Module bigint: Arbitrarily Large Integers

This module supports calculations with big integers. The maximum (or minimum) value for a big integer is limited only by available memory. All calculations are performed with full precision.

Big integers are native objects. Three functions convert between big integers and other representations:

• bigint.new creates a new big integer from a number, a string (in a given base, e.g. hexadecimal), or another big integer.
• bigint.num converts a big integer to a number (potentially loosing significant digits).
• bigint.str converts a big integer to a string encoded in a given base.

a=bigint.mul("33333333333333333333333333333333333", -2); print a, bigint.str(a) → bigint@414ffc -66666666666666666666666666666666666

• bigint.abs
• bigint.add
• bigint.cmp
• bigint.div
• bigint.mod
• bigint.mul
• bigint.neg
• bigint.new
• bigint.num
• bigint.pow
• bigint.str
• bigint.sub

bigint.abs

Computes the absolute value of p as a big integer.

r=bigint.abs("-314159265358979323846264"); print bigint.str(r) → 314159265358979323846264

bigint.add

Computes the sum of p and q as a big integer.

r=bigint.add("123456789012345678901234567890",              8765432110); print bigint.str(r) → 123456789012345678910000000000

bigint.cmp

Compares p and q:

• Returns -1 if p < q.
• Returns 0 if p = q.
• Returns 1 if p > q.

p=bigint.new("100000000", 16); q=bigint.new(4294967296); print bigint.cmp(p, q) → 0

bigint.div

Computes the quotient of p and q as a big integer. Throws ErrDivideByZero if q=0.

r=bigint.div("123456789012345678901234567890",              1234567890); print bigint.str(r) → 100000000010000000001

bigint.mod

Computes the remainder of p and q as a big integer. Throws ErrDivideByZero if q=0.

r=bigint.mod("123456789012345678901234567893",              1234567890); print bigint.str(r) → 3

bigint.mul

Computes the product of p and q as a big integer.

p=bigint.new(333333333333333); r=bigint.mul(p, p); print bigint.str(r) → 111111111111110888888888888889

bigint.neg

Computes the value of p with sign changed.

r=bigint.neg("314159265358979323846264") print bigint.str(r) → -314159265358979323846264

bigint.new

Creates a new big integer with the value of p. p can be:

• Another big integer. In this case a copy of p is returned.
• A number. Digits after the decimal points are ignored, and for values outside the range -2⁶³ to +2⁶³-1, the result is undefined.
• A string encoding an integer in the given base. Valid bases are in the range 2 (binary) and 36 (using letters A to Z and a to z for digits 11 to 36).

  Leading and trailing blanks in the string are ignored.

  Throws ErrArgument if the base is out of range or the string contains invalid characters.

m=bigint.new(-18513.7); print bigint.str(m) → -18513 m=bigint.new("ffffffffffffffff", 16); print bigint.str(m, 4) → 33333333333333333333333333333333

bigint.num

Converts the big integer p to a number. If p is outside the range -2⁶³ to +2⁶³-1, the result is undefined.

r=bigint.div("12345678901234567890", 1234567890); print bigint.num(r) / 2 → 5000000000.5

bigint.pow

Efficiently computes p^q as a big integer. With three arguments, computes the remainder of dividing p^q by m.

Throws ErrArgument if q<0. Throws ErrDivideByZero if m=0.

// perform RSA encryption with a 256-bit key e=bigint.new("7715580902129052762255348495586732516285"+              "0754331340849769128881931930089847467"); m=bigint.new("1157337135319357914338302274338009877449"+              "56524669244552124759012865929681230709"); c=bigint.pow("3695195570339388218205223153428883192073"+              "329889262155589752278898769206369823",               e, m); print bigint.str(c) → 2090963726256956961627254580276511758392932630933805 1745096332980705650678328

bigint.str

Converts the big integer p to a string in the given base. Valid bases are in the range 2 (binary) and 36 (using letters a to z for digits 11 to 36).

// convert a large decimal to a large hexadecimal number s=bigint.str("123456789012345678901234567890", 16); print s → 18ee90ff6c373e0ee4e3f0ad2

bigint.sub

Computes the difference of p and q as a big integer.

r=bigint.sub("123456789012345678901234567890",              -8765432110); print bigint.str(r) → 123456789012345678910000000000