mandel-6502/silly.js

// input range: 0..255 * 0..255
// output range: 16 bits

let logBits = 8;
let logEntries = 2 ** logBits;

let powBits = 16;
let powEntries = (2 ** powBits);

// Room to hold powers up to 4
let shift = 4;
let base = 2 ** (powBits - shift);

// 16-bit lookup table
let reduction = 0;

// 12-bit lookup table
//let reduction = 4;

function toFixed(float) {
    return Math.round(float * base);
}

function toFloat(fixed) {
    return fixed / base;
}

// 256x2 = 512 bytes
let enloggen = new Uint16Array(logEntries);
for (let i = 0; i < logEntries; i++) {
    enloggen[i] = toFixed(Math.log2(i));
}

// 64k entries
// 64kx2 = 128 KiB
// can reduce number by reducing precision
// or splitting into high & low vals
let powCount = powEntries >> reduction;
let empower = new Uint16Array(powCount);
for (let i = 0; i < powCount; i++) {
    let fixed = i << reduction;
    empower[i] = Math.round(2 ** toFloat(fixed));
}


// returns fixed
function log2(byte) {
    return enloggen[byte];
}

// returns 16-bit number
function pow2(fixed) {
    n = (fixed >> reduction);
    return empower[n];
}

function mul(a, b) {
    if (a == 0) return 0;
    if (b == 0) return 0;
    let la = log2(a);
    let lb = log2(b);
    return pow2(la + lb);
}

/*
for (let i = 0; i < logEntries; i++) {
    let l = log2(i);
    let p = pow2(l);
    console.log(`${i} ${l} ${p}`)
    if (i !== p) {
        //console.log(`mismatch ${i} expected, got ${p} via log value ${l} (${toFloat(l)})`);
    }
}
process.exit(1);
*/

// now just try multipling numbers
let deltas = 0;
let count = 0;
let deltaCount = 0;
let results = 0;

function round(n, x) {
    return Math.round(x * n) / n;
}

while (true) {
    let a = Math.trunc(Math.random() * logEntries);
    let b = Math.trunc(Math.random() * logEntries);
    let expected = a * b;
    let result = mul(a, b);

    let delta = Math.abs(result - expected);
    let epsilon = 1;

    if (delta >= epsilon) {
        let percent = 100 * (delta / expected);
        //console.log(`${a} * ${b} = ${expected}, but got ${result} delta ${delta} ${Math.round(percent * 100) / 100}%`);
        deltas += delta;
        deltaCount++;
    } else {
        //console.log(`${a} * ${b} = ${result}`);
    }
    count++;
    if (count == 100) {
        deltaAvg = deltas / deltaCount;
        console.log(`${count - deltaCount} of ${count} ok -- ${deltaCount} off by avg ${round(10,deltaAvg)})`);
        count = 0;
        deltas = 0;
        deltaCount = 0;
    }
}

console.log('done');