mandel-6502/fixed.js

// i/o range: 16 bits
let bits = 16;

// max Mandelbrot zx/zy addition range prior to checking distance
let inputRange = 4;

let reduction = 0;
let roundOffset = (2 ** (reduction - 1)) + 1;

// Room to hold power up to -12/+4 for 16-bit mandelbrot
let shift = 5;
let base = 2 ** (bits - shift);


let entries = 2 ** (bits - reduction);
let bytes = Math.ceil(bits / 8) * entries;

// try to keep all but the last few bits semi-accurate
let epsilonBits = 1;
let epsilon = 2 ** epsilonBits;

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

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

function toIndex(fixed) {
    let n = (fixed + roundOffset) >> reduction;
    if (n == entries) {
        // round down for the maxo for now
        n--;
    }
    return n;
}

// x -> log2 x
let enloggen = new Int32Array(entries);
for (let i = 0; i < entries; i++) {
    enloggen[i] = toFixed(Math.log2(toFloat(i << reduction)));
}

// x -> 2 ^ x
let empower = new Int32Array(entries * 2);
for (let i = 0; i < entries * 2; i++) {
    empower[i] = toFixed(2 ** toFloat(i - entries << reduction));
}


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

// returns rounded integer
export function pow2(fixed) {
    let n = toIndex(fixed);
    if (n > empower.length) {
        n = empower.length - 1;
    }
    return empower[entries + n];
}

export 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 * entries) {
        // 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 deltaAvg = 0;
let deltaCount = 0;
let count = 0;

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

while (true) {
    let a = toFixed(Math.random() * inputRange);
    let b = toFixed(Math.random() * inputRange);

    let expected = toFixed(toFloat(a) * toFloat(b));
    let result = mul(a, b);
    if (result === NaN || result === undefined) {
        console.log(a, b, result);
        console.log(log2(a), log2(b));
        throw new Error('invalid');
    }

    console.log(`fixed a ${a} b ${b} expected ${expected} result ${result} loga ${log2(a)} logb ${log2(b)} sum ${log2(a)+log2(b)} pow ${pow2(log2(a)+log2(b))}`);
    console.log(`float a ${toFloat(a)} b ${toFloat(b)} expected ${toFloat(expected)} result ${toFloat(result)} loga ${toFloat(log2(a))} logb ${toFloat(log2(b))} sum ${toFloat(log2(a)+log2(b))} pow ${toFloat(pow2(log2(a)+log2(b)))}`);

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

    if (delta >= epsilon) {
        let percent = 100 * (delta / expected);
        if (delta > epsilon) {
            console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(expected)}, but got ${toFloat(result)} delta ${toFloat(delta)} ${Math.round(percent * 100) / 100}%`);
        }
        deltas += delta;
        deltaCount++;
    } else {
        console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(result)}`);
    }
    count++;
    if (count > 10000) {
        break;
    }
}

deltaAvg = deltas / count;
console.log(`${count - deltaCount} of ${count} ok -- ${deltaCount} off by avg ${toFloat(deltaAvg)} -- fixed ${round(10,deltaAvg)}`);
count = 0;
deltas = 0;
deltaCount = 0;

console.log('done');



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

*/

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