The Extended Arithmetic Plugin

The extended_arithmetic_v1 plugin provides additional arithmetic operations over the basic addition and multiplication, easing the development of a broader range of statements.

Operations

The following operations are supported.

less_than

Compares two inputs, returning 1 if the first input is less than the second input, or 0 otherwise.

less_than_equal

Compares two inputs, returning 1 if the first input is less than or equal to the second input, or 0 otherwise.

division

Divides two inputs as if they were integers, returning first the quotient and then the remainder.

bit_decompose

Decomposes a single input into a bit vector, returning it as range whose length is the prime’s width.

@function(lt, @out: 0:1, @in: 0:1, 0:1)
  @plugin(extended_arithmetic_v1, less_than);
@function(lte, @out: 0:1, @in: 0:1, 0:1)
  @plugin(extended_arithmetic_v1, less_than_equal);
@function(div, @out: 0:1, 0:1, @in: 0:1, 0:1)
  @plugin(extended_arithmetic_v1, division);
@function(bit_decomp, @out: 0:7, @in: 0:1)
  @plugin(extended_arithmetic_v1, bit_decompose);

less_than and less_than_equal

These compare two inputs and indicate 1 or 0 for truth or false. For a given type t the following parameters are used.

Function Signature

  • Output t:1: 1 or 0

  • Input t:1: Left side of comparison

  • Input t:1: Right side of comparison

Plugin Binding:

  • Plugin Name: extended_arithmetic_v1

  • Operation: less_than or less_than_equal

division

This operation divides one input by the other, returning a quotient or a remainder. For a given type t the following parameters are used.

Function Signature

  • Output t:1: Quotient

  • Output t:1: Remainder

  • Input t:1: Numerator/dividend

  • Input t:1: Denominator/divisor

Plugin Binding:

  • Plugin Name: extended_arithmetic_v1

  • Operation: division

bit_decompose

The operation accepts one input, n, and decomposes it into a bit vector. The vector, v, is represented as a range of output wires with each element chosen from {0,1}, such that sum(vi * 2l-i) == n. The output vector’s length, l, must be exactly ceiling(log2(p)), where p is the field’s prime. The most significant bit is stored first and the least significant bit is last. For a given type t with prime p, the following parameters are used.

Function Signature

  • Output t:ceiling(log2(p)): The decomposed bits

  • Input t:1: Value to decompose

Plugin Binding:

  • Plugin Name: extended_arithmetic_v1

  • Operation: bit_decompose

Implementing the Wizkit Arithmetic Plugin

TODO: Coming Soon