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u32_xor.rs
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use crate::treepp::*;
use crate::u32::u32_zip::u32_copy_zip;
/// Bitwise XOR of two u8 elements, i denoting how many values are there in the stack after the table (including the input numbers A and B)
/// Expects the u8_xor_table on the stack and uses it to process even and odd bits separately
pub fn u8_xor(i: u32) -> Script {
script! {
// f_A = f(A)
OP_DUP
{i}
OP_ADD
OP_PICK
// A_even = f_A << 1
OP_DUP
OP_DUP
OP_ADD
// A_odd = A - A_even
OP_ROT
OP_SWAP
OP_SUB
// f_B = f(B)
OP_ROT
OP_DUP
{i + 1}
OP_ADD
OP_PICK
// B_even = f_B << 1
OP_DUP
OP_DUP
OP_ADD
// B_odd = B - B_even
OP_ROT
OP_SWAP
OP_SUB
// A_andxor_B_even = f_A + f_B
OP_SWAP
3
OP_ROLL
OP_ADD
// A_xor_B_even = A_andxor_B_even - (f(A_andxor_B_even) << 1)
OP_DUP
{i + 1}
OP_ADD
OP_PICK
OP_DUP
OP_ADD
OP_SUB
// A_andxor_B_odd = A_odd + B_odd
OP_SWAP
OP_ROT
OP_ADD
// A_xor_B_odd = A_andxor_B_odd - (f(A_andxor_B_odd) << 1)
OP_DUP
{i}
OP_ADD
OP_PICK
OP_DUP
OP_ADD
OP_SUB
// A_xor_B = A_xor_B_odd + (A_xor_B_even << 1)
OP_OVER
OP_ADD
OP_ADD
}
}
/// Bitwise XOR of a-th and b-th u32 elements from the top, keeps a-th element in the stack
/// Expects u8_xor_table on the stack to use u8_xor, and stack_size as a parameter to locate the table (which should be equal to 1 + number of the u32 elements in the stack after the table)
pub fn u32_xor(a: u32, b: u32, stack_size: u32) -> Script {
assert_ne!(a, b);
script! {
{u32_copy_zip(a, b)}
//
// XOR
//
{u8_xor(8 + (stack_size - 2) * 4)}
OP_TOALTSTACK
{u8_xor(6 + (stack_size - 2) * 4)}
OP_TOALTSTACK
{u8_xor(4 + (stack_size - 2) * 4)}
OP_TOALTSTACK
{u8_xor(2 + (stack_size - 2) * 4)}
OP_FROMALTSTACK
OP_FROMALTSTACK
OP_FROMALTSTACK
}
}
/// Pushes the u8 XOR table, for the function f(x) = (x & 0b10101010) >> 1
pub fn u8_push_xor_table() -> Script {
script! {
85
OP_DUP
84
OP_DUP
OP_2OVER
OP_2OVER
81
OP_DUP
80
OP_DUP
OP_2OVER
OP_2OVER
85
OP_DUP
84
OP_DUP
OP_2OVER
OP_2OVER
81
OP_DUP
80
OP_DUP
OP_2OVER
OP_2OVER
69
OP_DUP
68
OP_DUP
OP_2OVER
OP_2OVER
65
OP_DUP
64
OP_DUP
OP_2OVER
OP_2OVER
69
OP_DUP
68
OP_DUP
OP_2OVER
OP_2OVER
65
OP_DUP
64
OP_DUP
OP_2OVER
OP_2OVER
85
OP_DUP
84
OP_DUP
OP_2OVER
OP_2OVER
81
OP_DUP
80
OP_DUP
OP_2OVER
OP_2OVER
85
OP_DUP
84
OP_DUP
OP_2OVER
OP_2OVER
81
OP_DUP
80
OP_DUP
OP_2OVER
OP_2OVER
69
OP_DUP
68
OP_DUP
OP_2OVER
OP_2OVER
65
OP_DUP
64
OP_DUP
OP_2OVER
OP_2OVER
69
OP_DUP
68
OP_DUP
OP_2OVER
OP_2OVER
65
OP_DUP
64
OP_DUP
OP_2OVER
OP_2OVER
21
OP_DUP
20
OP_DUP
OP_2OVER
OP_2OVER
17
OP_DUP
16
OP_DUP
OP_2OVER
OP_2OVER
21
OP_DUP
20
OP_DUP
OP_2OVER
OP_2OVER
17
OP_DUP
16
OP_DUP
OP_2OVER
OP_2OVER
5
OP_DUP
4
OP_DUP
OP_2OVER
OP_2OVER
1
OP_DUP
0
OP_DUP
OP_2OVER
OP_2OVER
5
OP_DUP
4
OP_DUP
OP_2OVER
OP_2OVER
1
OP_DUP
0
OP_DUP
OP_2OVER
OP_2OVER
21
OP_DUP
20
OP_DUP
OP_2OVER
OP_2OVER
17
OP_DUP
16
OP_DUP
OP_2OVER
OP_2OVER
21
OP_DUP
20
OP_DUP
OP_2OVER
OP_2OVER
17
OP_DUP
16
OP_DUP
OP_2OVER
OP_2OVER
5
OP_DUP
4
OP_DUP
OP_2OVER
OP_2OVER
1
OP_DUP
0
OP_DUP
OP_2OVER
OP_2OVER
5
OP_DUP
4
OP_DUP
OP_2OVER
OP_2OVER
1
OP_DUP
0
OP_DUP
OP_2OVER
OP_2OVER
}
}
/// Drops the u8 XOR table
pub fn u8_drop_xor_table() -> Script {
script! {
for _ in 0..128{
OP_2DROP
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::u32::u32_std::*;
use rand::Rng;
#[test]
fn test_xor_table() {
let script = script! {
{ u8_push_xor_table() }
{ 1 } OP_TOALTSTACK
for x in 0..1<<8 {
{ x }
OP_PICK
{ (x & 0b10101010) >> 1 }
OP_EQUAL
OP_FROMALTSTACK
OP_BOOLAND
OP_TOALTSTACK
}
{ u8_drop_xor_table() }
OP_FROMALTSTACK
};
run(script);
}
#[test]
fn test_u32_xor() {
println!("u32 xor: {} bytes", u32_xor(0, 1, 3).len());
let mut rng = rand::thread_rng();
for _ in 0..1000 {
let x: u32 = rng.gen();
let y: u32 = rng.gen();
let script = script! {
{u8_push_xor_table()}
{u32_push(x)}
{u32_push(y)}
{u32_xor(0, 1, 3)}
{ u32_push(x ^ y) }
{u32_equal()}
OP_TOALTSTACK
{u32_drop()} // drop y
{u8_drop_xor_table()}
OP_FROMALTSTACK
};
run(script);
}
}
#[test]
fn test_u8_xor_exhaustive() {
for a in 0..256 {
for b in 0..256 {
let script = script! {
{ u8_push_xor_table() }
{ a }
{ b }
{ u8_xor(2) }
{ a ^ b }
OP_EQUAL
OP_TOALTSTACK
{ u8_drop_xor_table() }
OP_FROMALTSTACK
};
run(script);
}
}
}
}