2c783dc038
The Sqrt Newton method computes g(t) = f(t)/f'(t) and then iterates t2 = t1 - g(t1) We can save one operation by including the final subtraction in g(t) and evaluating the resulting expression symbolically. For example, for the direct method, g(t) = ½(t² - x)/t and we use 2 multiplications, 1 division and 1 subtraction in g(), plus 1 final subtraction; but if we compute t - g(t) = t - ½(t² - x)/t = ½(t² + x)/t we only use 2 multiplications, 1 division and 1 addition. A similar simplification can be done for the inverse method. name old time/op new time/op delta FloatSqrt/64-4 889ns ± 4% 790ns ± 1% -11.19% (p=0.000 n=8+7) FloatSqrt/128-4 1.82µs ± 0% 1.64µs ± 1% -10.07% (p=0.001 n=6+8) FloatSqrt/256-4 3.56µs ± 4% 3.10µs ± 3% -12.96% (p=0.000 n=7+8) FloatSqrt/1000-4 9.06µs ± 3% 8.86µs ± 1% -2.20% (p=0.001 n=7+7) FloatSqrt/10000-4 109µs ± 1% 107µs ± 1% -1.56% (p=0.000 n=8+8) FloatSqrt/100000-4 2.91ms ± 0% 2.89ms ± 2% -0.68% (p=0.026 n=7+7) FloatSqrt/1000000-4 237ms ± 1% 239ms ± 1% +0.72% (p=0.021 n=8+8) name old alloc/op new alloc/op delta FloatSqrt/64-4 448B ± 0% 416B ± 0% -7.14% (p=0.000 n=8+8) FloatSqrt/128-4 752B ± 0% 720B ± 0% -4.26% (p=0.000 n=8+8) FloatSqrt/256-4 2.05kB ± 0% 1.34kB ± 0% -34.38% (p=0.000 n=8+8) FloatSqrt/1000-4 6.91kB ± 0% 5.09kB ± 0% -26.39% (p=0.000 n=8+8) FloatSqrt/10000-4 60.5kB ± 0% 45.9kB ± 0% -24.17% (p=0.000 n=8+8) FloatSqrt/100000-4 617kB ± 0% 533kB ± 0% -13.57% (p=0.000 n=8+8) FloatSqrt/1000000-4 10.3MB ± 0% 9.2MB ± 0% -10.85% (p=0.000 n=8+8) name old allocs/op new allocs/op delta FloatSqrt/64-4 9.00 ± 0% 9.00 ± 0% ~ (all equal) FloatSqrt/128-4 13.0 ± 0% 13.0 ± 0% ~ (all equal) FloatSqrt/256-4 20.0 ± 0% 15.0 ± 0% -25.00% (p=0.000 n=8+8) FloatSqrt/1000-4 31.0 ± 0% 24.0 ± 0% -22.58% (p=0.000 n=8+8) FloatSqrt/10000-4 50.0 ± 0% 40.0 ± 0% -20.00% (p=0.000 n=8+8) FloatSqrt/100000-4 76.0 ± 0% 66.0 ± 0% -13.16% (p=0.000 n=8+8) FloatSqrt/1000000-4 146 ± 0% 143 ± 0% -2.05% (p=0.000 n=8+8) Change-Id: I271c00de1ca9740e585bf2af7bcd87b18c1fa68e Reviewed-on: https://go-review.googlesource.com/73879 Run-TryBot: Alberto Donizetti <alb.donizetti@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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