Forth Programmer’s Handbook

2.2 ARITHMETIC AND LOGICAL OPERATIONS

Forth offers a comprehensive set of commands for performing arithmetic and logical functions. The functions in a standard system are optimized for integer arithmetic, because not all processors have hardware floating-point capability and software floating point is too slow for most real-time applications. All Forth systems provide words to perform fast, precise, scaled-integer computations; many provide fixed-point fraction computations, as well. On systems with hardware floating-point capability, many implementations include an optional, complete set of floating-point operations, including an assembler. See Section 3.8 in this manual and the product documentation for these systems for details.

2.2.1 Arithmetic and Shift Operators

In order to achieve maximum performance, each version of Forth implements most arithmetic primitives to use the internal behavior of that particular processor’s hardware multiply and divide instructions. Therefore, to find out at the bit level what these primitives do, you should consult either the manufacturer’s hardware description or the implementation’s detailed description of these functions.

In particular, signed integer division where only one operand (either dividend or divisor) is negative and there is a remainder may produce different, but equally valid, results on different implementations. The two possibilities are floored and symmetric division. In floored division, the remainder carries the sign of the divisor and the quotient is rounded to its arithmetic floor (towards negative infinity). In symmetric division, the remainder carries the sign of the dividend and the quotient is rounded towards zero, or truncated. For example, dividing -10 by 7 can give a quotient of -2 and remainder of 4 (floored), or a quotient of -1 and remainder of -3 (symmetric).

Most hardware multiply and divide instructions are symmetric, so floored division operations are likely to be slower. However, some applications (such as graphics) require floored division in order to get a continuous function through zero. Consult your system’s documentation to learn its behavior.

The following general guidelines may help you use these arithmetic operators:

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Forth Programmer’s Handbook

!The order of arguments to order-dependent operators (e.g., - and /) is such that, if the operator were moved to an infix position, it would algebraically describe the result. Some examples:

Forth Algebraic

!All arithmetic words starting with the letter U are unsigned; others are normally signed. The exception to this rule is that, on most systems, M*/ requires a positive divisor.

!When executing operations involving address calculations, use the words CELL+, CELLS, CHAR+, and CHARS as appropriate to convert logical values to bytes, rather than to absolute numbers. For example, to increment an address by three cells on a 32-bit system, use 3 CELLS +, not 12 +; this makes the code portable to systems that may have different cell widths.

These operators perform arithmetic and logical functions on numbers that are on the stack. In general, the operands are removed (popped) from the stack and the results are left on the stack.

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Forth Programmer’s Handbook

the same data when exactly one argument is negative and there is a remainder.

“F-M-slash-mod”

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Multiply d1 by n1, producing a triple-cell intermediate result t. Divide t by the positive number n2 giving the double-cell quotient d2. If double-precision multiplication or division only is needed, this word may be used with either n1 or

Divide d by n1, using symmetric division, giving quotient n3 and remainder n2. All arguments are signed. This word and FM/MOD will produce different results on the same data when exactly one argument is negative and there is a remainder. “S-M-slash-rem”

Divide ud by u1, leaving remainder u2 and quotient u3. This operation is called UM/MOD because it assumes the arguments are unsigned, and it produces unsigned results. Compare with SM/REM and FM/MOD. “U-M-slash-mod”

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