5.6.9.3 Arithmetic Operators

Note

This section describes the implementation of MS-VBAL §5.6.9.3 Arithmetic Operators.

Runtime Semantics

Arithmetic operators are simple data operators (RD-VBAL §5.6.9.2 Simple Data Operators):

• They validate their operands through OperatorRuntimeSemantics.LetCoerceNonNullOperand.
• An integral or fixed-point result is computed in the effective type's own representation, never through a Double intermediate: Long in a 32-bit int, Currency and Decimal in decimal.
• A Single, Double or Date result of operands of declared types is computed in the 80-bit extended format, as extended intermediates describes.

Arithmetic runs in a checked context. An integral or fixed-point result that does not fit the effective type raises Overflow rather than wrapping or silently narrowing. A floating-point value is an overflow where it is stored as a Single or Double and that is not finite: s = s * 10 raises 6 for a Single of 3E+38. So is a result that is no number (NaN) of operands that are numbers: infinity less infinity. An operation of an infinity is otherwise IEEE-754's, with no error: infinity plus one is infinity, and an infinity compares as one.

Condition	Run-time error
An integral or fixed-point result does not fit the effective type.	6 — Overflow
A floating-point value stored as a Single or Double is past its range.	6 — Overflow
A floating-point result of operands that are numbers is NaN.	6 — Overflow
A floating-point number other than zero is divided by zero.	11 — Division by zero

The error carries the value IEEE-754 arithmetic gave the operation, and a Let assignment of it to a Single or Double variable assigns it before raising the error: after s = s * 10, s is infinite (RD-VBAL §5.4.3.8). MS-VBAL §5.6.9.3.5 says this of a division of operands declared Double; MS-VBA does it for every floating-point operation, and RD-VBA follows MS-VBA.

Extended intermediates

MS-VBAL §5.6.9.3 lets an implementation "perform floating point operations with a higher-precision than the effective value type (such as an 'extended' or 'long double' type)". MS-VBA does: it computes them as an x87 floating-point unit does, in 80 bits - a 64-bit significand and a 15-bit exponent - and RD-VBA computes them the same way (Float80). An expression of Single, Double and Date operations whose operands have declared types is computed operation after operation in that format, a Single's included, and rounded where its value is stored. So:

• (d * 10) / 10 is 1E+308 for a Double of 1E+308, with no overflow: the intermediate 1E+309 is a value.
• 0.1 + 0.2 - 0.3 is 2.77555756156289E-17, where an evaluation in Double gives 5.55111512312578E-17.
• s + 1 - s is 1 for a Single of 16777216, which no Single arithmetic gives.

Where the value goes decides what it is rounded to:

The value is…	It is…
Let-coerced to a declared numeric type: a variable, an element, a field, a parameter, a function's result, a For bound, a subscript, a ReDim bound, a condition, an operand of \, Mod, ^, And and the other logical operators, CLng and the other conversions to a number.	Converted to that type from its 80 bits: e = s + 1 assigns 16777217 to a Double, and 2.5 + 2^-60 is 3 as a Long.
Held as itself: by a Variant, written as a String (CStr included), made a Decimal, the selector of a Select Case.	Stored as the type of the expression first: a Single s + 1 held by a Variant is 16777216.
Compared.	Rounded to the precision of the comparison's effective type, in the extended range: d * 10 > 0 is True, and 1 + 2^-60 > 1 is False.
Given to Abs, Int, Fix, Sgn.	Computed on as it is.
Given to CDbl, or CSng.	Rounded to a Double - an infinity past its range, an overflow pending - and, by CSng, to the precision of a Single.

An invalid operation and a division by zero do not stop the evaluation: the exception is pending until the value is stored, and the error raised then. (1 / z) - (1 / z) assigns a NaN and raises 11, for z zero - a division by zero is raised before an invalid operation or an overflow.

An operation with an operand declared Variant is MS-VBA's Variant arithmetic, which rounds each result to its type (below): a typed operand of it is stored as its own type for it.

When an operand is declared Variant, an overflowing result is evaluated again in a wider type instead (RD-VBAL §5.0 Semantics); a result no Double holds is still 6. For an infinity and a NaN, MS-VBA's Variant arithmetic differs from typed arithmetic, and RD-VBA follows it:

Variant operation	Typed operation
A Single result that is not finite is a Double, with no error: a Variant holding a Single infinity, plus one, is a Double infinity.	A Single result of finite operands that is not finite is 6.
A Double result that is not finite is 6, an infinity's or a NaN's included, and assigns nothing.	A Double of an infinity is IEEE-754's, with no error: infinity plus one is infinity.

An infinity and a NaN are values of Single, Double and Variant: they are copied between them, and assigned, with no error. Converted to any other type, compared (a NaN), or given a sign by Sgn (a NaN), they are 6.

Run-time error 6 is VBRuntimeErrorId.Overflow. For division by zero, see RD-VBAL §5.6.9.3.6 \ Operator and Mod Operator.

5.6.9.3.1 Unary - Operator

This section corresponds to MS-VBAL §5.6.9.3.1 Unary - Operator.

Note

Reserved. This section has no content yet.

5.6.9.3.2 + Operator

Note

This section describes the implementation of MS-VBAL §5.6.9.3.2 + Operator.

🧩 RD-VBA explicitly adds runtime semantics for a unary + operator, as a language core extension (RD-VBAL §1.1.2 Language Core Extensions).

👉 A For loop's ForNext instruction adds step to the counter through the addition operator, RDCore.Runtime.Semantics.Operators.Arithmetic.BinaryAdditionOperatorRuntimeSemantics. The step addition is therefore an overflow-checked operation, not a plain CLR addition (RD-VBAL §5.4.2.3 For Statement).

5.6.9.3.3 Binary - Operator

This section corresponds to MS-VBAL §5.6.9.3.3 Binary - Operator.

Note

Reserved. This section has no content yet.

5.6.9.3.4 * Operator

This section corresponds to MS-VBAL §5.6.9.3.4 * Operator.

Note

Reserved. This section has no content yet.

5.6.9.3.5 / Operator

This section corresponds to MS-VBAL §5.6.9.3.5 / Operator.

Note

Reserved. This section has no content yet.

5.6.9.3.6 \ Operator and Mod Operator

Note

This section describes the implementation of MS-VBAL §5.6.9.3.6 \ Operator and Mod Operator.

Static Semantics

Note

Not implemented. The Mod operator token has no mapped static semantics rule. The static semantics of a Mod expression defer to VBUnknownType (RD-VBAL §5.0 Semantics).

Runtime Semantics

Condition	Run-time error
An integral division or Mod by zero.	11 — Division by zero

Run-time error 11 is VBRuntimeErrorId.DivisionByZero.

5.6.9.3.7 ^ Operator

Note

This section describes the implementation of MS-VBAL §5.6.9.3.7 ^ Operator.

The ^ operator is the sole exception to computation in the effective type (RD-VBAL §5.6.9.2 Simple Data Operators): its effective type is always Double. The ^ operator is evaluated as IEEE-754 exponentiation, except where that gives no finite number:

Condition	Run-time error
0 to a negative power.	5 — Invalid procedure call or argument
A negative number to a fractional power ((-8) ^ (1 / 3)), which has no real result.	5 — Invalid procedure call or argument
A result past the range of a Double (10 ^ 400).	6 — Overflow

A Variant operand doesn't change this: Double has nothing wider. 0 ^ 0 is 1.

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⏮️ RD-VBAL §5.6.9.2 Simple Data Operators | ⏭️ RD-VBAL §5.6.9.4 & Operator