hmm

silly.js

@@ -1,21 +1,20 @@
-// input range: 0..255 * 0..255
-// output range: 16 bits
+// i/o range: 16 bits
+let bits = 16;
 
-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
+// Room to hold values up to 15.9 for 16-bit mandelbrot
 let shift = 4;
-let base = 2 ** (powBits - shift);
+let base = 2 ** (bits - shift);
+
+let inputRange = 8; // max Mandelbrot zx/zy addition range prior to checking distance
 
-// total of 12-bit lookup table
 let reduction = 0;
+let roundOffset = (2 ** (reduction - 1)) + 1;
+let entries = 2 ** (bits - reduction);
+let bytes = Math.ceil(bits / 8) * entries;
 
-let powCount = powEntries >> reduction;
-
+// try to keep all but the last few bits semi-accurate
+let epsilonBits = 2;
+let epsilon = 2 ** epsilonBits;
 
 function toFixed(float) {
     return Math.round(float * base);
@@ -25,46 +24,36 @@ 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')
+function toIndex(fixed) {
+    let n = (fixed + roundOffset) >> reduction;
+    if (n == entries) {
+        // round down for the maxo for now
+        n--;
     }
+    return n;
 }
 
-// 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')
-    }
+// x -> log2 x
+let enloggen = new Uint32Array(entries);
+for (let i = 0; i < entries; i++) {
+    enloggen[i] = toFixed(Math.log2(toFloat(i << reduction)));
+}
+
+// x -> 2 ^ x
+let empower = new Uint32Array(entries * 2);
+for (let i = 0; i < entries * 2; i++) {
+    empower[i] = toFixed(2 ** toFloat(i << reduction));
 }
 
 
 // returns fixed point
-function log2(val) {
-    return enloggen[val];
+function log2(fixed) {
+    return enloggen[toIndex(fixed)];
 }
 
 // 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];
+    return empower[toIndex(fixed)];
 }
 
 function mul(a, b) {
@@ -73,7 +62,7 @@ function mul(a, b) {
     let la = log2(a)|0;
     let lb = log2(b)|0;
     let sum = la + lb;
-    if (sum >= (2 ** powBits)) {
+    if (sum >= 2 * entries) {
         // overflow
         throw new Error('overflow on mul');
     }
@@ -101,43 +90,44 @@ for (let i = 0; i < powEntries; i++) {
 
 // now just try multipling numbers
 let deltas = 0;
-let count = 0;
+let deltaAvg = 0;
 let deltaCount = 0;
-let results = 0;
+let count = 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 a = toFixed(Math.random() * inputRange);
+    let b = toFixed(Math.random() * inputRange);
 
-for (let i = 0; i < 65536; i++) {
-    let a = i & 0xff;
-    let b = (i >> 8) & 0xff;
-    let expected = a * b;
+    let expected = toFixed(toFloat(a) * toFloat(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))}`);
+
+    //console.log(`fixed a ${a} b ${b} expected ${expected} result ${result}`);
+    //console.log(`float a ${toFloat(a)} b ${toFloat(b)} expected ${toFloat(expected)} result ${toFloat(result)} loga ${toFloat(log2(a))} logb ${toFloat(log2(b))} pow ${toFloat(pow2(log2(a)+log2(b)))}`);
 
     let delta = Math.abs(result - expected);
-    let epsilon = 1;
 
-    if (delta >= epsilon || result === undefined) {
+    if (delta > 0) {
         let percent = 100 * (delta / expected);
-        console.log(`${a} * ${b} = ${expected}, but got ${result} delta ${delta} ${Math.round(percent * 100) / 100}%`);
+        if (delta > epsilon) {
+            console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(expected)}, but got ${toFloat(result)} delta ${toFloat(delta)} ${Math.round(percent * 100) / 100}%`);
+        }
         deltas += delta;
         deltaCount++;
     } else {
-        console.log(`${a} * ${b} = ${result}`);
+        //console.log(`${toFloat(a)} * ${toFloat(b)} = ${toFloat(result)}`);
     }
     count++;
+    if (count > 10000) {
+        break;
+    }
 }
 
-deltaAvg = deltas / deltaCount;
-console.log(`${count - deltaCount} of ${count} ok -- ${deltaCount} off by avg ${round(10,deltaAvg)})`);
+deltaAvg = deltas / count;
+console.log(`${count - deltaCount} of ${count} ok -- ${deltaCount} off by avg ${toFloat(deltaAvg)} -- fixed ${round(10,deltaAvg)}`);
 count = 0;
 deltas = 0;
 deltaCount = 0;
@@ -145,8 +135,8 @@ 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`);
+console.log(`size of enloggen table: ${entries * 2} 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++) {