expr2tc from_integer(const mp_integer &int_value, const type2tc &type)
{
switch(type->type_id)
{
case type2t::bool_id:
return !int_value.is_zero() ? gen_true_expr() : gen_false_expr();
case type2t::unsignedbv_id:
case type2t::signedbv_id:
return constant_int2tc(type, int_value);
case type2t::fixedbv_id:
{
constant_fixedbv2tc f(fixedbvt(fixedbv_spect(
to_fixedbv_type(type).width, to_fixedbv_type(type).integer_bits)));
f->value.from_integer(int_value);
return f;
}
case type2t::floatbv_id:
{
constant_floatbv2tc f(ieee_floatt(ieee_float_spect(
to_floatbv_type(type).fraction, to_floatbv_type(type).exponent)));
f->value.from_integer(int_value);
return f;
}
default:
abort();
}
}
typet long_double_type()
{
typet result;
if(config.ansi_c.use_fixed_for_float)
{
fixedbv_typet tmp;
tmp.set_width(config.ansi_c.long_double_width);
tmp.set_integer_bits(config.ansi_c.long_double_width/2);
result=tmp;
}
else
{
if(config.ansi_c.long_double_width==128)
result=ieee_float_spect::quadruple_precision().to_type();
else if(config.ansi_c.long_double_width==64)
result=ieee_float_spect::double_precision().to_type();
else if(config.ansi_c.long_double_width==80)
{
// x86 extended precision has 80 bits in total, and
// deviating from IEEE, does not use a hidden bit.
// We use the closest we have got, but the below isn't accurate.
result=ieee_float_spect(63, 15).to_type();
}
else if(config.ansi_c.long_double_width==96)
{
result=ieee_float_spect(80, 15).to_type();
// not quite right. The extra bits beyond 80 are usually padded.
}
else
assert(false);
}
result.set(ID_C_c_type, ID_long_double);
return result;
}
exprt convert_float_literal(const std::string &src)
{
mp_integer significand;
mp_integer exponent;
bool is_float, is_long, is_imaginary;
bool is_decimal, is_float80, is_float128; // GCC extensions
unsigned base;
parse_float(src, significand, exponent, base,
is_float, is_long, is_imaginary,
is_decimal, is_float80, is_float128);
exprt result=exprt(ID_constant);
result.set(ID_C_cformat, src);
// In ANSI-C, float literals are double by default,
// unless marked with 'f'.
// All of these can be complex as well.
// This can be overriden with
// config.ansi_c.single_precision_constant.
if(is_float)
result.type()=float_type();
else if(is_long)
result.type()=long_double_type();
else if(is_float80)
{
result.type()=ieee_float_spect(64, 15).to_type();
result.type().set(ID_C_c_type, ID_long_double);
}
else if(is_float128)
{
result.type()=ieee_float_spect::quadruple_precision().to_type();
result.type().set(ID_C_c_type, ID_gcc_float128);
}
else
{
// default
if(config.ansi_c.single_precision_constant)
result.type()=float_type(); // default
else
result.type()=double_type(); // default
}
if(is_decimal)
{
// TODO - should set ID_gcc_decimal32/ID_gcc_decimal64/ID_gcc_decimal128,
// but these aren't handled anywhere
}
if(config.ansi_c.use_fixed_for_float)
{
unsigned width=result.type().get_int(ID_width);
unsigned fraction_bits;
const irep_idt integer_bits=result.type().get(ID_integer_bits);
assert(width!=0);
if(integer_bits==irep_idt())
fraction_bits=width/2; // default
else
fraction_bits=width-safe_string2int(id2string(integer_bits));
mp_integer factor=mp_integer(1)<<fraction_bits;
mp_integer value=significand*factor;
if(value!=0)
{
if(exponent<0)
value/=power(base, -exponent);
else
{
value*=power(base, exponent);
if(value>=power(2, width-1))
{
// saturate: use "biggest value"
value=power(2, width-1)-1;
}
else if(value<=-power(2, width-1)-1)
{
// saturate: use "smallest value"
value=-power(2, width-1);
}
}
}
result.set(ID_value, integer2binary(value, width));
}
else
{
ieee_floatt a;
a.spec=to_floatbv_type(result.type());
if(base==10)
a.from_base10(significand, exponent);
else if(base==2) // hex
a.build(significand, exponent);
else
assert(false);
result.set(ID_value,
integer2binary(a.pack(), a.spec.width()));
}
if(is_imaginary)
{
complex_typet complex_type;
complex_type.subtype()=result.type();
exprt complex_expr(ID_complex, complex_type);
complex_expr.operands().resize(2);
complex_expr.op0()=gen_zero(result.type());
complex_expr.op1()=result;
return complex_expr;
}
return result;
}
void goto_checkt::nan_check(
const exprt &expr,
const guardt &guard)
{
if(!enable_nan_check)
return;
// first, check type
if(expr.type().id()!=ID_floatbv)
return;
if(expr.id()!=ID_plus &&
expr.id()!=ID_mult &&
expr.id()!=ID_div &&
expr.id()!=ID_minus)
return;
// add NaN subgoal
exprt isnan;
if(expr.id()==ID_div)
{
assert(expr.operands().size()==2);
// there a two ways to get a new NaN on division:
// 0/0 = NaN and x/inf = NaN
// (note that x/0 = +-inf for x!=0 and x!=inf)
exprt zero_div_zero=and_exprt(
ieee_float_equal_exprt(expr.op0(), gen_zero(expr.op0().type())),
ieee_float_equal_exprt(expr.op1(), gen_zero(expr.op1().type())));
exprt div_inf=unary_exprt(ID_isinf, expr.op1(), bool_typet());
isnan=or_exprt(zero_div_zero, div_inf);
}
else if(expr.id()==ID_mult)
{
if(expr.operands().size()>=3)
return nan_check(make_binary(expr), guard);
assert(expr.operands().size()==2);
// Inf * 0 is NaN
exprt inf_times_zero=and_exprt(
unary_exprt(ID_isinf, expr.op0(), bool_typet()),
ieee_float_equal_exprt(expr.op1(), gen_zero(expr.op1().type())));
exprt zero_times_inf=and_exprt(
ieee_float_equal_exprt(expr.op1(), gen_zero(expr.op1().type())),
unary_exprt(ID_isinf, expr.op0(), bool_typet()));
isnan=or_exprt(inf_times_zero, zero_times_inf);
}
else if(expr.id()==ID_plus)
{
if(expr.operands().size()>=3)
return nan_check(make_binary(expr), guard);
assert(expr.operands().size()==2);
// -inf + +inf = NaN and +inf + -inf = NaN,
// i.e., signs differ
ieee_float_spect spec=ieee_float_spect(to_floatbv_type(expr.type()));
exprt plus_inf=ieee_floatt::plus_infinity(spec).to_expr();
exprt minus_inf=ieee_floatt::minus_infinity(spec).to_expr();
isnan=or_exprt(
and_exprt(equal_exprt(expr.op0(), minus_inf), equal_exprt(expr.op1(), plus_inf)),
and_exprt(equal_exprt(expr.op0(), plus_inf), equal_exprt(expr.op1(), minus_inf)));
}
else if(expr.id()==ID_minus)
{
assert(expr.operands().size()==2);
// +inf - +inf = NaN and -inf - -inf = NaN,
// i.e., signs match
ieee_float_spect spec=ieee_float_spect(to_floatbv_type(expr.type()));
exprt plus_inf=ieee_floatt::plus_infinity(spec).to_expr();
exprt minus_inf=ieee_floatt::minus_infinity(spec).to_expr();
isnan=or_exprt(
and_exprt(equal_exprt(expr.op0(), plus_inf), equal_exprt(expr.op1(), plus_inf)),
and_exprt(equal_exprt(expr.op0(), minus_inf), equal_exprt(expr.op1(), minus_inf)));
}
else
assert(false);
isnan.make_not();
add_guarded_claim(
isnan,
"NaN on "+expr.id_string(),
"NaN",
expr.find_source_location(),
expr,
guard);
}
bool simplify_exprt::simplify_floatbv_typecast(exprt &expr)
{
// These casts usually reduce precision, and thus, usually round.
assert(expr.operands().size()==2);
const typet &dest_type=ns.follow(expr.type());
const typet &src_type=ns.follow(expr.op0().type());
// eliminate redundant casts
if(dest_type==src_type)
{
expr=expr.op0();
return false;
}
exprt op0=expr.op0();
exprt op1=expr.op1(); // rounding mode
// We can soundly re-write (float)((double)x op (double)y)
// to x op y. True for any rounding mode!
#if 0
if(op0.id()==ID_floatbv_div ||
op0.id()==ID_floatbv_mult ||
op0.id()==ID_floatbv_plus ||
op0.id()==ID_floatbv_minus)
{
if(op0.operands().size()==3 &&
op0.op0().id()==ID_typecast &&
op0.op1().id()==ID_typecast &&
op0.op0().operands().size()==1 &&
op0.op1().operands().size()==1 &&
ns.follow(op0.op0().type())==dest_type &&
ns.follow(op0.op1().type())==dest_type)
{
exprt result(op0.id(), expr.type());
result.operands().resize(3);
result.op0()=op0.op0().op0();
result.op1()=op0.op1().op0();
result.op2()=op1;
simplify_node(result);
expr.swap(result);
return false;
}
}
#endif
// constant folding
if(op0.is_constant() && op1.is_constant())
{
mp_integer rounding_mode;
if(!to_integer(op1, rounding_mode))
{
if(src_type.id()==ID_floatbv)
{
if(dest_type.id()==ID_floatbv) // float to float
{
ieee_floatt result(to_constant_expr(op0));
result.rounding_mode=
(ieee_floatt::rounding_modet)integer2size_t(rounding_mode);
result.change_spec(
ieee_float_spect(to_floatbv_type(dest_type)));
expr=result.to_expr();
return false;
}
else if(dest_type.id()==ID_signedbv ||
dest_type.id()==ID_unsignedbv)
{
if(rounding_mode==ieee_floatt::ROUND_TO_ZERO)
{
ieee_floatt result(to_constant_expr(op0));
result.rounding_mode=
(ieee_floatt::rounding_modet)integer2size_t(rounding_mode);
mp_integer value=result.to_integer();
expr=from_integer(value, dest_type);
return false;
}
}
}
else if(src_type.id()==ID_signedbv ||
src_type.id()==ID_unsignedbv)
{
mp_integer value;
if(!to_integer(op0, value))
{
if(dest_type.id()==ID_floatbv) // int to float
{
ieee_floatt result(to_floatbv_type(dest_type));
result.rounding_mode=
(ieee_floatt::rounding_modet)integer2size_t(rounding_mode);
result.from_integer(value);
expr=result.to_expr();
return false;
}
}
}
}
}
#if 0
// (T)(a?b:c) --> a?(T)b:(T)c
if(expr.op0().id()==ID_if &&
expr.op0().operands().size()==3)
{
exprt tmp_op1=
binary_exprt(
expr.op0().op1(),
ID_floatbv_typecast,
expr.op1(),
dest_type);
exprt tmp_op2=
binary_exprt(
expr.op0().op2(),
ID_floatbv_typecast,
expr.op1(),
dest_type);
simplify_floatbv_typecast(tmp_op1);
simplify_floatbv_typecast(tmp_op2);
expr=if_exprt(expr.op0().op0(), tmp_op1, tmp_op2, dest_type);
simplify_if(expr);
return false;
}
#endif
return true;
}
bool boolbvt::type_conversion(
const typet &src_type, const bvt &src,
const typet &dest_type, bvt &dest)
{
bvtypet dest_bvtype=get_bvtype(dest_type);
bvtypet src_bvtype=get_bvtype(src_type);
if(src_bvtype==IS_C_BIT_FIELD)
return
type_conversion(
c_bit_field_replacement_type(to_c_bit_field_type(src_type), ns),
src,
dest_type,
dest);
if(dest_bvtype==IS_C_BIT_FIELD)
return
type_conversion(
src_type,
src,
c_bit_field_replacement_type(to_c_bit_field_type(dest_type), ns),
dest);
std::size_t src_width=src.size();
std::size_t dest_width=boolbv_width(dest_type);
if(dest_width==0 || src_width==0)
return true;
dest.clear();
dest.reserve(dest_width);
if(dest_type.id()==ID_complex)
{
if(src_type==dest_type.subtype())
{
forall_literals(it, src)
dest.push_back(*it);
// pad with zeros
for(std::size_t i=src.size(); i<dest_width; i++)
dest.push_back(const_literal(false));
return false;
}
else if(src_type.id()==ID_complex)
{
// recursively do both halfs
bvt lower, upper, lower_res, upper_res;
lower.assign(src.begin(), src.begin()+src.size()/2);
upper.assign(src.begin()+src.size()/2, src.end());
type_conversion(
ns.follow(src_type.subtype()),
lower,
ns.follow(dest_type.subtype()),
lower_res);
type_conversion(
ns.follow(src_type.subtype()),
upper,
ns.follow(dest_type.subtype()),
upper_res);
assert(lower_res.size()+upper_res.size()==dest_width);
dest=lower_res;
dest.insert(dest.end(), upper_res.begin(), upper_res.end());
return false;
}
}
if(src_type.id()==ID_complex)
{
assert(dest_type.id()!=ID_complex);
if(dest_type.id()==ID_signedbv ||
dest_type.id()==ID_unsignedbv ||
dest_type.id()==ID_floatbv ||
dest_type.id()==ID_fixedbv ||
dest_type.id()==ID_c_enum ||
dest_type.id()==ID_c_enum_tag ||
dest_type.id()==ID_bool)
{
// A cast from complex x to real T
// is (T) __real__ x.
bvt tmp_src(src);
tmp_src.resize(src.size()/2); // cut off imag part
return type_conversion(src_type.subtype(), tmp_src, dest_type, dest);
}
}
switch(dest_bvtype)
{
case IS_RANGE:
if(src_bvtype==IS_UNSIGNED ||
src_bvtype==IS_SIGNED ||
src_bvtype==IS_C_BOOL)
{
mp_integer dest_from=to_range_type(dest_type).get_from();
if(dest_from==0)
{
// do zero extension
dest.resize(dest_width);
for(std::size_t i=0; i<dest.size(); i++)
dest[i]=(i<src.size()?src[i]:const_literal(false));
return false;
}
}
else if(src_bvtype==IS_RANGE) // range to range
{
mp_integer src_from=to_range_type(src_type).get_from();
mp_integer dest_from=to_range_type(dest_type).get_from();
if(dest_from==src_from)
{
// do zero extension, if needed
dest=bv_utils.zero_extension(src, dest_width);
return false;
}
else
{
// need to do arithmetic: add src_from-dest_from
mp_integer offset=src_from-dest_from;
dest=
bv_utils.add(
bv_utils.zero_extension(src, dest_width),
bv_utils.build_constant(offset, dest_width));
}
return false;
}
break;
case IS_FLOAT: // to float
{
float_utilst float_utils(prop);
switch(src_bvtype)
{
case IS_FLOAT: // float to float
// we don't have a rounding mode here,
// which is why we refuse.
break;
case IS_SIGNED: // signed to float
case IS_C_ENUM:
float_utils.spec=ieee_float_spect(to_floatbv_type(dest_type));
dest=float_utils.from_signed_integer(src);
return false;
case IS_UNSIGNED: // unsigned to float
case IS_C_BOOL: // _Bool to float
float_utils.spec=ieee_float_spect(to_floatbv_type(dest_type));
dest=float_utils.from_unsigned_integer(src);
return false;
case IS_BV:
assert(src_width==dest_width);
dest=src;
return false;
default:
if(src_type.id()==ID_bool)
{
// bool to float
// build a one
ieee_floatt f(to_floatbv_type(dest_type));
f.from_integer(1);
dest=convert_bv(f.to_expr());
assert(src_width==1);
Forall_literals(it, dest)
*it=prop.land(*it, src[0]);
return false;
}
}
}
break;
case IS_FIXED:
if(src_bvtype==IS_FIXED)
{
// fixed to fixed
std::size_t dest_fraction_bits=
to_fixedbv_type(dest_type).get_fraction_bits();
std::size_t dest_int_bits=dest_width-dest_fraction_bits;
std::size_t op_fraction_bits=
to_fixedbv_type(src_type).get_fraction_bits();
std::size_t op_int_bits=src_width-op_fraction_bits;
dest.resize(dest_width);
// i == position after dot
// i == 0: first position after dot
for(std::size_t i=0; i<dest_fraction_bits; i++)
{
// position in bv
std::size_t p=dest_fraction_bits-i-1;
if(i<op_fraction_bits)
dest[p]=src[op_fraction_bits-i-1];
else
dest[p]=const_literal(false); // zero padding
}
for(std::size_t i=0; i<dest_int_bits; i++)
{
// position in bv
std::size_t p=dest_fraction_bits+i;
assert(p<dest_width);
if(i<op_int_bits)
dest[p]=src[i+op_fraction_bits];
else
dest[p]=src[src_width-1]; // sign extension
}
return false;
}
else if(src_bvtype==IS_BV)
{
assert(src_width==dest_width);
dest=src;
return false;
}
else if(src_bvtype==IS_UNSIGNED ||
src_bvtype==IS_SIGNED ||
src_bvtype==IS_C_BOOL ||
src_bvtype==IS_C_ENUM)
{
// integer to fixed
std::size_t dest_fraction_bits=
to_fixedbv_type(dest_type).get_fraction_bits();
for(std::size_t i=0; i<dest_fraction_bits; i++)
dest.push_back(const_literal(false)); // zero padding
for(std::size_t i=0; i<dest_width-dest_fraction_bits; i++)
{
literalt l;
if(i<src_width)
l=src[i];
else
{
if(src_bvtype==IS_SIGNED || src_bvtype==IS_C_ENUM)
l=src[src_width-1]; // sign extension
else
l=const_literal(false); // zero extension
}
dest.push_back(l);
}
return false;
}
else if(src_type.id()==ID_bool)
{
// bool to fixed
std::size_t fraction_bits=
to_fixedbv_type(dest_type).get_fraction_bits();
assert(src_width==1);
for(std::size_t i=0; i<dest_width; i++)
{
if(i==fraction_bits)
dest.push_back(src[0]);
else
dest.push_back(const_literal(false));
}
return false;
}
break;
case IS_UNSIGNED:
case IS_SIGNED:
case IS_C_ENUM:
switch(src_bvtype)
{
case IS_FLOAT: // float to integer
// we don't have a rounding mode here,
// which is why we refuse.
break;
case IS_FIXED: // fixed to integer
{
std::size_t op_fraction_bits=
to_fixedbv_type(src_type).get_fraction_bits();
for(std::size_t i=0; i<dest_width; i++)
{
if(i<src_width-op_fraction_bits)
dest.push_back(src[i+op_fraction_bits]);
else
{
if(dest_bvtype==IS_SIGNED)
dest.push_back(src[src_width-1]); // sign extension
else
dest.push_back(const_literal(false)); // zero extension
}
}
// we might need to round up in case of negative numbers
// e.g., (int)(-1.00001)==1
bvt fraction_bits_bv=src;
fraction_bits_bv.resize(op_fraction_bits);
literalt round_up=
prop.land(prop.lor(fraction_bits_bv), src.back());
dest=bv_utils.incrementer(dest, round_up);
return false;
}
case IS_UNSIGNED: // integer to integer
case IS_SIGNED:
case IS_C_ENUM:
case IS_C_BOOL:
{
// We do sign extension for any source type
// that is signed, independently of the
// destination type.
// E.g., ((short)(ulong)(short)-1)==-1
bool sign_extension=
src_bvtype==IS_SIGNED || src_bvtype==IS_C_ENUM;
for(std::size_t i=0; i<dest_width; i++)
{
if(i<src_width)
dest.push_back(src[i]);
else if(sign_extension)
dest.push_back(src[src_width-1]); // sign extension
else
dest.push_back(const_literal(false));
}
return false;
}
case IS_VERILOG_UNSIGNED: // verilog_unsignedbv to signed/unsigned/enum
{
for(std::size_t i=0; i<dest_width; i++)
{
std::size_t src_index=i*2; // we take every second bit
if(src_index<src_width)
dest.push_back(src[src_index]);
else // always zero-extend
dest.push_back(const_literal(false));
}
return false;
}
break;
case IS_VERILOG_SIGNED: // verilog_signedbv to signed/unsigned/enum
{
for(std::size_t i=0; i<dest_width; i++)
{
std::size_t src_index=i*2; // we take every second bit
if(src_index<src_width)
dest.push_back(src[src_index]);
else // always sign-extend
dest.push_back(src.back());
}
return false;
}
break;
default:
if(src_type.id()==ID_bool)
{
// bool to integer
assert(src_width==1);
for(std::size_t i=0; i<dest_width; i++)
{
if(i==0)
dest.push_back(src[0]);
else
dest.push_back(const_literal(false));
}
return false;
}
}
break;
case IS_VERILOG_UNSIGNED:
if(src_bvtype==IS_UNSIGNED ||
src_bvtype==IS_C_BOOL ||
src_type.id()==ID_bool)
{
for(std::size_t i=0, j=0; i<dest_width; i+=2, j++)
{
if(j<src_width)
dest.push_back(src[j]);
else
dest.push_back(const_literal(false));
dest.push_back(const_literal(false));
}
return false;
}
else if(src_bvtype==IS_SIGNED)
{
for(std::size_t i=0, j=0; i<dest_width; i+=2, j++)
{
if(j<src_width)
dest.push_back(src[j]);
else
dest.push_back(src.back());
dest.push_back(const_literal(false));
}
return false;
}
else if(src_bvtype==IS_VERILOG_UNSIGNED)
{
// verilog_unsignedbv to verilog_unsignedbv
dest=src;
if(dest_width<src_width)
dest.resize(dest_width);
else
{
dest=src;
while(dest.size()<dest_width)
{
dest.push_back(const_literal(false));
dest.push_back(const_literal(false));
}
}
return false;
}
break;
case IS_BV:
assert(src_width==dest_width);
dest=src;
return false;
case IS_C_BOOL:
dest.resize(dest_width, const_literal(false));
if(src_bvtype==IS_FLOAT)
{
float_utilst float_utils(prop, to_floatbv_type(src_type));
dest[0]=!float_utils.is_zero(src);
}
else if(src_bvtype==IS_C_BOOL)
dest[0]=src[0];
else
dest[0]=!bv_utils.is_zero(src);
return false;
default:
if(dest_type.id()==ID_array)
{
if(src_width==dest_width)
{
dest=src;
return false;
}
}
else if(dest_type.id()==ID_struct)
{
const struct_typet &dest_struct=to_struct_type(dest_type);
if(src_type.id()==ID_struct)
{
// we do subsets
dest.resize(dest_width, const_literal(false));
const struct_typet &op_struct=to_struct_type(src_type);
const struct_typet::componentst &dest_comp=
dest_struct.components();
const struct_typet::componentst &op_comp=
op_struct.components();
// build offset maps
offset_mapt op_offsets, dest_offsets;
build_offset_map(op_struct, op_offsets);
build_offset_map(dest_struct, dest_offsets);
// build name map
typedef std::map<irep_idt, std::size_t> op_mapt;
op_mapt op_map;
for(std::size_t i=0; i<op_comp.size(); i++)
op_map[op_comp[i].get_name()]=i;
// now gather required fields
for(std::size_t i=0;
i<dest_comp.size();
i++)
{
std::size_t offset=dest_offsets[i];
std::size_t comp_width=boolbv_width(dest_comp[i].type());
if(comp_width==0)
continue;
op_mapt::const_iterator it=
op_map.find(dest_comp[i].get_name());
if(it==op_map.end())
{
// not found
// filling with free variables
for(std::size_t j=0; j<comp_width; j++)
dest[offset+j]=prop.new_variable();
}
else
{
// found
if(dest_comp[i].type()!=dest_comp[it->second].type())
{
// filling with free variables
for(std::size_t j=0; j<comp_width; j++)
dest[offset+j]=prop.new_variable();
}
else
{
std::size_t op_offset=op_offsets[it->second];
for(std::size_t j=0; j<comp_width; j++)
dest[offset+j]=src[op_offset+j];
}
}
}
return false;
}
}
}
return true;
}
void ieee_floatt::from_expr(const constant_exprt &expr)
{
spec=ieee_float_spect(to_floatbv_type(expr.type()));
unpack(binary2integer(id2string(expr.get_value()), false));
}