pokemon-showdown/sim/prng.ts
2020-03-05 08:33:06 -08:00

230 lines
7.2 KiB
TypeScript

/**
* PRNG
* Pokemon Showdown - http://pokemonshowdown.com/
*
* This file handles the random number generator for battles.
*
* @license MIT license
*/
/** 64-bit [high -> low] */
export type PRNGSeed = [number, number, number, number];
/**
* A PRNG intended to emulate the on-cartridge PRNG for Gen 5 with a 64-bit
* initial seed.
*/
export class PRNG {
readonly initialSeed: PRNGSeed;
seed: PRNGSeed;
/** Creates a new source of randomness for the given seed. */
constructor(seed: PRNGSeed | null = null) {
if (!seed) seed = PRNG.generateSeed();
this.initialSeed = seed.slice() as PRNGSeed; // make a copy
this.seed = seed.slice() as PRNGSeed;
}
/**
* Getter to the initial seed.
*
* This should be considered a hack and is only here for backwards compatibility.
*/
get startingSeed(): PRNGSeed {
return this.initialSeed;
}
/**
* Creates a clone of the current PRNG.
*
* The new PRNG will have its initial seed set to the seed of the current instance.
*/
clone(): PRNG {
return new PRNG(this.seed);
}
/**
* Retrieves the next random number in the sequence.
* This function has three different results, depending on arguments:
* - random() returns a real number in [0, 1), just like Math.random()
* - random(n) returns an integer in [0, n)
* - random(m, n) returns an integer in [m, n)
* m and n are converted to integers via Math.floor. If the result is NaN, they are ignored.
*/
next(from?: number, to?: number): number {
this.seed = this.nextFrame(this.seed); // Advance the RNG
let result = (this.seed[0] << 16 >>> 0) + this.seed[1]; // Use the upper 32 bits
if (from) from = Math.floor(from);
if (to) to = Math.floor(to);
if (from === undefined) {
result = result / 0x100000000;
} else if (!to) {
result = Math.floor(result * from / 0x100000000);
} else {
result = Math.floor(result * (to - from) / 0x100000000) + from;
}
return result;
}
/**
* Flip a coin (two-sided die), returning true or false.
*
* This function returns true with probability `P`, where `P = numerator
* / denominator`. This function returns false with probability `1 - P`.
*
* The numerator must be a non-negative integer (`>= 0`).
*
* The denominator must be a positive integer (`> 0`).
*/
randomChance(numerator: number, denominator: number): boolean {
return this.next(denominator) < numerator;
}
/**
* Return a random item from the given array.
*
* This function chooses items in the array with equal probability.
*
* If there are duplicate items in the array, each duplicate is
* considered separately. For example, sample(['x', 'x', 'y']) returns
* 'x' 67% of the time and 'y' 33% of the time.
*
* The array must contain at least one item.
*
* The array must not be sparse.
*/
sample<T>(items: readonly T[]): T {
if (items.length === 0) {
throw new RangeError(`Cannot sample an empty array`);
}
const index = this.next(items.length);
const item = items[index];
if (item === undefined && !Object.prototype.hasOwnProperty.call(items, index)) {
throw new RangeError(`Cannot sample a sparse array`);
}
return item;
}
/**
* This is how the game resolves speed ties.
*
* At least according to V4 in
* https://github.com/smogon/pokemon-showdown/issues/1157#issuecomment-214454873
*/
shuffle<T>(items: T[], start = 0, end: number = items.length) {
while (start < end - 1) {
const nextIndex = this.next(start, end);
if (start !== nextIndex) {
[items[start], items[nextIndex]] = [items[nextIndex], items[start]];
}
start++;
}
}
/**
* The RNG is a Linear Congruential Generator (LCG) in the form: `x_{n + 1} = (a x_n + c) % m`
*
* Where: `x_0` is the seed, `x_n` is the random number after n iterations,
*
* ````
* a = 0x5D588B656C078965
* c = 0x00269EC3
* m = 2^64
* ````
*
* Javascript doesnt handle such large numbers properly, so this function does it in 16-bit parts.
* ````
* x_{n + 1} = (x_n * a) + c
* ````
*
* Let any 64 bit number:
* ````
* n = (n[0] << 48) + (n[1] << 32) + (n[2] << 16) + n[3]
* ````
*
* Then:
* ````
* x_{n + 1} =
* ((a[3] x_n[0] + a[2] x_n[1] + a[1] x_n[2] + a[0] x_n[3] + c[0]) << 48) +
* ((a[3] x_n[1] + a[2] x_n[2] + a[1] x_n[3] + c[1]) << 32) +
* ((a[3] x_n[2] + a[2] x_n[3] + c[2]) << 16) +
* a[3] x_n[3] + c[3]
* ````
*
* Which can be generalised where b is the number of 16 bit words in the number:
* ````
* ((a[b-1] + x_n[b-1] + c[b-1]) << (16 * 0)) +
* ((a[b-1] x_n[b-2] + a[b-2] x_n[b-1] + c[b-2]) << (16 * 1)) +
* ((a[b-1] x_n[b-3] + a[b-2] x_n[b-2] + a[b-3] x_n[b-1] + c[b-3]) << (16 * 2)) +
* ...
* ((a[b-1] x_n[1] + a[b-2] x_n[2] + ... + a[2] x_n[b-2] + a[1] + x_n[b-1] + c[1]) << (16 * (b-2))) +
* ((a[b-1] x_n[0] + a[b-2] x_n[1] + ... + a[1] x_n[b-2] + a[0] + x_n[b-1] + c[0]) << (16 * (b-1)))
* ````
*
* Which produces this equation:
* ````
* \sum_{l=0}^{b-1}\left(\sum_{m=b-l-1}^{b-1}\left\{a[2b-m-l-2] x_n[m]\right\}+c[b-l-1]\ll16l\right)
* ````
*
* Notice how the `a[]` word starts at `b-1`, and decrements every time it appears again on the line;
* `x_n[]` starts at `b-<line#>-1` and increments to b-1 at the end of the line per line, limiting the
* length of the line; `c[]` is at `b-<line#>-1` for each line and the left shift is `16 * <line#>`)
*
* This is all ignoring overflow/carry because that cannot be shown in a pseudo-mathematical equation.
* The below code implements a optimised version of that equation while also checking for overflow/carry.
*/
nextFrame(initialSeed: PRNGSeed, framesToAdvance = 1): PRNGSeed {
// Use Slice so we don't actually alter the original seed.
let seed: PRNGSeed = initialSeed.slice() as PRNGSeed;
for (let frame = 0; frame < framesToAdvance; ++frame) {
const a = [0x5D58, 0x8B65, 0x6C07, 0x8965];
const c = [0, 0, 0x26, 0x9EC3];
const nextSeed: PRNGSeed = [0, 0, 0, 0];
let carry = 0;
for (let cN = seed.length - 1; cN >= 0; --cN) {
nextSeed[cN] = carry;
carry = 0;
let aN = seed.length - 1;
for (let seedN = cN; seedN < seed.length; --aN, ++seedN) {
const nextWord = a[aN] * seed[seedN];
carry += nextWord >>> 16;
nextSeed[cN] += nextWord & 0xFFFF;
}
nextSeed[cN] += c[cN];
carry += nextSeed[cN] >>> 16;
nextSeed[cN] &= 0xFFFF;
}
seed = nextSeed;
}
return seed;
}
static generateSeed() {
return [
Math.floor(Math.random() * 0x10000),
Math.floor(Math.random() * 0x10000),
Math.floor(Math.random() * 0x10000),
Math.floor(Math.random() * 0x10000),
] as PRNGSeed;
}
}
// The following commented-out function is designed to emulate the on-cartridge
// PRNG for Gens 3 and 4, as described in
// https://www.smogon.com/ingame/rng/pid_iv_creation#pokemon_random_number_generator
// This RNG uses a 32-bit initial seed
// m and n are converted to integers via Math.floor. If the result is NaN, they
// are ignored.
/*
random(m: number, n: number) {
this.seed = (this.seed * 0x41C64E6D + 0x6073) >>> 0; // truncate the result to the last 32 bits
let result = this.seed >>> 16; // the first 16 bits of the seed are the random value
m = Math.floor(m)
n = Math.floor(n)
return (m ? (n ? (result % (n - m)) + m : result % m) : result / 0x10000)
}
*/