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|
#include "rangeestimation.hh"
#include "consts.hh"
#ifdef FP_SUPPORT_OPTIMIZER
using namespace FUNCTIONPARSERTYPES;
using namespace FPoptimizer_CodeTree;
//#define DEBUG_SUBSTITUTIONS_extra_verbose
namespace FPoptimizer_CodeTree
{
template<typename Value_t>
range<Value_t> CalculateResultBoundaries(const CodeTree<Value_t>& tree)
#ifdef DEBUG_SUBSTITUTIONS_extra_verbose
{
using namespace FUNCTIONPARSERTYPES;
range<Value_t> tmp = CalculateResultBoundaries_do(tree);
std::cout << "Estimated boundaries: ";
if(tmp.min.known) std::cout << tmp.min.val; else std::cout << "-inf";
std::cout << " .. ";
if(tmp.max.known) std::cout << tmp.max.val; else std::cout << "+inf";
std::cout << ": ";
DumpTree(tree);
std::cout << std::endl;
return tmp;
}
template<typename Value_t>
range<Value_t> CodeTree<Value_t>::CalculateResultBoundaries_do(const CodeTree<Value_t>& tree)
#endif
{
static const range<Value_t> pihalf_limits
(-fp_const_pihalf<Value_t>(),
fp_const_pihalf<Value_t>());
static const range<Value_t> pi_limits
(-fp_const_pi<Value_t>(),
fp_const_pi<Value_t>());
static const range<Value_t> abs_pi_limits
( Value_t(0),
fp_const_pi<Value_t>());
static const range<Value_t> plusminus1_limits
( Value_t(-1),
Value_t(1) );
using namespace std;
switch( tree.GetOpcode() )
{
case cImmed:
return range<Value_t>(tree.GetImmed(), tree.GetImmed()); // a definite value.
case cAnd:
case cAbsAnd:
case cOr:
case cAbsOr:
case cNot:
case cAbsNot:
case cNotNot:
case cAbsNotNot:
case cEqual:
case cNEqual:
case cLess:
case cLessOrEq:
case cGreater:
case cGreaterOrEq:
{
/* These operations always produce truth values (0 or 1) */
/* Narrowing them down is a matter of performing Constant optimization */
return range<Value_t>( Value_t(0), Value_t(1) );
}
case cAbs:
{
/* cAbs always produces a positive value */
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.set_abs();
return m;
}
case cLog: /* Defined for 0.0 < x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.template set_if<cGreater>(Value_t(0), fp_log); // No boundaries
m.max.template set_if<cGreater>(Value_t(0), fp_log); // No boundaries
return m;
}
case cLog2: /* Defined for 0.0 < x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.template set_if<cGreater>(Value_t(0), fp_log2); // No boundaries
m.max.template set_if<cGreater>(Value_t(0), fp_log2); // No boundaries
return m;
}
case cLog10: /* Defined for 0.0 < x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.template set_if<cGreater>(Value_t(0), fp_log10); // No boundaries
m.max.template set_if<cGreater>(Value_t(0), fp_log10); // No boundaries
return m;
}
case cAcosh: /* defined for 1.0 <= x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.template set_if<cGreaterOrEq>(Value_t(1), fp_acosh); // No boundaries
m.max.template set_if<cGreaterOrEq>(Value_t(1), fp_acosh); // No boundaries
return m;
}
case cAsinh: /* defined for all values -inf <= x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_asinh); // No boundaries
m.max.set(fp_asinh); // No boundaries
return m;
}
case cAtanh: /* defined for -1.0 <= x < 1, results within -inf..+inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.template set_if<cGreater> (Value_t(-1), fp_atanh);
m.max.template set_if<cLess> (Value_t( 1), fp_atanh);
return m;
}
case cAcos: /* defined for -1.0 <= x <= 1, results within CONSTANT_PI..0 */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
return range<Value_t>( // Note that the range is flipped!
(m.max.known && (m.max.val) < Value_t(1))
? fp_acos(m.max.val) : Value_t(0),
(m.min.known && (m.min.val) >= Value_t(-1))
? fp_acos(m.min.val) : fp_const_pi<Value_t>()
);
}
case cAsin: /* defined for -1.0 <= x < 1, results within -CONSTANT_PIHALF..CONSTANT_PIHALF */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
/* Assuming that x is never outside valid limits */
m.min.template set_if<cGreater>(Value_t(-1), fp_asin, pihalf_limits.min.val);
m.max.template set_if<cLess >(Value_t( 1), fp_asin, pihalf_limits.max.val);
return m;
}
case cAtan: /* defined for all values -inf <= x <= inf, results within -CONSTANT_PIHALF..CONSTANT_PIHALF */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_atan, pihalf_limits.min.val);
m.max.set(fp_atan, pihalf_limits.max.val);
return m;
}
case cAtan2: /* too complicated to estimate */
{
//range<Value_t> p0 = CalculateResultBoundaries( tree.GetParam(0) );
//range<Value_t> p1 = CalculateResultBoundaries( tree.GetParam(1) );
if(tree.GetParam(0).IsImmed()
&& fp_equal(tree.GetParam(0).GetImmed(), Value_t(0))) // y == 0
{
// Either 0.0 or CONSTANT_PI
return abs_pi_limits;
}
if(tree.GetParam(1).IsImmed()
&& fp_equal(tree.GetParam(1).GetImmed(), Value_t(0))) // x == 0
{
// Either -CONSTANT_PIHALF or +CONSTANT_PIHALF
return pihalf_limits;
}
// Anything else
/* Somewhat complicated to narrow down from this */
/* TODO: A resourceful programmer may add it later. */
return pi_limits;
}
case cSin:
{
/* Quite difficult to estimate due to the cyclic nature of the function. */
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
bool covers_full_cycle
= !m.min.known || !m.max.known
|| (m.max.val - m.min.val) >= (fp_const_twopi<Value_t>());
if(covers_full_cycle)
return range<Value_t>(Value_t(-1), Value_t(1));
Value_t min = fp_mod(m.min.val, fp_const_twopi<Value_t>()); if(min<Value_t(0)) min+=fp_const_twopi<Value_t>();
Value_t max = fp_mod(m.max.val, fp_const_twopi<Value_t>()); if(max<Value_t(0)) max+=fp_const_twopi<Value_t>();
if(max < min) max += fp_const_twopi<Value_t>();
bool covers_plus1 = (min <= fp_const_pihalf<Value_t>() && max >= fp_const_pihalf<Value_t>());
bool covers_minus1 = (min <= Value_t(1.5)*fp_const_pi<Value_t>() && max >= Value_t(1.5)*fp_const_pi<Value_t>());
if(covers_plus1 && covers_minus1)
return range<Value_t>(Value_t(-1), Value_t(1));
if(covers_minus1)
return range<Value_t>(Value_t(-1), fp_max(fp_sin(min), fp_sin(max)));
if(covers_plus1)
return range<Value_t>(fp_min(fp_sin(min), fp_sin(max)), Value_t(1));
return range<Value_t>(fp_min(fp_sin(min), fp_sin(max)),
fp_max(fp_sin(min), fp_sin(max)));
}
case cCos:
{
/* Quite difficult to estimate due to the cyclic nature of the function. */
/* cos(x) = sin(pi/2 - x) = sin(x + pi/2) */
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
if(m.min.known) m.min.val += fp_const_pihalf<Value_t>();/*for cCos*/
if(m.max.known) m.max.val += fp_const_pihalf<Value_t>();/*for cCos*/
bool covers_full_cycle
= !m.min.known || !m.max.known
|| (m.max.val - m.min.val) >= (fp_const_twopi<Value_t>());
if(covers_full_cycle)
return range<Value_t>(Value_t(-1), Value_t(1));
Value_t min = fp_mod(m.min.val, fp_const_twopi<Value_t>()); if(min<Value_t(0)) min+=fp_const_twopi<Value_t>();
Value_t max = fp_mod(m.max.val, fp_const_twopi<Value_t>()); if(max<Value_t(0)) max+=fp_const_twopi<Value_t>();
if(max < min) max += fp_const_twopi<Value_t>();
bool covers_plus1 = (min <= fp_const_pihalf<Value_t>() && max >= fp_const_pihalf<Value_t>());
bool covers_minus1 = (min <= Value_t(1.5)*fp_const_pi<Value_t>() && max >= Value_t(1.5)*fp_const_pi<Value_t>());
if(covers_plus1 && covers_minus1)
return range<Value_t>(Value_t(-1), Value_t(1));
if(covers_minus1)
return range<Value_t>(Value_t(-1), fp_max(fp_sin(min), fp_sin(max)));
if(covers_plus1)
return range<Value_t>(fp_min(fp_sin(min), fp_sin(max)), Value_t(1));
return range<Value_t>(fp_min(fp_sin(min), fp_sin(max)),
fp_max(fp_sin(min), fp_sin(max)));
}
case cTan:
{
/* Could be narrowed down from here,
* but it's too complicated due to
* the cyclic nature of the function */
/* TODO: A resourceful programmer may add it later. */
return range<Value_t>(); // (CONSTANT_NEG_INF, CONSTANT_POS_INF);
}
case cCeil:
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.max.set(fp_ceil); // ceil() may increase the value, may not decrease
return m;
}
case cFloor:
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_floor); // floor() may decrease the value, may not increase
return m;
}
case cTrunc:
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_floor); // trunc() may either increase or decrease the value
m.max.set(fp_ceil); // for safety, we assume both
return m;
}
case cInt:
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_floor); // int() may either increase or decrease the value
m.max.set(fp_ceil); // for safety, we assume both
return m;
}
case cSinh: /* defined for all values -inf <= x <= inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_sinh); // No boundaries
m.max.set(fp_sinh); // No boundaries
return m;
}
case cTanh: /* defined for all values -inf <= x <= inf, results within -1..1 */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_tanh, plusminus1_limits.min);
m.max.set(fp_tanh, plusminus1_limits.max);
return m;
}
case cCosh: /* defined for all values -inf <= x <= inf, results within 1..inf */
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
if(m.min.known)
{
if(m.max.known) // max, min
{
if(m.min.val >= Value_t(0) && m.max.val >= Value_t(0)) // +x .. +y
{ m.min.val = fp_cosh(m.min.val); m.max.val = fp_cosh(m.max.val); }
else if((m.min.val) < Value_t(0) && m.max.val >= Value_t(0)) // -x .. +y
{ Value_t tmp = fp_cosh(m.min.val); m.max.val = fp_cosh(m.max.val);
if(tmp > m.max.val) m.max.val = tmp;
m.min.val = Value_t(1); }
else // -x .. -y
{ m.min.val = fp_cosh(m.min.val); m.max.val = fp_cosh(m.max.val);
std::swap(m.min.val, m.max.val); }
}
else // min, no max
{
if(m.min.val >= Value_t(0)) // 0..inf -> 1..inf
{ m.max.known = false; m.min.val = fp_cosh(m.min.val); }
else
{ m.max.known = false; m.min.val = Value_t(1); } // Anything between 1..inf
}
}
else // no min
{
m.min.known = true; m.min.val = Value_t(1); // always a lower boundary
if(m.max.known) // max, no min
{
m.min.val = fp_cosh(m.max.val); // n..inf
m.max.known = false; // No upper boundary
}
else // no max, no min
m.max.known = false; // No upper boundary
}
return m;
}
case cIf:
case cAbsIf:
{
// No guess which branch is chosen. Produce a spanning min & max.
range<Value_t> res1 = CalculateResultBoundaries( tree.GetParam(1) );
range<Value_t> res2 = CalculateResultBoundaries( tree.GetParam(2) );
if(!res2.min.known) res1.min.known = false; else if(res1.min.known && (res2.min.val) < res1.min.val) res1.min.val = res2.min.val;
if(!res2.max.known) res1.max.known = false; else if(res1.max.known && (res2.max.val) > res1.max.val) res1.max.val = res2.max.val;
return res1;
}
case cMin:
{
bool has_unknown_min = false;
bool has_unknown_max = false;
range<Value_t> result;
for(size_t a=0; a<tree.GetParamCount(); ++a)
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(a) );
if(!m.min.known)
has_unknown_min = true;
else if(!result.min.known || (m.min.val) < result.min.val)
result.min.val = m.min.val;
if(!m.max.known)
has_unknown_max = true;
else if(!result.max.known || (m.max.val) < result.max.val)
result.max.val = m.max.val;
}
if(has_unknown_min) result.min.known = false;
if(has_unknown_max) result.max.known = false;
return result;
}
case cMax:
{
bool has_unknown_min = false;
bool has_unknown_max = false;
range<Value_t> result;
for(size_t a=0; a<tree.GetParamCount(); ++a)
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(a) );
if(!m.min.known)
has_unknown_min = true;
else if(!result.min.known || m.min.val > result.min.val)
result.min.val = m.min.val;
if(!m.max.known)
has_unknown_max = true;
else if(!result.max.known || m.max.val > result.max.val)
result.max.val = m.max.val;
}
if(has_unknown_min) result.min.known = false;
if(has_unknown_max) result.max.known = false;
return result;
}
case cAdd:
{
/* It's complicated. Follow the logic below. */
/* Note: This also deals with the following opcodes:
* cNeg, cSub, cRSub
*/
range<Value_t> result(Value_t(0), Value_t(0));
for(size_t a=0; a<tree.GetParamCount(); ++a)
{
range<Value_t> item = CalculateResultBoundaries( tree.GetParam(a) );
if(item.min.known) result.min.val += item.min.val;
else result.min.known = false;
if(item.max.known) result.max.val += item.max.val;
else result.max.known = false;
if(!result.min.known && !result.max.known) break; // hopeless
}
if(result.min.known && result.max.known
&& result.min.val > result.max.val) std::swap(result.min.val, result.max.val);
return result;
}
case cMul:
{
/* It's very complicated. Follow the logic below. */
struct Value
{
enum ValueType { Finite, MinusInf, PlusInf };
ValueType valueType;
Value_t value;
Value(ValueType t): valueType(t), value(0) {}
Value(Value_t v): valueType(Finite), value(v) {}
bool isNegative() const
{
return valueType == MinusInf ||
(valueType == Finite && value < Value_t(0));
}
void operator*=(const Value& rhs)
{
if(valueType == Finite && rhs.valueType == Finite)
value *= rhs.value;
else
valueType = (isNegative() != rhs.isNegative() ?
MinusInf : PlusInf);
}
bool operator<(const Value& rhs) const
{
return
(valueType == MinusInf && rhs.valueType != MinusInf) ||
(valueType == Finite &&
(rhs.valueType == PlusInf ||
(rhs.valueType == Finite && value < rhs.value)));
}
};
struct MultiplicationRange
{
Value minValue, maxValue;
MultiplicationRange():
minValue(Value::PlusInf),
maxValue(Value::MinusInf) {}
void multiply(Value value1, const Value& value2)
{
value1 *= value2;
if(value1 < minValue) minValue = value1;
if(maxValue < value1) maxValue = value1;
}
};
range<Value_t> result(Value_t(1), Value_t(1));
for(size_t a=0; a<tree.GetParamCount(); ++a)
{
range<Value_t> item = CalculateResultBoundaries( tree.GetParam(a) );
if(!item.min.known && !item.max.known) return range<Value_t>(); // hopeless
Value minValue0 = result.min.known ? Value(result.min.val) : Value(Value::MinusInf);
Value maxValue0 = result.max.known ? Value(result.max.val) : Value(Value::PlusInf);
Value minValue1 = item.min.known ? Value(item.min.val) : Value(Value::MinusInf);
Value maxValue1 = item.max.known ? Value(item.max.val) : Value(Value::PlusInf);
MultiplicationRange range;
range.multiply(minValue0, minValue1);
range.multiply(minValue0, maxValue1);
range.multiply(maxValue0, minValue1);
range.multiply(maxValue0, maxValue1);
if(range.minValue.valueType == Value::Finite)
result.min.val = range.minValue.value;
else result.min.known = false;
if(range.maxValue.valueType == Value::Finite)
result.max.val = range.maxValue.value;
else result.max.known = false;
if(!result.min.known && !result.max.known) break; // hopeless
}
if(result.min.known && result.max.known
&& result.min.val > result.max.val) std::swap(result.min.val, result.max.val);
return result;
}
case cMod:
{
/* TODO: The boundaries of modulo operator could be estimated better. */
range<Value_t> x = CalculateResultBoundaries( tree.GetParam(0) );
range<Value_t> y = CalculateResultBoundaries( tree.GetParam(1) );
if(y.max.known)
{
if(y.max.val >= Value_t(0))
{
if(!x.min.known || (x.min.val) < Value_t(0))
return range<Value_t>(-y.max.val, y.max.val);
else
return range<Value_t>(Value_t(0), y.max.val);
}
else
{
if(!x.max.known || (x.max.val) >= Value_t(0))
return range<Value_t>(y.max.val, -y.max.val);
else
return range<Value_t>(y.max.val, fp_const_negativezero<Value_t>());
}
}
else
return range<Value_t>();
}
case cPow:
{
if(tree.GetParam(1).IsImmed() && tree.GetParam(1).GetImmed() == Value_t(0))
{
// Note: This makes 0^0 evaluate into 1.
return range<Value_t>(Value_t(1), Value_t(1)); // x^0 = 1
}
if(tree.GetParam(0).IsImmed() && tree.GetParam(0).GetImmed() == Value_t(0))
{
// Note: This makes 0^0 evaluate into 0.
return range<Value_t>(Value_t(0), Value_t(0)); // 0^x = 0
}
if(tree.GetParam(0).IsImmed() && fp_equal(tree.GetParam(0).GetImmed(), Value_t(1)))
{
return range<Value_t>(Value_t(1), Value_t(1)); // 1^x = 1
}
if(tree.GetParam(1).IsImmed()
&& tree.GetParam(1).GetImmed() > Value_t(0)
&& GetEvennessInfo(tree.GetParam(1)) == IsAlways)
{
// x ^ even_int_const always produces a non-negative value.
Value_t exponent = tree.GetParam(1).GetImmed();
range<Value_t> tmp = CalculateResultBoundaries( tree.GetParam(0) );
range<Value_t> result;
result.min.known = true;
result.min.val = 0;
if(tmp.min.known && tmp.min.val >= Value_t(0))
result.min.val = fp_pow(tmp.min.val, exponent);
else if(tmp.max.known && tmp.max.val <= Value_t(0))
result.min.val = fp_pow(tmp.max.val, exponent);
result.max.known = false;
if(tmp.min.known && tmp.max.known)
{
result.max.known = true;
result.max.val = fp_max(fp_abs(tmp.min.val), fp_abs(tmp.max.val));
result.max.val = fp_pow(result.max.val, exponent);
}
return result;
}
range<Value_t> p0 = CalculateResultBoundaries( tree.GetParam(0) );
range<Value_t> p1 = CalculateResultBoundaries( tree.GetParam(1) );
TriTruthValue p0_positivity =
(p0.min.known && (p0.min.val) >= Value_t(0)) ? IsAlways
: (p0.max.known && (p0.max.val) < Value_t(0) ? IsNever
: Unknown);
TriTruthValue p1_evenness = GetEvennessInfo(tree.GetParam(1));
/* If param0 IsAlways, the return value is also IsAlways */
/* If param1 is even, the return value is IsAlways */
/* If param1 is odd, the return value is same as param0's */
/* If param0 is negative and param1 is not integer,
* the return value is imaginary (assumed Unknown)
*
* Illustrated in this truth table:
* P=positive, N=negative
* E=even, O=odd, U=not integer
* *=unknown, X=invalid (unknown), x=maybe invalid (unknown)
*
* param1: PE PO P* NE NO N* PU NU *
* param0:
* PE P P P P P P P P P
* PO P P P P P P P P P
* PU P P P P P P P P P
* P* P P P P P P P P P
* NE P N * P N * X X x
* NO P N * P N * X X x
* NU P N * P N * X X x
* N* P N * P N * X X x
* * P * * P * * x x *
*
* Note: This also deals with the following opcodes:
* cSqrt (param0, PU) (x^0.5)
* cRSqrt (param0, NU) (x^-0.5)
* cExp (PU, param1) (CONSTANT_E^x)
*/
TriTruthValue result_positivity = Unknown;
switch(p0_positivity)
{
case IsAlways:
// e.g. 5^x = positive.
result_positivity = IsAlways;
break;
case IsNever:
{
result_positivity = p1_evenness;
break;
}
default:
switch(p1_evenness)
{
case IsAlways:
// e.g. x^( 4) = positive
// e.g. x^(-4) = positive
result_positivity = IsAlways;
break;
case IsNever:
break;
case Unknown:
{
/* If p1 is const non-integer,
* assume the result is positive
* though it may be NaN instead.
*/
if(tree.GetParam(1).IsImmed()
&& !isInteger(tree.GetParam(1).GetImmed())
&& tree.GetParam(1).GetImmed() >= Value_t(0))
{
result_positivity = IsAlways;
}
break;
}
}
}
switch(result_positivity)
{
case IsAlways:
{
/* The result is always positive.
* Figure out whether we know the minimum value. */
if((p1.max.known && p1.max.val < 0)
|| (p1.min.known && p1.min.val < 0))
{
// Fix regression 50/10:
// 1/abs(x) must not be estimated to be >=inf
// TODO: Better fix
return range<Value_t>();
}
Value_t min = Value_t(0);
if(p0.min.known && p1.min.known)
{
min = fp_pow(p0.min.val, p1.min.val);
if(p0.min.val < Value_t(0) && (!p1.max.known || p1.max.val >= Value_t(0)) && min >= Value_t(0))
min = Value_t(0);
}
if(p0.min.known && p0.min.val >= Value_t(0) && p0.max.known && p1.max.known)
{
Value_t max = fp_pow(p0.max.val, p1.max.val);
if(min > max) std::swap(min, max);
return range<Value_t>(min, max);
}
return range<Value_t>(min, false);
}
case IsNever:
{
/* The result is always negative.
* TODO: Figure out whether we know the maximum value.
*/
return range<Value_t>(false, fp_const_negativezero<Value_t>());
}
default:
{
/* It can be negative or positive.
* We know nothing about the boundaries. */
break;
}
}
break;
}
/* The following opcodes are processed by GenerateFrom()
* within fpoptimizer_bytecode_to_codetree.cc and thus
* they will never occur in the calling context for the
* most of the parsing context. They may however occur
* at the late phase, so we deal with them.
*/
case cNeg:
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.set_neg();
return m;
}
case cSub: // converted into cAdd(x, cNeg(y))
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cNeg);
tmp2.AddParam(tree.GetParam(1));
tmp.SetOpcode(cAdd);
tmp.AddParam(tree.GetParam(0));
tmp.AddParamMove(tmp2);
return CalculateResultBoundaries(tmp);
}
case cInv: // converted into cPow x -1
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cPow);
tmp.AddParam(tree.GetParam(0));
tmp.AddParam(CodeTreeImmed(Value_t(-1)));
return CalculateResultBoundaries(tmp);
}
case cDiv: // converted into cPow y -1
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cInv);
tmp2.AddParam(tree.GetParam(1));
tmp.SetOpcode(cMul);
tmp.AddParam(tree.GetParam(0));
tmp.AddParamMove(tmp2);
return CalculateResultBoundaries(tmp);
}
case cRad: // converted into cMul x CONSTANT_RD
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cMul);
tmp.AddParam(tree.GetParam(0));
tmp.AddParam(CodeTreeImmed(fp_const_rad_to_deg<Value_t>()));
return CalculateResultBoundaries(tmp);
}
case cDeg: // converted into cMul x CONSTANT_DR
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cMul);
tmp.AddParam(tree.GetParam(0));
tmp.AddParam(CodeTreeImmed(fp_const_deg_to_rad<Value_t>()));
return CalculateResultBoundaries(tmp);
}
case cSqr: // converted into cMul x x or cPow x 2
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cPow);
tmp.AddParam(tree.GetParam(0));
tmp.AddParam(CodeTreeImmed(Value_t(2)));
return CalculateResultBoundaries(tmp);
}
case cExp: // converted into cPow CONSTANT_E x
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cPow);
tmp.AddParam(CodeTreeImmed(fp_const_e<Value_t>()));
tmp.AddParam(tree.GetParam(0));
return CalculateResultBoundaries(tmp);
}
case cExp2: // converted into cPow 2 x
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cPow);
tmp.AddParam(CodeTreeImmed(Value_t(2)));
tmp.AddParam(tree.GetParam(0));
return CalculateResultBoundaries(tmp);
}
case cCbrt: // converted into cPow x 0.33333333
{
// However, contrary to x^(1/3), this allows
// negative values for x, and produces those
// as well.
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
m.min.set(fp_cbrt);
m.max.set(fp_cbrt);
return m;
}
case cSqrt: // converted into cPow x 0.5
{
range<Value_t> m = CalculateResultBoundaries( tree.GetParam(0) );
if(m.min.known) m.min.val = (m.min.val) < Value_t(0) ? 0 : fp_sqrt(m.min.val);
if(m.max.known) m.max.val = (m.max.val) < Value_t(0) ? 0 : fp_sqrt(m.max.val);
return m;
}
case cRSqrt: // converted into cPow x -0.5
{
CodeTree<Value_t> tmp;
tmp.SetOpcode(cPow);
tmp.AddParam(tree.GetParam(0));
tmp.AddParam(CodeTreeImmed( Value_t(-0.5) ));
return CalculateResultBoundaries(tmp);
}
case cHypot: // converted into cSqrt(cAdd(cMul(x x), cMul(y y)))
{
CodeTree<Value_t> xsqr, ysqr, add, sqrt;
xsqr.AddParam(tree.GetParam(0)); xsqr.AddParam(CodeTreeImmed( Value_t(2) ));
ysqr.AddParam(tree.GetParam(1)); ysqr.AddParam(CodeTreeImmed( Value_t(2) ));
xsqr.SetOpcode(cPow); ysqr.SetOpcode(cPow);
add.AddParamMove(xsqr); add.AddParamMove(ysqr);
add.SetOpcode(cAdd); sqrt.AddParamMove(add);
sqrt.SetOpcode(cSqrt);
return CalculateResultBoundaries(sqrt);
}
case cLog2by: // converted into cMul y CONSTANT_L2I (cLog x)
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cLog2);
tmp2.AddParam(tree.GetParam(0));
tmp.SetOpcode(cMul);
tmp.AddParamMove(tmp2);
tmp.AddParam(tree.GetParam(1));
return CalculateResultBoundaries(tmp);
}
case cCot: // converted into 1 / cTan
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cTan);
tmp2.AddParam(tree.GetParam(0));
tmp.SetOpcode(cInv);
tmp.AddParamMove(tmp2);
return CalculateResultBoundaries(tmp);
}
case cSec: // converted into 1 / cCos
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cCos);
tmp2.AddParam(tree.GetParam(0));
tmp.SetOpcode(cInv);
tmp.AddParamMove(tmp2);
return CalculateResultBoundaries(tmp);
}
case cCsc: // converted into 1 / cSin
{
CodeTree<Value_t> tmp, tmp2;
tmp2.SetOpcode(cSin);
tmp2.AddParam(tree.GetParam(0));
tmp.SetOpcode(cInv);
tmp.AddParamMove(tmp2);
return CalculateResultBoundaries(tmp);
}
/* The following opcodes are processed by GenerateFrom()
* within fpoptimizer_bytecode_to_codetree.cc and thus
* they will never occur in the calling context:
*/
break; /* Should never occur */
/* Opcodes that do not occur in the tree for other reasons */
case cRDiv: // version of cDiv
case cRSub: // version of cSub
case cDup:
case cFetch:
case cPopNMov:
case cSinCos:
case cSinhCosh:
case cNop:
case cJump:
case VarBegin:
break; /* Should never occur */
/* Complex functions */
case cArg:
case cConj:
case cImag:
case cReal:
case cPolar:
break; /* Should never occur */
/* Opcodes that are completely unpredictable */
case cPCall:
break;
case cFCall:
break; // Cannot deduce
}
return range<Value_t>(); /* Cannot deduce */
}
template<typename Value_t>
TriTruthValue GetIntegerInfo(const CodeTree<Value_t>& tree)
{
switch(tree.GetOpcode())
{
case cImmed:
return isInteger(tree.GetImmed()) ? IsAlways : IsNever;
case cFloor:
case cCeil:
case cTrunc:
case cInt:
return IsAlways;
case cAnd:
case cOr:
case cNot:
case cNotNot:
case cEqual:
case cNEqual:
case cLess:
case cLessOrEq:
case cGreater:
case cGreaterOrEq:
/* These operations always produce truth values (0 or 1) */
return IsAlways; /* 0 and 1 are both integers */
case cIf:
{
TriTruthValue a = GetIntegerInfo(tree.GetParam(1));
TriTruthValue b = GetIntegerInfo(tree.GetParam(2));
if(a == b) return a;
return Unknown;
}
case cAdd:
case cMul:
{
// It's integer if all the components are integer
// Otherwise, unknown whether it's integer
// A confirmed non-integer does not necessarily
// mean the result isn't an integer, because:
// 0.5 + 0.5 = 1.0; sqrt(2) * sqrt(2) = 2.0
for(size_t a=tree.GetParamCount(); a-- > 0; )
if(GetIntegerInfo(tree.GetParam(a)) != IsAlways)
return Unknown;
return IsAlways;
}
default:
break;
}
return Unknown; /* Don't know whether it's integer. */
}
template<typename Value_t>
bool IsLogicalValue(const CodeTree<Value_t>& tree)
{
switch(tree.GetOpcode())
{
case cImmed:
return fp_equal(tree.GetImmed(), Value_t(0))
|| fp_equal(tree.GetImmed(), Value_t(1));
case cAnd:
case cOr:
case cNot:
case cNotNot:
case cAbsAnd:
case cAbsOr:
case cAbsNot:
case cAbsNotNot:
case cEqual:
case cNEqual:
case cLess:
case cLessOrEq:
case cGreater:
case cGreaterOrEq:
/* These operations always produce truth values (0 or 1) */
return true;
case cMul:
{
for(size_t a=tree.GetParamCount(); a-- > 0; )
if(!IsLogicalValue(tree.GetParam(a)))
return false;
return true;
}
case cIf:
case cAbsIf:
{
return IsLogicalValue(tree.GetParam(1))
&& IsLogicalValue(tree.GetParam(2));
}
default:
break;
}
return false; // Not a logical value.
}
}
/* BEGIN_EXPLICIT_INSTANTATION */
#include "instantiate.hh"
namespace FPoptimizer_CodeTree
{
#define FP_INSTANTIATE(type) \
template range<type> CalculateResultBoundaries(const CodeTree<type> &); \
template bool IsLogicalValue(const CodeTree<type> &); \
template TriTruthValue GetIntegerInfo(const CodeTree<type> &);
FPOPTIMIZER_EXPLICITLY_INSTANTIATE(FP_INSTANTIATE)
#undef FP_INSTANTIATE
}
/* END_EXPLICIT_INSTANTATION */
#endif
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