function multiply(out, a, b) { let b0 = b[0] let b1 = b[1] let b2 = b[2] let b3 = b[3] out[0] = b0 * a[0] + b1 * a[4] + b2 * a[8] + b3 * a[12] out[1] = b0 * a[1] + b1 * a[5] + b2 * a[9] + b3 * a[13] out[2] = b0 * a[2] + b1 * a[6] + b2 * a[10] + b3 * a[14] out[3] = b0 * a[3] + b1 * a[7] + b2 * a[11] + b3 * a[15] b0 = b[4] b1 = b[5] b2 = b[6] b3 = b[7] out[4] = b0 * a[0] + b1 * a[4] + b2 * a[8] + b3 * a[12] out[5] = b0 * a[1] + b1 * a[5] + b2 * a[9] + b3 * a[13] out[6] = b0 * a[2] + b1 * a[6] + b2 * a[10] + b3 * a[14] out[7] = b0 * a[3] + b1 * a[7] + b2 * a[11] + b3 * a[15] b0 = b[8] b1 = b[9] b2 = b[10] b3 = b[11] out[8] = b0 * a[0] + b1 * a[4] + b2 * a[8] + b3 * a[12] out[9] = b0 * a[1] + b1 * a[5] + b2 * a[9] + b3 * a[13] out[10] = b0 * a[2] + b1 * a[6] + b2 * a[10] + b3 * a[14] out[11] = b0 * a[3] + b1 * a[7] + b2 * a[11] + b3 * a[15] b0 = b[12] b1 = b[13] b2 = b[14] b3 = b[15] out[12] = b0 * a[0] + b1 * a[4] + b2 * a[8] + b3 * a[12] out[13] = b0 * a[1] + b1 * a[5] + b2 * a[9] + b3 * a[13] out[14] = b0 * a[2] + b1 * a[6] + b2 * a[10] + b3 * a[14] out[15] = b0 * a[3] + b1 * a[7] + b2 * a[11] + b3 * a[15] return out }function multiplyCached(out, a, b) { let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3]; let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7]; let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11]; let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15]; // Cache only the current line of the second matrix let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3]; out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7]; out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11]; out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15]; out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31; out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32; out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33; return out;}let result = [0, 0, 0, 0]multiplyCached(result, [123.12, 131.31, 143.12, 0.123], [143.12, 0.123, 123.12, 131.31])let result = [0, 0, 0, 0]multiply(result, [123.12, 131.31, 143.12, 0.123], [143.12, 0.123, 123.12, 131.31])--enable-precise-memory-info flag.
| Test case name | Result |
|---|---|
| With cache | |
| Without cache |
| Test name | Executions per second |
|---|---|
| With cache | 6051233.5 Ops/sec |
| Without cache | 4273649.5 Ops/sec |
A challenging benchmarking problem!
After analyzing the provided code, I'll attempt to break down and explain it.
Code Analysis
The code appears to be a JavaScript function multiplyCached (or multiply) that multiplies two arrays: [a00, ..., a33] and [b0, ..., b3]. The multiplication is done using the standard matrix multiplication algorithm. The difference between multiplyCached and multiply lies in the caching mechanism.
In multiplyCached, there are 16 iterations (from out[0] to out[15]) that perform the same calculation: multiplying each row of [a00, ..., a33] with each column of [b0, ..., b3]. These calculations seem to be stored in cache (b0 to b15) and reused across iterations.
In contrast, multiply does not use caching. Each iteration performs the full calculation from scratch.
Benchmarking
The benchmarking data suggests that multiplyCached outperforms multiply, with a significant difference in executions per second (6051233.5 vs 4273649.5).
This outcome is likely due to the caching mechanism in multiplyCached. By reusing previously computed values, it avoids redundant calculations and reduces the computational overhead.
Conclusion
The provided code demonstrates an optimization technique using caching to improve the performance of matrix multiplication. The benchmarking data supports this claim, showing a substantial speedup for the cached version (multiplyCached) compared to the non-cached version (multiply).
