experimenting with fixed-point log lookup table

probably won't be enough precision to work with
at a size that fits in memory :D

fixed.js

@@ -0,0 +1,155 @@
+// i/o range: 16 bits
+let bits = 16;
+
+// max Mandelbrot zx/zy addition range prior to checking distance
+let inputRange = 4;
+
+// Room to hold power up to -12/+4 for 16-bit mandelbrot
+let shift = 4;
+let base = 2 ** (bits - shift);
+
+let reduction = 4;
+let roundOffset = (2 ** (reduction - 1)) + 1;
+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;
+
+function toFixed(float) {
+    return Math.round(float * base);
+}
+
+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
+function log2(fixed) {
+    return enloggen[toIndex(fixed)];
+}
+
+// returns rounded integer
+function pow2(fixed) {
+    let n = toIndex(fixed);
+    if (n > empower.length) {
+        n = empower.length - 1;
+    }
+    return empower[entries + 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 * 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');
+
+
+console.log(`size of enloggen table: ${entries} entries, ${bytes} bytes`);
+console.log(`size of empower table: ${entries * 2} entries, ${bytes * 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}`);