diff --git a/src/util/mpf.cpp b/src/util/mpf.cpp index de215c958..ceb407781 100644 --- a/src/util/mpf.cpp +++ b/src/util/mpf.cpp @@ -1214,6 +1214,154 @@ 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) { + 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; + + 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. + + // 2. Round a/b to integer Q/QQ + mpf_exp_t Q_exp = partial ? N : D; + scoped_mpz Q_sig(m_mpz_manager), Q_rem(m_mpz_manager); + 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); + } + 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); + 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++; + } + + 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); + tout << "Q=" << to_string_hexfloat(Q) << std::endl;); + + // 3. Compute Y*Q / Y*QQ*2^{D-N} + 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); + + 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; + 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); + 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; + 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;); + 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; + } + + 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); + } + 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;); + } + + 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))); + + // 5. Rounding + if (m_mpz_manager.is_zero(X_YQ_sig)) { + TRACE("mpf_dbg_rem", tout << "sig zero" << std::endl;); + 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)); + 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;); +} + void mpf_manager::rem(mpf const & x, mpf const & y, mpf & o) { SASSERT(x.sbits == y.sbits && x.ebits == y.ebits); @@ -1231,54 +1379,32 @@ void mpf_manager::rem(mpf const & x, mpf const & y, mpf & o) { else if (is_zero(x)) set(o, x); else { - // This is a generalized version of the algorithm for FPREM1 in the Intel + 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', - // Section 3-402 Vol. 2A FPREM1-Partial Remainder'. + // Section 3-402 Vol. 2A `FPREM1-Partial Remainder'. scoped_mpf ST0(*this), ST1(*this); set(ST0, x); set(ST1, y); + unpack(ST0, true); + unpack(ST1, true); - const mpf_exp_t B = x.sbits-1; // max bits per iteration. + const mpf_exp_t B = x.sbits; // max bits per iteration. mpf_exp_t D; do { D = ST0.exponent() - ST1.exponent(); - TRACE("mpf_dbg_rem", tout << "st0=" << to_string_hexfloat(ST0) << std::endl; - tout << "st1=" << to_string_hexfloat(ST1) << std::endl; + 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;); - if (D < B) { - scoped_mpf ST0_DIV_ST1(*this), Q(*this), ST1_MUL_Q(*this), ST0p(*this); - div(MPF_ROUND_NEAREST_TEVEN, ST0, ST1, ST0_DIV_ST1); - round_to_integral(MPF_ROUND_NEAREST_TEVEN, ST0_DIV_ST1, Q); - mul(MPF_ROUND_NEAREST_TEVEN, ST1, Q, ST1_MUL_Q); - sub(MPF_ROUND_NEAREST_TEVEN, ST0, ST1_MUL_Q, ST0p); - TRACE("mpf_dbg_rem", tout << "ST0/ST1=" << to_string_hexfloat(ST0_DIV_ST1) << std::endl; - tout << "Q=" << to_string_hexfloat(Q) << std::endl; - tout << "ST1*Q=" << to_string_hexfloat(ST1_MUL_Q) << std::endl; - tout << "ST0'=" << to_string_hexfloat(ST0p) << std::endl;); - set(ST0, ST0p); - } - else { - const mpf_exp_t N = B; - scoped_mpf ST0_DIV_ST1(*this), QQ(*this), ST1_MUL_QQ(*this), ST0p(*this); - div(MPF_ROUND_TOWARD_ZERO, ST0, ST1, ST0_DIV_ST1); - ST0_DIV_ST1.get().exponent -= D - N; - round_to_integral(MPF_ROUND_TOWARD_ZERO, ST0_DIV_ST1, QQ); - mul(MPF_ROUND_NEAREST_TEVEN, ST1, QQ, ST1_MUL_QQ); - ST1_MUL_QQ.get().exponent += D - N; - sub(MPF_ROUND_NEAREST_TEVEN, ST0, ST1_MUL_QQ, ST0p); - TRACE("mpf_dbg_rem", tout << "ST0/ST1/2^{D-N}=" << to_string_hexfloat(ST0_DIV_ST1) << std::endl; - tout << "QQ=" << to_string_hexfloat(QQ) << std::endl; - tout << "ST1*QQ*2^{D-N}=" << to_string_hexfloat(ST1_MUL_QQ) << std::endl; - tout << "ST0'=" << to_string_hexfloat(ST0p) << std::endl;); - SASSERT(!eq(ST0, ST0p)); - set(ST0, ST0p); - } - - SASSERT(ST0.exponent() - ST1.exponent() <= D); + prem(ST0, ST1, D, (D >= B)); } while (D >= B); - set(o, ST0); + set(o, x.ebits, x.sbits, MPF_ROUND_TOWARD_ZERO, ST0); if (is_zero(o)) o.sign = x.sign; } @@ -1364,9 +1490,9 @@ std::string mpf_manager::to_string(mpf const & x) { } } - //DEBUG_CODE( - // res += " " + to_string_hexfloat(x); - //); + DEBUG_CODE( + res += " " + to_string_raw(x); + ); return res; } @@ -1407,6 +1533,16 @@ std::string mpf_manager::to_string_raw(mpf const & x) { return res; } +scoped_mpf mpf_manager::to_packed_mpf(bool sgn, mpf_exp_t exp, scoped_mpz const & sig, unsigned ebits, unsigned sbits, unsigned rbits) { + scoped_mpf q(*this); + 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 + set(q, ebits, sbits, sgn, exp, q_sig); + return q; +} + std::string mpf_manager::to_string_hexfloat(mpf const & x) { std::stringstream ss(""); std::ios::fmtflags ff = ss.setf(std::ios_base::hex | std::ios_base::uppercase | diff --git a/src/util/mpf.h b/src/util/mpf.h index 1bd0ac952..e6bf3cd27 100644 --- a/src/util/mpf.h +++ b/src/util/mpf.h @@ -185,9 +185,6 @@ public: void mk_pinf(unsigned ebits, unsigned sbits, mpf & o); void mk_ninf(unsigned ebits, unsigned sbits, mpf & o); - std::string to_string_raw(mpf const & a); - std::string to_string_hexfloat(mpf const & a); - unsynch_mpz_manager & mpz_manager(void) { return m_mpz_manager; } unsynch_mpq_manager & mpq_manager(void) { return m_mpq_manager; } @@ -226,6 +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 mk_round_inf(mpf_rounding_mode rm, mpf & o); // Convert x into a mpz numeral. zm is the manager that owns o. @@ -284,6 +283,10 @@ protected: } }; + std::string to_string_raw(mpf const & a); + std::string to_string_hexfloat(mpf const & a); + scoped_mpf to_packed_mpf(bool sgn, mpf_exp_t exp, scoped_mpz const & sig, unsigned ebits, unsigned sbits, unsigned rbits); + public: powers2 m_powers2; }; @@ -291,6 +294,7 @@ public: class scoped_mpf : public _scoped_numeral { friend class mpf_manager; mpz & significand() { return get().significand; } + const mpz & significand() const { return get().significand; } bool sign() const { return get().sign; } mpf_exp_t exponent() const { return get().exponent; } unsigned sbits() const { return get().sbits; }