010579c237
The Newton sqrtInverse procedure we use to compute Float.Sqrt should not allocate a number of times proportional to the number of Newton iterations we need to reach the desired precision. At the beginning the function the target precision is known, so even if we do want to perform the early steps at low precisions (to save time), it's still possible to pre-allocate larger backing arrays, both for the temp variables in the loop and the variable that'll hold the final result. There's one complication. At the following line: u.Sub(three, u) the Sub method will allocate, because the receiver aliases one of the arguments, and the large backing array we initially allocated for u will be replaced by a smaller one allocated by Sub. We can work around this by introducing a second temp variable u2 that we use to hold the Sub call result. Overall, the sqrtInverse procedure still allocates a number of times proportional to the number of Newton steps, because unfortunately a few of the Mul calls in the Newton function allocate; but at least we allocate less in the function itself. FloatSqrt/256-4 1.97µs ± 1% 1.84µs ± 1% -6.61% (p=0.000 n=8+8) FloatSqrt/1000-4 4.80µs ± 3% 4.28µs ± 1% -10.78% (p=0.000 n=8+8) FloatSqrt/10000-4 40.0µs ± 1% 38.3µs ± 1% -4.15% (p=0.000 n=8+8) FloatSqrt/100000-4 955µs ± 1% 932µs ± 0% -2.49% (p=0.000 n=8+7) FloatSqrt/1000000-4 79.8ms ± 1% 79.4ms ± 1% ~ (p=0.105 n=8+8) name old alloc/op new alloc/op delta FloatSqrt/256-4 816B ± 0% 512B ± 0% -37.25% (p=0.000 n=8+8) FloatSqrt/1000-4 2.50kB ± 0% 1.47kB ± 0% -41.03% (p=0.000 n=8+8) FloatSqrt/10000-4 23.5kB ± 0% 18.2kB ± 0% -22.62% (p=0.000 n=8+8) FloatSqrt/100000-4 251kB ± 0% 173kB ± 0% -31.26% (p=0.000 n=8+8) FloatSqrt/1000000-4 4.61MB ± 0% 2.86MB ± 0% -37.90% (p=0.000 n=8+8) name old allocs/op new allocs/op delta FloatSqrt/256-4 12.0 ± 0% 8.0 ± 0% -33.33% (p=0.000 n=8+8) FloatSqrt/1000-4 19.0 ± 0% 9.0 ± 0% -52.63% (p=0.000 n=8+8) FloatSqrt/10000-4 35.0 ± 0% 14.0 ± 0% -60.00% (p=0.000 n=8+8) FloatSqrt/100000-4 55.0 ± 0% 23.0 ± 0% -58.18% (p=0.000 n=8+8) FloatSqrt/1000000-4 122 ± 0% 75 ± 0% -38.52% (p=0.000 n=8+8) Change-Id: I950dbf61a40267a6cca82ae72524c3024bcb149c Reviewed-on: https://go-review.googlesource.com/87659 Reviewed-by: Robert Griesemer <gri@golang.org> |
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