5.13.2 Number Conversion

This section describes the rules that the text interpreter uses when it tries to convert a string into a number.

Let <digit> represent any character that is a legal digit in the current number base²⁸.

Let <decimal digit> represent any character in the range 0-9.

Let {a b} represent the optional presence of any of the characters in the braces (a or b or neither).

Let * represent any number of instances of the previous character (including none).

Let any other character represent itself.

Now, the conversion rules are:

• A string of the form <digit><digit>* is treated as a single-precision (cell-sized) positive integer. Examples are 0 123 6784532 32343212343456 42
• A string of the form -<digit><digit>* is treated as a single-precision (cell-sized) negative integer, and is represented using 2’s-complement arithmetic. Examples are -45 -5681 -0
• A string of the form <digit><digit>*.<digit>* is treated as a double-precision (double-cell-sized) positive integer. Examples are 3465. 3.465 34.65 (all three of these represent the same number).
• A string of the form -<digit><digit>*.<digit>* is treated as a double-precision (double-cell-sized) negative integer, and is represented using 2’s-complement arithmetic. Examples are -3465. -3.465 -34.65 (all three of these represent the same number).
• A string of the form {+ -}<decimal digit>{.}<decimal digit>*{e E}{+ -}<decimal digit><decimal digit>* is treated as a floating-point number. Examples are 1e 1e0 1.e 1.e0 +1e+0 (which all represent the same number) +12.E-4

By default, the number base used for integer number conversion is given by the contents of the variable base. Note that a lot of confusion can result from unexpected values of base. If you change base anywhere, make sure to save the old value and restore it afterwards; better yet, use base-execute, which does this for you. In general I recommend keeping base decimal, and using the prefixes described below for the popular non-decimal bases.

dpl – a-addr  gforth “dpl” 

User variable – a-addr is the address of a cell that stores the position of the decimal point in the most recent numeric conversion. Initialised to -1. After the conversion of a number containing no decimal point, dpl is -1. After the conversion of 2. it holds 0. After the conversion of 234123.9 it contains 1, and so forth.

base-execute i*x xt u – j*x  gforth “base-execute” 

execute xt with the content of BASE being u, and restoring the original BASE afterwards.

base – a-addr  core “base” 

User variable – a-addr is the address of a cell that stores the number base used by default for number conversion during input and output. Don’t store to base, use base-execute instead.

hex –  core-ext “hex” 

Set base to &16 (hexadecimal). Don’t use hex, use base-execute instead.

decimal –  core “decimal” 

Set base to &10 (decimal). Don’t use decimal, use base-execute instead.

Gforth allows you to override the value of base by using a prefix²⁹ before the first digit of an (integer) number. The following prefixes are supported:

• & – decimal
• # – decimal
• % – binary
• $ – hexadecimal
• 0x – hexadecimal, if base<33.
• ' – numeric value (e.g., ASCII code) of next character; an optional ' may be present after the character.

Here are some examples, with the equivalent decimal number shown after in braces:

-$41 (-65), %1001101 (205), %1001.0001 (145 - a double-precision number), ’A (65), -’a’ (-97), &905 (905), $abc (2478), $ABC (2478).

Number conversion has a number of traps for the unwary:

• You cannot determine the current number base using the code sequence base @ . – the number base is always 10 in the current number base. Instead, use something like base @ dec.
• If the number base is set to a value greater than 14 (for example, hexadecimal), the number 123E4 is ambiguous; the conversion rules allow it to be intepreted as either a single-precision integer or a floating-point number (Gforth treats it as an integer). The ambiguity can be resolved by explicitly stating the sign of the mantissa and/or exponent: 123E+4 or +123E4 – if the number base is decimal, no ambiguity arises; either representation will be treated as a floating-point number.
• There is a word bin but it does not set the number base! It is used to specify file types.
• Standard Forth requires the . of a double-precision number to be the final character in the string. Gforth allows the . to be anywhere after the first digit.
• The number conversion process does not check for overflow.
• In a Standard Forth program base is required to be decimal when converting floating-point numbers. In Gforth, number conversion to floating-point numbers always uses base &10, irrespective of the value of base.

You can read numbers into your programs with the words described in Line input and conversion.