diff --git a/src/util/mpf.cpp b/src/util/mpf.cpp index ceb407781..32932522c 100644 --- a/src/util/mpf.cpp +++ b/src/util/mpf.cpp @@ -1214,149 +1214,192 @@ void mpf_manager::to_ieee_bv_mpz(const mpf & x, scoped_mpz & o) { } } -void mpf_manager::prem(scoped_mpf & x, scoped_mpf const & y, mpf_exp_t const & exp_diff, bool partial) { +void mpf_manager::renormalize(unsigned ebits, unsigned sbits, mpf_exp_t & exp, mpz & sig) { + if (m_mpz_manager.is_zero(sig)) + return; + + mpf_exp_t max_e = mk_max_exp(ebits); + mpf_exp_t min_e = mk_min_exp(ebits); + + const mpz & pg = m_powers2(sbits); + while (m_mpz_manager.ge(sig, pg)) { + m_mpz_manager.machine_div2k(sig, 1); + exp++; + } + + const mpz & pl = m_powers2(sbits-1); + while (m_mpz_manager.lt(sig, pl)) { + m_mpz_manager.mul2k(sig, 1); + exp--; + } +} + +void mpf_manager::partial_remainder(scoped_mpf & x, scoped_mpf const & y, mpf_exp_t const & exp_diff, bool partial) { unsigned ebits = x.get().ebits; unsigned sbits = x.get().sbits; bool sign = x.get().sign; - signed int D = (unsigned)(partial ? 0 : exp_diff); - mpf_exp_t N = sbits/2; + SASSERT(-1 <= exp_diff && exp_diff < INT64_MAX); + SASSERT(exp_diff < ebits+sbits || partial); + + signed int D = (signed int)(exp_diff); + mpf_exp_t N = (sbits+ebits)/2; TRACE("mpf_dbg_rem", tout << "x=" << to_string(x) << std::endl; tout << "y=" << to_string(y) << std::endl; tout << "d=" << D << std::endl; tout << "partial=" << partial << std::endl;); - // 1. Compute a/b - unsigned extra_bits = sbits + 2; - scoped_mpz x_sig_shifted(m_mpz_manager), x_div_y_sig_lrg(m_mpz_manager); - scoped_mpz x_div_y_sig(m_mpz_manager), x_rem_y_sig(m_mpz_manager); - m_mpz_manager.mul2k(x.significand(), sbits + extra_bits, x_sig_shifted); - m_mpz_manager.machine_div(x_sig_shifted, y.significand(), x_div_y_sig_lrg); - m_mpz_manager.machine_div_rem(x_div_y_sig_lrg, m_powers2(extra_bits-2), x_div_y_sig, x_rem_y_sig); - TRACE("mpf_dbg_rem", tout << "X/Y_sig=" << m_mpz_manager.to_string(x_div_y_sig) << std::endl; - tout << "X%Y_sig=" << m_mpz_manager.to_string(x_rem_y_sig) << std::endl; - tout << "X/Y=" << to_string_hexfloat( - to_packed_mpf(x.sign(), D, x_div_y_sig, ebits, sbits, 3)) << std::endl;); - SASSERT(m_mpz_manager.lt(x_div_y_sig, m_powers2(sbits + 3))); // 3 extra bits in x_div_y_sig. - SASSERT(m_mpz_manager.ge(x_div_y_sig, m_powers2(sbits - 1 + 3))); - // Bug: a_rem_b_sig is not used. + SASSERT(m_mpz_manager.lt(x.significand(), m_powers2(sbits))); + SASSERT(m_mpz_manager.ge(x.significand(), m_powers2(sbits - 1))); + SASSERT(m_mpz_manager.lt(y.significand(), m_powers2(sbits))); + SASSERT(m_mpz_manager.ge(y.significand(), m_powers2(sbits - 1))); + + // 1. Compute a/b + bool x_div_y_sgn = x.sign() ^ y.sign(); + mpf_exp_t x_div_y_exp = D; + scoped_mpz x_sig_shifted(m_mpz_manager), x_div_y_sig_lrg(m_mpz_manager), x_div_y_rem(m_mpz_manager); + scoped_mpz x_rem_y_sig(m_mpz_manager); + m_mpz_manager.mul2k(x.significand(), 2*sbits + 2, x_sig_shifted); + m_mpz_manager.machine_div_rem(x_sig_shifted, y.significand(), x_div_y_sig_lrg, x_div_y_rem); // rem useful? + // x/y is in x_diuv_y_sig_lrg and has sbits+3 extra bits. + + TRACE("mpf_dbg_rem", tout << "X/Y_exp=" << x_div_y_exp << std::endl; + tout << "X/Y_sig_lrg=" << m_mpz_manager.to_string(x_div_y_sig_lrg) << std::endl; + tout << "X/Y_rem=" << m_mpz_manager.to_string(x_div_y_rem) << std::endl; + scoped_mpf & XdY = to_packed_mpf(x_div_y_sgn, x_div_y_exp, x_div_y_sig_lrg, ebits, sbits, sbits+3); + tout << "X/Y~=" << to_string_hexfloat(XdY) << std::endl;); // 2. Round a/b to integer Q/QQ - mpf_exp_t Q_exp = partial ? N : D; + bool Q_sgn = x_div_y_sgn; + mpf_exp_t Q_exp = x_div_y_exp; scoped_mpz Q_sig(m_mpz_manager), Q_rem(m_mpz_manager); - if (partial) { + unsigned Q_shft = (sbits-1) + (sbits+3) - (unsigned) (partial ? N :Q_exp); + if (partial) { // Round according to MPF_ROUND_TOWARD_ZERO - SASSERT(N < D && D < INT_MAX); - unsigned D_N = (unsigned)(D-N); - unsigned Q_shft = (sbits - 1) - D_N; - m_mpz_manager.machine_div_rem(x_div_y_sig, m_powers2(Q_shft+3), Q_sig, Q_rem); - m_mpz_manager.mul2k(Q_sig, Q_shft); + SASSERT(0 < N && N < Q_exp && Q_exp < INT_MAX); + m_mpz_manager.machine_div2k(x_div_y_sig_lrg, Q_shft, Q_sig); } else { // Round according to MPF_ROUND_NEAREST_TEVEN - unsigned Q_shft = (sbits - 1) - D; - m_mpz_manager.machine_div_rem(x_div_y_sig, m_powers2(Q_shft+3), Q_sig, Q_rem); + m_mpz_manager.machine_div_rem(x_div_y_sig_lrg, m_powers2(Q_shft), Q_sig, Q_rem); const mpz & shiftm1_p = m_powers2(Q_shft-1); bool tie = m_mpz_manager.eq(Q_rem, shiftm1_p); bool more_than_tie = m_mpz_manager.gt(Q_rem, shiftm1_p); TRACE("mpf_dbg_rem", tout << "tie= " << tie << "; >tie= " << more_than_tie << std::endl;); if ((tie && m_mpz_manager.is_odd(Q_sig)) || more_than_tie) m_mpz_manager.inc(Q_sig); - m_mpz_manager.mul2k(Q_sig, Q_shft); - SASSERT(m_mpz_manager.ge(Q_sig, m_powers2(sbits-1))); - } - TRACE("mpf_dbg_rem", tout << "Q_sig'=" << m_mpz_manager.to_string(Q_sig) << std::endl; - tout << "Q_rem=" << m_mpz_manager.to_string(Q_rem) << std::endl; ); - - // re-normalize Q - while (m_mpz_manager.ge(Q_sig, m_powers2(sbits))) { - m_mpz_manager.machine_div2k(Q_sig, 1); - Q_exp++; } + m_mpz_manager.mul2k(Q_sig, Q_shft); + m_mpz_manager.machine_div2k(Q_sig, sbits+3); + renormalize(ebits, sbits, Q_exp, Q_sig); TRACE("mpf_dbg_rem", tout << "Q_exp=" << Q_exp << std::endl; tout << "Q_sig=" << m_mpz_manager.to_string(Q_sig) << std::endl; - scoped_mpf & Q = to_packed_mpf(x.sign(), Q_exp, Q_sig, ebits, sbits, 0); + scoped_mpf & Q = to_packed_mpf(Q_sgn, Q_exp, Q_sig, ebits, sbits, 0); tout << "Q=" << to_string_hexfloat(Q) << std::endl;); + + if ((D == -1 || partial) && m_mpz_manager.is_zero(Q_sig)) + return; // This means x % y = x. + + // no extra bits in Q_sig. + SASSERT(!m_mpz_manager.is_zero(Q_sig)); + SASSERT(m_mpz_manager.lt(Q_sig, m_powers2(sbits))); + SASSERT(m_mpz_manager.ge(Q_sig, m_powers2(sbits - 1))); + // 3. Compute Y*Q / Y*QQ*2^{D-N} + bool YQ_sgn = y.sign() ^ Q_sgn; scoped_mpz YQ_sig(m_mpz_manager); - mpf_exp_t YQ_exp = (Q_exp + y.exponent()) + (partial ? D-N : 0); - m_mpz_manager.mul(y.significand(), Q_sig, YQ_sig); + mpf_exp_t YQ_exp = Q_exp + y.exponent(); + m_mpz_manager.mul(y.significand(), Q_sig, YQ_sig); + renormalize(ebits, 2*sbits-1, YQ_exp, YQ_sig); // YQ_sig has `sbits-1' extra bits. - if (sbits >= 7) { - scoped_mpz sticky_rem(m_mpz_manager); - m_mpz_manager.machine_div_rem(YQ_sig, m_powers2(sbits-7), YQ_sig, sticky_rem); - if (!m_mpz_manager.is_zero(sticky_rem) && m_mpz_manager.is_even(YQ_sig)) - m_mpz_manager.inc(YQ_sig); - } - else - m_mpz_manager.mul2k(YQ_sig, 7-sbits, YQ_sig); - - TRACE("mpf_dbg_rem", tout << "YQ_exp=" << YQ_exp << std::endl; + TRACE("mpf_dbg_rem", tout << "YQ_sgn=" << YQ_sgn << std::endl; + tout << "YQ_exp=" << YQ_exp << std::endl; tout << "YQ_sig=" << m_mpz_manager.to_string(YQ_sig) << std::endl; - scoped_mpf & YQ = to_packed_mpf(x.sign(), YQ_exp, YQ_sig, ebits, sbits, 6); + scoped_mpf & YQ = to_packed_mpf(YQ_sgn, YQ_exp, YQ_sig, ebits, sbits, sbits-1); tout << "YQ=" << to_string_hexfloat(YQ) << std::endl;); - // 4. Compute X-Y*Q - bool YQ_sgn = !x.sign(); - mpf_exp_t X_YQ_exp = x.exponent() - 3; + // `sbits-1' extra bits in YQ_sig. + SASSERT(m_mpz_manager.lt(YQ_sig, m_powers2(2*sbits-1))); + SASSERT(m_mpz_manager.ge(YQ_sig, m_powers2(2*sbits-2)) || YQ_exp <= mk_bot_exp(ebits)); + + // 4. Compute X-Y*Q + mpf_exp_t X_YQ_exp = x.exponent(); scoped_mpz X_YQ_sig(m_mpz_manager); mpf_exp_t exp_delta = exp(x) - YQ_exp; TRACE("mpf_dbg_rem", tout << "exp_delta=" << exp_delta << std::endl;); + SASSERT(INT_MIN < exp_delta && exp_delta <= INT_MAX); scoped_mpz minuend(m_mpz_manager), subtrahend(m_mpz_manager); - if (exp_delta >= 0) { - m_mpz_manager.set(minuend, x.significand()); - m_mpz_manager.set(subtrahend, YQ_sig); - } - else if (exp_delta < 0) { - m_mpz_manager.set(minuend, YQ_sig); - m_mpz_manager.set(subtrahend, x.significand()); - YQ_sgn = !YQ_sgn; - exp_delta = -exp_delta; - } + scoped_mpz x_sig_lrg(m_mpz_manager); + m_mpz_manager.mul2k(x.significand(), sbits-1, x_sig_lrg); // sbits-1 extra bits into x + m_mpz_manager.set(minuend, x_sig_lrg); + m_mpz_manager.set(subtrahend, YQ_sig); + + SASSERT(m_mpz_manager.lt(minuend, m_powers2(2*sbits-1))); + SASSERT(m_mpz_manager.ge(minuend, m_powers2(2*sbits-2))); + SASSERT(m_mpz_manager.lt(subtrahend, m_powers2(2*sbits-1))); + SASSERT(m_mpz_manager.ge(subtrahend, m_powers2(2*sbits-2))); + if (exp_delta != 0) { scoped_mpz sticky_rem(m_mpz_manager); - if (exp_delta > sbits+5) { - m_mpz_manager.set(sticky_rem, 0); - sticky_rem.swap(subtrahend); + m_mpz_manager.set(sticky_rem, 0); + if (exp_delta > sbits+5) + sticky_rem.swap(subtrahend); + else if (exp_delta > 0) + m_mpz_manager.machine_div_rem(subtrahend, m_powers2((unsigned)exp_delta), subtrahend, sticky_rem); + else { + SASSERT(exp_delta < 0); + exp_delta = -exp_delta; + m_mpz_manager.mul2k(subtrahend, (int)exp_delta); } - else - m_mpz_manager.machine_div_rem(subtrahend, m_powers2((unsigned)exp_delta), subtrahend, sticky_rem); if (!m_mpz_manager.is_zero(sticky_rem) && m_mpz_manager.is_even(subtrahend)) m_mpz_manager.inc(subtrahend); TRACE("mpf_dbg_rem", tout << "aligned subtrahend=" << m_mpz_manager.to_string(subtrahend) << std::endl;); } + + m_mpz_manager.sub(minuend, subtrahend, X_YQ_sig); + TRACE("mpf_dbg_rem", tout << "X_YQ_sig'=" << m_mpz_manager.to_string(X_YQ_sig) << std::endl;); - scoped_mpz minuend_lrg(m_mpz_manager); - m_mpz_manager.mul2k(minuend, 6, minuend_lrg); // + 6 extra bits into X - m_mpz_manager.sub(minuend_lrg, subtrahend, X_YQ_sig); - - TRACE("mpf_dbg_rem", tout << "minuend=" << m_mpz_manager.to_string(minuend) << std::endl; - tout << "subtrahend=" << m_mpz_manager.to_string(subtrahend) << std::endl; - tout << "X_YQ_exp=" << X_YQ_exp << std::endl; - tout << "X_YQ_sig=" << m_mpz_manager.to_string(X_YQ_sig) << std::endl; - scoped_mpf & X_YQ = to_packed_mpf(YQ_sgn, X_YQ_exp, X_YQ_sig, ebits, sbits, 3); - tout << "X-YQ=" << to_string_hexfloat(X_YQ) << std::endl;); - - SASSERT(m_mpz_manager.lt(X_YQ_sig, m_powers2(sbits+5))); + bool neg = m_mpz_manager.is_neg(X_YQ_sig); + if (neg) m_mpz_manager.neg(X_YQ_sig); + bool X_YQ_sgn = ((!x.sign() && !YQ_sgn && neg) || + (x.sign() && YQ_sgn && !neg) || + (x.sign() && !YQ_sgn)); // 5. Rounding - if (m_mpz_manager.is_zero(X_YQ_sig)) { - TRACE("mpf_dbg_rem", tout << "sig zero" << std::endl;); + if (m_mpz_manager.is_zero(X_YQ_sig)) mk_zero(ebits, sbits, x.sign(), x); - } else { - bool neg = m_mpz_manager.is_neg(X_YQ_sig); - if (neg) m_mpz_manager.neg(X_YQ_sig); - bool X_YQ_sgn = ((!x.sign() && YQ_sgn && neg) || - (x.sign() && !YQ_sgn && !neg) || - (x.sign() && YQ_sgn)); + renormalize(ebits, 2*sbits-1, X_YQ_exp, X_YQ_sig); + + TRACE("mpf_dbg_rem", tout << "minuend=" << m_mpz_manager.to_string(minuend) << std::endl; + tout << "subtrahend=" << m_mpz_manager.to_string(subtrahend) << std::endl; + tout << "X_YQ_sgn=" << X_YQ_sgn << std::endl; + tout << "X_YQ_exp=" << X_YQ_exp << std::endl; + tout << "X_YQ_sig=" << m_mpz_manager.to_string(X_YQ_sig) << std::endl; + scoped_mpf & X_YQ = to_packed_mpf(X_YQ_sgn, X_YQ_exp, X_YQ_sig, ebits, sbits, sbits-1); + tout << "X-YQ=" << to_string_hexfloat(X_YQ) << std::endl;); + + // `sbits-1' extra bits in X_YQ_sig + SASSERT(m_mpz_manager.lt(X_YQ_sig, m_powers2(2*sbits-1))); + scoped_mpz rnd_bits(m_mpz_manager); + m_mpz_manager.machine_div_rem(X_YQ_sig, m_powers2(sbits-1), X_YQ_sig, rnd_bits); + TRACE("mpf_dbg_rem", tout << "final sticky=" << m_mpz_manager.to_string(rnd_bits) << std::endl; ); + + // Round to nearest, ties to even. + if (m_mpz_manager.eq(rnd_bits, mpz(32))) { // tie. + if (m_mpz_manager.is_odd(X_YQ_sig)) { + m_mpz_manager.inc(X_YQ_sig); + } + } + else if (m_mpz_manager.gt(rnd_bits, mpz(32))) + m_mpz_manager.inc(X_YQ_sig); + set(x, ebits, sbits, X_YQ_sgn, X_YQ_exp, X_YQ_sig); - round(MPF_ROUND_NEAREST_TEVEN, x); } TRACE("mpf_dbg_rem", tout << "partial remainder = " << to_string_hexfloat(x) << std::endl;); @@ -1365,8 +1408,8 @@ void mpf_manager::prem(scoped_mpf & x, scoped_mpf const & y, mpf_exp_t const & e void mpf_manager::rem(mpf const & x, mpf const & y, mpf & o) { SASSERT(x.sbits == y.sbits && x.ebits == y.ebits); - TRACE("mpf_dbg", tout << "X = " << to_string(x) << std::endl;); - TRACE("mpf_dbg", tout << "Y = " << to_string(y) << std::endl;); + TRACE("mpf_dbg_rem", tout << "X = " << to_string(x) << "=" << to_string_hexfloat(x) << std::endl; + tout << "Y = " << to_string(y) << "=" << to_string_hexfloat(y) << std::endl;); if (is_nan(x) || is_nan(y)) mk_nan(x.ebits, x.sbits, o); @@ -1380,7 +1423,6 @@ void mpf_manager::rem(mpf const & x, mpf const & y, mpf & o) { set(o, x); else { SASSERT(is_regular(x) && is_regular(y)); - SASSERT(x.exponent >= y.exponent); // This is a generalized version of the algorithm for FPREM1 in the `Intel // 64 and IA-32 Architectures Software Developer's Manual', @@ -1391,24 +1433,24 @@ void mpf_manager::rem(mpf const & x, mpf const & y, mpf & o) { unpack(ST0, true); unpack(ST1, true); - const mpf_exp_t B = x.sbits; // max bits per iteration. + const mpf_exp_t B = x.sbits+x.ebits; mpf_exp_t D; do { - D = ST0.exponent() - ST1.exponent(); - SASSERT(0 <= D && D < INT64_MAX); - - TRACE("mpf_dbg_rem", tout << "ST0=" << to_string_raw(ST0) << "=" << to_string_hexfloat(ST0) << std::endl; - tout << "ST1=" << to_string_raw(ST1) << "=" << to_string_hexfloat(ST1) << std::endl; - tout << "D=" << D << std::endl;); - - prem(ST0, ST1, D, (D >= B)); - } while (D >= B); + if (ST0.exponent() < (ST1.exponent()) - 1) { + D = 0; + } + else { + D = ST0.exponent() - ST1.exponent(); + partial_remainder(ST0, ST1, D, (D >= B)); + } + } while (D >= B && !ST0.is_zero()); + m_mpz_manager.mul2k(ST0.significand(), 3); set(o, x.ebits, x.sbits, MPF_ROUND_TOWARD_ZERO, ST0); - if (is_zero(o)) - o.sign = x.sign; + round(MPF_ROUND_NEAREST_TEVEN, o); } + TRACE("mpf_dbg_rem", tout << "R = " << to_string(o) << "=" << to_string_hexfloat(o) << std::endl; ); TRACE("mpf_dbg", tout << "REMAINDER = " << to_string(o) << std::endl;); } @@ -1538,7 +1580,10 @@ scoped_mpf mpf_manager::to_packed_mpf(bool sgn, mpf_exp_t exp, scoped_mpz const scoped_mpz q_sig(m_mpz_manager); m_mpz_manager.set(q_sig, sig); if (rbits != 0) m_mpz_manager.div(q_sig, m_powers2(rbits), q_sig); // restore scale - m_mpz_manager.sub(q_sig, m_powers2(sbits-1), q_sig); // strip hidden bit + if (m_mpz_manager.ge(q_sig, m_powers2(sbits-1))) + m_mpz_manager.sub(q_sig, m_powers2(sbits-1), q_sig); // strip hidden bit + else if (exp == mk_min_exp(ebits)) + exp = mk_bot_exp(ebits); set(q, ebits, sbits, sgn, exp, q_sig); return q; } diff --git a/src/util/mpf.h b/src/util/mpf.h index e6bf3cd27..ca2e3c605 100644 --- a/src/util/mpf.h +++ b/src/util/mpf.h @@ -223,7 +223,8 @@ protected: void round(mpf_rounding_mode rm, mpf & o); void round_sqrt(mpf_rounding_mode rm, mpf & o); - void prem(scoped_mpf & x, scoped_mpf const & y, mpf_exp_t const & exp_diff, bool partial); + void renormalize(unsigned ebits, unsigned sbits, mpf_exp_t & exp, mpz & sig); + void partial_remainder(scoped_mpf & x, scoped_mpf const & y, mpf_exp_t const & exp_diff, bool partial); void mk_round_inf(mpf_rounding_mode rm, mpf & o);