347 lines
8.9 KiB
TypeScript
347 lines
8.9 KiB
TypeScript
/**
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* Miscellaneous binary utility functions
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*
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* @module
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*/
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export {
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bytes_to_bigint,
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bigint_to_bytes,
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concat,
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strong_rand_bytes
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};
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/**
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* Concatenate two arrays
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*/
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function
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concat
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(arr1 : Uint8Array,
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arr2 : Uint8Array)
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: Uint8Array
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{
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let len1 : number = arr1.length;
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let len2 : number = arr2.length;
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let arr1_idx0_offset : number = 0;
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let arr2_idx0_offset : number = len1;
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let result_len : number = len1 + len2;
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let result : Uint8Array = new Uint8Array(result_len);
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// copy first array into result
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for (let arr1_idx0 = 0;
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arr1_idx0 < len1;
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arr1_idx0++)
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{
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// no offset here
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let result_idx0 : number = arr1_idx0 + arr1_idx0_offset;
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result[result_idx0] = arr1[arr1_idx0];
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}
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// copy second array into result
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for (let arr2_idx0 = 0;
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arr2_idx0 < len2;
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arr2_idx0++)
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{
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// offset by the length of the first array
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let result_idx0 : number = arr2_idx0 + arr2_idx0_offset;
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result[result_idx0] = arr2[arr2_idx0];
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}
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return result;
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}
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/**
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* Cryptographically random bytes
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*/
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function
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strong_rand_bytes
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(how_many : number)
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: Uint8Array
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{
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let arr = new Uint8Array(how_many);
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(new Crypto()).getRandomValues(arr);
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return arr;
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}
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/**
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* Convert a byte array to a bigint
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*
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* Equivalent to `binary:decode_unsigned/1` from Erlang
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*/
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function
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bytes_to_bigint
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(bytes: Uint8Array)
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: bigint
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{
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let n : bigint = 0n;
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for (let b of bytes) {
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// move first, then add
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// otherwise it ends on a move
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// imperative languages are for losers
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n <<= 8n;
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n += BigInt(b);
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}
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return n;
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}
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/**
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* Convert a bigint to a byte array
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*
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* Equivalent to `binary:encode_unsigned/1` from Erlang
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*
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* Requires input to be positive
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*/
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function
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bigint_to_bytes
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(q: bigint)
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: Uint8Array
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{
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if (q < 0n) {
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throw new Error('q < 0n: ' + q);
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}
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let arr_reverse = [];
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while (q > 0n) {
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let r = Number(q % 256n);
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q /= 256n;
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arr_reverse.push(r);
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}
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arr_reverse.reverse();
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return new Uint8Array(arr_reverse);
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}
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/**
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* Oh no, bitstrings in a language that only has bytestrings
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*
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* By convention these are `Uint8Array`s with byte length `ceil(bit_length /
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* 8)`, and all trailing bits are zero.
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*/
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type bits =
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{bit_length : number,
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bytes : Uint8Array};
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/**
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* Get an uninitialized bitstring
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*
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* @internal
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*/
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function
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bits_null
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(bit_length : number)
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: bits
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{
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let byte_length : number = Math.ceil(bit_length / 8);
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let result : Uint8Array = new Uint8Array(byte_length);
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return {bit_length : bit_length,
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bytes : result};
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}
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/**
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* Get a bitstring of a given length where every value is 0.
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*/
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function
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bits_zeros
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(bit_length : number)
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: bits
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{
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let byte_length : number = Math.ceil(bit_length / 8);
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let result : Uint8Array = new Uint8Array(byte_length);
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for (let i0 = 0;
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i0 < byte_length;
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i0++)
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{
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result[i0] = 0;
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}
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return {bit_length : bit_length,
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bytes : result};
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}
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/**
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* Get a bitstring of a given length where every value is 1.
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*/
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function
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bits_ones
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(bit_length : number)
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: bits
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{
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let byte_length : number = Math.ceil(bit_length / 8);
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let result : Uint8Array = new Uint8Array(byte_length);
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// fill everything except the last byte with 255s
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for (let i0 = 0;
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i0 < (byte_length - 1);
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i0++)
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{
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result[i0] = 255;
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}
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// alright so the last byte
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// ok so the number of leading 0s is
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// 8 - (bit_length % 8)
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let num_trailing_zero_bits : number = 8 - (bit_length % 8);
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// the trailing byte is 255 << that
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// e.g. 3 trailing 0s
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// 1111_1111 -> 1111_1000
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let last_byte : number = 255 << num_trailing_zero_bits;
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let last_byte_idx0 : number = byte_length - 1;
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result[last_byte_idx0] = last_byte;
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return {bit_length : bit_length,
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bytes : result};
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}
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/**
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* Get the bit at a given 0-index
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*/
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function
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bits_i0th
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(bit_idx0 : number,
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bits : bits)
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: number
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{
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// first task is figuring out what byte we're at
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// for instance if we want bit 27
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// 3*8 = 24 =< 27 < 4*8
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// so it's Math.floor(bit_idx0 / 8)
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let byte_idx0 : number = Math.floor(bit_idx0 / 8);
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// let's fetch the byte and work with that
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let the_byte : number = bits.bytes[byte_idx0];
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// ok so let's go with 27 again
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// 27 = 3 mod 8
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// so we bitshift right by (8 - 3)
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// and then take the remainder dividing by 2
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// --B-_---- -> ----_---B -> 0000_000B
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let bsr : number = 8 - (bit_idx0 % 8);
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return (the_byte >> bsr) % 2;
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}
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/**
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* Concatenate two bitstrings
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*/
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function
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bits_concat
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(bits1 : bits,
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bits2 : bits)
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: bits
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{
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let result_bit_length : number = bits1.bit_length + bits2.bit_length;
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let bytes1 : Uint8Array = bits1.bytes;
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let bytes2 : Uint8Array = bits2.bytes;
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// using zeros here because of our xor trick in a minute
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let result_bits : bits = bits_zeros(result_bit_length);
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let result_bytes : Uint8Array = result_bits.bytes;
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// alright so
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// we can start by copying the first bytes into result bytes
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for (let bytes1_idx0 = 0;
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bytes1_idx0 < bytes1.length;
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bytes1_idx0++)
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{
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result_bytes[bytes1_idx0] = bytes1[bytes1_idx0];
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}
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// next
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// we need to calculate the left-shift offset
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// this will be 8 - (bytes1.bit_length % 8)
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let num_trailing_zeros_in_first_array : number = 8 - (bits1.bit_length % 8);
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// so
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// bytes1: ABCD_EF00
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// bytes2: GH12_3000
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// result: ABCD_EFGH 1230_0000
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// ah ok, so we need to for each byte in the second array
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// take the first however many bits, xor it with the existing byte
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// then take the last however many bits and place them into the next byte
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// this is super confusing but
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// ABCD_EF00
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// GH12_3456
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// operation:
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// ABCD_EF00
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// xor 0000_00GH
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// = ABCD_EFGH 1234_5600
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//
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// then on the next iteration
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// 1234_5600
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// abcd_efgh
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// ->
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// 1234_56ab cdef_gh00
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//
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// ah so there's a pattern
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// however many trailing 0s there are in the first array
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// say there's 2
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// we take the first 2 bits of the upcoming byte
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// xor that against the current byte
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// take the last 6 bits of the upcoming byte
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// set the next byte to that
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//
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// have to think about edge behavior
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// this is ripe for off-by-1 errors
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// but i think the general idea is right
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//
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// so we start the iteration
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// on the last byte of the first array
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let last_byte_of_first_array_idx0 : number = bytes1.length - 1;
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// and we end
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// on the second-to-last-byte of the result array
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let second_to_last_byte_of_result_array_idx0 : number = result_bytes.length - 2;
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// the reason we do that is because we're doing this is because we are
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// going along, xoring against the current byte and then setting the next
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// byte
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//
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// ok so
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for (let this_result_byte_idx0 = last_byte_of_first_array_idx0;
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this_result_byte_idx0 <= second_to_last_byte_of_result_array_idx0;
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this_result_byte_idx0++)
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{
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let this_result_byte : number = result_bytes[this_result_byte_idx0];
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// ok here we need to fish out the relevant byte of the second array
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// gaaah
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// so this will be 0 at the start of the loop
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let relevant_byte_of_second_array_idx0 : number = this_result_byte_idx0 - last_byte_of_first_array_idx0;
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let relevant_byte_of_second_array : number = bytes2[relevant_byte_of_second_array_idx0];
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// ok so let's fish out the leading digits
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// the number of leading digits is the number of trailing 0s in the first array
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let num_leading_digits : number = num_trailing_zeros_in_first_array;
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let num_trailing_digits : number = 8 - num_leading_digits;
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// suppose there are 2 leading digits and 6 trailing digits
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// ABCD_EFGH
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// leading digits are
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// ABCD_EFGH >> 6 = 0000_00AB
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// trailing digits are
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// (ABCD_EFGH << 2) % 255 = CDEF_GH00
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let leading_digits : number = relevant_byte_of_second_array >> num_trailing_digits;
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let trailing_digits : number = (relevant_byte_of_second_array << num_leading_digits) % 255;
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// xor the current byte against the leading digits
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let new_this_result_byte : number = this_result_byte ^ leading_digits;
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result_bytes[this_result_byte_idx0] = new_this_result_byte;
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// set the next byte to the trailing digits
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result_bytes[this_result_byte_idx0 + 1] = trailing_digits;
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}
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// i think we're done
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return {bit_length : result_bit_length,
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bytes : result_bytes};
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}
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