##wc (X)) \ |
| { \ |
| X##_s = _FP_NANSIGN_##fs; \ |
| _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ |
| } \ |
| } \ |
| else \ |
| _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \ |
| } \ |
| while (0) |
| #define _FP_SETQNAN_SEMIRAW(fs, wc, X) \ |
| do \ |
| { \ |
| if (_FP_QNANNEGATEDP) \ |
| { \ |
| _FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \ |
| if (_FP_FRAC_ZEROP_##wc (X)) \ |
| { \ |
| X##_s = _FP_NANSIGN_##fs; \ |
| _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ |
| _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ |
| } \ |
| } \ |
| else \ |
| _FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \ |
| } \ |
| 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 \ |
| { \ |
| int _FP_PACK_SEMIRAW_is_tiny \ |
| = X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \ |
| if (_FP_TININESS_AFTER_ROUNDING \ |
| && _FP_PACK_SEMIRAW_is_tiny) \ |
| { \ |
| FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \ |
| _FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \ |
| _FP_PACK_SEMIRAW_T##_s = X##_s; \ |
| _FP_PACK_SEMIRAW_T##_e = X##_e; \ |
| _FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \ |
| _FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \ |
| if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \ |
| _FP_PACK_SEMIRAW_is_tiny = 0; \ |
| } \ |
| _FP_ROUND (wc, X); \ |
| if (_FP_PACK_SEMIRAW_is_tiny) \ |
| { \ |
| if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ |
| || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \ |
| FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ |
| } \ |
| 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 (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ |
| { \ |
| if (!_FP_KEEPNANFRACP) \ |
| { \ |
| _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ |
| X##_s = _FP_NANSIGN_##fs; \ |
| } \ |
| else \ |
| _FP_SETQNAN (fs, wc, X); \ |
| } \ |
| } \ |
| 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 |
| kinds of fp values, the original parts may not have been fully |
| extracted -- but that is ok, we can regenerate them now. */ |
| |
| #define _FP_PACK_CANONICAL(fs, wc, X) \ |
| do \ |
| { \ |
| switch (X##_c) \ |
| { \ |
| case FP_CLS_NORMAL: \ |
| X##_e += _FP_EXPBIAS_##fs; \ |
| if (X##_e > 0) \ |
| { \ |
| _FP_ROUND (wc, X); \ |
| if (_FP_FRAC_OVERP_##wc (fs, X)) \ |
| { \ |
| _FP_FRAC_CLEAR_OVERP_##wc (fs, X); \ |
| X##_e++; \ |
| } \ |
| _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ |
| if (X##_e >= _FP_EXPMAX_##fs) \ |
| { \ |
| /* Overflow. */ \ |
| switch (FP_ROUNDMODE) \ |
| { \ |
| case FP_RND_NEAREST: \ |
| X##_c = FP_CLS_INF; \ |
| break; \ |
| case FP_RND_PINF: \ |
| if (!X##_s) \ |
| X##_c = FP_CLS_INF; \ |
| break; \ |
| case FP_RND_MINF: \ |
| if (X##_s) \ |
| X##_c = FP_CLS_INF; \ |
| break; \ |
| } \ |
| if (X##_c == FP_CLS_INF) \ |
| { \ |
| /* Overflow to infinity. */ \ |
| X##_e = _FP_EXPMAX_##fs; \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| } \ |
| else \ |
| { \ |
| /* Overflow to maximum normal. */ \ |
| X##_e = _FP_EXPMAX_##fs - 1; \ |
| _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ |
| } \ |
| FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| } \ |
| } \ |
| else \ |
| { \ |
| /* We've got a denormalized number. */ \ |
| int _FP_PACK_CANONICAL_is_tiny = 1; \ |
| if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \ |
| { \ |
| FP_DECL_##fs (_FP_PACK_CANONICAL_T); \ |
| _FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \ |
| _FP_PACK_CANONICAL_T##_s = X##_s; \ |
| _FP_PACK_CANONICAL_T##_e = X##_e; \ |
| _FP_ROUND (wc, _FP_PACK_CANONICAL_T); \ |
| if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \ |
| _FP_PACK_CANONICAL_is_tiny = 0; \ |
| } \ |
| X##_e = -X##_e + 1; \ |
| if (X##_e <= _FP_WFRACBITS_##fs) \ |
| { \ |
| _FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \ |
| _FP_ROUND (wc, X); \ |
| if (_FP_FRAC_HIGH_##fs (X) \ |
| & (_FP_OVERFLOW_##fs >> 1)) \ |
| { \ |
| X##_e = 1; \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| } \ |
| else \ |
| { \ |
| X##_e = 0; \ |
| _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ |
| } \ |
| if (_FP_PACK_CANONICAL_is_tiny \ |
| && ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ |
| || (FP_TRAPPING_EXCEPTIONS \ |
| & FP_EX_UNDERFLOW))) \ |
| FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ |
| } \ |
| else \ |
| { \ |
| /* Underflow to zero. */ \ |
| X##_e = 0; \ |
| if (!_FP_FRAC_ZEROP_##wc (X)) \ |
| { \ |
| _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ |
| _FP_ROUND (wc, X); \ |
| _FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \ |
| } \ |
| FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ |
| } \ |
| } \ |
| break; \ |
| \ |
| case FP_CLS_ZERO: \ |
| X##_e = 0; \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| break; \ |
| \ |
| case FP_CLS_INF: \ |
| X##_e = _FP_EXPMAX_##fs; \ |
| _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ |
| break; \ |
| \ |
| case FP_CLS_NAN: \ |
| X##_e = _FP_EXPMAX_##fs; \ |
| if (!_FP_KEEPNANFRACP) \ |
| { \ |
| _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ |
| X##_s = _FP_NANSIGN_##fs; \ |
| } \ |
| else \ |
| _FP_SETQNAN (fs, wc, X); \ |
| break; \ |
| } \ |
| } \ |
| while (0) |
| |
| /* This one accepts raw argument and not cooked, returns |
| 1 if X is a signaling NaN. */ |
| #define _FP_ISSIGNAN(fs, wc, X) \ |
| ({ \ |
| int _FP_ISSIGNAN_ret = 0; \ |
| if (X##_e == _FP_EXPMAX_##fs) \ |
| { \ |
| if (!_FP_FRAC_ZEROP_##wc (X) \ |
| && _FP_FRAC_SNANP (fs, X)) \ |
| _FP_ISSIGNAN_ret = 1; \ |
| } \ |
| _FP_ISSIGNAN_ret; \ |
| }) |
| |
| |
| |
| |
| |
| /* Addition on semi-raw values. */ |
| #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ |
| do \ |
| { \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ |
| if (X##_s == Y##_s) \ |
| { \ |
| /* Addition. */ \ |
| R##_s = X##_s; \ |
| int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \ |
| if (_FP_ADD_INTERNAL_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); \ |
| _FP_ADD_INTERNAL_ediff--; \ |
| if (_FP_ADD_INTERNAL_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 \ |
| _FP_ADD_INTERNAL_EDIFF steps; remember to account \ |
| later for the implicit MSB of X. */ \ |
| if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ |
| _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \ |
| { \ |
| _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \ |
| _FP_ADD_INTERNAL_ediff--; \ |
| if (_FP_ADD_INTERNAL_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 \ |
| _FP_ADD_INTERNAL_EDIFF steps; remember to account \ |
| later for the implicit MSB of Y. */ \ |
| if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ |
| _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \ |
| { \ |
| /* _FP_ADD_INTERNAL_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 _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \ |
| if (_FP_ADD_INTERNAL_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); \ |
| _FP_ADD_INTERNAL_ediff--; \ |
| if (_FP_ADD_INTERNAL_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 \ |
| _FP_ADD_INTERNAL_EDIFF steps; remember to account \ |
| later for the implicit MSB of X. */ \ |
| if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ |
| _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \ |
| { \ |
| _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \ |
| _FP_ADD_INTERNAL_ediff--; \ |
| if (_FP_ADD_INTERNAL_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 \ |
| _FP_ADD_INTERNAL_EDIFF steps; remember to account \ |
| later for the implicit MSB of Y. */ \ |
| if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \ |
| _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \ |
| | FP_EX_INVALID_ISI); \ |
| } \ |
| 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 _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_diff, R); \ |
| _FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \ |
| _FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \ |
| if (R##_e <= _FP_ADD_INTERNAL_diff) \ |
| { \ |
| /* R is denormalized. */ \ |
| _FP_ADD_INTERNAL_diff \ |
| = _FP_ADD_INTERNAL_diff - R##_e + 1; \ |
| _FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \ |
| _FP_WFRACBITS_##fs); \ |
| R##_e = 0; \ |
| } \ |
| else \ |
| { \ |
| R##_e -= _FP_ADD_INTERNAL_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##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ |
| Y##_s ^= 1; \ |
| _FP_ADD_INTERNAL (fs, wc, R, X, Y, '-'); \ |
| } \ |
| while (0) |
| |
| |
| /* Main negation routine. The input value is raw. */ |
| |
| #define _FP_NEG(fs, wc, R, X) \ |
| do \ |
| { \ |
| _FP_FRAC_COPY_##wc (R, X); \ |
| R##_e = X##_e; \ |
| R##_s = 1 ^ X##_s; \ |
| } \ |
| while (0) |
| |
| |
| /* Main multiplication routine. The input values should be cooked. */ |
| |
| #define _FP_MUL(fs, wc, R, X, Y) \ |
| do \ |
| { \ |
| R##_s = X##_s ^ Y##_s; \ |
| R##_e = X##_e + Y##_e + 1; \ |
| switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ |
| { \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ |
| R##_c = FP_CLS_NORMAL; \ |
| \ |
| _FP_MUL_MEAT_##fs (R, X, Y); \ |
| \ |
| if (_FP_FRAC_OVERP_##wc (fs, R)) \ |
| _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ |
| else \ |
| R##_e--; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ |
| _FP_CHOOSENAN (fs, wc, R, X, Y, '*'); \ |
| break; \ |
| \ |
| 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): \ |
| R##_s = X##_s; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ |
| _FP_FRAC_COPY_##wc (R, X); \ |
| R##_c = X##_c; \ |
| break; \ |
| \ |
| 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): \ |
| R##_s = Y##_s; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ |
| _FP_FRAC_COPY_##wc (R, Y); \ |
| R##_c = Y##_c; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ |
| R##_s = _FP_NANSIGN_##fs; \ |
| R##_c = FP_CLS_NAN; \ |
| _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ); \ |
| break; \ |
| \ |
| default: \ |
| abort (); \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* Fused multiply-add. The input values should be cooked. */ |
| |
| #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \ |
| do \ |
| { \ |
| FP_DECL_##fs (_FP_FMA_T); \ |
| _FP_FMA_T##_s = X##_s ^ Y##_s; \ |
| _FP_FMA_T##_e = X##_e + Y##_e + 1; \ |
| switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ |
| { \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ |
| switch (Z##_c) \ |
| { \ |
| case FP_CLS_INF: \ |
| case FP_CLS_NAN: \ |
| R##_s = Z##_s; \ |
| _FP_FRAC_COPY_##wc (R, Z); \ |
| R##_c = Z##_c; \ |
| break; \ |
| \ |
| case FP_CLS_ZERO: \ |
| R##_c = FP_CLS_NORMAL; \ |
| R##_s = _FP_FMA_T##_s; \ |
| R##_e = _FP_FMA_T##_e; \ |
| \ |
| _FP_MUL_MEAT_##fs (R, X, Y); \ |
| \ |
| if (_FP_FRAC_OVERP_##wc (fs, R)) \ |
| _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ |
| else \ |
| R##_e--; \ |
| break; \ |
| \ |
| case FP_CLS_NORMAL:; \ |
| _FP_FRAC_DECL_##dwc (_FP_FMA_TD); \ |
| _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \ |
| _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \ |
| _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \ |
| R##_e = _FP_FMA_T##_e; \ |
| int _FP_FMA_tsh \ |
| = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \ |
| _FP_FMA_T##_e -= _FP_FMA_tsh; \ |
| int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \ |
| if (_FP_FMA_ediff >= 0) \ |
| { \ |
| int _FP_FMA_shift \ |
| = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \ |
| if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \ |
| _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \ |
| else \ |
| { \ |
| _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \ |
| if (_FP_FMA_shift < 0) \ |
| _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \ |
| _FP_WFRACBITS_DW_##fs); \ |
| else if (_FP_FMA_shift > 0) \ |
| _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \ |
| } \ |
| R##_s = _FP_FMA_T##_s; \ |
| if (_FP_FMA_T##_s == Z##_s) \ |
| _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \ |
| _FP_FMA_ZD); \ |
| else \ |
| { \ |
| _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \ |
| _FP_FMA_ZD); \ |
| if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \ |
| { \ |
| R##_s = Z##_s; \ |
| _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ |
| _FP_FMA_TD); \ |
| } \ |
| } \ |
| } \ |
| else \ |
| { \ |
| R##_e = Z##_e; \ |
| R##_s = Z##_s; \ |
| _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \ |
| _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \ |
| int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \ |
| if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \ |
| _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \ |
| else if (_FP_FMA_shift > 0) \ |
| _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \ |
| _FP_WFRACBITS_DW_##fs); \ |
| if (Z##_s == _FP_FMA_T##_s) \ |
| _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ |
| _FP_FMA_TD); \ |
| else \ |
| _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \ |
| _FP_FMA_TD); \ |
| } \ |
| if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \ |
| { \ |
| if (_FP_FMA_T##_s == Z##_s) \ |
| R##_s = Z##_s; \ |
| else \ |
| R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ |
| _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ |
| R##_c = FP_CLS_ZERO; \ |
| } \ |
| else \ |
| { \ |
| int _FP_FMA_rlz; \ |
| _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \ |
| _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \ |
| R##_e -= _FP_FMA_rlz; \ |
| int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \ |
| if (_FP_FMA_shift > 0) \ |
| _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \ |
| _FP_WFRACBITS_DW_##fs); \ |
| else if (_FP_FMA_shift < 0) \ |
| _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \ |
| _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \ |
| R##_c = FP_CLS_NORMAL; \ |
| } \ |
| break; \ |
| } \ |
| goto done_fma; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ |
| _FP_CHOOSENAN (fs, wc, _FP_FMA_T, X, Y, '*'); \ |
| break; \ |
| \ |
| 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_FMA_T##_s = X##_s; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ |
| _FP_FRAC_COPY_##wc (_FP_FMA_T, X); \ |
| _FP_FMA_T##_c = X##_c; \ |
| break; \ |
| \ |
| 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_FMA_T##_s = Y##_s; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ |
| _FP_FRAC_COPY_##wc (_FP_FMA_T, Y); \ |
| _FP_FMA_T##_c = Y##_c; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ |
| _FP_FMA_T##_s = _FP_NANSIGN_##fs; \ |
| _FP_FMA_T##_c = FP_CLS_NAN; \ |
| _FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \ |
| break; \ |
| \ |
| default: \ |
| abort (); \ |
| } \ |
| \ |
| /* T = X * Y is zero, infinity or NaN. */ \ |
| switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \ |
| { \ |
| case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ |
| _FP_CHOOSENAN (fs, wc, R, _FP_FMA_T, Z, '+'); \ |
| break; \ |
| \ |
| 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): \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ |
| R##_s = _FP_FMA_T##_s; \ |
| _FP_FRAC_COPY_##wc (R, _FP_FMA_T); \ |
| R##_c = _FP_FMA_T##_c; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ |
| R##_s = Z##_s; \ |
| _FP_FRAC_COPY_##wc (R, Z); \ |
| R##_c = Z##_c; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ |
| if (_FP_FMA_T##_s == Z##_s) \ |
| { \ |
| R##_s = Z##_s; \ |
| _FP_FRAC_COPY_##wc (R, Z); \ |
| R##_c = Z##_c; \ |
| } \ |
| else \ |
| { \ |
| R##_s = _FP_NANSIGN_##fs; \ |
| R##_c = FP_CLS_NAN; \ |
| _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_ISI); \ |
| } \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ |
| if (_FP_FMA_T##_s == Z##_s) \ |
| R##_s = Z##_s; \ |
| else \ |
| R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ |
| _FP_FRAC_COPY_##wc (R, Z); \ |
| R##_c = Z##_c; \ |
| break; \ |
| \ |
| default: \ |
| abort (); \ |
| } \ |
| done_fma: ; \ |
| } \ |
| while (0) |
| |
| |
| /* Main division routine. The input values should be cooked. */ |
| |
| #define _FP_DIV(fs, wc, R, X, Y) \ |
| do \ |
| { \ |
| R##_s = X##_s ^ Y##_s; \ |
| R##_e = X##_e - Y##_e; \ |
| switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ |
| { \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ |
| R##_c = FP_CLS_NORMAL; \ |
| \ |
| _FP_DIV_MEAT_##fs (R, X, Y); \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ |
| _FP_CHOOSENAN (fs, wc, R, X, Y, '/'); \ |
| break; \ |
| \ |
| 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): \ |
| R##_s = X##_s; \ |
| _FP_FRAC_COPY_##wc (R, X); \ |
| R##_c = X##_c; \ |
| break; \ |
| \ |
| 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): \ |
| R##_s = Y##_s; \ |
| _FP_FRAC_COPY_##wc (R, Y); \ |
| R##_c = Y##_c; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ |
| R##_c = FP_CLS_ZERO; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ |
| FP_SET_EXCEPTION (FP_EX_DIVZERO); \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ |
| R##_c = FP_CLS_INF; \ |
| break; \ |
| \ |
| case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ |
| case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ |
| R##_s = _FP_NANSIGN_##fs; \ |
| R##_c = FP_CLS_NAN; \ |
| _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID \ |
| | (X##_c == FP_CLS_INF \ |
| ? FP_EX_INVALID_IDI \ |
| : FP_EX_INVALID_ZDZ)); \ |
| break; \ |
| \ |
| default: \ |
| abort (); \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* Helper for comparisons. EX is 0 not to raise exceptions, 1 to |
| raise exceptions for signaling NaN operands, 2 to raise exceptions |
| for all NaN operands. Conditionals are organized to allow the |
| compiler to optimize away code based on the value of EX. */ |
| |
| #define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \ |
| do \ |
| { \ |
| /* The arguments are unordered, which may or may not result in \ |
| an exception. */ \ |
| if (ex) \ |
| { \ |
| /* At least some cases of unordered arguments result in \ |
| exceptions; check whether this is one. */ \ |
| if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \ |
| { \ |
| /* Check separately for each case of "invalid" \ |
| exceptions. */ \ |
| if ((ex) == 2) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \ |
| if (_FP_ISSIGNAN (fs, wc, X) \ |
| || _FP_ISSIGNAN (fs, wc, Y)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \ |
| } \ |
| /* Otherwise, we only need to check whether to raise an \ |
| exception, not which case or cases it is. */ \ |
| else if ((ex) == 2 \ |
| || _FP_ISSIGNAN (fs, wc, X) \ |
| || _FP_ISSIGNAN (fs, wc, Y)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID); \ |
| } \ |
| } \ |
| while (0) |
| |
| /* Main differential comparison routine. The inputs should be raw not |
| cooked. The return is -1, 0, 1 for normal values, UN |
| otherwise. */ |
| |
| #define _FP_CMP(fs, wc, ret, X, Y, un, ex) \ |
| 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) = (un); \ |
| _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ |
| } \ |
| else \ |
| { \ |
| int _FP_CMP_is_zero_x; \ |
| int _FP_CMP_is_zero_y; \ |
| \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ |
| \ |
| _FP_CMP_is_zero_x \ |
| = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \ |
| _FP_CMP_is_zero_y \ |
| = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \ |
| \ |
| if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \ |
| (ret) = 0; \ |
| else if (_FP_CMP_is_zero_x) \ |
| (ret) = Y##_s ? 1 : -1; \ |
| else if (_FP_CMP_is_zero_y) \ |
| (ret) = X##_s ? -1 : 1; \ |
| else if (X##_s != Y##_s) \ |
| (ret) = X##_s ? -1 : 1; \ |
| else if (X##_e > Y##_e) \ |
| (ret) = X##_s ? -1 : 1; \ |
| else if (X##_e < Y##_e) \ |
| (ret) = X##_s ? 1 : -1; \ |
| else if (_FP_FRAC_GT_##wc (X, Y)) \ |
| (ret) = X##_s ? -1 : 1; \ |
| else if (_FP_FRAC_GT_##wc (Y, X)) \ |
| (ret) = X##_s ? 1 : -1; \ |
| else \ |
| (ret) = 0; \ |
| } \ |
| } \ |
| while (0) |
| |
| |
| /* Simplification for strict equality. */ |
| |
| #define _FP_CMP_EQ(fs, wc, ret, X, Y, ex) \ |
| 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; \ |
| _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ |
| } \ |
| else \ |
| { \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ |
| _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ |
| \ |
| (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. */ |
| |
| #define _FP_CMP_UNORD(fs, wc, ret, X, Y, ex) \ |
| do \ |
| { \ |
| (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ |
| || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \ |
| if (ret) \ |
| _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \ |
| } \ |
| while (0) |
| |
| /* Main square root routine. The input value should be cooked. */ |
| |
| #define _FP_SQRT(fs, wc, R, X) \ |
| do \ |
| { \ |
| _FP_FRAC_DECL_##wc (_FP_SQRT_T); \ |
| _FP_FRAC_DECL_##wc (_FP_SQRT_S); \ |
| _FP_W_TYPE _FP_SQRT_q; \ |
| switch (X##_c) \ |
| { \ |
| case FP_CLS_NAN: \ |
| _FP_FRAC_COPY_##wc (R, X); \ |
| R##_s = X##_s; \ |
| R##_c = FP_CLS_NAN; \ |
| break; \ |
| case FP_CLS_INF: \ |
| if (X##_s) \ |
| { \ |
| R##_s = _FP_NANSIGN_##fs; \ |
| R##_c = FP_CLS_NAN; /* NAN */ \ |
| _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \ |
| } \ |
| else \ |
| { \ |
| R##_s = 0; \ |
| R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \ |
| } \ |
| break; \ |
| case FP_CLS_ZERO: \ |
| R##_s = X##_s; \ |
| R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \ |
| break; \ |
| case FP_CLS_NORMAL: \ |
| R##_s = 0; \ |
| if (X##_s) \ |
| { \ |
| R##_c = FP_CLS_NAN; /* NAN */ \ |
| R##_s = _FP_NANSIGN_##fs; \ |
| _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \ |
| break; \ |
| } \ |
| R##_c = FP_CLS_NORMAL; \ |
| if (X##_e & 1) \ |
| _FP_FRAC_SLL_##wc (X, 1); \ |
| R##_e = X##_e >> 1; \ |
| _FP_FRAC_SET_##wc (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \ |
| _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ |
| _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \ |
| _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \ |
| _FP_SQRT_q); \ |
| } \ |
| } \ |
| while (0) |
| |
| /* 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. |
| 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, |
| NV is set plus the result is reduced modulo 2^rsize. |
| -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. */ |
| #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)) \ |
| { \ |
| if (!FP_DENORM_ZERO) \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| } \ |
| } \ |
| else \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| } \ |
| else if ((rsigned) == 2 \ |
| && (X##_e \ |
| >= ((_FP_EXPMAX_##fs \ |
| < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \ |
| ? _FP_EXPMAX_##fs \ |
| : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \ |
| { \ |
| /* Overflow resulting in 0. */ \ |
| (r) = 0; \ |
| FP_SET_EXCEPTION (FP_EX_INVALID \ |
| | FP_EX_INVALID_CVI \ |
| | ((FP_EX_INVALID_SNAN \ |
| && _FP_ISSIGNAN (fs, wc, X)) \ |
| ? FP_EX_INVALID_SNAN \ |
| : 0)); \ |
| } \ |
| else if ((rsigned) != 2 \ |
| && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \ |
| ? _FP_EXPMAX_##fs \ |
| : (_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_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \ |
| && (rsigned) \ |
| && X##_s \ |
| && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \ |
| { \ |
| /* Possibly converting to most negative integer; check the \ |
| mantissa. */ \ |
| int _FP_TO_INT_inexact = 0; \ |
| (void) ((_FP_FRACBITS_##fs > (rsize)) \ |
| ? ({ \ |
| _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \ |
| _FP_FRACBITS_##fs - (rsize), \ |
| _FP_FRACBITS_##fs); \ |
| 0; \ |
| }) \ |
| : 0); \ |
| if (!_FP_FRAC_ZEROP_##wc (X)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ |
| else if (_FP_TO_INT_inexact) \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| } \ |
| else \ |
| FP_SET_EXCEPTION (FP_EX_INVALID \ |
| | FP_EX_INVALID_CVI \ |
| | ((FP_EX_INVALID_SNAN \ |
| && _FP_ISSIGNAN (fs, wc, X)) \ |
| ? FP_EX_INVALID_SNAN \ |
| : 0)); \ |
| } \ |
| else \ |
| { \ |
| int _FP_TO_INT_inexact = 0; \ |
| _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 \ |
| { \ |
| _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \ |
| (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \ |
| - X##_e), \ |
| _FP_FRACBITS_##fs); \ |
| _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \ |
| } \ |
| if ((rsigned) && X##_s) \ |
| (r) = -(r); \ |
| if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \ |
| { \ |
| /* Overflow or converting to the most negative integer. */ \ |
| if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \ |
| || !X##_s \ |
| || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \ |
| { \ |
| _FP_TO_INT_inexact = 0; \ |
| FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ |
| } \ |
| } \ |
| if (_FP_TO_INT_inexact) \ |
| FP_SET_EXCEPTION (FP_EX_INEXACT); \ |
| } \ |
| } \ |
| 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 _FP_FROM_INT_ur; \ |
| \ |
| if ((X##_s = ((r) < 0))) \ |
| (r) = -(rtype) (r); \ |
| \ |
| _FP_FROM_INT_ur = (rtype) (r); \ |
| (void) (((rsize) <= _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| int _FP_FROM_INT_lz; \ |
| __FP_CLZ (_FP_FROM_INT_lz, \ |
| (_FP_W_TYPE) _FP_FROM_INT_ur); \ |
| X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \ |
| - _FP_FROM_INT_lz); \ |
| }) \ |
| : (((rsize) <= 2 * _FP_W_TYPE_SIZE) \ |
| ? ({ \ |
| int _FP_FROM_INT_lz; \ |
| __FP_CLZ_2 (_FP_FROM_INT_lz, \ |
| (_FP_W_TYPE) (_FP_FROM_INT_ur \ |
| >> _FP_W_TYPE_SIZE), \ |
| (_FP_W_TYPE) _FP_FROM_INT_ur); \ |
| X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \ |
| - _FP_FROM_INT_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, _FP_FROM_INT_ur, (rsize)); \ |
| if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \ |
| _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) \ |
| _FP_FROM_INT_ur \ |
| = ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \ |
| - _FP_WFRACBITS_##fs + 1)) \ |
| | ((_FP_FROM_INT_ur \ |
| << ((rsize) - (X##_e - _FP_EXPBIAS_##fs \ |
| - _FP_WFRACBITS_##fs + 1))) \ |
| != 0)); \ |
| _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_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) |
| |
| |
| /* 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 \ |
| && _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \ |
| 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) \ |
| { \ |
| _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \ |
| if (_FP_FRAC_ZEROP_##swc (S)) \ |
| D##_e = 0; \ |
| else if (_FP_EXPBIAS_##dfs \ |
| < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \ |
| { \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ |
| - _FP_FRACBITS_##sfs)); \ |
| D##_e = 0; \ |
| if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \ |
| FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ |
| } \ |
| else \ |
| { \ |
| int FP_EXTEND_lz; \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| _FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \ |
| _FP_FRAC_SLL_##dwc (D, \ |
| FP_EXTEND_lz + _FP_FRACBITS_##dfs \ |
| - _FP_FRACTBITS_##sfs); \ |
| D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \ |
| + _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \ |
| } \ |
| } \ |
| else \ |
| { \ |
| D##_e = _FP_EXPMAX_##dfs; \ |
| if (!_FP_FRAC_ZEROP_##swc (S)) \ |
| { \ |
| if (_FP_FRAC_SNANP (sfs, S)) \ |
| FP_SET_EXCEPTION (FP_EX_INVALID \ |
| | FP_EX_INVALID_SNAN); \ |
| _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ |
| - _FP_FRACBITS_##sfs)); \ |
| _FP_SETQNAN (dfs, dwc, D); \ |
| } \ |
| } \ |
| } \ |
| } \ |
| 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 \ |
| && _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \ |
| 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); \ |
| _FP_FRAC_LOW_##swc (S) |= 1; \ |
| } \ |
| 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) \ |
| { \ |
| _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \ |
| D##_e = 0; \ |
| if (_FP_FRAC_ZEROP_##swc (S)) \ |
| _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ |
| else \ |
| { \ |
| FP_SET_EXCEPTION (FP_EX_DENORM); \ |
| if (_FP_EXPBIAS_##sfs \ |
| < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \ |
| { \ |
| _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ |
| - _FP_WFRACBITS_##dfs), \ |
| _FP_WFRACBITS_##sfs); \ |
| _FP_FRAC_COPY_##dwc##_##swc (D, S); \ |
| } \ |
| else \ |
| { \ |
| _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ |
| _FP_FRAC_LOW_##dwc (D) |= 1; \ |
| } \ |
| } \ |
| } \ |
| 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); \ |
| /* Semi-raw NaN must have all workbits cleared. */ \ |
| _FP_FRAC_LOW_##dwc (D) \ |
| &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \ |
| _FP_SETQNAN_SEMIRAW (dfs, dwc, D); \ |
| } \ |
| } \ |
| } \ |
| } \ |
| while (0) |
| |
| /* Helper primitives. */ |
| |
| /* Count leading zeros in a word. */ |
| |
| #ifndef __FP_CLZ |
| /* GCC 3.4 and later provide the builtins for us. */ |
| # define __FP_CLZ(r, x) \ |
| do \ |
| { \ |
| if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \ |
| (r) = __builtin_clz (x); \ |
| else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \ |
| (r) = __builtin_clzl (x); \ |
| else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \ |
| (r) = __builtin_clzll (x); \ |
| else \ |
| abort (); \ |
| } \ |
| while (0) |
| #endif /* ndef __FP_CLZ */ |
| |
| #define _FP_DIV_HELP_imm(q, r, n, d) \ |
| do \ |
| { \ |
| (q) = (n) / (d), (r) = (n) % (d); \ |
| } \ |
| while (0) |
| |
| |
| /* A restoring bit-by-bit division primitive. */ |
| |
| #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \ |
| do \ |
| { \ |
| int _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \ |
| _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \ |
| _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \ |
| _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \ |
| _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \ |
| _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ |
| /* Normalize _FP_DIV_MEAT_N_LOOP_U and _FP_DIV_MEAT_N_LOOP_V. */ \ |
| _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \ |
| _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_v, _FP_WFRACXBITS_##fs); \ |
| /* First round. Since the operands are normalized, either the \ |
| first or second bit will be set in the fraction. Produce a \ |
| normalized result by checking which and adjusting the loop \ |
| count and exponent accordingly. */ \ |
| if (_FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \ |
| { \ |
| _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \ |
| _FP_DIV_MEAT_N_loop_u, \ |
| _FP_DIV_MEAT_N_loop_v); \ |
| _FP_FRAC_LOW_##wc (R) |= 1; \ |
| _FP_DIV_MEAT_N_loop_count--; \ |
| } \ |
| else \ |
| R##_e--; \ |
| /* Subsequent rounds. */ \ |
| do \ |
| { \ |
| int _FP_DIV_MEAT_N_loop_msb \ |
| = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \ |
| _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \ |
| _FP_FRAC_SLL_##wc (R, 1); \ |
| if (_FP_DIV_MEAT_N_loop_msb \ |
| || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \ |
| _FP_DIV_MEAT_N_loop_v)) \ |
| { \ |
| _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \ |
| _FP_DIV_MEAT_N_loop_u, \ |
| _FP_DIV_MEAT_N_loop_v); \ |
| _FP_FRAC_LOW_##wc (R) |= 1; \ |
| } \ |
| } \ |
| while (--_FP_DIV_MEAT_N_loop_count > 0); \ |
| /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \ |
| is inexact. */ \ |
| _FP_FRAC_LOW_##wc (R) \ |
| |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \ |
| } \ |
| while (0) |
| |
| #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y) |
| #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y) |
| #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y) |
