static int reduce_trig_arg(int expDiff, int &zSign, Bit64u &aSig0, Bit64u &aSig1) { Bit64u term0, term1, q = 0; if (expDiff < 0) { shift128Right(aSig0, 0, 1, &aSig0, &aSig1); expDiff = 0; } if (expDiff > 0) { q = argument_reduction_kernel(aSig0, expDiff, &aSig0, &aSig1); } else { if (FLOAT_PI_HI <= aSig0) { aSig0 -= FLOAT_PI_HI; q = 1; } } shift128Right(FLOAT_PI_HI, FLOAT_PI_LO, 1, &term0, &term1); if (! lt128(aSig0, aSig1, term0, term1)) { int lt = lt128(term0, term1, aSig0, aSig1); int eq = eq128(aSig0, aSig1, term0, term1); if ((eq && (q & 1)) || lt) { zSign = !zSign; ++q; } if (lt) sub128(FLOAT_PI_HI, FLOAT_PI_LO, aSig0, aSig1, &aSig0, &aSig1); } return (int)(q & 3); }
void float128_rem () { signed int expDiff; long long int aSig1; long long int sigMean1; if (-64 < expDiff) shift128Right (-expDiff, &aSig1); add128 (&sigMean1); }
static floatx80 fyl2x(floatx80 a, floatx80 b) { UINT64 aSig = extractFloatx80Frac(a); INT32 aExp = extractFloatx80Exp(a); int aSign = extractFloatx80Sign(a); UINT64 bSig = extractFloatx80Frac(b); INT32 bExp = extractFloatx80Exp(b); int bSign = extractFloatx80Sign(b); int zSign = bSign ^ 1; if (aExp == 0x7FFF) { if ((UINT64) (aSig<<1) || ((bExp == 0x7FFF) && (UINT64) (bSig<<1))) { return propagateFloatx80NaN(a, b); } if (aSign) { invalid: float_raise(float_flag_invalid); return floatx80_default_nan; } else { if (bExp == 0) { if (bSig == 0) goto invalid; float_raise(float_flag_denormal); } return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000)); } } if (bExp == 0x7FFF) { if ((UINT64) (bSig<<1)) return propagateFloatx80NaN(a, b); if (aSign && (UINT64)(aExp | aSig)) goto invalid; if (aSig && (aExp == 0)) float_raise(float_flag_denormal); if (aExp < 0x3FFF) { return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000)); } if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0)) goto invalid; return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000)); } if (aExp == 0) { if (aSig == 0) { if ((bExp | bSig) == 0) goto invalid; float_raise(float_flag_divbyzero); return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000)); } if (aSign) goto invalid; float_raise(float_flag_denormal); normalizeFloatx80Subnormal(aSig, &aExp, &aSig); } if (aSign) goto invalid; if (bExp == 0) { if (bSig == 0) { if (aExp < 0x3FFF) return packFloatx80(zSign, 0, 0); return packFloatx80(bSign, 0, 0); } float_raise(float_flag_denormal); normalizeFloatx80Subnormal(bSig, &bExp, &bSig); } if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0)) return packFloatx80(bSign, 0, 0); float_raise(float_flag_inexact); int ExpDiff = aExp - 0x3FFF; aExp = 0; if (aSig >= SQRT2_HALF_SIG) { ExpDiff++; aExp--; } /* ******************************** */ /* using float128 for approximation */ /* ******************************** */ UINT64 zSig0, zSig1; shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1); float128 x = packFloat128(0, aExp+0x3FFF, zSig0, zSig1); x = poly_l2(x); x = float128_add(x, int64_to_float128((INT64) ExpDiff)); return floatx80_mul(b, float128_to_floatx80(x)); }
floatx80 fyl2xp1(floatx80 a, floatx80 b) { INT32 aExp, bExp; UINT64 aSig, bSig, zSig0, zSig1, zSig2; int aSign, bSign; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); bSig = extractFloatx80Frac(b); bExp = extractFloatx80Exp(b); bSign = extractFloatx80Sign(b); int zSign = aSign ^ bSign; if (aExp == 0x7FFF) { if ((UINT64) (aSig<<1) || ((bExp == 0x7FFF) && (UINT64) (bSig<<1))) { return propagateFloatx80NaN(a, b); } if (aSign) { invalid: float_raise(float_flag_invalid); return floatx80_default_nan; } else { if (bExp == 0) { if (bSig == 0) goto invalid; float_raise(float_flag_denormal); } return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000)); } } if (bExp == 0x7FFF) { if ((UINT64) (bSig<<1)) return propagateFloatx80NaN(a, b); if (aExp == 0) { if (aSig == 0) goto invalid; float_raise(float_flag_denormal); } return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000)); } if (aExp == 0) { if (aSig == 0) { if (bSig && (bExp == 0)) float_raise(float_flag_denormal); return packFloatx80(zSign, 0, 0); } float_raise(float_flag_denormal); normalizeFloatx80Subnormal(aSig, &aExp, &aSig); } if (bExp == 0) { if (bSig == 0) return packFloatx80(zSign, 0, 0); float_raise(float_flag_denormal); normalizeFloatx80Subnormal(bSig, &bExp, &bSig); } float_raise(float_flag_inexact); if (aSign && aExp >= 0x3FFF) return a; if (aExp >= 0x3FFC) // big argument { return fyl2x(floatx80_add(a, floatx80_one), b); } // handle tiny argument if (aExp < EXP_BIAS-70) { // first order approximation, return (a*b)/ln(2) INT32 zExp = aExp + FLOAT_LN2INV_EXP - 0x3FFE; mul128By64To192(FLOAT_LN2INV_HI, FLOAT_LN2INV_LO, aSig, &zSig0, &zSig1, &zSig2); if (0 < (INT64) zSig0) { shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1); --zExp; } zExp = zExp + bExp - 0x3FFE; mul128By64To192(zSig0, zSig1, bSig, &zSig0, &zSig1, &zSig2); if (0 < (INT64) zSig0) { shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1); --zExp; } return roundAndPackFloatx80(80, aSign ^ bSign, zExp, zSig0, zSig1); } /* ******************************** */ /* using float128 for approximation */ /* ******************************** */ shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1); float128 x = packFloat128(aSign, aExp, zSig0, zSig1); x = poly_l2p1(x); return floatx80_mul(b, float128_to_floatx80(x)); }
static floatx80 do_fprem(floatx80 a, floatx80 b, Bit64u &q, int rounding_mode, float_status_t &status) { Bit32s aExp, bExp, zExp, expDiff; Bit64u aSig0, aSig1, bSig; int aSign; q = 0; // handle unsupported extended double-precision floating encodings if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b)) { float_raise(status, float_flag_invalid); return floatx80_default_nan; } aSig0 = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); bSig = extractFloatx80Frac(b); bExp = extractFloatx80Exp(b); if (aExp == 0x7FFF) { if ((Bit64u) (aSig0<<1) || ((bExp == 0x7FFF) && (Bit64u) (bSig<<1))) { return propagateFloatx80NaN(a, b, status); } goto invalid; } if (bExp == 0x7FFF) { if ((Bit64u) (bSig<<1)) return propagateFloatx80NaN(a, b, status); return a; } if (bExp == 0) { if (bSig == 0) { invalid: float_raise(status, float_flag_invalid); return floatx80_default_nan; } float_raise(status, float_flag_denormal); normalizeFloatx80Subnormal(bSig, &bExp, &bSig); } if (aExp == 0) { if ((Bit64u) (aSig0<<1) == 0) return a; float_raise(status, float_flag_denormal); normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0); } expDiff = aExp - bExp; aSig1 = 0; if (expDiff >= 64) { int n = (expDiff & 0x1f) | 0x20; remainder_kernel(aSig0, bSig, n, &aSig0, &aSig1); zExp = aExp - n; q = (Bit64u) -1; } else { zExp = bExp; if (expDiff < 0) { if (expDiff < -1) return (a.fraction & BX_CONST64(0x8000000000000000)) ? packFloatx80(aSign, aExp, aSig0) : a; shift128Right(aSig0, 0, 1, &aSig0, &aSig1); expDiff = 0; } if (expDiff > 0) { q = remainder_kernel(aSig0, bSig, expDiff, &aSig0, &aSig1); } else { if (bSig <= aSig0) { aSig0 -= bSig; q = 1; } } if (rounding_mode == float_round_nearest_even) { Bit64u term0, term1; shift128Right(bSig, 0, 1, &term0, &term1); if (! lt128(aSig0, aSig1, term0, term1)) { int lt = lt128(term0, term1, aSig0, aSig1); int eq = eq128(aSig0, aSig1, term0, term1); if ((eq && (q & 1)) || lt) { aSign = !aSign; ++q; } if (lt) sub128(bSig, 0, aSig0, aSig1, &aSig0, &aSig1); } } } return normalizeRoundAndPackFloatx80(80, aSign, zExp, aSig0, aSig1, status); }