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z3/src/tactic/fpa/fpa2bv_converter.cpp
Christoph M. Wintersteiger 0e74362ecb Added support for the final draft of the FPA standard (and fpa2bv conversion). 
Signed-off-by: Christoph M. Wintersteiger <cwinter@microsoft.com>
2014-01-24 15:36:23 +00:00

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/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
fpa2bv_converter.cpp
Abstract:
Conversion routines for Floating Point -> Bit-Vector
Author:
Christoph (cwinter) 2012-02-09
Notes:
--*/
#include"ast_smt2_pp.h"
#include"well_sorted.h"
#include"fpa2bv_converter.h"
#define BVULT(X,Y,R) { expr_ref bvult_eq(m), bvult_not(m); m_simp.mk_eq(X, Y, bvult_eq); m_simp.mk_not(bvult_eq, bvult_not); expr_ref t(m); t = m_bv_util.mk_ule(X,Y); m_simp.mk_and(t, bvult_not, R); }
#define BVSLT(X,Y,R) { expr_ref bvslt_eq(m), bvslt_not(m); m_simp.mk_eq(X, Y, bvslt_eq); m_simp.mk_not(bvslt_eq, bvslt_not); expr_ref t(m); t = m_bv_util.mk_sle(X,Y); m_simp.mk_and(t, bvslt_not, R); }
fpa2bv_converter::fpa2bv_converter(ast_manager & m) :
m(m),
m_simp(m),
m_util(m),
m_mpf_manager(m_util.fm()),
m_mpz_manager(m_mpf_manager.mpz_manager()),
m_bv_util(m),
extra_assertions(m) {
m_plugin = static_cast<float_decl_plugin*>(m.get_plugin(m.mk_family_id("float")));
}
fpa2bv_converter::~fpa2bv_converter() {
dec_ref_map_key_values(m, m_const2bv);
dec_ref_map_key_values(m, m_rm_const2bv);
dec_ref_map_key_values(m, m_uf2bvuf);
obj_map<func_decl, func_decl_triple>::iterator it = m_uf23bvuf.begin();
obj_map<func_decl, func_decl_triple>::iterator end = m_uf23bvuf.end();
for (; it != end; ++it) {
m.dec_ref(it->m_key);
m.dec_ref(it->m_value.f_sgn);
m.dec_ref(it->m_value.f_sig);
m.dec_ref(it->m_value.f_exp);
}
m_uf23bvuf.reset();
}
void fpa2bv_converter::mk_eq(expr * a, expr * b, expr_ref & result) {
SASSERT(is_app_of(a, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(is_app_of(b, m_plugin->get_family_id(), OP_TO_FLOAT));
expr_ref sgn(m), s(m), e(m);
m_simp.mk_eq(to_app(a)->get_arg(0), to_app(b)->get_arg(0), sgn);
m_simp.mk_eq(to_app(a)->get_arg(1), to_app(b)->get_arg(1), s);
m_simp.mk_eq(to_app(a)->get_arg(2), to_app(b)->get_arg(2), e);
// The SMT FPA theory asks for _one_ NaN value, but the bit-blasting
// has many, like IEEE754. This encoding of equality makes it look like
// a single NaN again.
expr_ref both_the_same(m), a_is_nan(m), b_is_nan(m), both_are_nan(m);
m_simp.mk_and(sgn, s, e, both_the_same);
mk_is_nan(a, a_is_nan);
mk_is_nan(b, b_is_nan);
m_simp.mk_and(a_is_nan, b_is_nan, both_are_nan);
m_simp.mk_or(both_are_nan, both_the_same, result);
}
void fpa2bv_converter::mk_ite(expr * c, expr * t, expr * f, expr_ref & result) {
SASSERT(is_app_of(t, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(is_app_of(f, m_plugin->get_family_id(), OP_TO_FLOAT));
expr_ref sgn(m), s(m), e(m);
m_simp.mk_ite(c, to_app(t)->get_arg(0), to_app(f)->get_arg(0), sgn);
m_simp.mk_ite(c, to_app(t)->get_arg(1), to_app(f)->get_arg(1), s);
m_simp.mk_ite(c, to_app(t)->get_arg(2), to_app(f)->get_arg(2), e);
mk_triple(sgn, s, e, result);
}
void fpa2bv_converter::mk_value(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 0);
SASSERT(f->get_num_parameters() == 1);
SASSERT(f->get_parameter(0).is_external());
unsigned p_id = f->get_parameter(0).get_ext_id();
mpf const & v = m_plugin->get_value(p_id);
unsigned sbits = v.get_sbits();
unsigned ebits = v.get_ebits();
bool sign = m_util.fm().sgn(v);
mpz const & sig = m_util.fm().sig(v);
mpf_exp_t const & exp = m_util.fm().exp(v);
if (m_util.fm().is_nan(v))
mk_nan(f, result);
else if (m_util.fm().is_inf(v)) {
if (m_util.fm().sgn(v))
mk_minus_inf(f, result);
else
mk_plus_inf(f, result);
}
else {
expr_ref bv_sgn(m), bv_sig(m), e(m), biased_exp(m);
bv_sgn = m_bv_util.mk_numeral( (sign) ? 1 : 0, 1);
bv_sig = m_bv_util.mk_numeral(rational(sig), sbits-1);
e = m_bv_util.mk_numeral(exp, ebits);
mk_bias(e, biased_exp);
mk_triple(bv_sgn, bv_sig, biased_exp, result);
TRACE("fpa2bv_dbg", tout << "value of [" << sign << " " << m_mpz_manager.to_string(sig) << " " << exp << "] is "
<< mk_ismt2_pp(result, m) << std::endl;);
}
}
void fpa2bv_converter::mk_const(func_decl * f, expr_ref & result) {
SASSERT(f->get_family_id() == null_family_id);
SASSERT(f->get_arity() == 0);
expr * r;
if (m_const2bv.find(f, r)) {
result = r;
}
else {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned ebits = m_util.get_ebits(srt);
unsigned sbits = m_util.get_sbits(srt);
expr_ref sgn(m), s(m), e(m);
sort_ref s_sgn(m), s_sig(m), s_exp(m);
s_sgn = m_bv_util.mk_sort(1);
s_sig = m_bv_util.mk_sort(sbits-1);
s_exp = m_bv_util.mk_sort(ebits);
#ifdef Z3DEBUG
std::string p("fpa2bv");
std::string name = f->get_name().str();
sgn = m.mk_fresh_const((p + "_sgn_" + name).c_str(), s_sgn);
s = m.mk_fresh_const((p + "_sig_" + name).c_str(), s_sig);
e = m.mk_fresh_const((p + "_exp_" + name).c_str(), s_exp);
#else
sgn = m.mk_fresh_const(0, s_sgn);
s = m.mk_fresh_const(0, s_sig);
e = m.mk_fresh_const(0, s_exp);
#endif
mk_triple(sgn, s, e, result);
m_const2bv.insert(f, result);
m.inc_ref(f);
m.inc_ref(result);
}
}
void fpa2bv_converter::mk_var(unsigned base_inx, sort * srt, expr_ref & result) {
SASSERT(is_float(srt));
unsigned ebits = m_util.get_ebits(srt);
unsigned sbits = m_util.get_sbits(srt);
expr_ref sgn(m), s(m), e(m);
sgn = m.mk_var(base_inx, m_bv_util.mk_sort(1));
s = m.mk_var(base_inx + 1, m_bv_util.mk_sort(sbits-1));
e = m.mk_var(base_inx + 2, m_bv_util.mk_sort(ebits));
mk_triple(sgn, s, e, result);
}
void fpa2bv_converter::mk_uninterpreted_function(func_decl * f, unsigned num, expr * const * args, expr_ref & result)
{
TRACE("fpa2bv_dbg", tout << "UF: " << mk_ismt2_pp(f, m) << std::endl; );
SASSERT(f->get_arity() == num);
expr_ref_buffer new_args(m);
for (unsigned i = 0; i < num ; i ++)
if (is_float(args[i]))
{
expr * sgn, * sig, * exp;
split(args[i], sgn, sig, exp);
new_args.push_back(sgn);
new_args.push_back(sig);
new_args.push_back(exp);
}
else
new_args.push_back(args[i]);
func_decl * fd;
func_decl_triple fd3;
if (m_uf2bvuf.find(f, fd)) {
result = m.mk_app(fd, new_args.size(), new_args.c_ptr());
}
else if (m_uf23bvuf.find(f, fd3))
{
expr_ref a_sgn(m), a_sig(m), a_exp(m);
a_sgn = m.mk_app(fd3.f_sgn, new_args.size(), new_args.c_ptr());
a_sig = m.mk_app(fd3.f_sig, new_args.size(), new_args.c_ptr());
a_exp = m.mk_app(fd3.f_exp, new_args.size(), new_args.c_ptr());
mk_triple(a_sgn, a_sig, a_exp, result);
}
else {
sort_ref_buffer new_domain(m);
for (unsigned i = 0; i < f->get_arity() ; i ++)
if (is_float(f->get_domain()[i]))
{
new_domain.push_back(m_bv_util.mk_sort(1));
new_domain.push_back(m_bv_util.mk_sort(m_util.get_sbits(f->get_domain()[i])-1));
new_domain.push_back(m_bv_util.mk_sort(m_util.get_ebits(f->get_domain()[i])));
}
else
new_domain.push_back(f->get_domain()[i]);
if (!is_float(f->get_range()))
{
func_decl * fbv = m.mk_func_decl(f->get_name(), new_domain.size(), new_domain.c_ptr(), f->get_range(), *f->get_info());
TRACE("fpa2bv_dbg", tout << "New UF func_decl : " << mk_ismt2_pp(fbv, m) << std::endl; );
m_uf2bvuf.insert(f, fbv);
m.inc_ref(f);
m.inc_ref(fbv);
result = m.mk_app(fbv, new_args.size(), new_args.c_ptr());
}
else
{
string_buffer<> name_buffer;
name_buffer.reset(); name_buffer << f->get_name() << ".sgn";
func_decl * f_sgn = m.mk_func_decl(symbol(name_buffer.c_str()), new_domain.size(), new_domain.c_ptr(), m_bv_util.mk_sort(1));
name_buffer.reset(); name_buffer << f->get_name() << ".sig";
func_decl * f_sig = m.mk_func_decl(symbol(name_buffer.c_str()), new_domain.size(), new_domain.c_ptr(), m_bv_util.mk_sort(m_util.get_sbits(f->get_range())-1));
name_buffer.reset(); name_buffer << f->get_name() << ".exp";
func_decl * f_exp = m.mk_func_decl(symbol(name_buffer.c_str()), new_domain.size(), new_domain.c_ptr(), m_bv_util.mk_sort(m_util.get_ebits(f->get_range())));
expr_ref a_sgn(m), a_sig(m), a_exp(m);
a_sgn = m.mk_app(f_sgn, new_args.size(), new_args.c_ptr());
a_sig = m.mk_app(f_sig, new_args.size(), new_args.c_ptr());
a_exp = m.mk_app(f_exp, new_args.size(), new_args.c_ptr());
TRACE("fpa2bv_dbg", tout << "New UF func_decls : " << std::endl;
tout << mk_ismt2_pp(f_sgn, m) << std::endl;
tout << mk_ismt2_pp(f_sig, m) << std::endl;
tout << mk_ismt2_pp(f_exp, m) << std::endl; );
m_uf23bvuf.insert(f, func_decl_triple(f_sgn, f_sig, f_exp));
m.inc_ref(f);
m.inc_ref(f_sgn);
m.inc_ref(f_sig);
m.inc_ref(f_exp);
mk_triple(a_sgn, a_sig, a_exp, result);
}
}
TRACE("fpa2bv_dbg", tout << "UF result: " << mk_ismt2_pp(result, m) << std::endl; );
SASSERT(is_well_sorted(m, result));
}
void fpa2bv_converter::mk_rm_const(func_decl * f, expr_ref & result) {
SASSERT(f->get_family_id() == null_family_id);
SASSERT(f->get_arity() == 0);
expr * r;
if (m_rm_const2bv.find(f, r)) {
result = r;
}
else {
SASSERT(is_rm_sort(f->get_range()));
result = m.mk_fresh_const(
#ifdef Z3DEBUG
"fpa2bv_rm"
#else
0
#endif
, m_bv_util.mk_sort(3));
m_rm_const2bv.insert(f, result);
m.inc_ref(f);
m.inc_ref(result);
}
}
void fpa2bv_converter::mk_plus_inf(func_decl * f, expr_ref & result) {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
expr_ref top_exp(m);
mk_top_exp(ebits, top_exp);
mk_triple(m_bv_util.mk_numeral(0, 1),
m_bv_util.mk_numeral(0, sbits-1),
top_exp,
result);
}
void fpa2bv_converter::mk_minus_inf(func_decl * f, expr_ref & result) {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
expr_ref top_exp(m);
mk_top_exp(ebits, top_exp);
mk_triple(m_bv_util.mk_numeral(1, 1),
m_bv_util.mk_numeral(0, sbits-1),
top_exp,
result);
}
void fpa2bv_converter::mk_nan(func_decl * f, expr_ref & result) {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
expr_ref top_exp(m);
mk_top_exp(ebits, top_exp);
mk_triple(m_bv_util.mk_numeral(0, 1),
m_bv_util.mk_numeral(1, sbits-1),
top_exp,
result);
}
void fpa2bv_converter::mk_nzero(func_decl *f, expr_ref & result) {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
expr_ref bot_exp(m);
mk_bot_exp(ebits, bot_exp);
mk_triple(m_bv_util.mk_numeral(1, 1),
m_bv_util.mk_numeral(0, sbits-1),
bot_exp,
result);
}
void fpa2bv_converter::mk_pzero(func_decl *f, expr_ref & result) {
sort * srt = f->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
expr_ref bot_exp(m);
mk_bot_exp(ebits, bot_exp);
mk_triple(m_bv_util.mk_numeral(0, 1),
m_bv_util.mk_numeral(0, sbits-1),
bot_exp,
result);
}
void fpa2bv_converter::add_core(unsigned sbits, unsigned ebits, expr_ref & rm,
expr_ref & c_sgn, expr_ref & c_sig, expr_ref & c_exp, expr_ref & d_sgn, expr_ref & d_sig, expr_ref & d_exp,
expr_ref & res_sgn, expr_ref & res_sig, expr_ref & res_exp)
{
// c/d are now such that c_exp >= d_exp.
expr_ref exp_delta(m);
exp_delta = m_bv_util.mk_bv_sub(c_exp, d_exp);
dbg_decouple("fpa2bv_add_exp_delta", exp_delta);
// cap the delta
expr_ref cap(m), cap_le_delta(m);
cap = m_bv_util.mk_numeral(sbits+2, ebits);
cap_le_delta = m_bv_util.mk_ule(cap, exp_delta);
m_simp.mk_ite(cap_le_delta, cap, exp_delta, exp_delta);
dbg_decouple("fpa2bv_add_exp_delta_capped", exp_delta);
// Three extra bits for c/d
c_sig = m_bv_util.mk_concat(c_sig, m_bv_util.mk_numeral(0, 3));
d_sig = m_bv_util.mk_concat(d_sig, m_bv_util.mk_numeral(0, 3));
SASSERT(is_well_sorted(m, c_sig));
SASSERT(is_well_sorted(m, d_sig));
// Alignment shift with sticky bit computation.
expr_ref big_d_sig(m);
big_d_sig = m_bv_util.mk_concat(d_sig, m_bv_util.mk_numeral(0, sbits+3));
SASSERT(is_well_sorted(m, big_d_sig));
expr_ref shifted_big(m), shifted_d_sig(m), sticky_raw(m), sticky(m);
shifted_big = m_bv_util.mk_bv_lshr(big_d_sig, m_bv_util.mk_concat(m_bv_util.mk_numeral(0, (2*(sbits+3))-ebits), exp_delta));
shifted_d_sig = m_bv_util.mk_extract((2*(sbits+3)-1), (sbits+3), shifted_big);
SASSERT(is_well_sorted(m, shifted_d_sig));
sticky_raw = m_bv_util.mk_extract(sbits+2, 0, shifted_big);
expr_ref sticky_eq(m), nil_sbit3(m), one_sbit3(m);
nil_sbit3 = m_bv_util.mk_numeral(0, sbits+3);
one_sbit3 = m_bv_util.mk_numeral(1, sbits+3);
m_simp.mk_eq(sticky_raw, nil_sbit3, sticky_eq);
m_simp.mk_ite(sticky_eq, nil_sbit3, one_sbit3, sticky);
SASSERT(is_well_sorted(m, sticky));
expr * or_args[2] = { shifted_d_sig, sticky };
shifted_d_sig = m_bv_util.mk_bv_or(2, or_args);
SASSERT(is_well_sorted(m, shifted_d_sig));
expr_ref eq_sgn(m);
m_simp.mk_eq(c_sgn, d_sgn, eq_sgn);
// dbg_decouple("fpa2bv_add_eq_sgn", eq_sgn);
TRACE("fpa2bv_add_core", tout << "EQ_SGN = " << mk_ismt2_pp(eq_sgn, m) << std::endl; );
// two extra bits for catching the overflow.
c_sig = m_bv_util.mk_zero_extend(2, c_sig);
shifted_d_sig = m_bv_util.mk_zero_extend(2, shifted_d_sig);
SASSERT(m_bv_util.get_bv_size(c_sig) == sbits+5);
SASSERT(m_bv_util.get_bv_size(shifted_d_sig) == sbits+5);
dbg_decouple("fpa2bv_add_c_sig", c_sig);
dbg_decouple("fpa2bv_add_shifted_d_sig", shifted_d_sig);
expr_ref sum(m);
m_simp.mk_ite(eq_sgn,
m_bv_util.mk_bv_add(c_sig, shifted_d_sig),
m_bv_util.mk_bv_sub(c_sig, shifted_d_sig),
sum);
SASSERT(is_well_sorted(m, sum));
dbg_decouple("fpa2bv_add_sum", sum);
expr_ref sign_bv(m), n_sum(m);
sign_bv = m_bv_util.mk_extract(sbits+4, sbits+4, sum);
n_sum = m_bv_util.mk_bv_neg(sum);
dbg_decouple("fpa2bv_add_sign_bv", sign_bv);
dbg_decouple("fpa2bv_add_n_sum", n_sum);
family_id bvfid = m_bv_util.get_fid();
expr_ref res_sgn_c1(m), res_sgn_c2(m), res_sgn_c3(m);
expr_ref not_c_sgn(m), not_d_sgn(m), not_sign_bv(m);
not_c_sgn = m_bv_util.mk_bv_not(c_sgn);
not_d_sgn = m_bv_util.mk_bv_not(d_sgn);
not_sign_bv = m_bv_util.mk_bv_not(sign_bv);
res_sgn_c1 = m.mk_app(bvfid, OP_BAND, not_c_sgn, d_sgn, sign_bv);
res_sgn_c2 = m.mk_app(bvfid, OP_BAND, c_sgn, not_d_sgn, not_sign_bv);
res_sgn_c3 = m.mk_app(bvfid, OP_BAND, c_sgn, d_sgn);
expr * res_sgn_or_args[3] = { res_sgn_c1, res_sgn_c2, res_sgn_c3 };
res_sgn = m_bv_util.mk_bv_or(3, res_sgn_or_args);
expr_ref res_sig_eq(m), sig_abs(m), one_1(m);
one_1 = m_bv_util.mk_numeral(1, 1);
m_simp.mk_eq(sign_bv, one_1, res_sig_eq);
m_simp.mk_ite(res_sig_eq, n_sum, sum, sig_abs);
dbg_decouple("fpa2bv_add_sig_abs", sig_abs);
res_sig = m_bv_util.mk_extract(sbits+3, 0, sig_abs);
res_exp = m_bv_util.mk_sign_extend(2, c_exp); // rounder requires 2 extra bits!
}
void fpa2bv_converter::mk_add(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 3);
expr_ref rm(m), x(m), y(m);
rm = args[0];
x = args[1];
y = args[2];
expr_ref nan(m), nzero(m), pzero(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_neg(m), x_is_inf(m);
expr_ref y_is_nan(m), y_is_zero(m), y_is_pos(m), y_is_neg(m), y_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_neg(x, x_is_neg);
mk_is_inf(x, x_is_inf);
mk_is_nan(y, y_is_nan);
mk_is_zero(y, y_is_zero);
mk_is_pos(y, y_is_pos);
mk_is_neg(y, y_is_neg);
mk_is_inf(y, y_is_inf);
dbg_decouple("fpa2bv_add_x_is_nan", x_is_nan);
dbg_decouple("fpa2bv_add_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_add_x_is_pos", x_is_pos);
dbg_decouple("fpa2bv_add_x_is_neg", x_is_neg);
dbg_decouple("fpa2bv_add_x_is_inf", x_is_inf);
dbg_decouple("fpa2bv_add_y_is_nan", y_is_nan);
dbg_decouple("fpa2bv_add_y_is_zero", y_is_zero);
dbg_decouple("fpa2bv_add_y_is_pos", y_is_pos);
dbg_decouple("fpa2bv_add_y_is_neg", y_is_neg);
dbg_decouple("fpa2bv_add_y_is_inf", y_is_inf);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m);
m_simp.mk_or(x_is_nan, y_is_nan, c1);
v1 = nan;
mk_is_inf(x, c2);
expr_ref nx(m), ny(m), nx_xor_ny(m), inf_xor(m);
mk_is_neg(x, nx);
mk_is_neg(y, ny);
m_simp.mk_xor(nx, ny, nx_xor_ny);
m_simp.mk_and(y_is_inf, nx_xor_ny, inf_xor);
mk_ite(inf_xor, nan, x, v2);
mk_is_inf(y, c3);
expr_ref xy_is_neg(m), v3_and(m);
m_simp.mk_xor(x_is_neg, y_is_neg, xy_is_neg);
m_simp.mk_and(x_is_inf, xy_is_neg, v3_and);
mk_ite(v3_and, nan, y, v3);
expr_ref rm_is_to_neg(m), signs_and(m), signs_xor(m), v4_and(m), rm_and_xor(m), neg_cond(m);
m_simp.mk_and(x_is_zero, y_is_zero, c4);
m_simp.mk_and(x_is_neg, y_is_neg, signs_and);
m_simp.mk_xor(x_is_neg, y_is_neg, signs_xor);
mk_is_rm(rm, BV_RM_TO_NEGATIVE, rm_is_to_neg);
m_simp.mk_and(rm_is_to_neg, signs_xor, rm_and_xor);
m_simp.mk_or(signs_and, rm_and_xor, neg_cond);
mk_ite(neg_cond, nzero, pzero, v4);
m_simp.mk_and(x_is_neg, y_is_neg, v4_and);
mk_ite(v4_and, x, v4, v4);
c5 = x_is_zero;
v5 = y;
c6 = y_is_zero;
v6 = x;
// Actual addition.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m), b_sgn(m), b_sig(m), b_exp(m), b_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, false);
unpack(y, b_sgn, b_sig, b_exp, b_lz, false);
dbg_decouple("fpa2bv_add_unpack_a_sgn", a_sgn);
dbg_decouple("fpa2bv_add_unpack_a_sig", a_sig);
dbg_decouple("fpa2bv_add_unpack_a_exp", a_exp);
dbg_decouple("fpa2bv_add_unpack_b_sgn", b_sgn);
dbg_decouple("fpa2bv_add_unpack_b_sig", b_sig);
dbg_decouple("fpa2bv_add_unpack_b_exp", b_exp);
expr_ref swap_cond(m);
swap_cond = m_bv_util.mk_sle(a_exp, b_exp);
expr_ref c_sgn(m), c_sig(m), c_exp(m), d_sgn(m), d_sig(m), d_exp(m);
m_simp.mk_ite(swap_cond, b_sgn, a_sgn, c_sgn);
m_simp.mk_ite(swap_cond, b_sig, a_sig, c_sig); // has sbits
m_simp.mk_ite(swap_cond, b_exp, a_exp, c_exp); // has ebits
m_simp.mk_ite(swap_cond, a_sgn, b_sgn, d_sgn);
m_simp.mk_ite(swap_cond, a_sig, b_sig, d_sig); // has sbits
m_simp.mk_ite(swap_cond, a_exp, b_exp, d_exp); // has ebits
expr_ref res_sgn(m), res_sig(m), res_exp(m);
add_core(sbits, ebits, rm,
c_sgn, c_sig, c_exp, d_sgn, d_sig, d_exp,
res_sgn, res_sig, res_exp);
expr_ref is_zero_sig(m), nil_sbit4(m);
nil_sbit4 = m_bv_util.mk_numeral(0, sbits+4);
m_simp.mk_eq(res_sig, nil_sbit4, is_zero_sig);
SASSERT(is_well_sorted(m, is_zero_sig));
dbg_decouple("fpa2bv_add_is_zero_sig", is_zero_sig);
expr_ref zero_case(m);
mk_ite(rm_is_to_neg, nzero, pzero, zero_case);
expr_ref rounded(m);
round(f->get_range(), rm, res_sgn, res_sig, res_exp, rounded);
mk_ite(is_zero_sig, zero_case, rounded, v7);
mk_ite(c6, v6, v7, result);
mk_ite(c5, v5, result, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_add", tout << "ADD = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_sub(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 3);
expr_ref t(m);
mk_uminus(f, 1, &args[2], t);
expr * nargs[3] = { args[0], args[1], t };
mk_add(f, 3, nargs, result);
}
void fpa2bv_converter::mk_uminus(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
expr * sgn, * s, * e;
split(args[0], sgn, s, e);
expr_ref c(m), nsgn(m);
mk_is_nan(args[0], c);
nsgn = m_bv_util.mk_bv_not(sgn);
expr_ref r_sgn(m);
m_simp.mk_ite(c, sgn, nsgn, r_sgn);
mk_triple(r_sgn, s, e, result);
}
void fpa2bv_converter::mk_mul(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 3);
expr_ref rm(m), x(m), y(m);
rm = args[0];
x = args[1];
y = args[2];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
mk_minus_inf(f, ninf);
mk_plus_inf(f, pinf);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_inf(m);
expr_ref y_is_nan(m), y_is_zero(m), y_is_pos(m), y_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_inf(x, x_is_inf);
mk_is_nan(y, y_is_nan);
mk_is_zero(y, y_is_zero);
mk_is_pos(y, y_is_pos);
mk_is_inf(y, y_is_inf);
dbg_decouple("fpa2bv_mul_x_is_nan", x_is_nan);
dbg_decouple("fpa2bv_mul_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_mul_x_is_pos", x_is_pos);
dbg_decouple("fpa2bv_mul_x_is_inf", x_is_inf);
dbg_decouple("fpa2bv_mul_y_is_nan", y_is_nan);
dbg_decouple("fpa2bv_mul_y_is_zero", y_is_zero);
dbg_decouple("fpa2bv_mul_y_is_pos", y_is_pos);
dbg_decouple("fpa2bv_mul_y_is_inf", y_is_inf);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m);
// (x is NaN) || (y is NaN) -> NaN
m_simp.mk_or(x_is_nan, y_is_nan, c1);
v1 = nan;
// (x is +oo) -> if (y is 0) then NaN else inf with y's sign.
mk_is_pinf(x, c2);
expr_ref y_sgn_inf(m);
mk_ite(y_is_pos, pinf, ninf, y_sgn_inf);
mk_ite(y_is_zero, nan, y_sgn_inf, v2);
// (y is +oo) -> if (x is 0) then NaN else inf with x's sign.
mk_is_pinf(y, c3);
expr_ref x_sgn_inf(m);
mk_ite(x_is_pos, pinf, ninf, x_sgn_inf);
mk_ite(x_is_zero, nan, x_sgn_inf, v3);
// (x is -oo) -> if (y is 0) then NaN else inf with -y's sign.
mk_is_ninf(x, c4);
expr_ref neg_y_sgn_inf(m);
mk_ite(y_is_pos, ninf, pinf, neg_y_sgn_inf);
mk_ite(y_is_zero, nan, neg_y_sgn_inf, v4);
// (y is -oo) -> if (x is 0) then NaN else inf with -x's sign.
mk_is_ninf(y, c5);
expr_ref neg_x_sgn_inf(m);
mk_ite(x_is_pos, ninf, pinf, neg_x_sgn_inf);
mk_ite(x_is_zero, nan, neg_x_sgn_inf, v5);
// (x is 0) || (y is 0) -> x but with sign = x.sign ^ y.sign
m_simp.mk_or(x_is_zero, y_is_zero, c6);
expr_ref sign_xor(m);
m_simp.mk_xor(x_is_pos, y_is_pos, sign_xor);
mk_ite(sign_xor, nzero, pzero, v6);
// else comes the actual multiplication.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(ebits <= sbits);
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m), b_sgn(m), b_sig(m), b_exp(m), b_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
unpack(y, b_sgn, b_sig, b_exp, b_lz, true);
dbg_decouple("fpa2bv_mul_a_sig", a_sig);
dbg_decouple("fpa2bv_mul_a_exp", a_exp);
dbg_decouple("fpa2bv_mul_b_sig", b_sig);
dbg_decouple("fpa2bv_mul_b_exp", b_exp);
expr_ref a_lz_ext(m), b_lz_ext(m);
a_lz_ext = m_bv_util.mk_zero_extend(2, a_lz);
b_lz_ext = m_bv_util.mk_zero_extend(2, b_lz);
dbg_decouple("fpa2bv_mul_lz_a", a_lz);
dbg_decouple("fpa2bv_mul_lz_b", b_lz);
expr_ref a_sig_ext(m), b_sig_ext(m);
a_sig_ext = m_bv_util.mk_zero_extend(sbits, a_sig);
b_sig_ext = m_bv_util.mk_zero_extend(sbits, b_sig);
expr_ref a_exp_ext(m), b_exp_ext(m);
a_exp_ext = m_bv_util.mk_sign_extend(2, a_exp);
b_exp_ext = m_bv_util.mk_sign_extend(2, b_exp);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
expr * signs[2] = { a_sgn, b_sgn };
res_sgn = m_bv_util.mk_bv_xor(2, signs);
dbg_decouple("fpa2bv_mul_res_sgn", res_sgn);
res_exp = m_bv_util.mk_bv_add(
m_bv_util.mk_bv_sub(a_exp_ext, a_lz_ext),
m_bv_util.mk_bv_sub(b_exp_ext, b_lz_ext));
expr_ref product(m);
product = m_bv_util.mk_bv_mul(a_sig_ext, b_sig_ext);
dbg_decouple("fpa2bv_mul_product", product);
SASSERT(m_bv_util.get_bv_size(product) == 2*sbits);
expr_ref h_p(m), l_p(m), rbits(m);
h_p = m_bv_util.mk_extract(2*sbits-1, sbits, product);
l_p = m_bv_util.mk_extract(sbits-1, 0, product);
if (sbits >= 4) {
expr_ref sticky(m);
sticky = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, m_bv_util.mk_extract(sbits-4, 0, product));
rbits = m_bv_util.mk_concat(m_bv_util.mk_extract(sbits-1, sbits-3, product), sticky);
}
else
rbits = m_bv_util.mk_concat(l_p, m_bv_util.mk_numeral(0, 4 - sbits));
SASSERT(m_bv_util.get_bv_size(rbits) == 4);
res_sig = m_bv_util.mk_concat(h_p, rbits);
round(f->get_range(), rm, res_sgn, res_sig, res_exp, v7);
// And finally, we tie them together.
mk_ite(c6, v6, v7, result);
mk_ite(c5, v5, result, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_mul", tout << "MUL = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_div(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 3);
expr_ref rm(m), x(m), y(m);
rm = args[0];
x = args[1];
y = args[2];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
mk_minus_inf(f, ninf);
mk_plus_inf(f, pinf);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_inf(m);
expr_ref y_is_nan(m), y_is_zero(m), y_is_pos(m), y_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_inf(x, x_is_inf);
mk_is_nan(y, y_is_nan);
mk_is_zero(y, y_is_zero);
mk_is_pos(y, y_is_pos);
mk_is_inf(y, y_is_inf);
dbg_decouple("fpa2bv_div_x_is_nan", x_is_nan);
dbg_decouple("fpa2bv_div_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_div_x_is_pos", x_is_pos);
dbg_decouple("fpa2bv_div_x_is_inf", x_is_inf);
dbg_decouple("fpa2bv_div_y_is_nan", y_is_nan);
dbg_decouple("fpa2bv_div_y_is_zero", y_is_zero);
dbg_decouple("fpa2bv_div_y_is_pos", y_is_pos);
dbg_decouple("fpa2bv_div_y_is_inf", y_is_inf);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m), c7(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m), v8(m);
// (x is NaN) || (y is NaN) -> NaN
m_simp.mk_or(x_is_nan, y_is_nan, c1);
v1 = nan;
// (x is +oo) -> if (y is oo) then NaN else inf with y's sign.
mk_is_pinf(x, c2);
expr_ref y_sgn_inf(m);
mk_ite(y_is_pos, pinf, ninf, y_sgn_inf);
mk_ite(y_is_inf, nan, y_sgn_inf, v2);
// (y is +oo) -> if (x is oo) then NaN else 0 with sign x.sgn ^ y.sgn
mk_is_pinf(y, c3);
expr_ref xy_zero(m), signs_xor(m);
m_simp.mk_xor(x_is_pos, y_is_pos, signs_xor);
mk_ite(signs_xor, nzero, pzero, xy_zero);
mk_ite(x_is_inf, nan, xy_zero, v3);
// (x is -oo) -> if (y is oo) then NaN else inf with -y's sign.
mk_is_ninf(x, c4);
expr_ref neg_y_sgn_inf(m);
mk_ite(y_is_pos, ninf, pinf, neg_y_sgn_inf);
mk_ite(y_is_inf, nan, neg_y_sgn_inf, v4);
// (y is -oo) -> if (x is oo) then NaN else 0 with sign x.sgn ^ y.sgn
mk_is_ninf(y, c5);
mk_ite(x_is_inf, nan, xy_zero, v5);
// (y is 0) -> if (x is 0) then NaN else inf with xor sign.
c6 = y_is_zero;
expr_ref sgn_inf(m);
mk_ite(signs_xor, ninf, pinf, sgn_inf);
mk_ite(x_is_zero, nan, sgn_inf, v6);
// (x is 0) -> result is zero with sgn = x.sgn^y.sgn
// This is a special case to avoid problems with the unpacking of zero.
c7 = x_is_zero;
mk_ite(signs_xor, nzero, pzero, v7);
// else comes the actual division.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(ebits <= sbits);
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m), b_sgn(m), b_sig(m), b_exp(m), b_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
unpack(y, b_sgn, b_sig, b_exp, b_lz, true);
unsigned extra_bits = sbits+2;
expr_ref a_sig_ext(m), b_sig_ext(m);
a_sig_ext = m_bv_util.mk_concat(a_sig, m_bv_util.mk_numeral(0, sbits + extra_bits));
b_sig_ext = m_bv_util.mk_zero_extend(sbits + extra_bits, b_sig);
expr_ref a_exp_ext(m), b_exp_ext(m);
a_exp_ext = m_bv_util.mk_sign_extend(2, a_exp);
b_exp_ext = m_bv_util.mk_sign_extend(2, b_exp);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
expr * signs[2] = { a_sgn, b_sgn };
res_sgn = m_bv_util.mk_bv_xor(2, signs);
expr_ref a_lz_ext(m), b_lz_ext(m);
a_lz_ext = m_bv_util.mk_zero_extend(2, a_lz);
b_lz_ext = m_bv_util.mk_zero_extend(2, b_lz);
res_exp = m_bv_util.mk_bv_sub(
m_bv_util.mk_bv_sub(a_exp_ext, a_lz_ext),
m_bv_util.mk_bv_sub(b_exp_ext, b_lz_ext));
expr_ref quotient(m);
quotient = m.mk_app(m_bv_util.get_fid(), OP_BUDIV, a_sig_ext, b_sig_ext);
dbg_decouple("fpa2bv_div_quotient", quotient);
SASSERT(m_bv_util.get_bv_size(quotient) == (sbits + sbits + extra_bits));
expr_ref sticky(m);
sticky = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, m_bv_util.mk_extract(extra_bits-2, 0, quotient));
res_sig = m_bv_util.mk_concat(m_bv_util.mk_extract(extra_bits+sbits+1, extra_bits-1, quotient), sticky);
SASSERT(m_bv_util.get_bv_size(res_sig) == (sbits + 4));
round(f->get_range(), rm, res_sgn, res_sig, res_exp, v8);
// And finally, we tie them together.
mk_ite(c7, v7, v8, result);
mk_ite(c6, v6, result, result);
mk_ite(c5, v5, result, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_div", tout << "DIV = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_remainder(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
// Remainder is always exact, so there is no rounding mode.
expr_ref x(m), y(m);
x = args[0];
y = args[1];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
mk_minus_inf(f, ninf);
mk_plus_inf(f, pinf);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_inf(m);
expr_ref y_is_nan(m), y_is_zero(m), y_is_pos(m), y_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_inf(x, x_is_inf);
mk_is_nan(y, y_is_nan);
mk_is_zero(y, y_is_zero);
mk_is_pos(y, y_is_pos);
mk_is_inf(y, y_is_inf);
dbg_decouple("fpa2bv_rem_x_is_nan", x_is_nan);
dbg_decouple("fpa2bv_rem_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_rem_x_is_pos", x_is_pos);
dbg_decouple("fpa2bv_rem_x_is_inf", x_is_inf);
dbg_decouple("fpa2bv_rem_y_is_nan", y_is_nan);
dbg_decouple("fpa2bv_rem_y_is_zero", y_is_zero);
dbg_decouple("fpa2bv_rem_y_is_pos", y_is_pos);
dbg_decouple("fpa2bv_rem_y_is_inf", y_is_inf);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m);
// (x is NaN) || (y is NaN) -> NaN
m_simp.mk_or(x_is_nan, y_is_nan, c1);
v1 = nan;
// (x is +-oo) -> NaN
c2 = x_is_inf;
v2 = nan;
// (y is +-oo) -> x
c3 = y_is_inf;
v3 = x;
// (x is 0) -> x
c4 = x_is_zero;
v4 = pzero;
// (y is 0) -> NaN.
c5 = y_is_zero;
v5 = nan;
// else the actual remainder.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m);
expr_ref b_sgn(m), b_sig(m), b_exp(m), b_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
unpack(y, b_sgn, b_sig, b_exp, b_lz, true);
BVSLT(a_exp, b_exp, c6);
v6 = x;
// max. exponent difference is (2^ebits) - 3
const mpz & two_to_ebits = fu().fm().m_powers2(ebits);
mpz max_exp_diff;
m_mpz_manager.sub(two_to_ebits, 3, max_exp_diff);
SASSERT(m_mpz_manager.is_int64(max_exp_diff));
SASSERT(m_mpz_manager.get_uint64(max_exp_diff) <= UINT_MAX);
unsigned int max_exp_diff_ui = (unsigned int)m_mpz_manager.get_uint64(max_exp_diff);
m_mpz_manager.del(max_exp_diff);
expr_ref exp_diff(m);
exp_diff = m_bv_util.mk_bv_sub(a_exp, b_exp);
dbg_decouple("fpa2bv_rem_exp_diff", exp_diff);
// CMW: This creates _huge_ bit-vectors, which is potentially sub-optimal,
// but calculating this via rem = x - y * nearest(x/y) creates huge circuits.
expr_ref huge_sig(m), shifted_sig(m), huge_rem(m);
huge_sig = m_bv_util.mk_zero_extend(max_exp_diff_ui, a_sig);
shifted_sig = m_bv_util.mk_bv_shl(huge_sig, m_bv_util.mk_zero_extend(max_exp_diff_ui + sbits - ebits, exp_diff));
huge_rem = m_bv_util.mk_bv_urem(shifted_sig, m_bv_util.mk_zero_extend(max_exp_diff_ui, b_sig));
dbg_decouple("fpa2bv_rem_huge_rem", huge_rem);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
res_sgn = a_sgn;
res_sig = m_bv_util.mk_concat(m_bv_util.mk_extract(sbits, 0, huge_rem),
m_bv_util.mk_numeral(0, 3));
res_exp = m_bv_util.mk_sign_extend(2, b_exp);
expr_ref rm(m);
rm = m_bv_util.mk_numeral(BV_RM_TIES_TO_EVEN, 3);
round(f->get_range(), rm, res_sgn, res_sig, res_exp, v7);
// And finally, we tie them together.
mk_ite(c6, v6, v7, result);
mk_ite(c5, v5, result, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_rem", tout << "REM = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_abs(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
expr * sgn, * s, * e;
split(args[0], sgn, s, e);
mk_triple(m_bv_util.mk_numeral(0, 1), s, e, result);
}
void fpa2bv_converter::mk_min(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr * x = args[0], * y = args[1];
expr * x_sgn, * x_sig, * x_exp;
expr * y_sgn, * y_sig, * y_exp;
split(x, x_sgn, x_sig, x_exp);
split(y, y_sgn, y_sig, y_exp);
expr_ref c1(m), c2(m), x_is_nan(m), y_is_nan(m), x_is_zero(m), y_is_zero(m), c1_and(m);
mk_is_zero(x, x_is_zero);
mk_is_zero(y, y_is_zero);
m_simp.mk_and(x_is_zero, y_is_zero, c1_and);
mk_is_nan(x, x_is_nan);
m_simp.mk_or(x_is_nan, c1_and, c1);
mk_is_nan(y, y_is_nan);
c2 = y_is_nan;
expr_ref c3(m);
mk_float_lt(f, num, args, c3);
expr_ref r_sgn(m), r_sig(m), r_exp(m);
expr_ref c3xy(m), c2c3(m);
m_simp.mk_ite(c3, x_sgn, y_sgn, c3xy);
m_simp.mk_ite(c2, x_sgn, c3xy, c2c3);
m_simp.mk_ite(c1, y_sgn, c2c3, r_sgn);
expr_ref c3xy_sig(m), c2c3_sig(m);
m_simp.mk_ite(c3, x_sig, y_sig, c3xy_sig);
m_simp.mk_ite(c2, x_sig, c3xy_sig, c2c3_sig);
m_simp.mk_ite(c1, y_sig, c2c3_sig, r_sig);
expr_ref c3xy_exp(m), c2c3_exp(m);
m_simp.mk_ite(c3, x_exp, y_exp, c3xy_exp);
m_simp.mk_ite(c2, x_exp, c3xy_exp, c2c3_exp);
m_simp.mk_ite(c1, y_exp, c2c3_exp, r_exp);
mk_triple(r_sgn, r_sig, r_exp, result);
}
void fpa2bv_converter::mk_max(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr * x = args[0], * y = args[1];
expr * x_sgn, * x_sig, * x_exp;
expr * y_sgn, * y_sig, * y_exp;
split(x, x_sgn, x_sig, x_exp);
split(y, y_sgn, y_sig, y_exp);
expr_ref c1(m), c2(m), x_is_nan(m), y_is_nan(m), y_is_zero(m), x_is_zero(m), c1_and(m);
mk_is_zero(y, y_is_zero);
mk_is_zero(x, x_is_zero);
m_simp.mk_and(y_is_zero, x_is_zero, c1_and);
mk_is_nan(x, x_is_nan);
m_simp.mk_or(x_is_nan, c1_and, c1);
mk_is_nan(y, y_is_nan);
c2 = y_is_nan;
expr_ref c3(m);
mk_float_gt(f, num, args, c3);
expr_ref r_sgn(m), r_sig(m), r_exp(m);
expr_ref c3xy_sgn(m), c2c3_sgn(m);
m_simp.mk_ite(c3, x_sgn, y_sgn, c3xy_sgn);
m_simp.mk_ite(c2, x_sgn, c3xy_sgn, c2c3_sgn);
m_simp.mk_ite(c1, y_sgn, c2c3_sgn, r_sgn);
expr_ref c3xy_sig(m), c2c3_sig(m);
m_simp.mk_ite(c3, x_sig, y_sig, c3xy_sig);
m_simp.mk_ite(c2, x_sig, c3xy_sig, c2c3_sig);
m_simp.mk_ite(c1, y_sig, c2c3_sig, r_sig);
expr_ref c3xy_exp(m), c2c3_exp(m);
m_simp.mk_ite(c3, x_exp, y_exp, c3xy_exp);
m_simp.mk_ite(c2, x_exp, c3xy_exp, c2c3_exp);
m_simp.mk_ite(c1, y_exp, c2c3_exp, r_exp);
mk_triple(r_sgn, r_sig, r_exp, result);
}
void fpa2bv_converter::mk_fusedma(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 4);
// fusedma means (x * y) + z
expr_ref rm(m), x(m), y(m), z(m);
rm = args[0];
x = args[1];
y = args[2];
z = args[3];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
mk_minus_inf(f, ninf);
mk_plus_inf(f, pinf);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_neg(m), x_is_inf(m);
expr_ref y_is_nan(m), y_is_zero(m), y_is_pos(m), y_is_neg(m), y_is_inf(m);
expr_ref z_is_nan(m), z_is_zero(m), z_is_pos(m), z_is_neg(m), z_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_neg(x, x_is_neg);
mk_is_inf(x, x_is_inf);
mk_is_nan(y, y_is_nan);
mk_is_zero(y, y_is_zero);
mk_is_pos(y, y_is_pos);
mk_is_neg(y, y_is_neg);
mk_is_inf(y, y_is_inf);
mk_is_nan(z, z_is_nan);
mk_is_zero(z, z_is_zero);
mk_is_pos(z, z_is_pos);
mk_is_neg(z, z_is_neg);
mk_is_inf(z, z_is_inf);
expr_ref rm_is_to_neg(m);
mk_is_rm(rm, BV_RM_TO_NEGATIVE, rm_is_to_neg);
dbg_decouple("fpa2bv_fma_x_is_nan", x_is_nan);
dbg_decouple("fpa2bv_fma_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_fma_x_is_pos", x_is_pos);
dbg_decouple("fpa2bv_fma_x_is_inf", x_is_inf);
dbg_decouple("fpa2bv_fma_y_is_nan", y_is_nan);
dbg_decouple("fpa2bv_fma_y_is_zero", y_is_zero);
dbg_decouple("fpa2bv_fma_y_is_pos", y_is_pos);
dbg_decouple("fpa2bv_fma_y_is_inf", y_is_inf);
dbg_decouple("fpa2bv_fma_z_is_nan", z_is_nan);
dbg_decouple("fpa2bv_fma_z_is_zero", z_is_zero);
dbg_decouple("fpa2bv_fma_z_is_pos", z_is_pos);
dbg_decouple("fpa2bv_fma_z_is_inf", z_is_inf);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m), c7(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m), v8(m);
expr_ref inf_xor(m), inf_cond(m);
m_simp.mk_xor(x_is_neg, y_is_neg, inf_xor);
m_simp.mk_xor(inf_xor, z_is_neg, inf_xor);
m_simp.mk_and(z_is_inf, inf_xor, inf_cond);
// (x is NaN) || (y is NaN) || (z is Nan) -> NaN
m_simp.mk_or(x_is_nan, y_is_nan, z_is_nan, c1);
v1 = nan;
// (x is +oo) -> if (y is 0) then NaN else inf with y's sign.
mk_is_pinf(x, c2);
expr_ref y_sgn_inf(m), inf_or(m);
mk_ite(y_is_pos, pinf, ninf, y_sgn_inf);
m_simp.mk_or(y_is_zero, inf_cond, inf_or);
mk_ite(inf_or, nan, y_sgn_inf, v2);
// (y is +oo) -> if (x is 0) then NaN else inf with x's sign.
mk_is_pinf(y, c3);
expr_ref x_sgn_inf(m);
mk_ite(x_is_pos, pinf, ninf, x_sgn_inf);
m_simp.mk_or(x_is_zero, inf_cond, inf_or);
mk_ite(inf_or, nan, x_sgn_inf, v3);
// (x is -oo) -> if (y is 0) then NaN else inf with -y's sign.
mk_is_ninf(x, c4);
expr_ref neg_y_sgn_inf(m);
mk_ite(y_is_pos, ninf, pinf, neg_y_sgn_inf);
m_simp.mk_or(y_is_zero, inf_cond, inf_or);
mk_ite(inf_or, nan, neg_y_sgn_inf, v4);
// (y is -oo) -> if (x is 0) then NaN else inf with -x's sign.
mk_is_ninf(y, c5);
expr_ref neg_x_sgn_inf(m);
mk_ite(x_is_pos, ninf, pinf, neg_x_sgn_inf);
m_simp.mk_or(x_is_zero, inf_cond, inf_or);
mk_ite(inf_or, nan, neg_x_sgn_inf, v5);
// z is +-INF -> z.
mk_is_inf(z, c6);
v6 = z;
// (x is 0) || (y is 0) -> z
m_simp.mk_or(x_is_zero, y_is_zero, c7);
expr_ref ite_c(m);
m_simp.mk_and(z_is_zero, m.mk_not(rm_is_to_neg), ite_c);
mk_ite(ite_c, pzero, z, v7);
// else comes the fused multiplication.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(ebits <= sbits);
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m);
expr_ref b_sgn(m), b_sig(m), b_exp(m), b_lz(m);
expr_ref c_sgn(m), c_sig(m), c_exp(m), c_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
unpack(y, b_sgn, b_sig, b_exp, b_lz, true);
unpack(z, c_sgn, c_sig, c_exp, c_lz, true);
expr_ref a_lz_ext(m), b_lz_ext(m), c_lz_ext(m);
a_lz_ext = m_bv_util.mk_zero_extend(2, a_lz);
b_lz_ext = m_bv_util.mk_zero_extend(2, b_lz);
c_lz_ext = m_bv_util.mk_zero_extend(2, c_lz);
expr_ref a_sig_ext(m), b_sig_ext(m);
a_sig_ext = m_bv_util.mk_zero_extend(sbits, a_sig);
b_sig_ext = m_bv_util.mk_zero_extend(sbits, b_sig);
expr_ref a_exp_ext(m), b_exp_ext(m), c_exp_ext(m);
a_exp_ext = m_bv_util.mk_sign_extend(2, a_exp);
b_exp_ext = m_bv_util.mk_sign_extend(2, b_exp);
c_exp_ext = m_bv_util.mk_sign_extend(2, c_exp);
dbg_decouple("fpa2bv_fma_a_sig", a_sig_ext);
dbg_decouple("fpa2bv_fma_b_sig", b_sig_ext);
dbg_decouple("fpa2bv_fma_c_sig", c_sig);
dbg_decouple("fpa2bv_fma_a_exp", a_exp_ext);
dbg_decouple("fpa2bv_fma_b_exp", b_exp_ext);
dbg_decouple("fpa2bv_fma_c_exp", c_exp_ext);
dbg_decouple("fpa2bv_fma_a_lz", a_lz_ext);
dbg_decouple("fpa2bv_fma_b_lz", b_lz_ext);
dbg_decouple("fpa2bv_fma_c_lz", c_lz_ext);
expr_ref mul_sgn(m), mul_sig(m), mul_exp(m);
expr * signs[2] = { a_sgn, b_sgn };
mul_sgn = m_bv_util.mk_bv_xor(2, signs);
dbg_decouple("fpa2bv_fma_mul_sgn", mul_sgn);
mul_exp = m_bv_util.mk_bv_add(m_bv_util.mk_bv_sub(a_exp_ext, a_lz_ext),
m_bv_util.mk_bv_sub(b_exp_ext, b_lz_ext));
dbg_decouple("fpa2bv_fma_mul_exp", mul_exp);
mul_sig = m_bv_util.mk_bv_mul(a_sig_ext, b_sig_ext);
dbg_decouple("fpa2bv_fma_mul_sig", mul_sig);
SASSERT(m_bv_util.get_bv_size(mul_sig) == 2*sbits);
SASSERT(m_bv_util.get_bv_size(mul_exp) == ebits + 2);
// The product has the form [-1][0].[2*sbits - 2].
// Extend c
c_sig = m_bv_util.mk_zero_extend(1, m_bv_util.mk_concat(c_sig, m_bv_util.mk_numeral(0, sbits-1)));
c_exp_ext = m_bv_util.mk_bv_sub(c_exp_ext, c_lz_ext);
SASSERT(m_bv_util.get_bv_size(mul_sig) == 2 * sbits);
SASSERT(m_bv_util.get_bv_size(c_sig) == 2 * sbits);
expr_ref swap_cond(m);
swap_cond = m_bv_util.mk_sle(mul_exp, c_exp_ext);
SASSERT(is_well_sorted(m, swap_cond));
dbg_decouple("fpa2bv_fma_swap_cond", swap_cond);
expr_ref e_sgn(m), e_sig(m), e_exp(m), f_sgn(m), f_sig(m), f_exp(m);
m_simp.mk_ite(swap_cond, c_sgn, mul_sgn, e_sgn);
m_simp.mk_ite(swap_cond, c_sig, mul_sig, e_sig); // has 2 * sbits
m_simp.mk_ite(swap_cond, c_exp_ext, mul_exp, e_exp); // has ebits + 2
m_simp.mk_ite(swap_cond, mul_sgn, c_sgn, f_sgn);
m_simp.mk_ite(swap_cond, mul_sig, c_sig, f_sig); // has 2 * sbits
m_simp.mk_ite(swap_cond, mul_exp, c_exp_ext, f_exp); // has ebits + 2
SASSERT(is_well_sorted(m, e_sgn));
SASSERT(is_well_sorted(m, e_sig));
SASSERT(is_well_sorted(m, e_exp));
SASSERT(is_well_sorted(m, f_sgn));
SASSERT(is_well_sorted(m, f_sig));
SASSERT(is_well_sorted(m, f_exp));
SASSERT(m_bv_util.get_bv_size(e_sig) == 2 * sbits);
SASSERT(m_bv_util.get_bv_size(f_sig) == 2 * sbits);
SASSERT(m_bv_util.get_bv_size(e_exp) == ebits + 2);
SASSERT(m_bv_util.get_bv_size(f_exp) == ebits + 2);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
expr_ref exp_delta(m);
exp_delta = m_bv_util.mk_bv_sub(e_exp, f_exp);
dbg_decouple("fpa2bv_fma_add_exp_delta", exp_delta);
// cap the delta
expr_ref cap(m), cap_le_delta(m);
cap = m_bv_util.mk_numeral(2*sbits, ebits+2);
cap_le_delta = m_bv_util.mk_ule(cap, exp_delta);
m_simp.mk_ite(cap_le_delta, cap, exp_delta, exp_delta);
SASSERT(m_bv_util.get_bv_size(exp_delta) == ebits+2);
SASSERT(is_well_sorted(m, exp_delta));
dbg_decouple("fpa2bv_fma_add_exp_delta_capped", exp_delta);
// Alignment shift with sticky bit computation.
expr_ref shifted_big(m), shifted_f_sig(m), sticky_raw(m);
shifted_big = m_bv_util.mk_bv_lshr(
m_bv_util.mk_concat(f_sig, m_bv_util.mk_numeral(0, sbits)),
m_bv_util.mk_zero_extend((3*sbits)-(ebits+2), exp_delta));
shifted_f_sig = m_bv_util.mk_extract(3*sbits-1, sbits, shifted_big);
sticky_raw = m_bv_util.mk_extract(sbits-1, 0, shifted_big);
SASSERT(m_bv_util.get_bv_size(shifted_f_sig) == 2 * sbits);
SASSERT(is_well_sorted(m, shifted_f_sig));
expr_ref sticky(m);
sticky = m_bv_util.mk_zero_extend(2*sbits-1, m.mk_app(m_bv_util.get_fid(), OP_BREDOR, sticky_raw.get()));
SASSERT(is_well_sorted(m, sticky));
dbg_decouple("fpa2bv_fma_f_sig_sticky_raw", sticky_raw);
dbg_decouple("fpa2bv_fma_f_sig_sticky", sticky);
expr * or_args[2] = { shifted_f_sig, sticky };
shifted_f_sig = m_bv_util.mk_bv_or(2, or_args);
SASSERT(is_well_sorted(m, shifted_f_sig));
// Significant addition.
// Two extra bits for catching the overflow.
e_sig = m_bv_util.mk_zero_extend(2, e_sig);
shifted_f_sig = m_bv_util.mk_zero_extend(2, shifted_f_sig);
expr_ref eq_sgn(m);
m_simp.mk_eq(e_sgn, f_sgn, eq_sgn);
SASSERT(m_bv_util.get_bv_size(e_sig) == 2*sbits + 2);
SASSERT(m_bv_util.get_bv_size(shifted_f_sig) == 2*sbits + 2);
dbg_decouple("fpa2bv_fma_add_e_sig", e_sig);
dbg_decouple("fpa2bv_fma_add_shifted_f_sig", shifted_f_sig);
expr_ref sum(m);
m_simp.mk_ite(eq_sgn,
m_bv_util.mk_bv_add(e_sig, shifted_f_sig),
m_bv_util.mk_bv_sub(e_sig, shifted_f_sig),
sum);
SASSERT(is_well_sorted(m, sum));
dbg_decouple("fpa2bv_fma_add_sum", sum);
expr_ref sign_bv(m), n_sum(m);
sign_bv = m_bv_util.mk_extract(2*sbits+1, 2*sbits+1, sum);
n_sum = m_bv_util.mk_bv_neg(sum);
expr_ref res_sig_eq(m), sig_abs(m), one_1(m);
one_1 = m_bv_util.mk_numeral(1, 1);
m_simp.mk_eq(sign_bv, one_1, res_sig_eq);
m_simp.mk_ite(res_sig_eq, n_sum, sum, sig_abs);
dbg_decouple("fpa2bv_fma_add_sign_bv", sign_bv);
dbg_decouple("fpa2bv_fma_add_n_sum", n_sum);
dbg_decouple("fpa2bv_fma_add_sig_abs", sig_abs);
res_exp = e_exp;
// Result could overflow into 4.xxx ...
family_id bvfid = m_bv_util.get_fid();
expr_ref res_sgn_c1(m), res_sgn_c2(m), res_sgn_c3(m);
expr_ref not_e_sgn(m), not_f_sgn(m), not_sign_bv(m);
not_e_sgn = m_bv_util.mk_bv_not(e_sgn);
not_f_sgn = m_bv_util.mk_bv_not(f_sgn);
not_sign_bv = m_bv_util.mk_bv_not(sign_bv);
res_sgn_c1 = m.mk_app(bvfid, OP_BAND, not_e_sgn, e_sgn, sign_bv);
res_sgn_c2 = m.mk_app(bvfid, OP_BAND, e_sgn, not_f_sgn, not_sign_bv);
res_sgn_c3 = m.mk_app(bvfid, OP_BAND, e_sgn, f_sgn);
expr * res_sgn_or_args[3] = { res_sgn_c1, res_sgn_c2, res_sgn_c3 };
res_sgn = m_bv_util.mk_bv_or(3, res_sgn_or_args);
sticky_raw = m_bv_util.mk_extract(sbits-5, 0, sig_abs);
sticky = m_bv_util.mk_zero_extend(sbits+3, m.mk_app(bvfid, OP_BREDOR, sticky_raw.get()));
dbg_decouple("fpa2bv_fma_add_sum_sticky", sticky);
expr * res_or_args[2] = { m_bv_util.mk_extract(2*sbits-1, sbits-4, sig_abs), sticky };
res_sig = m_bv_util.mk_bv_or(2, res_or_args);
SASSERT(m_bv_util.get_bv_size(res_sig) == sbits+4);
expr_ref is_zero_sig(m), nil_sbits4(m);
nil_sbits4 = m_bv_util.mk_numeral(0, sbits+4);
m_simp.mk_eq(res_sig, nil_sbits4, is_zero_sig);
SASSERT(is_well_sorted(m, is_zero_sig));
dbg_decouple("fpa2bv_fma_is_zero_sig", is_zero_sig);
expr_ref zero_case(m);
mk_ite(rm_is_to_neg, nzero, pzero, zero_case);
expr_ref rounded(m);
round(f->get_range(), rm, res_sgn, res_sig, res_exp, rounded);
mk_ite(is_zero_sig, zero_case, rounded, v8);
// And finally, we tie them together.
mk_ite(c7, v7, v8, result);
mk_ite(c6, v6, result, result);
mk_ite(c5, v5, result, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_fma_", tout << "FMA = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_sqrt(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr_ref rm(m), x(m);
rm = args[0];
x = args[1];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
mk_minus_inf(f, ninf);
mk_plus_inf(f, pinf);
expr_ref x_is_nan(m), x_is_zero(m), x_is_pos(m), x_is_inf(m);
mk_is_nan(x, x_is_nan);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
mk_is_inf(x, x_is_inf);
expr_ref zero1(m), one1(m);
zero1 = m_bv_util.mk_numeral(0, 1);
one1 = m_bv_util.mk_numeral(1, 1);
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m), c6(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m), v7(m);
// (x is NaN) -> NaN
c1 = x_is_nan;
v1 = x;
// (x is +oo) -> +oo
mk_is_pinf(x, c2);
v2 = x;
// (x is +-0) -> +-0
mk_is_zero(x, c3);
v3 = x;
// (x < 0) -> NaN
mk_is_neg(x, c4);
v4 = nan;
// else comes the actual square root.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(ebits <= sbits);
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
dbg_decouple("fpa2bv_sqrt_sig", a_sig);
dbg_decouple("fpa2bv_sqrt_exp", a_exp);
SASSERT(m_bv_util.get_bv_size(a_sig) == sbits);
SASSERT(m_bv_util.get_bv_size(a_exp) == ebits);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
res_sgn = zero1;
expr_ref real_exp(m);
real_exp = m_bv_util.mk_bv_sub(m_bv_util.mk_sign_extend(1, a_exp), m_bv_util.mk_zero_extend(1, a_lz));
res_exp = m_bv_util.mk_sign_extend(2, m_bv_util.mk_extract(ebits, 1, real_exp));
expr_ref e_is_odd(m);
e_is_odd = m.mk_eq(m_bv_util.mk_extract(0, 0, real_exp), one1);
dbg_decouple("fpa2bv_sqrt_e_is_odd", e_is_odd);
dbg_decouple("fpa2bv_sqrt_real_exp", real_exp);
expr_ref sig_prime(m);
m_simp.mk_ite(e_is_odd, m_bv_util.mk_concat(a_sig, zero1),
m_bv_util.mk_concat(zero1, a_sig),
sig_prime);
SASSERT(m_bv_util.get_bv_size(sig_prime) == sbits+1);
dbg_decouple("fpa2bv_sqrt_sig_prime", sig_prime);
// This is algorithm 10.2 in the Handbook of Floating-Point Arithmetic
expr_ref Q(m), R(m), S(m), T(m);
const mpz & p2 = fu().fm().m_powers2(sbits+3);
Q = m_bv_util.mk_numeral(p2, sbits+5);
R = m_bv_util.mk_bv_sub(m_bv_util.mk_concat(sig_prime, m_bv_util.mk_numeral(0, 4)), Q);
S = Q;
for (unsigned i = 0; i < sbits + 3; i++) {
dbg_decouple("fpa2bv_sqrt_Q", Q);
dbg_decouple("fpa2bv_sqrt_R", R);
S = m_bv_util.mk_concat(zero1, m_bv_util.mk_extract(sbits+4, 1, S));
expr_ref twoQ_plus_S(m);
twoQ_plus_S = m_bv_util.mk_bv_add(m_bv_util.mk_concat(Q, zero1), m_bv_util.mk_concat(zero1, S));
T = m_bv_util.mk_bv_sub(m_bv_util.mk_concat(R, zero1), twoQ_plus_S);
dbg_decouple("fpa2bv_sqrt_T", T);
SASSERT(m_bv_util.get_bv_size(Q) == sbits + 5);
SASSERT(m_bv_util.get_bv_size(R) == sbits + 5);
SASSERT(m_bv_util.get_bv_size(S) == sbits + 5);
SASSERT(m_bv_util.get_bv_size(T) == sbits + 6);
expr_ref t_lt_0(m);
m_simp.mk_eq(m_bv_util.mk_extract(sbits+5, sbits+5, T), one1, t_lt_0);
expr * or_args[2] = { Q, S };
m_simp.mk_ite(t_lt_0, Q,
m_bv_util.mk_bv_or(2, or_args),
Q);
m_simp.mk_ite(t_lt_0, m_bv_util.mk_concat(m_bv_util.mk_extract(sbits+3, 0, R), zero1),
m_bv_util.mk_extract(sbits+4, 0, T),
R);
}
expr_ref is_exact(m);
m_simp.mk_eq(R, m_bv_util.mk_numeral(0, sbits+5), is_exact);
dbg_decouple("fpa2bv_sqrt_is_exact", is_exact);
expr_ref rest(m), last(m), q_is_odd(m), rest_ext(m);
last = m_bv_util.mk_extract(0, 0, Q);
rest = m_bv_util.mk_extract(sbits+3, 1, Q);
dbg_decouple("fpa2bv_sqrt_last", last);
dbg_decouple("fpa2bv_sqrt_rest", rest);
rest_ext = m_bv_util.mk_zero_extend(1, rest);
expr_ref sticky(m);
m_simp.mk_ite(is_exact, m_bv_util.mk_zero_extend(sbits+3, last),
m_bv_util.mk_numeral(1, sbits+4),
sticky);
expr * or_args[2] = { rest_ext, sticky };
res_sig = m_bv_util.mk_bv_or(2, or_args);
SASSERT(m_bv_util.get_bv_size(res_sig) == sbits + 4);
expr_ref rounded(m);
round(f->get_range(), rm, res_sgn, res_sig, res_exp, rounded);
v5 = rounded;
// And finally, we tie them together.
mk_ite(c4, v4, v5, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
}
void fpa2bv_converter::mk_round_to_integral(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr_ref rm(m), x(m);
rm = args[0];
x = args[1];
expr_ref nan(m), nzero(m), pzero(m), ninf(m), pinf(m);
mk_nan(f, nan);
mk_nzero(f, nzero);
mk_pzero(f, pzero);
expr_ref x_is_zero(m), x_is_pos(m);
mk_is_zero(x, x_is_zero);
mk_is_pos(x, x_is_pos);
dbg_decouple("fpa2bv_r2i_x_is_zero", x_is_zero);
dbg_decouple("fpa2bv_r2i_x_is_pos", x_is_pos);
expr_ref c1(m), c2(m), c3(m), c4(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m);
mk_is_nan(x, c1);
v1 = nan;
mk_is_inf(x, c2);
v2 = x;
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
expr_ref a_sgn(m), a_sig(m), a_exp(m), a_lz(m);
unpack(x, a_sgn, a_sig, a_exp, a_lz, true);
dbg_decouple("fpa2bv_r2i_unpacked_sig", a_sig);
dbg_decouple("fpa2bv_r2i_unpacked_exp", a_exp);
expr_ref exp_is_small(m), exp_h(m), one_1(m);
exp_h = m_bv_util.mk_extract(ebits-1, ebits-1, a_exp);
one_1 = m_bv_util.mk_numeral(1, 1);
m_simp.mk_eq(exp_h, one_1, exp_is_small);
dbg_decouple("fpa2bv_r2i_exp_is_small", exp_is_small);
c3 = exp_is_small;
mk_ite(x_is_pos, pzero, nzero, v3);
expr_ref exp_is_large(m);
exp_is_large = m_bv_util.mk_sle(m_bv_util.mk_numeral(sbits-1, ebits), a_exp);
dbg_decouple("fpa2bv_r2i_exp_is_large", exp_is_large);
c4 = exp_is_large;
v4 = x;
// The actual rounding.
expr_ref res_sgn(m), res_sig(m), res_exp(m);
res_sgn = a_sgn;
res_exp = m_bv_util.mk_concat(m_bv_util.mk_numeral(0, 2), a_exp);
expr_ref shift(m), r_shifted(m), l_shifted(m);
shift = m_bv_util.mk_bv_sub(m_bv_util.mk_numeral(sbits-1, ebits+1),
m_bv_util.mk_sign_extend(1, a_exp));
if (sbits > (ebits+1))
r_shifted = m_bv_util.mk_bv_lshr(a_sig, m_bv_util.mk_zero_extend(sbits-(ebits+1), shift));
else if (sbits < (ebits+1))
r_shifted = m_bv_util.mk_extract(ebits, ebits-sbits+1, m_bv_util.mk_bv_lshr(m_bv_util.mk_zero_extend(ebits+1-sbits, a_sig), shift));
else // sbits == ebits+1
r_shifted = m_bv_util.mk_bv_lshr(a_sig, shift);
SASSERT(is_well_sorted(m, r_shifted));
SASSERT(m_bv_util.get_bv_size(r_shifted) == sbits);
if (sbits > (ebits+1))
l_shifted = m_bv_util.mk_bv_shl(r_shifted, m_bv_util.mk_zero_extend(sbits-(ebits+1), shift));
else if (sbits < (ebits+1))
l_shifted = m_bv_util.mk_extract(ebits, ebits-sbits+1, m_bv_util.mk_bv_shl(m_bv_util.mk_zero_extend(ebits+1-sbits, r_shifted), shift));
else // sbits == ebits+1
l_shifted = m_bv_util.mk_bv_shl(r_shifted, shift);
SASSERT(is_well_sorted(m, l_shifted));
SASSERT(m_bv_util.get_bv_size(l_shifted) == sbits);
res_sig = m_bv_util.mk_concat(m_bv_util.mk_numeral(0, 1),
m_bv_util.mk_concat(l_shifted,
m_bv_util.mk_numeral(0, 3)));
SASSERT(m_bv_util.get_bv_size(res_sig) == (sbits + 4));
round(f->get_range(), rm, res_sgn, res_sig, res_exp, v5);
// And finally, we tie them together.
mk_ite(c4, v4, v5, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
SASSERT(is_well_sorted(m, result));
TRACE("fpa2bv_round_to_integral", tout << "ROUND2INTEGRAL = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_float_eq(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr * x = args[0], * y = args[1];
TRACE("fpa2bv_float_eq", tout << "X = " << mk_ismt2_pp(x, m) << std::endl;
tout << "Y = " << mk_ismt2_pp(y, m) << std::endl;);
expr_ref c1(m), c2(m), x_is_nan(m), y_is_nan(m), x_is_zero(m), y_is_zero(m);
mk_is_nan(x, x_is_nan);
mk_is_nan(y, y_is_nan);
m_simp.mk_or(x_is_nan, y_is_nan, c1);
mk_is_zero(x, x_is_zero);
mk_is_zero(y, y_is_zero);
m_simp.mk_and(x_is_zero, y_is_zero, c2);
expr * x_sgn, * x_sig, * x_exp;
expr * y_sgn, * y_sig, * y_exp;
split(x, x_sgn, x_sig, x_exp);
split(y, y_sgn, y_sig, y_exp);
expr_ref x_eq_y_sgn(m), x_eq_y_exp(m), x_eq_y_sig(m);
m_simp.mk_eq(x_sgn, y_sgn, x_eq_y_sgn);
m_simp.mk_eq(x_exp, y_exp, x_eq_y_exp);
m_simp.mk_eq(x_sig, y_sig, x_eq_y_sig);
expr_ref c3(m), t4(m);
m_simp.mk_not(x_eq_y_sgn, c3);
m_simp.mk_and(x_eq_y_exp, x_eq_y_sig, t4);
expr_ref c3t4(m), c2else(m);
m_simp.mk_ite(c3, m.mk_false(), t4, c3t4);
m_simp.mk_ite(c2, m.mk_true(), c3t4, c2else);
m_simp.mk_ite(c1, m.mk_false(), c2else, result);
TRACE("fpa2bv_float_eq", tout << "FLOAT_EQ = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_converter::mk_float_lt(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr * x = args[0], * y = args[1];
expr_ref c1(m), c2(m), x_is_nan(m), y_is_nan(m), x_is_zero(m), y_is_zero(m);
mk_is_nan(x, x_is_nan);
mk_is_nan(y, y_is_nan);
m_simp.mk_or(x_is_nan, y_is_nan, c1);
mk_is_zero(x, x_is_zero);
mk_is_zero(y, y_is_zero);
m_simp.mk_and(x_is_zero, y_is_zero, c2);
expr * x_sgn, * x_sig, * x_exp;
expr * y_sgn, * y_sig, * y_exp;
split(x, x_sgn, x_sig, x_exp);
split(y, y_sgn, y_sig, y_exp);
expr_ref c3(m), t3(m), t4(m), one_1(m), nil_1(m);
one_1 = m_bv_util.mk_numeral(1, 1);
nil_1 = m_bv_util.mk_numeral(0, 1);
m_simp.mk_eq(x_sgn, one_1, c3);
expr_ref y_sgn_eq_0(m), y_lt_x_exp(m), y_lt_x_sig(m), y_eq_x_exp(m), y_le_x_sig_exp(m), t3_or(m);
m_simp.mk_eq(y_sgn, nil_1, y_sgn_eq_0);
BVULT(y_exp, x_exp, y_lt_x_exp);
BVULT(y_sig, x_sig, y_lt_x_sig);
m_simp.mk_eq(y_exp, x_exp, y_eq_x_exp);
m_simp.mk_and(y_eq_x_exp, y_lt_x_sig, y_le_x_sig_exp);
m_simp.mk_or(y_lt_x_exp, y_le_x_sig_exp, t3_or);
m_simp.mk_ite(y_sgn_eq_0, m.mk_true(), t3_or, t3);
expr_ref y_sgn_eq_1(m), x_lt_y_exp(m), x_eq_y_exp(m), x_lt_y_sig(m), x_le_y_sig_exp(m), t4_or(m);
m_simp.mk_eq(y_sgn, one_1, y_sgn_eq_1);
BVULT(x_exp, y_exp, x_lt_y_exp);
m_simp.mk_eq(x_exp, y_exp, x_eq_y_exp);
BVULT(x_sig, y_sig, x_lt_y_sig);
m_simp.mk_and(x_eq_y_exp, x_lt_y_sig, x_le_y_sig_exp);
m_simp.mk_or(x_lt_y_exp, x_le_y_sig_exp, t4_or);
m_simp.mk_ite(y_sgn_eq_1, m.mk_false(), t4_or, t4);
expr_ref c3t3t4(m), c2else(m);
m_simp.mk_ite(c3, t3, t4, c3t3t4);
m_simp.mk_ite(c2, m.mk_false(), c3t3t4, c2else);
m_simp.mk_ite(c1, m.mk_false(), c2else, result);
}
void fpa2bv_converter::mk_float_gt(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr * x = args[0], * y = args[1];
expr_ref t3(m);
mk_float_le(f, num, args, t3);
expr_ref nan_or(m), xy_zero(m), not_t3(m), r_else(m);
expr_ref x_is_nan(m), y_is_nan(m), x_is_zero(m), y_is_zero(m);
mk_is_nan(x, x_is_nan);
mk_is_nan(y, y_is_nan);
m_simp.mk_or(x_is_nan, y_is_nan, nan_or);
mk_is_zero(x, x_is_zero);
mk_is_zero(y, y_is_zero);
m_simp.mk_and(x_is_zero, y_is_zero, xy_zero);
m_simp.mk_not(t3, not_t3);
m_simp.mk_ite(xy_zero, m.mk_false(), not_t3, r_else);
m_simp.mk_ite(nan_or, m.mk_false(), r_else, result);
}
void fpa2bv_converter::mk_float_le(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr_ref a(m), b(m);
mk_float_lt(f, num, args, a);
mk_float_eq(f, num, args, b);
m_simp.mk_or(a, b, result);
}
void fpa2bv_converter::mk_float_ge(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 2);
expr_ref a(m), b(m);
mk_float_gt(f, num, args, a);
mk_float_eq(f, num, args, b);
m_simp.mk_or(a, b, result);
}
void fpa2bv_converter::mk_is_zero(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_zero(args[0], result);
}
void fpa2bv_converter::mk_is_nzero(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
expr_ref a0_is_neg(m), a0_is_zero(m);
mk_is_neg(args[0], a0_is_neg);
mk_is_zero(args[0], a0_is_zero);
m_simp.mk_and(a0_is_neg, a0_is_zero, result);
}
void fpa2bv_converter::mk_is_pzero(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
expr_ref a0_is_pos(m), a0_is_zero(m);
mk_is_pos(args[0], a0_is_pos);
mk_is_zero(args[0], a0_is_zero);
m_simp.mk_and(a0_is_pos, a0_is_zero, result);
}
void fpa2bv_converter::mk_is_nan(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_nan(args[0], result);
}
void fpa2bv_converter::mk_is_inf(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_inf(args[0], result);
}
void fpa2bv_converter::mk_is_normal(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_normal(args[0], result);
}
void fpa2bv_converter::mk_is_subnormal(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_denormal(args[0], result);
}
void fpa2bv_converter::mk_is_sign_minus(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
mk_is_neg(args[0], result);
}
void fpa2bv_converter::mk_to_float(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
TRACE("fpa2bv_to_float", for (unsigned i=0; i < num; i++)
tout << "arg" << i << " = " << mk_ismt2_pp(args[i], m) << std::endl; );
if (num == 3 &&
m_bv_util.is_bv(args[0]) &&
m_bv_util.is_bv(args[1]) &&
m_bv_util.is_bv(args[2])) {
// Theoretically, the user could have thrown in it's own triple of bit-vectors.
// Just keep it here, as there will be something else that uses it.
mk_triple(args[0], args[1], args[2], result);
}
else if (num == 1 && m_bv_util.is_bv(args[0])) {
sort * s = f->get_range();
unsigned to_sbits = m_util.get_sbits(s);
unsigned to_ebits = m_util.get_ebits(s);
expr * bv = args[0];
int sz = m_bv_util.get_bv_size(bv);
SASSERT((unsigned)sz == to_sbits + to_ebits);
m_bv_util.mk_extract(sz - 1, sz - 1, bv);
mk_triple(m_bv_util.mk_extract(sz - 1, sz - 1, bv),
m_bv_util.mk_extract(sz - to_ebits - 2, 0, bv),
m_bv_util.mk_extract(sz - 2, sz - to_ebits - 1, bv),
result);
}
else if (num == 2 && is_app(args[1]) && m_util.is_float(m.get_sort(args[1]))) {
// We also support float to float conversion
sort * s = f->get_range();
expr_ref rm(m), x(m);
rm = args[0];
x = args[1];
unsigned from_sbits = m_util.get_sbits(m.get_sort(x));
unsigned from_ebits = m_util.get_ebits(m.get_sort(x));
unsigned to_sbits = m_util.get_sbits(s);
unsigned to_ebits = m_util.get_ebits(s);
if (from_sbits == to_sbits && from_ebits == to_ebits)
result = x;
else {
expr_ref c1(m), c2(m), c3(m), c4(m), c5(m);
expr_ref v1(m), v2(m), v3(m), v4(m), v5(m), v6(m);
expr_ref one1(m);
one1 = m_bv_util.mk_numeral(1, 1);
expr_ref ninf(m), pinf(m);
mk_plus_inf(f, pinf);
mk_minus_inf(f, ninf);
// NaN -> NaN
mk_is_nan(x, c1);
mk_nan(f, v1);
// +0 -> +0
mk_is_pzero(x, c2);
mk_pzero(f, v2);
// -0 -> -0
mk_is_nzero(x, c3);
mk_nzero(f, v3);
// +oo -> +oo
mk_is_pinf(x, c4);
v4 = pinf;
// -oo -> -oo
mk_is_ninf(x, c5);
v5 = ninf;
// otherwise: the actual conversion with rounding.
expr_ref sgn(m), sig(m), exp(m), lz(m);
unpack(x, sgn, sig, exp, lz, true);
dbg_decouple("fpa2bv_to_float_x_sig", sig);
dbg_decouple("fpa2bv_to_float_x_exp", exp);
dbg_decouple("fpa2bv_to_float_lz", lz);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
res_sgn = sgn;
SASSERT(m_bv_util.get_bv_size(sgn) == 1);
SASSERT(m_bv_util.get_bv_size(sig) == from_sbits);
SASSERT(m_bv_util.get_bv_size(exp) == from_ebits);
SASSERT(m_bv_util.get_bv_size(lz) == from_ebits);
if (from_sbits < (to_sbits + 3))
{
// make sure that sig has at least to_sbits + 3
res_sig = m_bv_util.mk_concat(sig, m_bv_util.mk_numeral(0, to_sbits+3-from_sbits));
}
else if (from_sbits > (to_sbits + 3))
{
// collapse the extra bits into a sticky bit.
expr_ref sticky(m), low(m), high(m);
low = m_bv_util.mk_extract(from_sbits - to_sbits - 3, 0, sig);
high = m_bv_util.mk_extract(from_sbits - 1, from_sbits - to_sbits - 2, sig);
sticky = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, low.get());
res_sig = m_bv_util.mk_concat(high, sticky);
}
else
res_sig = sig;
res_sig = m_bv_util.mk_zero_extend(1, res_sig); // extra zero in the front for the rounder.
unsigned sig_sz = m_bv_util.get_bv_size(res_sig);
SASSERT(sig_sz == to_sbits+4);
expr_ref exponent_overflow(m);
exponent_overflow = m.mk_false();
if (from_ebits < (to_ebits + 2))
{
res_exp = m_bv_util.mk_sign_extend(to_ebits-from_ebits+2, exp);
// subtract lz for subnormal numbers.
expr_ref lz_ext(m);
lz_ext = m_bv_util.mk_zero_extend(to_ebits-from_ebits+2, lz);
res_exp = m_bv_util.mk_bv_sub(res_exp, lz_ext);
}
else if (from_ebits > (to_ebits + 2))
{
expr_ref high(m), low(m), lows(m), high_red_or(m), high_red_and(m), h_or_eq(m), h_and_eq(m);
expr_ref no_ovf(m), zero1(m), s_is_one(m), s_is_zero(m);
high = m_bv_util.mk_extract(from_ebits - 1, to_ebits + 2, exp);
low = m_bv_util.mk_extract(to_ebits+1, 0, exp);
lows = m_bv_util.mk_extract(to_ebits+1, to_ebits+1, low);
high_red_or = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, high.get());
high_red_and = m.mk_app(m_bv_util.get_fid(), OP_BREDAND, high.get());
zero1 = m_bv_util.mk_numeral(0, 1);
m_simp.mk_eq(high_red_and, one1, h_and_eq);
m_simp.mk_eq(high_red_or, zero1, h_or_eq);
m_simp.mk_eq(lows, zero1, s_is_zero);
m_simp.mk_eq(lows, one1, s_is_one);
expr_ref c2(m);
m_simp.mk_ite(h_or_eq, s_is_one, m.mk_false(), c2);
m_simp.mk_ite(h_and_eq, s_is_zero, c2, exponent_overflow);
// Note: Upon overflow, we _could_ try to shift the significand around...
// subtract lz for subnormal numbers.
expr_ref lz_ext(m), lz_rest(m), lz_redor(m), lz_redor_bool(m);
lz_ext = m_bv_util.mk_extract(to_ebits+1, 0, lz);
lz_rest = m_bv_util.mk_extract(from_ebits-1, to_ebits+2, lz);
lz_redor = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, lz_rest.get());
m_simp.mk_eq(lz_redor, one1, lz_redor_bool);
m_simp.mk_or(exponent_overflow, lz_redor_bool, exponent_overflow);
res_exp = m_bv_util.mk_bv_sub(low, lz_ext);
}
else // from_ebits == (to_ebits + 2)
res_exp = m_bv_util.mk_bv_sub(exp, lz);
SASSERT(m_bv_util.get_bv_size(res_exp) == to_ebits+2);
SASSERT(is_well_sorted(m, res_exp));
dbg_decouple("fpa2bv_to_float_res_sig", res_sig);
dbg_decouple("fpa2bv_to_float_res_exp", res_exp);
expr_ref rounded(m);
round(s, rm, res_sgn, res_sig, res_exp, rounded);
expr_ref is_neg(m), sig_inf(m);
m_simp.mk_eq(sgn, one1, is_neg);
mk_ite(is_neg, ninf, pinf, sig_inf);
dbg_decouple("fpa2bv_to_float_exp_ovf", exponent_overflow);
mk_ite(exponent_overflow, sig_inf, rounded, v6);
// And finally, we tie them together.
mk_ite(c5, v5, v6, result);
mk_ite(c4, v4, result, result);
mk_ite(c3, v3, result, result);
mk_ite(c2, v2, result, result);
mk_ite(c1, v1, result, result);
}
}
else {
// .. other than that, we only support rationals for asFloat
SASSERT(num == 2);
SASSERT(m_util.is_float(f->get_range()));
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(m_bv_util.is_numeral(args[0]));
rational tmp_rat; unsigned sz;
m_bv_util.is_numeral(to_expr(args[0]), tmp_rat, sz);
SASSERT(tmp_rat.is_int32());
SASSERT(sz == 3);
BV_RM_VAL bv_rm = (BV_RM_VAL) tmp_rat.get_unsigned();
mpf_rounding_mode rm;
switch(bv_rm)
{
case BV_RM_TIES_TO_AWAY: rm = MPF_ROUND_NEAREST_TAWAY; break;
case BV_RM_TIES_TO_EVEN: rm = MPF_ROUND_NEAREST_TEVEN; break;
case BV_RM_TO_NEGATIVE: rm = MPF_ROUND_TOWARD_NEGATIVE; break;
case BV_RM_TO_POSITIVE: rm = MPF_ROUND_TOWARD_POSITIVE; break;
case BV_RM_TO_ZERO: rm = MPF_ROUND_TOWARD_ZERO; break;
default: UNREACHABLE();
}
SASSERT(m_util.au().is_numeral(args[1]));
rational q;
SASSERT(m_util.au().is_numeral(args[1]));
m_util.au().is_numeral(args[1], q);
mpf v;
m_util.fm().set(v, ebits, sbits, rm, q.to_mpq());
expr * sgn = m_bv_util.mk_numeral((m_util.fm().sgn(v)) ? 1 : 0, 1);
expr * s = m_bv_util.mk_numeral(m_util.fm().sig(v), sbits-1);
expr * e = m_bv_util.mk_numeral(m_util.fm().exp(v), ebits);
mk_triple(sgn, s, e, result);
m_util.fm().del(v);
}
SASSERT(is_well_sorted(m, result));
}
void fpa2bv_converter::mk_to_ieee_bv(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 1);
expr * sgn, * s, * e;
split(args[0], sgn, s, e);
result = m_bv_util.mk_concat(m_bv_util.mk_concat(sgn, e), s);
}
void fpa2bv_converter::mk_fp(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
SASSERT(num == 3);
mk_triple(args[0], args[2], args[1], result);
}
void fpa2bv_converter::mk_to_fp_unsigned(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
NOT_IMPLEMENTED_YET();
}
void fpa2bv_converter::mk_to_ubv(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
NOT_IMPLEMENTED_YET();
}
void fpa2bv_converter::mk_to_sbv(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
NOT_IMPLEMENTED_YET();
}
void fpa2bv_converter::mk_to_real(func_decl * f, unsigned num, expr * const * args, expr_ref & result) {
NOT_IMPLEMENTED_YET();
}
void fpa2bv_converter::split(expr * e, expr * & sgn, expr * & sig, expr * & exp) const {
SASSERT(is_app_of(e, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(to_app(e)->get_num_args() == 3);
sgn = to_app(e)->get_arg(0);
sig = to_app(e)->get_arg(1);
exp = to_app(e)->get_arg(2);
}
void fpa2bv_converter::mk_is_nan(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
// exp == 1^n , sig != 0
expr_ref sig_is_zero(m), sig_is_not_zero(m), exp_is_top(m), top_exp(m), zero(m);
mk_top_exp(m_bv_util.get_bv_size(exp), top_exp);
zero = m_bv_util.mk_numeral(0, m_bv_util.get_bv_size(sig));
m_simp.mk_eq(sig, zero, sig_is_zero);
m_simp.mk_not(sig_is_zero, sig_is_not_zero);
m_simp.mk_eq(exp, top_exp, exp_is_top);
m_simp.mk_and(exp_is_top, sig_is_not_zero, result);
}
void fpa2bv_converter::mk_is_inf(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref eq1(m), eq2(m), top_exp(m), zero(m);
mk_top_exp(m_bv_util.get_bv_size(exp), top_exp);
zero = m_bv_util.mk_numeral(0, m_bv_util.get_bv_size(sig));
m_simp.mk_eq(sig, zero, eq1);
m_simp.mk_eq(exp, top_exp, eq2);
m_simp.mk_and(eq1, eq2, result);
}
void fpa2bv_converter::mk_is_pinf(expr * e, expr_ref & result) {
expr_ref e_is_pos(m), e_is_inf(m);
mk_is_pos(e, e_is_pos);
mk_is_inf(e, e_is_inf);
m_simp.mk_and(e_is_pos, e_is_inf, result);
}
void fpa2bv_converter::mk_is_ninf(expr * e, expr_ref & result) {
expr_ref e_is_neg(m), e_is_inf(m);
mk_is_neg(e, e_is_neg);
mk_is_inf(e, e_is_inf);
m_simp.mk_and(e_is_neg, e_is_inf, result);
}
void fpa2bv_converter::mk_is_pos(expr * e, expr_ref & result) {
SASSERT(is_app_of(e, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(to_app(e)->get_num_args() == 3);
expr * a0 = to_app(e)->get_arg(0);
expr_ref zero(m);
zero = m_bv_util.mk_numeral(0, m_bv_util.get_bv_size(a0));
m_simp.mk_eq(a0, zero, result);
}
void fpa2bv_converter::mk_is_neg(expr * e, expr_ref & result) {
SASSERT(is_app_of(e, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(to_app(e)->get_num_args() == 3);
expr * a0 = to_app(e)->get_arg(0);
expr_ref one(m);
one = m_bv_util.mk_numeral(1, m_bv_util.get_bv_size(a0));
m_simp.mk_eq(a0, one, result);
}
void fpa2bv_converter::mk_is_zero(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref eq1(m), eq2(m), bot_exp(m), zero(m);
mk_bot_exp(m_bv_util.get_bv_size(exp), bot_exp);
zero = m_bv_util.mk_numeral(0, m_bv_util.get_bv_size(sig));
m_simp.mk_eq(sig, zero, eq1);
m_simp.mk_eq(exp, bot_exp, eq2);
m_simp.mk_and(eq1, eq2, result);
}
void fpa2bv_converter::mk_is_nzero(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref e_is_zero(m), eq(m), one_1(m);
mk_is_zero(e, e_is_zero);
one_1 = m_bv_util.mk_numeral(1, 1);
m_simp.mk_eq(sgn, one_1, eq);
m_simp.mk_and(eq, e_is_zero, result);
}
void fpa2bv_converter::mk_is_pzero(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref e_is_zero(m), eq(m), nil_1(m);
mk_is_zero(e, e_is_zero);
nil_1 = m_bv_util.mk_numeral(0, 1);
m_simp.mk_eq(sgn, nil_1, eq);
m_simp.mk_and(eq, e_is_zero, result);
}
void fpa2bv_converter::mk_is_denormal(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref zero(m);
zero = m_bv_util.mk_numeral(0, m_bv_util.get_bv_size(exp));
m_simp.mk_eq(exp, zero, result);
}
void fpa2bv_converter::mk_is_normal(expr * e, expr_ref & result) {
expr * sgn, * sig, * exp;
split(e, sgn, sig, exp);
expr_ref is_special(m), is_denormal(m), p(m);
mk_is_denormal(e, is_denormal);
unsigned ebits = m_bv_util.get_bv_size(exp);
p = m_bv_util.mk_numeral(fu().fm().m_powers2.m1(ebits), ebits);
m_simp.mk_eq(exp, p, is_special);
expr_ref or_ex(m);
m_simp.mk_or(is_special, is_denormal, or_ex);
m_simp.mk_not(or_ex, result);
}
void fpa2bv_converter::mk_is_rm(expr * e, BV_RM_VAL rm, expr_ref & result) {
SASSERT(m_bv_util.is_bv(e) && m_bv_util.get_bv_size(e) == 3);
expr_ref rm_num(m);
rm_num = m_bv_util.mk_numeral(rm, 3);
switch(rm)
{
case BV_RM_TIES_TO_AWAY:
case BV_RM_TIES_TO_EVEN:
case BV_RM_TO_NEGATIVE:
case BV_RM_TO_POSITIVE: return m_simp.mk_eq(e, rm_num, result);
case BV_RM_TO_ZERO:
default:
rm_num = m_bv_util.mk_numeral(BV_RM_TO_POSITIVE, 3);
expr_ref r(m); r = m_bv_util.mk_ule(e, rm_num);
return m_simp.mk_not(r, result);
}
}
void fpa2bv_converter::mk_top_exp(unsigned sz, expr_ref & result) {
result = m_bv_util.mk_numeral(fu().fm().m_powers2.m1(sz), sz);
}
void fpa2bv_converter::mk_bot_exp(unsigned sz, expr_ref & result) {
result = m_bv_util.mk_numeral(0, sz);
}
void fpa2bv_converter::mk_min_exp(unsigned ebits, expr_ref & result) {
SASSERT(ebits >= 2);
const mpz & z = m_mpf_manager.m_powers2.m1(ebits-1, true);
result = m_bv_util.mk_numeral(z + mpz(1), ebits);
}
void fpa2bv_converter::mk_max_exp(unsigned ebits, expr_ref & result) {
SASSERT(ebits >= 2);
result = m_bv_util.mk_numeral(m_mpf_manager.m_powers2.m1(ebits-1, false), ebits);
}
void fpa2bv_converter::mk_leading_zeros(expr * e, unsigned max_bits, expr_ref & result) {
SASSERT(m_bv_util.is_bv(e));
unsigned bv_sz = m_bv_util.get_bv_size(e);
if (bv_sz == 0)
result = m_bv_util.mk_numeral(0, max_bits);
else if (bv_sz == 1) {
expr_ref eq(m), nil_1(m), one_m(m), nil_m(m);
nil_1 = m_bv_util.mk_numeral(0, 1);
one_m = m_bv_util.mk_numeral(1, max_bits);
nil_m = m_bv_util.mk_numeral(0, max_bits);
m_simp.mk_eq(e, nil_1, eq);
m_simp.mk_ite(eq, one_m, nil_m, result);
}
else {
expr_ref H(m), L(m);
H = m_bv_util.mk_extract(bv_sz-1, bv_sz/2, e);
L = m_bv_util.mk_extract(bv_sz/2-1, 0, e);
unsigned H_size = m_bv_util.get_bv_size(H);
// unsigned L_size = m_bv_util.get_bv_size(L);
expr_ref lzH(m), lzL(m);
mk_leading_zeros(H, max_bits, lzH); /* recursive! */
mk_leading_zeros(L, max_bits, lzL);
expr_ref H_is_zero(m), nil_h(m);
nil_h = m_bv_util.mk_numeral(0, H_size);
m_simp.mk_eq(H, nil_h, H_is_zero);
expr_ref sum(m), h_m(m);
h_m = m_bv_util.mk_numeral(H_size, max_bits);
sum = m_bv_util.mk_bv_add(h_m, lzL);
m_simp.mk_ite(H_is_zero, sum, lzH, result);
}
SASSERT(is_well_sorted(m, result));
}
void fpa2bv_converter::mk_bias(expr * e, expr_ref & result) {
unsigned ebits = m_bv_util.get_bv_size(e);
SASSERT(ebits >= 2);
expr_ref bias(m);
bias = m_bv_util.mk_numeral(fu().fm().m_powers2.m1(ebits-1), ebits);
result = m_bv_util.mk_bv_add(e, bias);
}
void fpa2bv_converter::mk_unbias(expr * e, expr_ref & result) {
unsigned ebits = m_bv_util.get_bv_size(e);
SASSERT(ebits >= 3);
expr_ref e_plus_one(m);
e_plus_one = m_bv_util.mk_bv_add(e, m_bv_util.mk_numeral(1, ebits));
expr_ref leading(m), n_leading(m), rest(m);
leading = m_bv_util.mk_extract(ebits-1, ebits-1, e_plus_one);
n_leading = m_bv_util.mk_bv_not(leading);
rest = m_bv_util.mk_extract(ebits-2, 0, e_plus_one);
result = m_bv_util.mk_concat(n_leading, rest);
}
void fpa2bv_converter::unpack(expr * e, expr_ref & sgn, expr_ref & sig, expr_ref & exp, expr_ref & lz, bool normalize) {
SASSERT(is_app_of(e, m_plugin->get_family_id(), OP_TO_FLOAT));
SASSERT(to_app(e)->get_num_args() == 3);
sort * srt = to_app(e)->get_decl()->get_range();
SASSERT(is_float(srt));
unsigned sbits = m_util.get_sbits(srt);
unsigned ebits = m_util.get_ebits(srt);
sgn = to_app(e)->get_arg(0);
sig = to_app(e)->get_arg(1);
exp = to_app(e)->get_arg(2);
expr_ref is_normal(m);
mk_is_normal(e, is_normal);
expr_ref normal_sig(m), normal_exp(m);
normal_sig = m_bv_util.mk_concat(m_bv_util.mk_numeral(1, 1), sig);
mk_unbias(exp, normal_exp);
dbg_decouple("fpa2bv_unpack_normal_exp", normal_exp);
expr_ref denormal_sig(m), denormal_exp(m);
denormal_sig = m_bv_util.mk_zero_extend(1, sig);
SASSERT(ebits >= 3); // Note: when ebits=2 there is no 1-exponent, so mk_unbias will produce a 0.
denormal_exp = m_bv_util.mk_numeral(1, ebits);
mk_unbias(denormal_exp, denormal_exp);
dbg_decouple("fpa2bv_unpack_denormal_exp", denormal_exp);
expr_ref zero_e(m);
zero_e = m_bv_util.mk_numeral(0, ebits);
if (normalize) {
expr_ref is_sig_zero(m), zero_s(m);
zero_s = m_bv_util.mk_numeral(0, sbits);
m_simp.mk_eq(zero_s, denormal_sig, is_sig_zero);
expr_ref lz_d(m);
mk_leading_zeros(denormal_sig, ebits, lz_d);
m_simp.mk_ite(m.mk_or(is_normal, is_sig_zero), zero_e, lz_d, lz);
dbg_decouple("fpa2bv_unpack_lz", lz);
expr_ref shift(m);
m_simp.mk_ite(is_sig_zero, zero_e, lz, shift);
dbg_decouple("fpa2bv_unpack_shift", shift);
SASSERT(is_well_sorted(m, is_sig_zero));
SASSERT(is_well_sorted(m, shift));
SASSERT(m_bv_util.get_bv_size(shift) == ebits);
if (ebits <= sbits) {
expr_ref q(m);
q = m_bv_util.mk_zero_extend(sbits-ebits, shift);
denormal_sig = m_bv_util.mk_bv_shl(denormal_sig, q);
}
else {
// the maximum shift is `sbits', because after that the mantissa
// would be zero anyways. So we can safely cut the shift variable down,
// as long as we check the higher bits.
expr_ref sh(m), is_sh_zero(m), sl(m), zero_s(m), sbits_s(m), short_shift(m);
zero_s = m_bv_util.mk_numeral(0, sbits-1);
sbits_s = m_bv_util.mk_numeral(sbits, sbits);
sh = m_bv_util.mk_extract(ebits-1, sbits, shift);
m_simp.mk_eq(zero_s, sh, is_sh_zero);
short_shift = m_bv_util.mk_extract(sbits-1, 0, shift);
m_simp.mk_ite(is_sh_zero, short_shift, sbits_s, sl);
denormal_sig = m_bv_util.mk_bv_shl(denormal_sig, sl);
}
}
else
lz = zero_e;
SASSERT(is_well_sorted(m, normal_sig));
SASSERT(is_well_sorted(m, denormal_sig));
SASSERT(is_well_sorted(m, normal_exp));
SASSERT(is_well_sorted(m, denormal_exp));
dbg_decouple("fpa2bv_unpack_is_normal", is_normal);
m_simp.mk_ite(is_normal, normal_sig, denormal_sig, sig);
m_simp.mk_ite(is_normal, normal_exp, denormal_exp, exp);
SASSERT(is_well_sorted(m, sgn));
SASSERT(is_well_sorted(m, sig));
SASSERT(is_well_sorted(m, exp));
SASSERT(m_bv_util.get_bv_size(sgn) == 1);
SASSERT(m_bv_util.get_bv_size(sig) == sbits);
SASSERT(m_bv_util.get_bv_size(exp) == ebits);
TRACE("fpa2bv_unpack", tout << "UNPACK SGN = " << mk_ismt2_pp(sgn, m) << std::endl; );
TRACE("fpa2bv_unpack", tout << "UNPACK SIG = " << mk_ismt2_pp(sig, m) << std::endl; );
TRACE("fpa2bv_unpack", tout << "UNPACK EXP = " << mk_ismt2_pp(exp, m) << std::endl; );
}
void fpa2bv_converter::mk_rounding_mode(func_decl * f, expr_ref & result)
{
switch(f->get_decl_kind())
{
case OP_RM_NEAREST_TIES_TO_AWAY: result = m_bv_util.mk_numeral(BV_RM_TIES_TO_AWAY, 3); break;
case OP_RM_NEAREST_TIES_TO_EVEN: result = m_bv_util.mk_numeral(BV_RM_TIES_TO_EVEN, 3); break;
case OP_RM_TOWARD_NEGATIVE: result = m_bv_util.mk_numeral(BV_RM_TO_NEGATIVE, 3); break;
case OP_RM_TOWARD_POSITIVE: result = m_bv_util.mk_numeral(BV_RM_TO_POSITIVE, 3); break;
case OP_RM_TOWARD_ZERO: result = m_bv_util.mk_numeral(BV_RM_TO_ZERO, 3); break;
default: UNREACHABLE();
}
}
void fpa2bv_converter::dbg_decouple(const char * prefix, expr_ref & e) {
#ifdef Z3DEBUG
return;
// CMW: This works only for quantifier-free formulas.
expr_ref new_e(m);
new_e = m.mk_fresh_const(prefix, m.get_sort(e));
extra_assertions.push_back(m.mk_eq(new_e, e));
e = new_e;
#endif
}
void fpa2bv_converter::round(sort * s, expr_ref & rm, expr_ref & sgn, expr_ref & sig, expr_ref & exp, expr_ref & result) {
unsigned ebits = m_util.get_ebits(s);
unsigned sbits = m_util.get_sbits(s);
dbg_decouple("fpa2bv_rnd_rm", rm);
dbg_decouple("fpa2bv_rnd_sgn", sgn);
dbg_decouple("fpa2bv_rnd_sig", sig);
dbg_decouple("fpa2bv_rnd_exp", exp);
SASSERT(is_well_sorted(m, rm));
SASSERT(is_well_sorted(m, sgn));
SASSERT(is_well_sorted(m, sig));
SASSERT(is_well_sorted(m, exp));
TRACE("fpa2bv_dbg", tout << "RND: " << std::endl <<
"ebits = " << ebits << std::endl <<
"sbits = " << sbits << std::endl <<
"sgn = " << mk_ismt2_pp(sgn, m) << std::endl <<
"sig = " << mk_ismt2_pp(sig, m) << std::endl <<
"exp = " << mk_ismt2_pp(exp, m) << std::endl; );
// Assumptions: sig is of the form f[-1:0] . f[1:sbits-1] [guard,round,sticky],
// i.e., it has 2 + (sbits-1) + 3 = sbits + 4 bits, where the first one is in sgn.
// Furthermore, note that sig is an unsigned bit-vector, while exp is signed.
SASSERT(ebits <= sbits);
SASSERT(m_bv_util.is_bv(rm) && m_bv_util.get_bv_size(rm) == 3);
SASSERT(m_bv_util.is_bv(sgn) && m_bv_util.get_bv_size(sgn) == 1);
SASSERT(m_bv_util.is_bv(sig) && m_bv_util.get_bv_size(sig) >= 5);
SASSERT(m_bv_util.is_bv(exp) && m_bv_util.get_bv_size(exp) >= 4);
SASSERT(m_bv_util.get_bv_size(sig) == sbits+4);
SASSERT(m_bv_util.get_bv_size(exp) == ebits+2);
// bool UNFen = false;
// bool OVFen = false;
expr_ref e_min(m), e_max(m);
mk_min_exp(ebits, e_min);
mk_max_exp(ebits, e_max);
TRACE("fpa2bv_dbg", tout << "e_min = " << mk_ismt2_pp(e_min, m) << std::endl <<
"e_max = " << mk_ismt2_pp(e_max, m) << std::endl;);
expr_ref OVF1(m), e_top_three(m), sigm1(m), e_eq_emax_and_sigm1(m), e_eq_emax(m);
expr_ref e3(m), ne3(m), e2(m), e1(m), e21(m), one_1(m), h_exp(m), sh_exp(m), th_exp(m);
one_1 = m_bv_util.mk_numeral(1, 1);
h_exp = m_bv_util.mk_extract(ebits+1, ebits+1, exp);
sh_exp = m_bv_util.mk_extract(ebits, ebits, exp);
th_exp = m_bv_util.mk_extract(ebits-1, ebits-1, exp);
m_simp.mk_eq(h_exp, one_1, e3);
m_simp.mk_eq(sh_exp, one_1, e2);
m_simp.mk_eq(th_exp, one_1, e1);
m_simp.mk_or(e2, e1, e21);
m_simp.mk_not(e3, ne3);
m_simp.mk_and(ne3, e21, e_top_three);
expr_ref ext_emax(m), t_sig(m);
ext_emax = m_bv_util.mk_zero_extend(2, e_max);
t_sig = m_bv_util.mk_extract(sbits+3, sbits+3, sig);
m_simp.mk_eq(ext_emax, exp, e_eq_emax);
m_simp.mk_eq(t_sig, one_1, sigm1);
m_simp.mk_and(e_eq_emax, sigm1, e_eq_emax_and_sigm1);
m_simp.mk_or(e_top_three, e_eq_emax_and_sigm1, OVF1);
dbg_decouple("fpa2bv_rnd_OVF1", OVF1);
TRACE("fpa2bv_dbg", tout << "OVF1 = " << mk_ismt2_pp(OVF1, m) << std::endl;);
SASSERT(is_well_sorted(m, OVF1));
expr_ref lz(m);
mk_leading_zeros(sig, ebits+2, lz); // CMW: is this always large enough?
dbg_decouple("fpa2bv_rnd_lz", lz);
TRACE("fpa2bv_dbg", tout << "LZ = " << mk_ismt2_pp(lz, m) << std::endl;);
expr_ref t(m);
t = m_bv_util.mk_bv_add(exp, m_bv_util.mk_numeral(1, ebits+2));
t = m_bv_util.mk_bv_sub(t, lz);
t = m_bv_util.mk_bv_sub(t, m_bv_util.mk_sign_extend(2, e_min));
dbg_decouple("fpa2bv_rnd_t", t);
expr_ref TINY(m);
TINY = m_bv_util.mk_sle(t, m_bv_util.mk_numeral((unsigned)-1, ebits+2));
dbg_decouple("fpa2bv_rnd_TINY", TINY);
TRACE("fpa2bv_dbg", tout << "TINY = " << mk_ismt2_pp(TINY, m) << std::endl;);
SASSERT(is_well_sorted(m, TINY));
expr_ref beta(m);
beta = m_bv_util.mk_bv_add(m_bv_util.mk_bv_sub(exp, lz), m_bv_util.mk_numeral(1, ebits+2));
TRACE("fpa2bv_dbg", tout << "beta = " << mk_ismt2_pp(beta, m)<< std::endl; );
SASSERT(is_well_sorted(m, beta));
dbg_decouple("fpa2bv_rnd_beta", beta);
dbg_decouple("fpa2bv_rnd_e_min", e_min);
dbg_decouple("fpa2bv_rnd_e_max", e_max);
expr_ref sigma(m), sigma_add(m);
sigma_add = m_bv_util.mk_bv_sub(exp, m_bv_util.mk_sign_extend(2, e_min));
sigma_add = m_bv_util.mk_bv_add(sigma_add, m_bv_util.mk_numeral(1, ebits+2));
m_simp.mk_ite(TINY, sigma_add, lz, sigma);
dbg_decouple("fpa2bv_rnd_sigma", sigma);
TRACE("fpa2bv_dbg", tout << "Shift distance: " << mk_ismt2_pp(sigma, m) << std::endl;);
SASSERT(is_well_sorted(m, sigma));
// Normalization shift
dbg_decouple("fpa2bv_rnd_sig_before_shift", sig);
unsigned sig_size = m_bv_util.get_bv_size(sig);
SASSERT(sig_size == sbits+4);
SASSERT(m_bv_util.get_bv_size(sigma) == ebits+2);
unsigned sigma_size = ebits+2;
expr_ref sigma_neg(m), sigma_cap(m), sigma_neg_capped(m), sigma_lt_zero(m), sig_ext(m),
rs_sig(m), ls_sig(m), big_sh_sig(m), sigma_le_cap(m);
sigma_neg = m_bv_util.mk_bv_neg(sigma);
sigma_cap = m_bv_util.mk_numeral(sbits+2, sigma_size);
sigma_le_cap = m_bv_util.mk_ule(sigma_neg, sigma_cap);
m_simp.mk_ite(sigma_le_cap, sigma_neg, sigma_cap, sigma_neg_capped);
dbg_decouple("fpa2bv_rnd_sigma_neg", sigma_neg);
dbg_decouple("fpa2bv_rnd_sigma_cap", sigma_cap);
dbg_decouple("fpa2bv_rnd_sigma_neg_capped", sigma_neg_capped);
sigma_lt_zero = m_bv_util.mk_sle(sigma, m_bv_util.mk_numeral((unsigned)-1, sigma_size));
dbg_decouple("fpa2bv_rnd_sigma_lt_zero", sigma_lt_zero);
sig_ext = m_bv_util.mk_concat(sig, m_bv_util.mk_numeral(0, sig_size));
rs_sig = m_bv_util.mk_bv_lshr(sig_ext, m_bv_util.mk_zero_extend(2*sig_size - sigma_size, sigma_neg_capped));
ls_sig = m_bv_util.mk_bv_shl(sig_ext, m_bv_util.mk_zero_extend(2*sig_size - sigma_size, sigma));
m_simp.mk_ite(sigma_lt_zero, rs_sig, ls_sig, big_sh_sig);
SASSERT(m_bv_util.get_bv_size(big_sh_sig) == 2*sig_size);
dbg_decouple("fpa2bv_rnd_big_sh_sig", big_sh_sig);
unsigned sig_extract_low_bit = (2*sig_size-1)-(sbits+2)+1;
sig = m_bv_util.mk_extract(2*sig_size-1, sig_extract_low_bit, big_sh_sig);
SASSERT(m_bv_util.get_bv_size(sig) == sbits+2);
dbg_decouple("fpa2bv_rnd_shifted_sig", sig);
expr_ref sticky(m);
sticky = m.mk_app(m_bv_util.get_fid(), OP_BREDOR, m_bv_util.mk_extract(sig_extract_low_bit-1, 0, big_sh_sig));
SASSERT(is_well_sorted(m, sticky));
SASSERT(is_well_sorted(m, sig));
// put the sticky bit into the significand.
expr_ref ext_sticky(m);
ext_sticky = m_bv_util.mk_zero_extend(sbits+1, sticky);
expr * tmp[] = { sig, ext_sticky };
sig = m_bv_util.mk_bv_or(2, tmp);
SASSERT(is_well_sorted(m, sig));
SASSERT(m_bv_util.get_bv_size(sig) == sbits+2);
// CMW: The (OVF1 && OVFen) and (TINY && UNFen) cases are never taken.
expr_ref ext_emin(m);
ext_emin = m_bv_util.mk_zero_extend(2, e_min);
m_simp.mk_ite(TINY, ext_emin, beta, exp);
SASSERT(is_well_sorted(m, exp));
// Significand rounding
expr_ref round(m), last(m);
sticky = m_bv_util.mk_extract(0, 0, sig); // new sticky bit!
round = m_bv_util.mk_extract(1, 1, sig);
last = m_bv_util.mk_extract(2, 2, sig);
TRACE("fpa2bv_dbg", tout << "sticky = " << mk_ismt2_pp(sticky, m) << std::endl;);
dbg_decouple("fpa2bv_rnd_sticky", sticky);
dbg_decouple("fpa2bv_rnd_round", round);
dbg_decouple("fpa2bv_rnd_last", last);
sig = m_bv_util.mk_extract(sbits+1, 2, sig);
expr_ref last_or_sticky(m), round_or_sticky(m), not_round(m), not_lors(m), not_rors(m), not_sgn(m);
expr * last_sticky[2] = { last, sticky };
expr * round_sticky[2] = { round, sticky };
last_or_sticky = m_bv_util.mk_bv_or(2, last_sticky);
round_or_sticky = m_bv_util.mk_bv_or(2, round_sticky);
not_round = m_bv_util.mk_bv_not(round);
not_lors = m_bv_util.mk_bv_not(last_or_sticky);
not_rors = m_bv_util.mk_bv_not(round_or_sticky);
not_sgn = m_bv_util.mk_bv_not(sgn);
expr * round_lors[2] = { not_round, not_lors};
expr * pos_args[2] = { sgn, not_rors };
expr * neg_args[2] = { not_sgn, not_rors };
expr_ref inc_teven(m), inc_taway(m), inc_pos(m), inc_neg(m);
inc_teven = m_bv_util.mk_bv_not(m_bv_util.mk_bv_or(2, round_lors));
inc_taway = round;
inc_pos = m_bv_util.mk_bv_not(m_bv_util.mk_bv_or(2, pos_args));
inc_neg = m_bv_util.mk_bv_not(m_bv_util.mk_bv_or(2, neg_args));
expr_ref inc(m), inc_c2(m), inc_c3(m), inc_c4(m);
expr_ref rm_is_to_neg(m), rm_is_to_pos(m), rm_is_away(m), rm_is_even(m), nil_1(m);
nil_1 = m_bv_util.mk_numeral(0, 1);
mk_is_rm(rm, BV_RM_TO_NEGATIVE, rm_is_to_neg);
mk_is_rm(rm, BV_RM_TO_POSITIVE, rm_is_to_pos);
mk_is_rm(rm, BV_RM_TIES_TO_AWAY, rm_is_away);
mk_is_rm(rm, BV_RM_TIES_TO_EVEN, rm_is_even);
m_simp.mk_ite(rm_is_to_neg, inc_neg, nil_1, inc_c4);
m_simp.mk_ite(rm_is_to_pos, inc_pos, inc_c4, inc_c3);
m_simp.mk_ite(rm_is_away, inc_taway, inc_c3, inc_c2);
m_simp.mk_ite(rm_is_even, inc_teven, inc_c2, inc);
SASSERT(m_bv_util.get_bv_size(inc) == 1 && is_well_sorted(m, inc));
dbg_decouple("fpa2bv_rnd_inc", inc);
sig = m_bv_util.mk_bv_add(m_bv_util.mk_zero_extend(1, sig),
m_bv_util.mk_zero_extend(sbits, inc));
SASSERT(is_well_sorted(m, sig));
dbg_decouple("fpa2bv_rnd_sig_plus_inc", sig);
// Post normalization
SASSERT(m_bv_util.get_bv_size(sig) == sbits + 1);
expr_ref SIGovf(m);
t_sig = m_bv_util.mk_extract(sbits, sbits, sig);
m_simp.mk_eq(t_sig, one_1, SIGovf);
SASSERT(is_well_sorted(m, SIGovf));
dbg_decouple("fpa2bv_rnd_SIGovf", SIGovf);
expr_ref hallbut1_sig(m), lallbut1_sig(m);
hallbut1_sig = m_bv_util.mk_extract(sbits, 1, sig);
lallbut1_sig = m_bv_util.mk_extract(sbits-1, 0, sig);
m_simp.mk_ite(SIGovf, hallbut1_sig, lallbut1_sig, sig);
SASSERT(m_bv_util.get_bv_size(exp) == ebits + 2);
expr_ref exp_p1(m);
exp_p1 = m_bv_util.mk_bv_add(exp, m_bv_util.mk_numeral(1, ebits+2));
m_simp.mk_ite(SIGovf, exp_p1, exp, exp);
SASSERT(is_well_sorted(m, sig));
SASSERT(is_well_sorted(m, exp));
dbg_decouple("fpa2bv_rnd_sig_postnormalized", sig);
dbg_decouple("fpa2bv_rnd_exp_postnormalized", exp);
SASSERT(m_bv_util.get_bv_size(sig) == sbits);
SASSERT(m_bv_util.get_bv_size(exp) == ebits + 2);
SASSERT(m_bv_util.get_bv_size(e_max) == ebits);
// Exponent adjustment and rounding
expr_ref biased_exp(m);
mk_bias(m_bv_util.mk_extract(ebits-1, 0, exp), biased_exp);
dbg_decouple("fpa2bv_rnd_unbiased_exp", exp);
dbg_decouple("fpa2bv_rnd_biased_exp", biased_exp);
// AdjustExp
SASSERT(is_well_sorted(m, OVF1));
SASSERT(m.is_bool(OVF1));
expr_ref preOVF2(m), OVF2(m), OVF(m), exp_redand(m), pem2m1(m);
exp_redand = m.mk_app(m_bv_util.get_fid(), OP_BREDAND, biased_exp.get());
m_simp.mk_eq(exp_redand, one_1, preOVF2);
m_simp.mk_and(SIGovf, preOVF2, OVF2);
pem2m1 = m_bv_util.mk_numeral(fu().fm().m_powers2.m1(ebits-2), ebits);
m_simp.mk_ite(OVF2, pem2m1, biased_exp, biased_exp);
m_simp.mk_or(OVF1, OVF2, OVF);
SASSERT(is_well_sorted(m, OVF2));
SASSERT(is_well_sorted(m, OVF));
SASSERT(m.is_bool(OVF2));
SASSERT(m.is_bool(OVF));
dbg_decouple("fpa2bv_rnd_OVF2", OVF2);
dbg_decouple("fpa2bv_rnd_OVF", OVF);
// ExpRnd
expr_ref top_exp(m), bot_exp(m);
mk_top_exp(ebits, top_exp);
mk_bot_exp(ebits, bot_exp);
expr_ref rm_is_to_zero(m), rm_zero_or_neg(m), rm_zero_or_pos(m);
mk_is_rm(rm, BV_RM_TO_ZERO, rm_is_to_zero);
m_simp.mk_or(rm_is_to_zero, rm_is_to_neg, rm_zero_or_neg);
m_simp.mk_or(rm_is_to_zero, rm_is_to_pos, rm_zero_or_pos);
expr_ref sgn_is_zero(m);
m_simp.mk_eq(sgn, m_bv_util.mk_numeral(0, 1), sgn_is_zero);
expr_ref max_sig(m), max_exp(m), inf_sig(m), inf_exp(m);
max_sig = m_bv_util.mk_numeral(fu().fm().m_powers2.m1(sbits-1, false), sbits-1);
max_exp = m_bv_util.mk_concat(m_bv_util.mk_numeral(fu().fm().m_powers2.m1(ebits-1, false), ebits-1),
m_bv_util.mk_numeral(0, 1));
inf_sig = m_bv_util.mk_numeral(0, sbits-1);
inf_exp = top_exp;
dbg_decouple("fpa2bv_rnd_max_exp", max_exp);
expr_ref ovfl_exp(m), max_inf_exp_neg(m), max_inf_exp_pos(m), n_d_check(m), n_d_exp(m);
m_simp.mk_ite(rm_zero_or_neg, max_exp, inf_exp, max_inf_exp_neg);
m_simp.mk_ite(rm_zero_or_pos, max_exp, inf_exp, max_inf_exp_pos);
m_simp.mk_ite(sgn_is_zero, max_inf_exp_neg, max_inf_exp_pos, ovfl_exp);
t_sig = m_bv_util.mk_extract(sbits-1, sbits-1, sig);
m_simp.mk_eq(t_sig, nil_1, n_d_check);
m_simp.mk_ite(n_d_check, bot_exp /* denormal */, biased_exp, n_d_exp);
m_simp.mk_ite(OVF, ovfl_exp, n_d_exp, exp);
expr_ref max_inf_sig_neg(m), max_inf_sig_pos(m), ovfl_sig(m), rest_sig(m);
m_simp.mk_ite(rm_zero_or_neg, max_sig, inf_sig, max_inf_sig_neg);
m_simp.mk_ite(rm_zero_or_pos, max_sig, inf_sig, max_inf_sig_pos);
m_simp.mk_ite(sgn_is_zero, max_inf_sig_neg, max_inf_sig_pos, ovfl_sig);
rest_sig = m_bv_util.mk_extract(sbits-2, 0, sig);
m_simp.mk_ite(OVF, ovfl_sig, rest_sig, sig);
dbg_decouple("fpa2bv_rnd_sgn_final", sgn);
dbg_decouple("fpa2bv_rnd_sig_final", sig);
dbg_decouple("fpa2bv_rnd_exp_final", exp);
expr_ref res_sgn(m), res_sig(m), res_exp(m);
res_sgn = sgn;
res_sig = sig;
res_exp = exp;
SASSERT(m_bv_util.get_bv_size(res_sgn) == 1);
SASSERT(is_well_sorted(m, res_sgn));
SASSERT(m_bv_util.get_bv_size(res_sig) == sbits-1);
SASSERT(is_well_sorted(m, res_sig));
SASSERT(m_bv_util.get_bv_size(res_exp) == ebits);
SASSERT(is_well_sorted(m, res_exp));
mk_triple(res_sgn, res_sig, res_exp, result);
TRACE("fpa2bv_round", tout << "ROUND = " << mk_ismt2_pp(result, m) << std::endl; );
}
void fpa2bv_model_converter::display(std::ostream & out) {
out << "(fpa2bv-model-converter";
for (obj_map<func_decl, expr*>::iterator it = m_const2bv.begin();
it != m_const2bv.end();
it++) {
const symbol & n = it->m_key->get_name();
out << "\n (" << n << " ";
unsigned indent = n.size() + 4;
out << mk_ismt2_pp(it->m_value, m, indent) << ")";
}
for (obj_map<func_decl, expr*>::iterator it = m_rm_const2bv.begin();
it != m_rm_const2bv.end();
it++) {
const symbol & n = it->m_key->get_name();
out << "\n (" << n << " ";
unsigned indent = n.size() + 4;
out << mk_ismt2_pp(it->m_value, m, indent) << ")";
}
for (obj_map<func_decl, func_decl*>::iterator it = m_uf2bvuf.begin();
it != m_uf2bvuf.end();
it++) {
const symbol & n = it->m_key->get_name();
out << "\n (" << n << " ";
unsigned indent = n.size() + 4;
out << mk_ismt2_pp(it->m_value, m, indent) << ")";
}
for (obj_map<func_decl, func_decl_triple>::iterator it = m_uf23bvuf.begin();
it != m_uf23bvuf.end();
it++) {
const symbol & n = it->m_key->get_name();
out << "\n (" << n << " ";
unsigned indent = n.size() + 4;
out << mk_ismt2_pp(it->m_value.f_sgn, m, indent) << " ; " <<
mk_ismt2_pp(it->m_value.f_sig, m, indent) << " ; " <<
mk_ismt2_pp(it->m_value.f_exp, m, indent) << " ; " <<
")";
}
out << ")" << std::endl;
}
model_converter * fpa2bv_model_converter::translate(ast_translation & translator) {
fpa2bv_model_converter * res = alloc(fpa2bv_model_converter, translator.to());
for (obj_map<func_decl, expr*>::iterator it = m_const2bv.begin();
it != m_const2bv.end();
it++)
{
func_decl * k = translator(it->m_key);
expr * v = translator(it->m_value);
res->m_const2bv.insert(k, v);
translator.to().inc_ref(k);
translator.to().inc_ref(v);
}
for (obj_map<func_decl, expr*>::iterator it = m_rm_const2bv.begin();
it != m_rm_const2bv.end();
it++)
{
func_decl * k = translator(it->m_key);
expr * v = translator(it->m_value);
res->m_rm_const2bv.insert(k, v);
translator.to().inc_ref(k);
translator.to().inc_ref(v);
}
return res;
}
void fpa2bv_model_converter::convert(model * bv_mdl, model * float_mdl) {
float_util fu(m);
bv_util bu(m);
mpf fp_val;
unsynch_mpz_manager & mpzm = fu.fm().mpz_manager();
unsynch_mpq_manager & mpqm = fu.fm().mpq_manager();
TRACE("fpa2bv_mc", tout << "BV Model: " << std::endl;
for (unsigned i = 0 ; i < bv_mdl->get_num_constants(); i++)
tout << bv_mdl->get_constant(i)->get_name() << " --> " <<
mk_ismt2_pp(bv_mdl->get_const_interp(bv_mdl->get_constant(i)), m) << std::endl;
);
obj_hashtable<func_decl> seen;
for (obj_map<func_decl, expr*>::iterator it = m_const2bv.begin();
it != m_const2bv.end();
it++)
{
func_decl * var = it->m_key;
app * a = to_app(it->m_value);
SASSERT(fu.is_float(var->get_range()));
SASSERT(var->get_range()->get_num_parameters() == 2);
unsigned ebits = fu.get_ebits(var->get_range());
unsigned sbits = fu.get_sbits(var->get_range());
expr_ref sgn(m), sig(m), exp(m);
sgn = bv_mdl->get_const_interp(to_app(a->get_arg(0))->get_decl());
sig = bv_mdl->get_const_interp(to_app(a->get_arg(1))->get_decl());
exp = bv_mdl->get_const_interp(to_app(a->get_arg(2))->get_decl());
seen.insert(to_app(a->get_arg(0))->get_decl());
seen.insert(to_app(a->get_arg(1))->get_decl());
seen.insert(to_app(a->get_arg(2))->get_decl());
if (!sgn && !sig && !exp)
continue;
unsigned sgn_sz = bu.get_bv_size(m.get_sort(a->get_arg(0)));
unsigned sig_sz = bu.get_bv_size(m.get_sort(a->get_arg(1))) - 1;
unsigned exp_sz = bu.get_bv_size(m.get_sort(a->get_arg(2)));
rational sgn_q(0), sig_q(0), exp_q(0);
if (sgn) bu.is_numeral(sgn, sgn_q, sgn_sz);
if (sig) bu.is_numeral(sig, sig_q, sig_sz);
if (exp) bu.is_numeral(exp, exp_q, exp_sz);
// un-bias exponent
rational exp_unbiased_q;
exp_unbiased_q = exp_q - fu.fm().m_powers2.m1(ebits-1);
mpz sig_z; mpf_exp_t exp_z;
mpzm.set(sig_z, sig_q.to_mpq().numerator());
exp_z = mpzm.get_int64(exp_unbiased_q.to_mpq().numerator());
TRACE("fpa2bv_mc", tout << var->get_name() << " == [" << sgn_q.to_string() << " " <<
mpzm.to_string(sig_z) << " " << exp_z << "(" << exp_q.to_string() << ")]" << std::endl; );
fu.fm().set(fp_val, ebits, sbits, !mpqm.is_zero(sgn_q.to_mpq()), sig_z, exp_z);
float_mdl->register_decl(var, fu.mk_value(fp_val));
mpzm.del(sig_z);
}
for (obj_map<func_decl, expr*>::iterator it = m_rm_const2bv.begin();
it != m_rm_const2bv.end();
it++)
{
func_decl * var = it->m_key;
app * a = to_app(it->m_value);
SASSERT(fu.is_rm(var->get_range()));
rational val(0);
unsigned sz = 0;
if (a && bu.is_numeral(a, val, sz)) {
TRACE("fpa2bv_mc", tout << var->get_name() << " == " << val.to_string() << std::endl; );
SASSERT(val.is_uint64());
switch (val.get_uint64())
{
case BV_RM_TIES_TO_AWAY: float_mdl->register_decl(var, fu.mk_round_nearest_ties_to_away()); break;
case BV_RM_TIES_TO_EVEN: float_mdl->register_decl(var, fu.mk_round_nearest_ties_to_even()); break;
case BV_RM_TO_NEGATIVE: float_mdl->register_decl(var, fu.mk_round_toward_negative()); break;
case BV_RM_TO_POSITIVE: float_mdl->register_decl(var, fu.mk_round_toward_positive()); break;
case BV_RM_TO_ZERO:
default: float_mdl->register_decl(var, fu.mk_round_toward_zero());
}
seen.insert(var);
}
}
for (obj_map<func_decl, func_decl*>::iterator it = m_uf2bvuf.begin();
it != m_uf2bvuf.end();
it++)
seen.insert(it->m_value);
for (obj_map<func_decl, func_decl_triple>::iterator it = m_uf23bvuf.begin();
it != m_uf23bvuf.end();
it++)
{
seen.insert(it->m_value.f_sgn);
seen.insert(it->m_value.f_sig);
seen.insert(it->m_value.f_exp);
}
fu.fm().del(fp_val);
// Keep all the non-float constants.
unsigned sz = bv_mdl->get_num_constants();
for (unsigned i = 0; i < sz; i++)
{
func_decl * c = bv_mdl->get_constant(i);
if (!seen.contains(c))
float_mdl->register_decl(c, bv_mdl->get_const_interp(c));
}
// And keep everything else
sz = bv_mdl->get_num_functions();
for (unsigned i = 0; i < sz; i++)
{
func_decl * f = bv_mdl->get_function(i);
if (!seen.contains(f))
{
TRACE("fpa2bv_mc", tout << "Keeping: " << mk_ismt2_pp(f, m) << std::endl; );
func_interp * val = bv_mdl->get_func_interp(f);
float_mdl->register_decl(f, val);
}
}
sz = bv_mdl->get_num_uninterpreted_sorts();
for (unsigned i = 0; i < sz; i++)
{
sort * s = bv_mdl->get_uninterpreted_sort(i);
ptr_vector<expr> u = bv_mdl->get_universe(s);
float_mdl->register_usort(s, u.size(), u.c_ptr());
}
}
model_converter * mk_fpa2bv_model_converter(ast_manager & m,
obj_map<func_decl, expr*> const & const2bv,
obj_map<func_decl, expr*> const & rm_const2bv,
obj_map<func_decl, func_decl*> const & uf2bvuf,
obj_map<func_decl, func_decl_triple> const & uf23bvuf) {
return alloc(fpa2bv_model_converter, m, const2bv, rm_const2bv, uf2bvuf, uf23bvuf);
}
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