162 lines
4 KiB
JavaScript
162 lines
4 KiB
JavaScript
// i/o range: 16 bits
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let bits = 16;
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// max Mandelbrot zx/zy addition range prior to checking distance
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let inputRange = 4;
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let reduction = 0;
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let roundOffset = (2 ** (reduction - 1)) + 1;
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// Room to hold power up to -12/+4 for 16-bit mandelbrot
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let shift = 5;
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let base = 2 ** (bits - shift);
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let entries = 2 ** (bits - reduction);
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let bytes = Math.ceil(bits / 8) * entries;
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// try to keep all but the last few bits semi-accurate
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let epsilonBits = 1;
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let epsilon = 2 ** epsilonBits;
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export function toFixed(float) {
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return Math.round(float * base);
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}
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export function toFloat(fixed) {
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return fixed / base;
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}
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function toIndex(fixed) {
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let n = (fixed + roundOffset) >> reduction;
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if (n == entries) {
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// round down for the maxo for now
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n--;
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}
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return n;
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}
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// x -> log2 x
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let enloggen = new Int32Array(entries);
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for (let i = 0; i < entries; i++) {
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enloggen[i] = toFixed(Math.log2(toFloat(i << reduction)));
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}
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// x -> 2 ^ x
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let empower = new Int32Array(entries * 2);
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for (let i = 0; i < entries * 2; i++) {
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empower[i] = toFixed(2 ** toFloat(i - entries << reduction));
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}
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// returns fixed point
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export function log2(fixed) {
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return enloggen[toIndex(fixed)];
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}
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// returns rounded integer
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export function pow2(fixed) {
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let n = toIndex(fixed);
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if (n > empower.length) {
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n = empower.length - 1;
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}
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return empower[entries + n];
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}
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export function mul(a, b) {
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if (a == 0) return 0;
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if (b == 0) return 0;
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let la = log2(a)|0;
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let lb = log2(b)|0;
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let sum = la + lb;
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if (sum >= 2 * entries) {
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// overflow
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//throw new Error('overflow on mul');
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}
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return pow2(la + lb);
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}
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/*
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for (let i = 0; i < logEntries; i++) {
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let l = log2(i);
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let p = pow2(l);
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console.log(`${i} ${l} ${p}`)
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if (i !== p) {
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console.log(`mismatch ${i} expected, got ${p} via log value ${l} (${toFloat(l)})`);
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}
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}
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console.log('empower');
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for (let i = 0; i < powEntries; i++) {
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let fixed = i << reduction;
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let float = toFloat(fixed);
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let val = pow2(fixed);
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console.log(`${i} ${fixed} ${float} ${val}`)
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}
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*/
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/*
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// now just try multipling numbers
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let deltas = 0;
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let deltaAvg = 0;
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let deltaCount = 0;
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let count = 0;
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function round(n, x) {
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return Math.round(x * n) / n;
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}
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while (true) {
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let a = toFixed(Math.random() * inputRange);
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let b = toFixed(Math.random() * inputRange);
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let expected = toFixed(toFloat(a) * toFloat(b));
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let result = mul(a, b);
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if (result === NaN || result === undefined) {
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console.log(a, b, result);
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console.log(log2(a), log2(b));
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throw new Error('invalid');
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}
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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))}`);
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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 ${toFloat(pow2(log2(a)+log2(b)))}`);
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let delta = Math.abs(result - expected);
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if (delta >= epsilon) {
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let percent = 100 * (delta / expected);
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if (delta > epsilon) {
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console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(expected)}, but got ${toFloat(result)} delta ${toFloat(delta)} ${Math.round(percent * 100) / 100}%`);
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}
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deltas += delta;
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deltaCount++;
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} else {
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console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(result)}`);
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}
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count++;
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if (count > 10000) {
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break;
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}
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}
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deltaAvg = deltas / count;
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console.log(`${count - deltaCount} of ${count} ok -- ${deltaCount} off by avg ${toFloat(deltaAvg)} -- fixed ${round(10,deltaAvg)}`);
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count = 0;
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deltas = 0;
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deltaCount = 0;
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console.log('done');
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let m = 0;
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for (let i = 0; i < enloggen.length; i++) {
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m = Math.max(m, enloggen[i]);
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}
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console.log(`max enloggen entry is ${m}`);
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*/
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console.log(`size of enloggen table: ${entries} entries, ${bytes} bytes`);
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console.log(`size of empower table: ${entries * 2} entries, ${bytes * 2} bytes`);
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