big.apl

Arbitrary-precision integer arithmetic for Dyalog APL.

All operations use a string-based interface: pass numbers as character vectors (e.g., '123456789012345678901234567890') and get strings back. This lets you work with integers of any size, limited only by available workspace.

Functions

Arithmetic

Function	Example	Result
a PLUS b	'999' big.PLUS '1'	'1000'
a MINUS b	'1000' big.MINUS '1'	'999'
a TIMES b	'123' big.TIMES '456'	'56088'
a DIVBY b	'123' big.DIVBY '56'	'2' '11'
a MOD b	'10' big.MOD '3'	'1'
a POWER b	'2' big.POWER '100'	'1267650600228229401496703205376'
NEGATE a	big.NEGATE '42'	'-42'
ABS a	big.ABS '-42'	'42'

DIVBY returns a two-element vector: quotient and remainder. MOD uses floored division, matching APL's | operator.

Comparison

Function	Example	Result
a CMP b	'100' big.CMP '99'	¯1
a GT b	'100' big.GT '99'	1
a LT b	'99' big.LT '100'	1
a GE b	'100' big.GE '100'	1
a LE b	'99' big.LE '100'	1
a MAX b	'5' big.MAX '10'	'10'
a MIN b	'5' big.MIN '10'	'5'

CMP returns ¯1 if the left argument is larger, 1 if the right is larger, and 0 if equal.

Number Theory

Function	Example	Result
a GCD b	'12' big.GCD '8'	'4'
a LCM b	'4' big.LCM '6'	'12'
base MODPOW exp mod	'4' big.MODPOW '13' '497'	'445'

Combinatorics

Function	Example	Result
FACTORIAL n	big.FACTORIAL '20'	'2432902008176640000'
k PERM n	'3' big.PERM '5'	'60'
k COMB n	'2' big.COMB '5'	'10'

PERM and COMB follow APL's convention where k is the left argument, matching k!n.

Negative Numbers

Negative numbers are represented with a leading '-', e.g., '-123'. All arithmetic and comparison functions handle negative arguments correctly.

Multiplication Strategy

TIMES automatically selects between two algorithms depending on available workspace:

• Outer product for numbers that fit in memory (fast for small-to-medium inputs)
• Karatsuba divide-and-conquer for large numbers that would otherwise exhaust the workspace

Division by Zero

DIVBY respects the ⎕DIV system variable:

• ⎕DIV=0 (default): '0' DIVBY '0' returns '1' '0'; non-zero divided by zero signals DOMAIN ERROR
• ⎕DIV=1: any x DIVBY '0' returns '0' '0'

Tests

A built-in test suite is included as an inner namespace:

      big.Test.Run
84 of 84 tests passed

Requirements

Dyalog APL (tested on version 16, Windows). The source file requires UTF-8 with BOM encoding.