/* * Copyright (c) 2013, Andreas Sandberg * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. */ #include #include #include "fpbits.h" #include #include #include const fp80_t fp80_pinf = BUILD_FP80(0, 0, FP80_EXP_SPECIAL); const fp80_t fp80_ninf = BUILD_FP80(1, 0, FP80_EXP_SPECIAL); const fp80_t fp80_qnan = BUILD_FP80(0, FP80_FRAC_QNAN, FP80_EXP_SPECIAL); const fp80_t fp80_qnani = BUILD_FP80(1, FP80_FRAC_QNANI, FP80_EXP_SPECIAL); const fp80_t fp80_snan = BUILD_FP80(0, FP80_FRAC_SNAN, FP80_EXP_SPECIAL); const fp80_t fp80_nan = BUILD_FP80(0, FP80_FRAC_QNAN, FP80_EXP_SPECIAL); int fp80_sgn(fp80_t fp80) { return (fp80.repr.se & FP80_SIGN_BIT) ? -1 : 1; } int fp80_isspecial(fp80_t fp80) { const int exp = FP80_EXP(fp80); return exp == FP80_EXP_SPECIAL; } int fp80_isinf(fp80_t fp80) { const uint64_t frac = FP80_FRAC(fp80); return fp80_isspecial(fp80) && frac == 0 ? fp80_sgn(fp80) : 0; } int fp80_isqnan(fp80_t fp80) { const uint64_t frac = FP80_FRAC(fp80); return fp80_isspecial(fp80) && (frac & FP80_QNAN_BIT); } int fp80_isqnani(fp80_t fp80) { const uint64_t frac_low = fp80.repr.fi & (FP80_FRAC_MASK >> 1); return fp80_isqnan(fp80) && (fp80.repr.se & FP80_SIGN_BIT) && !frac_low; } int fp80_issnan(fp80_t fp80) { const uint64_t frac = FP80_FRAC(fp80); return fp80_isspecial(fp80) && !(frac & FP80_QNAN_BIT) && frac; } int fp80_isfinite(fp80_t fp80) { return !fp80_isnan(fp80) && !fp80_isinf(fp80); } int fp80_isnan(fp80_t fp80) { return fp80_issnan(fp80) || fp80_isqnan(fp80) ? fp80_sgn(fp80) : 0; } int fp80_iszero(fp80_t fp80) { return fp80.repr.fi == 0 && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0; } int fp80_isnormal(fp80_t fp80) { return FP80_EXP(fp80) != 0 && !fp80_isspecial(fp80) ? fp80_sgn(fp80) : 0; } int fp80_issubnormal(fp80_t fp80) { return FP80_FRAC(fp80) && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0; } int fp80_classify(fp80_t fp80) { if (fp80_issubnormal(fp80)) { return FP_SUBNORMAL; } else if (fp80_iszero(fp80)) { return FP_ZERO; } else if (fp80_isinf(fp80)) { return FP_INFINITE; } else if (fp80_isnan(fp80)) { return FP_NAN; } else { assert(fp80_isfinite(fp80)); return FP_NORMAL; } } double fp80_cvtd(fp80_t fp80) { return fp80_cvtfp64(fp80).value; } fp64_t fp80_cvtfp64(fp80_t fp80) { const int sign = fp80.repr.se & FP80_SIGN_BIT; if (!fp80_isspecial(fp80)) { const uint64_t frac = fp80.repr.fi; const int unb_exp = FP80_EXP(fp80) - FP80_EXP_BIAS; const int fp64_exp = unb_exp + FP64_EXP_BIAS; const uint64_t fp64_frac = frac >> (FP80_FRAC_BITS - FP64_FRAC_BITS); if (fp64_exp > 0 && fp64_exp < FP64_EXP_SPECIAL) { /* These numbers fall in the range of what we can express * as normals */ return build_fp64(sign, fp64_frac, fp64_exp); } else if (fp64_exp <= 0) { uint64_t fp64_denormal_frac = fp64_frac >> (-fp64_exp); /* Generate a denormal or zero */ return build_fp64(sign, fp64_denormal_frac, 0); } else { /* Infinity */ return build_fp64(sign, 0, FP64_EXP_SPECIAL); } } else { if (fp80_isinf(fp80)) { return build_fp64(sign, 0, FP64_EXP_SPECIAL); } else if (fp80_issnan(fp80)) { return fp80_sgn(fp80) > 0 ? fp64_snan : fp64_nsnan; } else if (fp80_isqnani(fp80)) { return fp64_qnani; } else { assert(fp80_isqnan(fp80)); return fp80_sgn(fp80) > 0 ? fp64_qnan : fp64_nqnan; } } } fp80_t fp80_cvfd(double value) { const fp64_t fp64 = { .value = value }; return fp80_cvffp64(fp64); } fp80_t fp80_cvffp64(fp64_t fp64) { const uint64_t frac = FP64_FRAC(fp64); const unsigned exp = FP64_EXP(fp64); const int unb_exp = exp - FP64_EXP_BIAS; const uint64_t fp80_frac = frac << (FP80_FRAC_BITS - FP64_FRAC_BITS); if (exp != 0) { // Normal, inf, nan const unsigned fp80_exp = exp == FP64_EXP_SPECIAL ? FP80_EXP_SPECIAL : (unb_exp + FP80_EXP_BIAS); const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, fp80_frac, fp80_exp); return fp80; } else if (exp == 0 && frac == 0) { // Zero const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, 0, 0); return fp80; } else { // Denormal uint64_t fp80_fi = fp80_frac; int shift_amt = 0; while (!(fp80_fi & FP80_INT_BIT)) { fp80_fi <<= 1; ++shift_amt; } const unsigned fp80_exp = (unb_exp - shift_amt) + FP80_EXP_BIAS; const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, fp80_fi, fp80_exp); return fp80; } } void fp80_debug_dump(FILE *fout, fp80_t fp80) { fprintf(fout, "sgn: %i, int: %i, frac: 0x%llx, exp: 0x%x (%i)\n", fp80_sgn(fp80), !!(fp80.repr.fi & FP80_INT_BIT), FP80_FRAC(fp80), FP80_EXP(fp80), FP80_EXP(fp80) - FP80_EXP_BIAS); }