Speed up integer log10.
This is achieved with a branchless bit-twiddling implementation of the case x < 100_000, and using this as building block. Benchmark on an Intel i7-8700K (Coffee Lake): name old ns/iter new ns/iter diff ns/iter diff % speedup num::int_log::u8_log10_predictable 165 169 4 2.42% x 0.98 num::int_log::u8_log10_random 438 423 -15 -3.42% x 1.04 num::int_log::u8_log10_random_small 438 423 -15 -3.42% x 1.04 num::int_log::u16_log10_predictable 633 417 -216 -34.12% x 1.52 num::int_log::u16_log10_random 908 471 -437 -48.13% x 1.93 num::int_log::u16_log10_random_small 945 471 -474 -50.16% x 2.01 num::int_log::u32_log10_predictable 1,496 1,340 -156 -10.43% x 1.12 num::int_log::u32_log10_random 1,076 873 -203 -18.87% x 1.23 num::int_log::u32_log10_random_small 1,145 874 -271 -23.67% x 1.31 num::int_log::u64_log10_predictable 4,005 3,171 -834 -20.82% x 1.26 num::int_log::u64_log10_random 1,247 1,021 -226 -18.12% x 1.22 num::int_log::u64_log10_random_small 1,265 921 -344 -27.19% x 1.37 num::int_log::u128_log10_predictable 39,667 39,579 -88 -0.22% x 1.00 num::int_log::u128_log10_random 6,456 6,696 240 3.72% x 0.96 num::int_log::u128_log10_random_small 4,108 3,903 -205 -4.99% x 1.05 Benchmark on an M1 Mac Mini: name old ns/iter new ns/iter diff ns/iter diff % speedup num::int_log::u8_log10_predictable 143 130 -13 -9.09% x 1.10 num::int_log::u8_log10_random 375 325 -50 -13.33% x 1.15 num::int_log::u8_log10_random_small 376 325 -51 -13.56% x 1.16 num::int_log::u16_log10_predictable 500 322 -178 -35.60% x 1.55 num::int_log::u16_log10_random 794 405 -389 -48.99% x 1.96 num::int_log::u16_log10_random_small 1,035 405 -630 -60.87% x 2.56 num::int_log::u32_log10_predictable 1,144 894 -250 -21.85% x 1.28 num::int_log::u32_log10_random 832 786 -46 -5.53% x 1.06 num::int_log::u32_log10_random_small 832 787 -45 -5.41% x 1.06 num::int_log::u64_log10_predictable 2,681 2,057 -624 -23.27% x 1.30 num::int_log::u64_log10_random 1,015 806 -209 -20.59% x 1.26 num::int_log::u64_log10_random_small 1,004 795 -209 -20.82% x 1.26 num::int_log::u128_log10_predictable 56,825 56,526 -299 -0.53% x 1.01 num::int_log::u128_log10_random 9,056 8,861 -195 -2.15% x 1.02 num::int_log::u128_log10_random_small 1,528 1,527 -1 -0.07% x 1.00 The 128 bit case remains ridiculously slow because llvm fails to optimize division by a constant 128-bit value to multiplications. This could be worked around but it seems preferable to fix this in llvm. From u32 up, table lookup (like suggested here https://github.com/rust-lang/rust/issues/70887#issuecomment-881099813) is still faster, but requires a hardware leading_zero to be viable, and might clog up the cache.
This commit is contained in:
Falk Hüffner
parent
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commit
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@ -1,76 +1,71 @@
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mod unchecked {
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// 0 < val <= u8::MAX
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pub const fn u8(val: u8) -> u32 {
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if val >= 100 {
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2
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} else if val >= 10 {
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1
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} else {
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0
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}
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let val = val as u32;
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// For better performance, avoid branches by assembling the solution
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// in the bits above the low 8 bits.
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// Adding c1 to val gives 10 in the top bits for val < 10, 11 for val >= 10
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let c1 = 0b11_00000000 - 10; // 758
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// Adding c2 to val gives 01 in the top bits for val < 100, 10 for val >= 100
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let c2 = 0b10_00000000 - 100; // 412
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// Value of top bits:
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// +c1 +c2 1&2
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// 0..=9 10 01 00 = 0
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// 10..=99 11 01 01 = 1
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// 100..=255 11 10 10 = 2
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((val + c1) & (val + c2)) >> 8
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}
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// 0 < val < 100_000
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const fn less_than_5(val: u32) -> u32 {
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// Similar to u8, when adding one of these constants to val,
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// we get two possible bit patterns above the low 17 bits,
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// depending on whether val is below or above the threshold.
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let c1 = 0b011_00000000000000000 - 10; // 393206
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let c2 = 0b100_00000000000000000 - 100; // 524188
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let c3 = 0b111_00000000000000000 - 1000; // 916504
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let c4 = 0b100_00000000000000000 - 10000; // 514288
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// Value of top bits:
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// +c1 +c2 1&2 +c3 +c4 3&4 ^
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// 0..=9 010 011 010 110 011 010 000 = 0
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// 10..=99 011 011 011 110 011 010 001 = 1
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// 100..=999 011 100 000 110 011 010 010 = 2
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// 1000..=9999 011 100 000 111 011 011 011 = 3
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// 10000..=99999 011 100 000 111 100 100 100 = 4
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(((val + c1) & (val + c2)) ^ ((val + c3) & (val + c4))) >> 17
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}
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// 0 < val <= u16::MAX
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pub const fn u16(val: u16) -> u32 {
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if val >= 10_000 {
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4
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} else if val >= 1000 {
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3
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} else if val >= 100 {
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2
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} else if val >= 10 {
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1
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} else {
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0
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}
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}
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// 0 < val < 100_000_000
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const fn less_than_8(mut val: u32) -> u32 {
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let mut log = 0;
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if val >= 10_000 {
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val /= 10_000;
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log += 4;
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}
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log + if val >= 1000 {
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3
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} else if val >= 100 {
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2
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} else if val >= 10 {
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1
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} else {
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0
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}
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less_than_5(val as u32)
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}
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// 0 < val <= u32::MAX
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pub const fn u32(mut val: u32) -> u32 {
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let mut log = 0;
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if val >= 100_000_000 {
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val /= 100_000_000;
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log += 8;
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if val >= 100_000 {
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val /= 100_000;
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log += 5;
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}
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log + less_than_8(val)
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}
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// 0 < val < 10_000_000_000_000_000
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const fn less_than_16(mut val: u64) -> u32 {
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let mut log = 0;
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if val >= 100_000_000 {
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val /= 100_000_000;
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log += 8;
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}
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log + less_than_8(val as u32)
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log + less_than_5(val)
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}
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// 0 < val <= u64::MAX
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pub const fn u64(mut val: u64) -> u32 {
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let mut log = 0;
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if val >= 10_000_000_000_000_000 {
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val /= 10_000_000_000_000_000;
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log += 16;
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if val >= 10_000_000_000 {
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val /= 10_000_000_000;
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log += 10;
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}
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log + less_than_16(val)
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if val >= 100_000 {
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val /= 100_000;
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log += 5;
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}
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log + less_than_5(val as u32)
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}
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// 0 < val <= u128::MAX
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@ -79,13 +74,13 @@ mod unchecked {
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if val >= 100_000_000_000_000_000_000_000_000_000_000 {
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val /= 100_000_000_000_000_000_000_000_000_000_000;
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log += 32;
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return log + less_than_8(val as u32);
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return log + u32(val as u32);
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}
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if val >= 10_000_000_000_000_000 {
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val /= 10_000_000_000_000_000;
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log += 16;
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}
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log + less_than_16(val as u64)
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log + u64(val as u64)
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}
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// 0 < val <= i8::MAX
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@ -96,6 +96,9 @@ fn checked_log10() {
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for i in 1..=u16::MAX {
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assert_eq!(i.checked_log10(), Some((i as f32).log10() as u32));
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}
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for i in 1..=100_000u32 {
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assert_eq!(i.checked_log10(), Some((i as f32).log10() as u32));
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}
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}
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macro_rules! log10_loop {
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