private Expression constructArIntExprMod(
final ILocation loc,
final Expression exp1,
final Expression exp2,
final boolean bothAreIntegerLiterals,
final BigInteger leftValue,
final BigInteger rightValue) {
final BinaryExpression.Operator operator;
operator = Operator.ARITHMOD;
/*
* In C the semantics of integer division is "rounding towards zero". In Boogie euclidian division is used. We
* translate a % b into (a < 0 && a%b != 0) ? ( (b < 0) ? (a%b)-b : (a%b)+b) : a%b
*/
// modulo on bigInteger does not seem to follow the "multiply, add, and get the result
// back"-rule, together
// with its division..
if (bothAreIntegerLiterals) {
final String constantResult;
if (leftValue.signum() == 1 || leftValue.signum() == 0) {
if (rightValue.signum() == 1) {
constantResult = leftValue.mod(rightValue).toString();
} else if (rightValue.signum() == -1) {
constantResult = leftValue.mod(rightValue.negate()).toString();
} else {
constantResult = "0";
}
} else if (leftValue.signum() == -1) {
if (rightValue.signum() == 1) {
constantResult = (leftValue.negate().mod(rightValue)).negate().toString();
} else if (rightValue.signum() == -1) {
constantResult = (leftValue.negate().mod(rightValue.negate())).negate().toString();
} else {
constantResult = "0";
}
} else {
throw new UnsupportedOperationException("constant is not assigned");
}
return new IntegerLiteral(loc, constantResult);
} else {
final Expression leftSmallerZeroAndThereIsRemainder =
getLeftSmallerZeroAndThereIsRemainder(loc, exp1, exp2);
final Expression rightSmallerZero =
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.COMPLT, exp2, new IntegerLiteral(loc, SFO.NR0));
final Expression normalModulo =
ExpressionFactory.newBinaryExpression(loc, operator, exp1, exp2);
if (exp1 instanceof IntegerLiteral) {
if (leftValue.signum() == 1) {
return normalModulo;
} else if (leftValue.signum() == -1) {
return ExpressionFactory.newIfThenElseExpression(
loc,
rightSmallerZero,
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHPLUS, normalModulo, exp2),
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHMINUS, normalModulo, exp2));
} else {
return new IntegerLiteral(loc, SFO.NR0);
}
} else if (exp2 instanceof IntegerLiteral) {
if (rightValue.signum() == 1 || rightValue.signum() == 0) {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHMINUS, normalModulo, exp2),
normalModulo);
} else if (rightValue.signum() == -1) {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHPLUS, normalModulo, exp2),
normalModulo);
}
throw new UnsupportedOperationException(
"Is it expected that this is a fall-through switch?");
} else {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newIfThenElseExpression(
loc,
rightSmallerZero,
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHPLUS, normalModulo, exp2),
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.ARITHMINUS, normalModulo, exp2)),
normalModulo);
}
}
}
private void convertToIntegerType(
final ILocation loc, final ExpressionResult operand, final CPrimitive resultType) {
assert resultType.isIntegerType();
final CPrimitive oldType = (CPrimitive) operand.lrVal.getCType();
if (oldType.isIntegerType()) {
final Expression newExpression;
if (mTypeSizes.isUnsigned(resultType)) {
final Expression oldWrappedIfNeeded;
if (mTypeSizes.isUnsigned(oldType)
&& mTypeSizes.getSize(resultType.getType()) > mTypeSizes.getSize(oldType.getType())) {
// required for sound Nutz transformation
// (see examples/programs/regression/c/NutzTransformation03.c)
oldWrappedIfNeeded = applyWraparound(loc, mTypeSizes, oldType, operand.lrVal.getValue());
} else {
oldWrappedIfNeeded = operand.lrVal.getValue();
}
if (mUnsignedTreatment == UnsignedTreatment.ASSERT) {
final BigInteger maxValuePlusOne =
mTypeSizes.getMaxValueOfPrimitiveType(resultType).add(BigInteger.ONE);
final AssertStatement assertGeq0 =
new AssertStatement(
loc,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.COMPGEQ,
oldWrappedIfNeeded,
new IntegerLiteral(loc, SFO.NR0)));
final Check chk1 = new Check(Spec.UINT_OVERFLOW);
chk1.addToNodeAnnot(assertGeq0);
operand.stmt.add(assertGeq0);
final AssertStatement assertLtMax =
new AssertStatement(
loc,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.COMPLT,
oldWrappedIfNeeded,
new IntegerLiteral(loc, maxValuePlusOne.toString())));
final Check chk2 = new Check(Spec.UINT_OVERFLOW);
chk2.addToNodeAnnot(assertLtMax);
operand.stmt.add(assertLtMax);
} else {
// do nothing
}
newExpression = oldWrappedIfNeeded;
} else {
assert !mTypeSizes.isUnsigned(resultType);
final Expression oldWrappedIfUnsigned;
if (mTypeSizes.isUnsigned(oldType)) {
// required for sound Nutz transformation
// (see examples/programs/regression/c/NutzTransformation01.c)
oldWrappedIfUnsigned =
applyWraparound(loc, mTypeSizes, oldType, operand.lrVal.getValue());
} else {
oldWrappedIfUnsigned = operand.lrVal.getValue();
}
if (mTypeSizes.getSize(resultType.getType()) > mTypeSizes.getSize(oldType.getType())
|| (mTypeSizes
.getSize(resultType.getType())
.equals(mTypeSizes.getSize(oldType.getType()))
&& !mTypeSizes.isUnsigned(oldType))) {
newExpression = oldWrappedIfUnsigned;
} else {
// According to C11 6.3.1.3.3 the result is implementation-defined
// it the value cannot be represented by the new type
// We have chosen an implementation that is similar to
// taking the lowest bits in a two's complement representation:
// First we take the value modulo the cardinality of the
// data range (which is 2*(MAX_VALUE+1) for signed )
// If the number is strictly larger than MAX_VALUE we
// subtract the cardinality of the data range.
final CPrimitive correspondingUnsignedType =
mTypeSizes.getCorrespondingUnsignedType(resultType);
final Expression wrapped =
applyWraparound(loc, mTypeSizes, correspondingUnsignedType, oldWrappedIfUnsigned);
final Expression maxValue =
constructLiteralForIntegerType(
loc, oldType, mTypeSizes.getMaxValueOfPrimitiveType(resultType));
final Expression condition =
ExpressionFactory.newBinaryExpression(loc, Operator.COMPLEQ, wrapped, maxValue);
final Expression range =
constructLiteralForIntegerType(
loc,
oldType,
mTypeSizes
.getMaxValueOfPrimitiveType(correspondingUnsignedType)
.add(BigInteger.ONE));
newExpression =
ExpressionFactory.newIfThenElseExpression(
loc,
condition,
wrapped,
ExpressionFactory.newBinaryExpression(loc, Operator.ARITHMINUS, wrapped, range));
}
}
final RValue newRValue = new RValue(newExpression, resultType, false, false);
operand.lrVal = newRValue;
} else {
throw new UnsupportedOperationException("not yet supported: conversion from " + oldType);
}
}
private Expression constructArIntExprDiv(
final ILocation loc,
final Expression exp1,
final Expression exp2,
final boolean bothAreIntegerLiterals,
final BigInteger leftValue,
final BigInteger rightValue) {
final BinaryExpression.Operator operator;
operator = Operator.ARITHDIV;
/*
* In C the semantics of integer division is "rounding towards zero". In Boogie euclidian division is used. We
* translate a / b into (a < 0 && a%b != 0) ? ( (b < 0) ? (a/b)+1 : (a/b)-1) : a/b
*/
if (bothAreIntegerLiterals) {
final String constantResult = leftValue.divide(rightValue).toString();
return new IntegerLiteral(loc, constantResult);
} else {
final Expression leftSmallerZeroAndThereIsRemainder =
getLeftSmallerZeroAndThereIsRemainder(loc, exp1, exp2);
final Expression rightSmallerZero =
ExpressionFactory.newBinaryExpression(
loc, BinaryExpression.Operator.COMPLT, exp2, new IntegerLiteral(loc, SFO.NR0));
final Expression normalDivision =
ExpressionFactory.newBinaryExpression(loc, operator, exp1, exp2);
if (exp1 instanceof IntegerLiteral) {
if (leftValue.signum() == 1) {
return normalDivision;
} else if (leftValue.signum() == -1) {
return ExpressionFactory.newIfThenElseExpression(
loc,
rightSmallerZero,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHMINUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1)),
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHPLUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1)));
} else {
return new IntegerLiteral(loc, SFO.NR0);
}
} else if (exp2 instanceof IntegerLiteral) {
if (rightValue.signum() == 1 || rightValue.signum() == 0) {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHPLUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1)),
normalDivision);
} else if (rightValue.signum() == -1) {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHMINUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1)),
normalDivision);
}
throw new UnsupportedOperationException(
"Is it expected that this is a fall-through switch?");
} else {
return ExpressionFactory.newIfThenElseExpression(
loc,
leftSmallerZeroAndThereIsRemainder,
ExpressionFactory.newIfThenElseExpression(
loc,
rightSmallerZero,
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHMINUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1)),
ExpressionFactory.newBinaryExpression(
loc,
BinaryExpression.Operator.ARITHPLUS,
normalDivision,
new IntegerLiteral(loc, SFO.NR1))),
normalDivision);
}
}
}