diff options
Diffstat (limited to 'REORG.TODO/soft-fp/op-common.h')
| -rw-r--r-- | REORG.TODO/soft-fp/op-common.h | 2134 |
1 files changed, 2134 insertions, 0 deletions
diff --git a/REORG.TODO/soft-fp/op-common.h b/REORG.TODO/soft-fp/op-common.h new file mode 100644 index 0000000000..f52194ecd1 --- /dev/null +++ b/REORG.TODO/soft-fp/op-common.h @@ -0,0 +1,2134 @@ +/* Software floating-point emulation. Common operations. + Copyright (C) 1997-2017 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/>. */ + +#ifndef SOFT_FP_OP_COMMON_H +#define SOFT_FP_OP_COMMON_H 1 + +#define _FP_DECL(wc, X) \ + _FP_I_TYPE X##_c __attribute__ ((unused)) _FP_ZERO_INIT; \ + _FP_I_TYPE X##_s __attribute__ ((unused)) _FP_ZERO_INIT; \ + _FP_I_TYPE X##_e __attribute__ ((unused)) _FP_ZERO_INIT; \ + _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. */ \ + __label__ add1, add2, add3, add_done; \ + 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. */ \ + __label__ sub1, sub2, sub3, norm, sub_done; \ + 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; \ + /* FALLTHRU */ \ + \ + 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; \ + /* FALLTHRU */ \ + \ + 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: \ + _FP_UNREACHABLE; \ + } \ + } \ + while (0) + + +/* Fused multiply-add. The input values should be cooked. */ + +#define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \ + do \ + { \ + __label__ done_fma; \ + 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; \ + /* FALLTHRU */ \ + \ + 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; \ + /* FALLTHRU */ \ + \ + 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: \ + _FP_UNREACHABLE; \ + } \ + \ + /* 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; \ + R##_e = Z##_e; \ + 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: \ + _FP_UNREACHABLE; \ + } \ + 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); \ + /* FALLTHRU */ \ + 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: \ + _FP_UNREACHABLE; \ + } \ + } \ + 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) + +/* Helper for comparisons. If denormal operands would raise an + exception, check for them, and flush to zero as appropriate + (otherwise, we need only check and flush to zero if it might affect + the result, which is done later with _FP_CMP_CHECK_FLUSH_ZERO). */ +#define _FP_CMP_CHECK_DENORM(fs, wc, X, Y) \ + do \ + { \ + if (FP_EX_DENORM != 0) \ + { \ + /* We must ensure the correct exceptions are raised for \ + denormal operands, even though this may not affect the \ + result of the comparison. */ \ + if (FP_DENORM_ZERO) \ + { \ + _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ + _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ + } \ + else \ + { \ + if ((X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X)) \ + || (Y##_e == 0 && !_FP_FRAC_ZEROP_##wc (Y))) \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + } \ + } \ + } \ + while (0) + +/* Helper for comparisons. Check for flushing denormals for zero if + we didn't need to check earlier for any denormal operands. */ +#define _FP_CMP_CHECK_FLUSH_ZERO(fs, wc, X, Y) \ + do \ + { \ + if (FP_EX_DENORM == 0) \ + { \ + _FP_CHECK_FLUSH_ZERO (fs, wc, X); \ + _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \ + } \ + } \ + 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 \ + { \ + _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \ + /* 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_CMP_CHECK_FLUSH_ZERO (fs, wc, X, 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 \ + { \ + _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \ + /* 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_CMP_CHECK_FLUSH_ZERO (fs, wc, X, 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 \ + { \ + _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \ + (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 from floating point to integer, rounding according to the + current rounding direction. Input is raw. RSIGNED is as for + _FP_TO_INT. */ +#define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \ + do \ + { \ + __label__ _FP_TO_INT_ROUND_done; \ + if (X##_e < _FP_EXPBIAS_##fs) \ + { \ + int _FP_TO_INT_ROUND_rounds_away = 0; \ + if (X##_e == 0) \ + { \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + (r) = 0; \ + goto _FP_TO_INT_ROUND_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + if (FP_DENORM_ZERO) \ + { \ + (r) = 0; \ + goto _FP_TO_INT_ROUND_done; \ + } \ + } \ + } \ + /* The result is 0, 1 or -1 depending on the rounding mode; \ + -1 may cause overflow in the unsigned case. */ \ + switch (FP_ROUNDMODE) \ + { \ + case FP_RND_NEAREST: \ + _FP_TO_INT_ROUND_rounds_away \ + = (X##_e == _FP_EXPBIAS_##fs - 1 \ + && !_FP_FRAC_ZEROP_##wc (X)); \ + break; \ + case FP_RND_ZERO: \ + /* _FP_TO_INT_ROUND_rounds_away is already 0. */ \ + break; \ + case FP_RND_PINF: \ + _FP_TO_INT_ROUND_rounds_away = !X##_s; \ + break; \ + case FP_RND_MINF: \ + _FP_TO_INT_ROUND_rounds_away = X##_s; \ + break; \ + } \ + if ((rsigned) == 0 && _FP_TO_INT_ROUND_rounds_away && X##_s) \ + { \ + /* Result of -1 for an unsigned conversion. */ \ + (r) = 0; \ + FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ + } \ + else if ((rsize) == 1 && (rsigned) > 0 \ + && _FP_TO_INT_ROUND_rounds_away && !X##_s) \ + { \ + /* Converting to a 1-bit signed bit-field, which cannot \ + represent +1. */ \ + (r) = ((rsigned) == 2 ? -1 : 0); \ + FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ + } \ + else \ + { \ + (r) = (_FP_TO_INT_ROUND_rounds_away \ + ? (X##_s ? -1 : 1) \ + : 0); \ + 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) == 0 && X##_s))) \ + { \ + /* Definite overflow (does not require rounding to tell). */ \ + if ((rsigned) != 0) \ + { \ + (r) = 1; \ + (r) <<= (rsize) - 1; \ + (r) -= 1 - X##_s; \ + } \ + else \ + { \ + (r) = 0; \ + if (!X##_s) \ + (r) = ~(r); \ + } \ + \ + 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 \ + { \ + /* The value is finite, with magnitude at least 1. If \ + the conversion is unsigned, the value is positive. \ + If RSIGNED is not 2, the value does not definitely \ + overflow by virtue of its exponent, but may still turn \ + out to overflow after rounding; if RSIGNED is 2, the \ + exponent may be such that the value definitely overflows, \ + but at least one mantissa bit will not be shifted out. */ \ + int _FP_TO_INT_ROUND_inexact = 0; \ + _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ + if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \ + { \ + /* The value is an integer, no rounding needed. */ \ + _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \ + (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \ + } \ + else \ + { \ + /* May need to shift in order to round (unless there \ + are exactly _FP_WORKBITS fractional bits already). */ \ + int _FP_TO_INT_ROUND_rshift \ + = (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs \ + - 1 - _FP_WORKBITS - X##_e); \ + if (_FP_TO_INT_ROUND_rshift > 0) \ + _FP_FRAC_SRS_##wc (X, _FP_TO_INT_ROUND_rshift, \ + _FP_WFRACBITS_##fs); \ + else if (_FP_TO_INT_ROUND_rshift < 0) \ + _FP_FRAC_SLL_##wc (X, -_FP_TO_INT_ROUND_rshift); \ + /* Round like _FP_ROUND, but setting \ + _FP_TO_INT_ROUND_inexact instead of directly setting \ + the "inexact" exception, since it may turn out we \ + should set "invalid" instead. */ \ + if (_FP_FRAC_LOW_##wc (X) & 7) \ + { \ + _FP_TO_INT_ROUND_inexact = 1; \ + switch (FP_ROUNDMODE) \ + { \ + case FP_RND_NEAREST: \ + _FP_ROUND_NEAREST (wc, X); \ + break; \ + case FP_RND_ZERO: \ + _FP_ROUND_ZERO (wc, X); \ + break; \ + case FP_RND_PINF: \ + _FP_ROUND_PINF (wc, X); \ + break; \ + case FP_RND_MINF: \ + _FP_ROUND_MINF (wc, X); \ + break; \ + } \ + } \ + _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ + _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \ + } \ + if ((rsigned) != 0 && X##_s) \ + (r) = -(r); \ + /* An exponent of RSIZE - 1 always needs testing for \ + overflow (either directly overflowing, or overflowing \ + when rounding up results in 2^RSIZE). An exponent of \ + RSIZE - 2 can overflow for positive values when rounding \ + up to 2^(RSIZE-1), but cannot overflow for negative \ + values. Smaller exponents cannot overflow. */ \ + if (X##_e >= (_FP_EXPBIAS_##fs + (rsize) - 1 \ + - ((rsigned) > 0 && !X##_s))) \ + { \ + if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \ + || (X##_e == _FP_EXPBIAS_##fs + (rsize) - 1 \ + && (X##_s \ + ? (r) != (((typeof (r)) 1) << ((rsize) - 1)) \ + : ((rsigned) > 0 || (r) == 0))) \ + || ((rsigned) > 0 \ + && !X##_s \ + && X##_e == _FP_EXPBIAS_##fs + (rsize) - 2 \ + && (r) == (((typeof (r)) 1) << ((rsize) - 1)))) \ + { \ + if ((rsigned) != 2) \ + { \ + if ((rsigned) != 0) \ + { \ + (r) = 1; \ + (r) <<= (rsize) - 1; \ + (r) -= 1 - X##_s; \ + } \ + else \ + { \ + (r) = 0; \ + (r) = ~(r); \ + } \ + } \ + _FP_TO_INT_ROUND_inexact = 0; \ + FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \ + } \ + } \ + if (_FP_TO_INT_ROUND_inexact) \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + } \ + _FP_TO_INT_ROUND_done: ; \ + } \ + 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 \ + { \ + __label__ pack_semiraw; \ + if (r) \ + { \ + rtype _FP_FROM_INT_ur = (r); \ + \ + if ((X##_s = ((r) < 0))) \ + _FP_FROM_INT_ur = -_FP_FROM_INT_ur; \ + \ + _FP_STATIC_ASSERT ((rsize) <= 2 * _FP_W_TYPE_SIZE, \ + "rsize too large"); \ + (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); \ + }) \ + : ({ \ + 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); \ + })); \ + \ + 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. If CHECK_NAN, then signaling NaNs are + converted to quiet with the "invalid" exception raised; otherwise + signaling NaNs remain signaling with no exception. */ +#define _FP_EXTEND_CNAN(dfs, sfs, dwc, swc, D, S, check_nan) \ + do \ + { \ + _FP_STATIC_ASSERT (_FP_FRACBITS_##dfs >= _FP_FRACBITS_##sfs, \ + "destination mantissa narrower than source"); \ + _FP_STATIC_ASSERT ((_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \ + >= _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs), \ + "destination max exponent smaller" \ + " than source"); \ + _FP_STATIC_ASSERT (((_FP_EXPBIAS_##dfs \ + >= (_FP_EXPBIAS_##sfs \ + + _FP_FRACBITS_##sfs - 1)) \ + || (_FP_EXPBIAS_##dfs == _FP_EXPBIAS_##sfs)), \ + "source subnormals do not all become normal," \ + " but bias not the same"); \ + 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 (check_nan && _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)); \ + if (check_nan) \ + _FP_SETQNAN (dfs, dwc, D); \ + } \ + } \ + } \ + } \ + while (0) + +#define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \ + _FP_EXTEND_CNAN (dfs, sfs, dwc, swc, D, S, 1) + +/* 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 \ + { \ + _FP_STATIC_ASSERT (_FP_FRACBITS_##sfs >= _FP_FRACBITS_##dfs, \ + "destination mantissa wider than source"); \ + _FP_STATIC_ASSERT (((_FP_EXPBIAS_##sfs \ + >= (_FP_EXPBIAS_##dfs \ + + _FP_FRACBITS_##dfs - 1)) \ + || _FP_EXPBIAS_##sfs == _FP_EXPBIAS_##dfs), \ + "source subnormals do not all become same," \ + " but bias not the same"); \ + 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 \ + { \ + _FP_STATIC_ASSERT ((sizeof (_FP_W_TYPE) == sizeof (unsigned int) \ + || (sizeof (_FP_W_TYPE) \ + == sizeof (unsigned long)) \ + || (sizeof (_FP_W_TYPE) \ + == sizeof (unsigned long long))), \ + "_FP_W_TYPE size unsupported for clz"); \ + 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 /* sizeof (_FP_W_TYPE) == sizeof (unsigned long long). */ \ + (r) = __builtin_clzll (x); \ + } \ + 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) + +#endif /* !SOFT_FP_OP_COMMON_H */ |