mandel-6502/silly.js

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

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

let powBits = 21;
let powEntries = 2 ** powBits;

// Room to hold exponents up to 15.9 for 16-bit output
let shift = 4;
let base = 2 ** (powBits - shift);

// total of 12-bit lookup table
let reduction = 0;

let powCount = powEntries >> reduction;


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

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

// 256x2 = 512 bytes
let enloggen = new Uint32Array(logEntries);
for (let i = 0; i < logEntries; i++) {
    enloggen[i] = toFixed(Math.log2(i));
    if (enloggen[i] > powEntries) {
        throw new Error('enloggen entry out of range')
    }
}

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


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

// returns rounded integer
function pow2(fixed) {
    let n = fixed >> reduction;
    if (n >= empower.length) {
        /*
        console.log(`ERROR float ${toFloat(fixed)} fixed ${fixed} n ${n} max ${empower.length}`);
        
        throw new Error('whoops');
        */
        // Overflow? Round down.
        return empower[empower.length - 1];
    }
    return empower[n];
}

function mul(a, b) {
    if (a == 0) return 0;
    if (b == 0) return 0;
    let la = log2(a)|0;
    let lb = log2(b)|0;
    let sum = la + lb;
    if (sum >= (2 ** powBits)) {
        // overflow
        throw new Error('overflow on mul');
    }
    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)})`);
    }
}

console.log('empower');
for (let i = 0; i < powEntries; i++) {
    let fixed = i << reduction;
    let float = toFloat(fixed);
    let val = pow2(fixed);
    console.log(`${i} ${fixed} ${float} ${val}`)
}
*/

// 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);
*/

for (let i = 0; i < 65536; i++) {
    let a = i & 0xff;
    let b = (i >> 8) & 0xff;
    let expected = a * b;
    let result = mul(a, b);
    console.log(`a ${a} b ${b} expected ${expected} result ${result} loga ${log2(a)} logb ${log2(b)} pow ${pow2(log2(a)+log2(b))}`);

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

    if (delta >= epsilon || result === undefined) {
        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++;
}

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');


console.log(`size of enloggen table: ${enloggen.length} entries, ${enloggen.length * 3} bytes`);
console.log(`size of empower table: ${empower.length} entries, ${empower.length * 2} bytes`);

let m = 0;
for (let i = 0; i < enloggen.length; i++) {
    m = Math.max(m, enloggen[i]);
}
console.log(`max enloggen entry is ${m}`);