/// <summary>
/// Performs an ISO/IEC 10967 operation rem-f, i.e. reminder with flooring truncation towards negative infinity.
/// </summary>
/// <remarks>
/// See ISO/IEC 10967:
/// 4.1 Symbols (... about truncation)
/// 5.1.3 Axioms
/// Defined as:
/// divI-f(x,y): x - ( div-f(x, y) * y )
/// </remarks>
private Expression ReminderIntF(Expression arg1, Expression arg2, Type type1, Type type2)
{
if (BuiltInPrimitiveEncoder.IsUnsignedType(type1) && BuiltInPrimitiveEncoder.IsUnsignedType(type2))
{
return(Expression.Modulo(arg1, arg2));
}
Expression zero1 = this.GetZero(type1);
Expression zero2 = this.GetZero(type2);
// C# pseudocode:
// if (arg1 >= 0)
// if (arg2 => 0)
// return arg1 % arg2;
// else
// return -(arg1 % -arg2);
// else
// if (arg2 => 0)
// return -arg1 % arg2;
// else
// return arg1 % arg2; // same as: -(-arg1 % -arg2)
Expression modulo = Expression.Modulo(
Expression.Condition(
Expression.GreaterThanOrEqual(arg1, zero1),
arg1,
Expression.Negate(arg1)),
arg2);
return(Expression.Condition(
Expression.GreaterThanOrEqual(arg2, zero2),
modulo,
Expression.Negate(modulo)));
}
/// <summary>
/// Performs an ISO/IEC 10967 integer operation divI-f, i.e. division with flooring truncation towards negative infinity.
/// </summary>
/// <remarks>
/// See ISO/IEC 10967:
/// 4.1 Symbols (... about truncation)
/// 5.1.3 Axioms
/// Defined as:
/// divI-f(x,y): [x/y]
/// [x]: Largest integer where: x-1 ˂ [x] ˂= x
/// Example:
/// divI-f( -3, 2) =˃ -2
/// divI-f( -2, 2) =˃ -1
/// divI-f( -1, 2) =˃ -1
/// divI-f( 0, 2) =˃ 0
/// divI-f( 1, 2) =˃ 0
/// divI-f( 2, 2) =˃ 1
/// divI-f( 3, 2) =˃ 1
/// </remarks>
private Expression DivideIntF(Expression arg1, Expression arg2, Type type1, Type type2)
{
// BUGBUG: Do we throw an OverflowException?
if (BuiltInPrimitiveEncoder.IsUnsignedType(type1) && BuiltInPrimitiveEncoder.IsUnsignedType(type2))
{
return(Expression.Divide(arg1, arg2));
}
// C# pseudocode:
// if ((arg1 >= 0) ^ (arg2 >= 0))
// if ((arg1 % arg2) == 0)
// return arg1 / arg2;
// else
// return (arg1 / arg2) - 1;
// else
// return arg1 / arg2;
Expression zero = this.GetZero(type1);
Expression one = this.GetOne(type1);
Expression division = Expression.Divide(arg1, arg2);
Expression modulo = Expression.Modulo(arg1, arg2);
return(Expression.Condition(
Expression.ExclusiveOr(
Expression.GreaterThanOrEqual(arg1, zero),
Expression.GreaterThanOrEqual(arg2, zero)),
Expression.Condition(
Expression.Equal(modulo, zero),
division,
Expression.Subtract(division, one)),
division));
}
