mirror of https://github.com/golang/go.git
328 Commits
| Author | SHA1 | Message | Date |
|---|---|---|---|
Ville Skyttä
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440f7d6404 |
all: fix a bunch of misspellings
Change-Id: I5b909df0fd048cd66c5a27fca1b06466d3bcaac7
GitHub-Last-Rev:
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Rémy Oudompheng
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7ad27481f8 |
math/big: fix out-of-bounds panic in divRecursive
The bounds in the last carry branch were wrong as there is no reason for len(u) >= n+n/2 to always hold true. We also adjust test to avoid using a remainder of 1 (in which case, the last step of the algorithm computes (qhatv+1) - qhatv which rarely produces a carry). Change-Id: I69fbab9c5e19d0db1c087fbfcd5b89352c2d26fb Reviewed-on: https://go-review.googlesource.com/c/go/+/206839 Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Robert Griesemer
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1fe33e3cb2 |
math/big: ensure correct test input
There is a (theoretical, but possible) chance that the random number values a, b used for TestDiv are 0 or 1, in which case the test would fail. This CL makes sure that a >= 1 and b >= 2 at all times. Fixes #35523. Change-Id: I6451feb94241249516a821cd0066e95a0c65b0ed Reviewed-on: https://go-review.googlesource.com/c/go/+/206818 Run-TryBot: Robert Griesemer <gri@golang.org> Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
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Rémy Oudompheng
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194ae3236d |
math/big: implement recursive algorithm for division
The current division algorithm produces one word of result at a time, using 2-word division to compute the top word and mulAddVWW to compute the remainder. The top word may need to be adjusted by 1 or 2 units. The recursive version, based on Burnikel, Ziegler, "Fast Recursive Division", uses the same principles, but in a multi-word setting, so that multiplication benefits from the Karatsuba algorithm (and possibly later improvements). benchmark old ns/op new ns/op delta BenchmarkDiv/20/10-4 38.2 38.3 +0.26% BenchmarkDiv/40/20-4 38.7 38.5 -0.52% BenchmarkDiv/100/50-4 62.5 62.6 +0.16% BenchmarkDiv/200/100-4 238 259 +8.82% BenchmarkDiv/400/200-4 311 338 +8.68% BenchmarkDiv/1000/500-4 604 649 +7.45% BenchmarkDiv/2000/1000-4 1214 1278 +5.27% BenchmarkDiv/20000/10000-4 38279 36510 -4.62% BenchmarkDiv/200000/100000-4 3022057 1359615 -55.01% BenchmarkDiv/2000000/1000000-4 310827664 54012939 -82.62% BenchmarkDiv/20000000/10000000-4 33272829421 1965401359 -94.09% BenchmarkString/10/Base10-4 158 156 -1.27% BenchmarkString/100/Base10-4 797 792 -0.63% BenchmarkString/1000/Base10-4 3677 3814 +3.73% BenchmarkString/10000/Base10-4 16633 17116 +2.90% BenchmarkString/100000/Base10-4 5779029 1793808 -68.96% BenchmarkString/1000000/Base10-4 889840820 85524031 -90.39% BenchmarkString/10000000/Base10-4 134338236860 4935657026 -96.33% Fixes #21960 Updates #30943 Change-Id: I134c6f81a47870c688ca95b6081eb9211def15a2 Reviewed-on: https://go-review.googlesource.com/c/go/+/172018 Reviewed-by: Robert Griesemer <gri@golang.org> Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
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Brian Kessler
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f5949b6067 |
math/big: allow all values for GCD
Allow the inputs a and b to be zero or negative to GCD with the following definitions. If x or y are not nil, GCD sets their value such that z = a*x + b*y. Regardless of the signs of a and b, z is always >= 0. If a == b == 0, GCD sets z = x = y = 0. If a == 0 and b != 0, GCD sets z = |b|, x = 0, y = sign(b) * 1. If a != 0 and b == 0, GCD sets z = |a|, x = sign(a) * 1, y = 0. Fixes #28878 Change-Id: Ia83fce66912a96545c95cd8df0549bfd852652f3 Reviewed-on: https://go-review.googlesource.com/c/go/+/164972 Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Rémy Oudompheng
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8f30d25168 |
math/big: use nat pool to reduce allocations in mul and sqr
This notably allows to reuse temporaries across the karatsubaSqr recursion. benchmark old ns/op new ns/op delta BenchmarkNatMul/10-4 227 228 +0.44% BenchmarkNatMul/100-4 8339 8589 +3.00% BenchmarkNatMul/1000-4 313796 312272 -0.49% BenchmarkNatMul/10000-4 11924720 11873589 -0.43% BenchmarkNatMul/100000-4 503813354 503839058 +0.01% BenchmarkNatSqr/20-4 549 513 -6.56% BenchmarkNatSqr/30-4 945 874 -7.51% BenchmarkNatSqr/50-4 1993 1832 -8.08% BenchmarkNatSqr/80-4 4096 3874 -5.42% BenchmarkNatSqr/100-4 6192 5712 -7.75% BenchmarkNatSqr/200-4 20388 19543 -4.14% BenchmarkNatSqr/300-4 38735 36715 -5.21% BenchmarkNatSqr/500-4 99562 93542 -6.05% BenchmarkNatSqr/800-4 195554 184907 -5.44% BenchmarkNatSqr/1000-4 286302 275053 -3.93% BenchmarkNatSqr/10000-4 9817057 9441641 -3.82% BenchmarkNatSqr/100000-4 390713416 379696789 -2.82% benchmark old allocs new allocs delta BenchmarkNatMul/10-4 1 1 +0.00% BenchmarkNatMul/100-4 1 1 +0.00% BenchmarkNatMul/1000-4 2 1 -50.00% BenchmarkNatMul/10000-4 2 1 -50.00% BenchmarkNatMul/100000-4 9 11 +22.22% BenchmarkNatSqr/20-4 2 1 -50.00% BenchmarkNatSqr/30-4 2 1 -50.00% BenchmarkNatSqr/50-4 2 1 -50.00% BenchmarkNatSqr/80-4 2 1 -50.00% BenchmarkNatSqr/100-4 2 1 -50.00% BenchmarkNatSqr/200-4 2 1 -50.00% BenchmarkNatSqr/300-4 4 1 -75.00% BenchmarkNatSqr/500-4 4 1 -75.00% BenchmarkNatSqr/800-4 10 1 -90.00% BenchmarkNatSqr/1000-4 10 1 -90.00% BenchmarkNatSqr/10000-4 731 1 -99.86% BenchmarkNatSqr/100000-4 19687 6 -99.97% benchmark old bytes new bytes delta BenchmarkNatMul/10-4 192 192 +0.00% BenchmarkNatMul/100-4 4864 4864 +0.00% BenchmarkNatMul/1000-4 57344 49224 -14.16% BenchmarkNatMul/10000-4 565248 498772 -11.76% BenchmarkNatMul/100000-4 5749504 7263720 +26.34% BenchmarkNatSqr/20-4 672 352 -47.62% BenchmarkNatSqr/30-4 992 512 -48.39% BenchmarkNatSqr/50-4 1792 896 -50.00% BenchmarkNatSqr/80-4 2688 1408 -47.62% BenchmarkNatSqr/100-4 3584 1792 -50.00% BenchmarkNatSqr/200-4 6656 3456 -48.08% BenchmarkNatSqr/300-4 24448 16387 -32.97% BenchmarkNatSqr/500-4 36864 24591 -33.29% BenchmarkNatSqr/800-4 69760 40981 -41.25% BenchmarkNatSqr/1000-4 86016 49180 -42.82% BenchmarkNatSqr/10000-4 2524800 487368 -80.70% BenchmarkNatSqr/100000-4 68599808 5876581 -91.43% Change-Id: I8e6e409ae1cb48be9d5aa9b5f428d6cbe487673a Reviewed-on: https://go-review.googlesource.com/c/go/+/172017 Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Robert Griesemer
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a52c0a1992 |
math/big: make Rat.Denom side-effect free
A Rat is represented via a quotient a/b where a and b are Int values. To make it possible to use an uninitialized Rat value (with a and b uninitialized and thus == 0), the implementation treats a 0 denominator as 1. Rat.Num and Rat.Denom return pointers to these values a and b. Because b may be 0, Rat.Denom used to first initialize it to 1 and thus produce an undesirable side-effect (by changing the Rat's denominator). This CL changes Denom to return a new (not shared) *Int with value 1 in the rare case where the Rat was not initialized. This eliminates the side effect and returns the correct denominator value. While this is changing behavior of the API, the impact should now be minor because together with (prior) CL https://golang.org/cl/202997, which initializes Rats ASAP, Denom is unlikely used to access the denominator of an uninitialized (and thus 0) Rat. Any operation that will somehow set a Rat value will ensure that the denominator is not 0. Fixes #33792. Updates #3521. Change-Id: I0bf15ac60513cf52162bfb62440817ba36f0c3fc Reviewed-on: https://go-review.googlesource.com/c/go/+/203059 Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> |
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Robert Griesemer
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4412181e7c |
math/big: normalize unitialized denominators ASAP
A Rat is represented via a quotient a/b where a and b are Int values. To make it possible to use an uninitialized Rat value (with a and b uninitialized and thus == 0), the implementation treats a 0 denominator as 1. For each operation we check if the denominator is 0, and then treat it as 1 (if necessary). Operations that create a new Rat result, normalize that value such that a result denominator 1 is represened as 0 again. This CL changes this behavior slightly: 0 denominators are still interpreted as 1, but whenever we (safely) can, we set an uninitialized 0 denominator to 1. This simplifies the code overall. Also: Improved some doc strings. Preparation for addressing issue #33792. Updates #33792. Change-Id: I3040587c8d0dad2e840022f96ca027d8470878a0 Reviewed-on: https://go-review.googlesource.com/c/go/+/202997 Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> |
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Robert Griesemer
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898f9db81f |
math/big: make Rat accessors safe for concurrent use
Do not modify the underlying Rat denominator when calling one of the accessors Float32, Float64; verify that we don't modify the Rat denominator when calling Inv, Sign, IsInt, Num. Fixes #34919. Reopens #33792. Change-Id: Ife6d1252373f493a597398ee51e7b5695b708df5 Reviewed-on: https://go-review.googlesource.com/c/go/+/201205 Reviewed-by: Ian Lance Taylor <iant@golang.org> |
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Brad Fitzpatrick
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07b4abd62e |
all: remove the nacl port (part 2, amd64p32 + toolchain)
This is part two if the nacl removal. Part 1 was CL 199499. This CL removes amd64p32 support, which might be useful in the future if we implement the x32 ABI. It also removes the nacl bits in the toolchain, and some remaining nacl bits. Updates #30439 Change-Id: I2475d5bb066d1b474e00e40d95b520e7c2e286e1 Reviewed-on: https://go-review.googlesource.com/c/go/+/200077 Reviewed-by: Ian Lance Taylor <iant@golang.org> |
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Robert Griesemer
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770fac4586 |
math/big: avoid MinExp exponent wrap-around in 'x' Text format
Fixes #34343. Change-Id: I74240c8f431f6596338633a86a7a5ee1fce70a65 Reviewed-on: https://go-review.googlesource.com/c/go/+/196057 Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Ian Lance Taylor <iant@golang.org> |
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Ainar Garipov
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0efbd10157 |
all: fix typos
Use the following (suboptimal) script to obtain a list of possible
typos:
#!/usr/bin/env sh
set -x
git ls-files |\
grep -e '\.\(c\|cc\|go\)$' |\
xargs -n 1\
awk\
'/\/\// { gsub(/.*\/\//, ""); print; } /\/\*/, /\*\// { gsub(/.*\/\*/, ""); gsub(/\*\/.*/, ""); }' |\
hunspell -d en_US -l |\
grep '^[[:upper:]]\{0,1\}[[:lower:]]\{1,\}$' |\
grep -v -e '^.\{1,4\}$' -e '^.\{16,\}$' |\
sort -f |\
uniq -c |\
awk '$1 == 1 { print $2; }'
Then, go through the results manually and fix the most obvious typos in
the non-vendored code.
Change-Id: I3cb5830a176850e1a0584b8a40b47bde7b260eae
Reviewed-on: https://go-review.googlesource.com/c/go/+/193848
Reviewed-by: Robert Griesemer <gri@golang.org>
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peter zhang
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d5fe73393c |
math/big: fix a duplicate "the" in a comment
Change-Id: Ib637381ab8a12aeb798576b781e1b3c458ba812d
GitHub-Last-Rev:
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Eric Lagergren
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9dfa4cb026 |
math/big: document that Rat.Denom might modify the receiver
Fixes #33792 Change-Id: I306a95883c3db2d674d3294a6feb50adc50ee5d6 Reviewed-on: https://go-review.googlesource.com/c/go/+/192017 Reviewed-by: Robert Griesemer <gri@golang.org> |
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Illya Yalovyy
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be452cea42 |
math/big: fast path for Cmp if same
math/big.Int Cmp method does not have a fast path for the case if x and y are the same. Fixes #30856 Change-Id: Ia9a5b5f72db9d73af1b13ed6ac39ecff87d10393 Reviewed-on: https://go-review.googlesource.com/c/go/+/178957 Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Russ Cox
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06b0babf31 |
all: shorten some tests
Shorten some of the longest tests that run during all.bash. Removes 7r 50u 21s from all.bash. After this change, all.bash is under 5 minutes again on my laptop. For #26473. Change-Id: Ie0460aa935808d65460408feaed210fbaa1d5d79 Reviewed-on: https://go-review.googlesource.com/c/go/+/177559 Run-TryBot: Russ Cox <rsc@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Ian Lance Taylor <iant@golang.org> |
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JT Olio
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5a2da5624a |
math/big: stack allocate scaleDenom return value
benchmark old ns/op new ns/op delta BenchmarkRatCmp-4 154 77.9 -49.42% Change-Id: I932710ad8b6905879e232168b1777927f86ba22a Reviewed-on: https://go-review.googlesource.com/c/go/+/175460 Run-TryBot: Robert Griesemer <gri@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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erifan01
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503e6ccd74 |
math/big: fix the bug in assembly implementation of shlVU on arm64
For the case where the addresses of parameter z and x of the function shlVU overlap and the address of z is greater than x, x (input value) can be polluted during the calculation when the high words of x are overlapped with the low words of z (output value). Fixes #31084 Change-Id: I9bb0266a1d7856b8faa9a9b1975d6f57dece0479 Reviewed-on: https://go-review.googlesource.com/c/go/+/169780 Run-TryBot: Cherry Zhang <cherryyz@google.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Cherry Zhang <cherryyz@google.com> |
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Brian Kessler
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689ee112df |
math/big: document Int.String
Int.String had no documentation and the documentation for Int.Text did not mention the handling of the nil pointer case. Change-Id: I9f21921e431c948545b7cabc7829e4b4e574bbe9 Reviewed-on: https://go-review.googlesource.com/c/go/+/175118 Reviewed-by: Robert Griesemer <gri@golang.org> |
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erifan01
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d17d41e58d |
math/big: optimize mulAddVWW on arm64 for better performance
Unroll the cycle 4 times to reduce load overhead. Benchmarks: name old time/op new time/op delta MulAddVWW/1-8 15.9ns ± 0% 11.9ns ± 0% -24.92% (p=0.000 n=8+8) MulAddVWW/2-8 16.1ns ± 0% 13.9ns ± 1% -13.82% (p=0.000 n=8+8) MulAddVWW/3-8 18.9ns ± 0% 17.3ns ± 0% -8.47% (p=0.000 n=8+8) MulAddVWW/4-8 21.7ns ± 0% 19.5ns ± 0% -10.14% (p=0.000 n=8+8) MulAddVWW/5-8 25.1ns ± 0% 22.5ns ± 0% -10.27% (p=0.000 n=8+8) MulAddVWW/10-8 41.6ns ± 0% 40.0ns ± 0% -3.79% (p=0.000 n=8+8) MulAddVWW/100-8 368ns ± 0% 363ns ± 0% -1.36% (p=0.000 n=8+8) MulAddVWW/1000-8 3.52µs ± 0% 3.52µs ± 0% -0.14% (p=0.000 n=8+8) MulAddVWW/10000-8 35.1µs ± 0% 35.1µs ± 0% -0.01% (p=0.000 n=7+6) MulAddVWW/100000-8 351µs ± 0% 351µs ± 0% +0.15% (p=0.038 n=8+8) Change-Id: I052a4db286ac6e4f3293289c7e9a82027da0405e Reviewed-on: https://go-review.googlesource.com/c/go/+/155780 Run-TryBot: Cherry Zhang <cherryyz@google.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Cherry Zhang <cherryyz@google.com> |
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Robert Griesemer
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f8c6f986fd |
math/big: don't clobber shared underlying array in pow5 computation
Rearranged code slightly to make lifetime of underlying array of pow5 more explicit in code. Fixes #31184. Change-Id: I063081f0e54097c499988d268a23813746592654 Reviewed-on: https://go-review.googlesource.com/c/go/+/170641 Reviewed-by: Filippo Valsorda <filippo@golang.org> |
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Neven Sajko
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7756a72b35 |
all: change the old assembly style AX:CX to CX, AX
Assembly files with "/vendor/" or "testdata" in their paths were ignored.
Change-Id: I3882ff07eb4426abb9f8ee96f82dff73c81cd61f
GitHub-Last-Rev:
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Filippo Valsorda
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ead895688d |
math/big: do not panic in Exp when y < 0 and x doesn't have an inverse
If x does not have an inverse modulo m, and a negative exponent is used, return nil just like ModInverse does now. Change-Id: I8fa72f7a851e8cf77c5fab529ede88408740626f Reviewed-on: https://go-review.googlesource.com/c/go/+/170757 Run-TryBot: Filippo Valsorda <filippo@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Neven Sajko
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964fe4b80f |
math/big: simplify shlVU_g and shrVU_g
Rewrote a few lines to be more idiomatic/less assembly-ish.
Benchmarked with `go test -bench Float -tags math_big_pure_go`:
name old time/op new time/op delta
FloatString/100-8 751ns ± 0% 746ns ± 1% -0.71% (p=0.000 n=10+10)
FloatString/1000-8 22.9µs ± 0% 22.9µs ± 0% ~ (p=0.271 n=10+10)
FloatString/10000-8 1.89ms ± 0% 1.89ms ± 0% ~ (p=0.481 n=10+10)
FloatString/100000-8 184ms ± 0% 184ms ± 0% ~ (p=0.094 n=9+9)
FloatAdd/10-8 56.4ns ± 1% 56.5ns ± 0% ~ (p=0.170 n=9+9)
FloatAdd/100-8 59.7ns ± 0% 59.3ns ± 0% -0.70% (p=0.000 n=8+9)
FloatAdd/1000-8 101ns ± 0% 99ns ± 0% -1.89% (p=0.000 n=8+8)
FloatAdd/10000-8 553ns ± 0% 536ns ± 0% -3.00% (p=0.000 n=9+10)
FloatAdd/100000-8 4.94µs ± 0% 4.74µs ± 0% -3.94% (p=0.000 n=9+10)
FloatSub/10-8 50.3ns ± 0% 50.5ns ± 0% +0.52% (p=0.000 n=8+8)
FloatSub/100-8 52.0ns ± 0% 52.2ns ± 1% +0.46% (p=0.012 n=8+10)
FloatSub/1000-8 77.9ns ± 0% 77.3ns ± 0% -0.80% (p=0.000 n=7+8)
FloatSub/10000-8 371ns ± 0% 362ns ± 0% -2.67% (p=0.000 n=10+10)
FloatSub/100000-8 3.20µs ± 0% 3.10µs ± 0% -3.16% (p=0.000 n=10+10)
ParseFloatSmallExp-8 7.84µs ± 0% 7.82µs ± 0% -0.17% (p=0.037 n=9+9)
ParseFloatLargeExp-8 29.3µs ± 1% 29.5µs ± 0% ~ (p=0.059 n=9+8)
FloatSqrt/64-8 516ns ± 0% 519ns ± 0% +0.54% (p=0.000 n=9+9)
FloatSqrt/128-8 1.07µs ± 0% 1.07µs ± 0% ~ (p=0.109 n=8+9)
FloatSqrt/256-8 1.23µs ± 0% 1.23µs ± 0% +0.50% (p=0.000 n=9+9)
FloatSqrt/1000-8 3.43µs ± 0% 3.44µs ± 0% +0.53% (p=0.000 n=9+8)
FloatSqrt/10000-8 40.9µs ± 0% 40.7µs ± 0% -0.39% (p=0.000 n=9+8)
FloatSqrt/100000-8 1.07ms ± 0% 1.07ms ± 0% -0.10% (p=0.017 n=10+9)
FloatSqrt/1000000-8 89.3ms ± 0% 89.2ms ± 0% -0.07% (p=0.015 n=9+8)
Change-Id: Ibf07c6142719d11bc7f329246957d87a9f3ba3d2
GitHub-Last-Rev:
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Robert Griesemer
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4dce6dbb1e |
math/big: temporarily disable buggy shlVU assembly for arm64
This addresses the failures we have seen in #31084. The correct fix is to find the actual bug in the assembly code. Updates #31084. Change-Id: I437780c53d0c4423d742e2e3b650b899ce845372 Reviewed-on: https://go-review.googlesource.com/c/go/+/169721 Run-TryBot: Robert Griesemer <gri@golang.org> Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
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Brian Kessler
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5ee2290420 |
math/big: implement Rat.SetUint64
Implemented via the underlying Int.SetUint64. Added tests for Rat.SetInt64 and Rat.SetUint64. Fixes #29579 Change-Id: I03faaffc93e36873b202b58ae72b139dea5c40f9 Reviewed-on: https://go-review.googlesource.com/c/go/+/160682 Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Robert Griesemer
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e4ba40030f |
math/big: accept non-decimal floats with Rat.SetString
This fixes an old oversight. Rat.SetString already permitted fractions a/b where both a and b could independently specify a base prefix. With this CL, it now also accepts non-decimal floating-point numbers. Fixes #29799. Change-Id: I9cc65666a5cebb00f0202da2e4fc5654a02e3234 Reviewed-on: https://go-review.googlesource.com/c/go/+/168237 Reviewed-by: Emmanuel Odeke <emm.odeke@gmail.com> |
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Robert Griesemer
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cfa93ba51f |
math/big: add support for underscores '_' in numbers
The primary change is in nat.scan which now accepts underscores for base 0. While at it, streamlined error handling in that function as well. Also, improved the corresponding test significantly by checking the expected result values also in case of scan errors. The second major change is in scanExponent which now accepts underscores when the new sepOk argument is set. While at it, essentially rewrote that function to match error and underscore handling of nat.scan more closely. Added a new test for scanExponent which until now was only tested indirectly. Finally, updated the documentation for several functions and added many new test cases to clients of nat.scan. A major portion of this CL is due to much better test coverage. Updates #28493. Change-Id: I7f17b361b633fbe6c798619d891bd5e0a045b5c5 Reviewed-on: https://go-review.googlesource.com/c/go/+/166157 Reviewed-by: Emmanuel Odeke <emm.odeke@gmail.com> |
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Brian Kessler
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ef891e1c83 |
math/big: implement Int.TrailingZeroBits
Implemented via the underlying nat.trailingZeroBits. Fixes #29578 Change-Id: If9876c5a74b107cbabceb7547bef4e44501f6745 Reviewed-on: https://go-review.googlesource.com/c/go/+/160681 Reviewed-by: Robert Griesemer <gri@golang.org> Run-TryBot: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
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Josh Bleecher Snyder
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4d10aba35e |
math/big: add fast path for amd64 addVW for large z
This matches the pure Go fast path added in the previous commit. I will leave other architectures to those with ready access to hardware. name old time/op new time/op delta AddVW/1-8 3.60ns ± 3% 3.59ns ± 1% ~ (p=0.147 n=91+86) AddVW/2-8 3.92ns ± 1% 3.91ns ± 2% -0.36% (p=0.000 n=86+92) AddVW/3-8 4.33ns ± 5% 4.46ns ± 5% +2.94% (p=0.000 n=96+97) AddVW/4-8 4.76ns ± 5% 4.82ns ± 5% +1.28% (p=0.000 n=95+92) AddVW/5-8 5.40ns ± 1% 5.42ns ± 0% +0.47% (p=0.000 n=76+71) AddVW/10-8 8.03ns ± 1% 7.80ns ± 5% -2.90% (p=0.000 n=73+96) AddVW/100-8 43.8ns ± 5% 17.9ns ± 1% -59.12% (p=0.000 n=94+81) AddVW/1000-8 428ns ± 4% 85ns ± 6% -80.20% (p=0.000 n=96+99) AddVW/10000-8 4.22µs ± 2% 1.80µs ± 3% -57.32% (p=0.000 n=69+92) AddVW/100000-8 44.8µs ± 8% 31.5µs ± 3% -29.76% (p=0.000 n=99+90) name old time/op new time/op delta SubVW/1-8 3.53ns ± 2% 3.63ns ± 5% +2.97% (p=0.000 n=94+93) SubVW/2-8 4.33ns ± 5% 4.01ns ± 2% -7.36% (p=0.000 n=90+85) SubVW/3-8 4.32ns ± 2% 4.32ns ± 5% ~ (p=0.084 n=87+97) SubVW/4-8 4.70ns ± 2% 4.83ns ± 6% +2.77% (p=0.000 n=85+96) SubVW/5-8 5.84ns ± 1% 5.35ns ± 1% -8.35% (p=0.000 n=87+87) SubVW/10-8 8.01ns ± 4% 7.54ns ± 4% -5.84% (p=0.000 n=98+97) SubVW/100-8 43.9ns ± 5% 17.9ns ± 1% -59.20% (p=0.000 n=98+76) SubVW/1000-8 426ns ± 2% 85ns ± 3% -80.13% (p=0.000 n=90+98) SubVW/10000-8 4.24µs ± 2% 1.81µs ± 3% -57.28% (p=0.000 n=74+91) SubVW/100000-8 44.5µs ± 4% 31.5µs ± 2% -29.33% (p=0.000 n=84+91) Change-Id: I10dd361cbaca22197c27e7734c0f50065292afbb Reviewed-on: https://go-review.googlesource.com/c/go/+/164969 Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Josh Bleecher Snyder
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fe24837c4d |
math/big: add fast path for pure Go addVW for large z
In the normal case, only a few words have to be updated when adding a word to a vector. When that happens, we can simply copy the rest of the words, which is much faster. However, the overhead of that makes it prohibitive for small vectors, so we check the size at the beginning. The implementation is a bit weird to allow addVW to continued to be inlined; see #30548. The AddVW benchmarks are surprising, but fully repeatable. The SubVW benchmarks are more or less as expected. I expect that removing the indirect function call will help both and make them a bit more normal. name old time/op new time/op delta AddVW/1-8 4.27ns ± 2% 3.81ns ± 3% -10.83% (p=0.000 n=89+90) AddVW/2-8 4.91ns ± 2% 4.34ns ± 1% -11.60% (p=0.000 n=83+90) AddVW/3-8 5.77ns ± 4% 5.76ns ± 2% ~ (p=0.365 n=91+87) AddVW/4-8 6.03ns ± 1% 6.03ns ± 1% ~ (p=0.392 n=80+76) AddVW/5-8 6.48ns ± 2% 6.63ns ± 1% +2.27% (p=0.000 n=76+74) AddVW/10-8 9.56ns ± 2% 9.56ns ± 1% -0.02% (p=0.002 n=69+76) AddVW/100-8 90.6ns ± 0% 18.1ns ± 4% -79.99% (p=0.000 n=72+94) AddVW/1000-8 865ns ± 0% 85ns ± 6% -90.14% (p=0.000 n=66+96) AddVW/10000-8 8.57µs ± 2% 1.82µs ± 3% -78.73% (p=0.000 n=99+94) AddVW/100000-8 84.4µs ± 2% 31.8µs ± 4% -62.29% (p=0.000 n=93+98) name old time/op new time/op delta SubVW/1-8 3.90ns ± 2% 4.13ns ± 4% +6.02% (p=0.000 n=92+95) SubVW/2-8 4.15ns ± 1% 5.20ns ± 1% +25.22% (p=0.000 n=83+85) SubVW/3-8 5.50ns ± 2% 6.22ns ± 6% +13.21% (p=0.000 n=91+97) SubVW/4-8 5.99ns ± 1% 6.63ns ± 1% +10.63% (p=0.000 n=79+61) SubVW/5-8 6.75ns ± 4% 6.88ns ± 2% +1.82% (p=0.000 n=98+73) SubVW/10-8 9.57ns ± 1% 9.56ns ± 1% -0.13% (p=0.000 n=77+64) SubVW/100-8 90.3ns ± 1% 18.1ns ± 2% -80.00% (p=0.000 n=75+94) SubVW/1000-8 860ns ± 4% 85ns ± 7% -90.14% (p=0.000 n=97+99) SubVW/10000-8 8.51µs ± 3% 1.77µs ± 6% -79.21% (p=0.000 n=100+97) SubVW/100000-8 84.4µs ± 3% 31.5µs ± 3% -62.66% (p=0.000 n=92+92) Change-Id: I721d7031d40f245b4a284f5bdd93e7bb85e7e937 Reviewed-on: https://go-review.googlesource.com/c/go/+/164968 Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Josh Bleecher Snyder
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4c227a091e |
math/big: remove bounds checks in pure Go implementations
These routines are quite sensitive to BCE.
This change eliminates bounds checks from loops.
It does so at the cost of a bit of safety:
malformed input will now return incorrect answers
instead of panicking.
This isn't as bad as it sounds: math/big has very good
test coverage, and the alternative implementations are in
assembly, which could do much worse things with malformed input.
If the compiler's BCE improves, so could these routines.
Notable BCE improvements for these routines would be:
* Allowing and propagating more cross-slice length hints.
Then hints like _ = y[:len(z)] would eliminate bounds checks for y[i].
* Propagating enough information so that we could do
n := len(x)
if len(z) < n {
n = len(z)
}
and then have i < n eliminate the same bounds checks as
i < len(x) && i < len(z) currently does.
* Providing some way to do BCE for unrolled loops.
Now that we have math/bits implementations,
it is possible to write things like ADC chains in
pure Go, if you can reasonably unroll loops.
Benchmarks below are for amd64, using -tags=math_big_pure_go.
name old time/op new time/op delta
AddVV/1-8 5.15ns ± 3% 4.65ns ± 4% -9.81% (p=0.000 n=93+86)
AddVV/2-8 6.40ns ± 2% 5.58ns ± 4% -12.78% (p=0.000 n=90+95)
AddVV/3-8 7.07ns ± 2% 6.66ns ± 2% -5.88% (p=0.000 n=87+83)
AddVV/4-8 7.94ns ± 5% 7.41ns ± 4% -6.65% (p=0.000 n=94+98)
AddVV/5-8 8.55ns ± 1% 8.80ns ± 0% +2.92% (p=0.000 n=87+92)
AddVV/10-8 12.7ns ± 1% 12.3ns ± 1% -3.12% (p=0.000 n=83+71)
AddVV/100-8 119ns ± 5% 117ns ± 4% -1.60% (p=0.000 n=93+90)
AddVV/1000-8 1.14µs ± 4% 1.14µs ± 5% ~ (p=0.812 n=95+91)
AddVV/10000-8 11.4µs ± 5% 11.3µs ± 5% ~ (p=0.503 n=97+96)
AddVV/100000-8 114µs ± 4% 113µs ± 5% -0.98% (p=0.002 n=97+90)
name old time/op new time/op delta
SubVV/1-8 5.23ns ± 5% 4.65ns ± 3% -11.18% (p=0.000 n=89+91)
SubVV/2-8 6.49ns ± 5% 5.58ns ± 3% -14.04% (p=0.000 n=92+94)
SubVV/3-8 7.10ns ± 3% 6.65ns ± 2% -6.28% (p=0.000 n=87+80)
SubVV/4-8 8.04ns ± 1% 7.44ns ± 5% -7.49% (p=0.000 n=83+98)
SubVV/5-8 8.55ns ± 2% 8.32ns ± 1% -2.75% (p=0.000 n=84+92)
SubVV/10-8 12.7ns ± 1% 12.3ns ± 1% -3.09% (p=0.000 n=80+75)
SubVV/100-8 119ns ± 0% 116ns ± 3% -1.83% (p=0.000 n=87+98)
SubVV/1000-8 1.13µs ± 5% 1.13µs ± 3% ~ (p=0.082 n=96+98)
SubVV/10000-8 11.2µs ± 1% 11.3µs ± 3% +0.76% (p=0.000 n=87+97)
SubVV/100000-8 112µs ± 2% 113µs ± 3% +0.55% (p=0.000 n=76+88)
name old time/op new time/op delta
AddVW/1-8 4.30ns ± 4% 3.96ns ± 6% -8.02% (p=0.000 n=89+97)
AddVW/2-8 5.15ns ± 2% 4.91ns ± 1% -4.56% (p=0.000 n=87+80)
AddVW/3-8 5.59ns ± 3% 5.75ns ± 2% +2.91% (p=0.000 n=91+88)
AddVW/4-8 6.20ns ± 1% 6.03ns ± 1% -2.71% (p=0.000 n=75+90)
AddVW/5-8 6.93ns ± 3% 6.49ns ± 2% -6.35% (p=0.000 n=100+82)
AddVW/10-8 10.0ns ± 7% 9.6ns ± 0% -4.02% (p=0.000 n=98+74)
AddVW/100-8 91.1ns ± 1% 90.6ns ± 1% -0.55% (p=0.000 n=84+80)
AddVW/1000-8 866ns ± 1% 856ns ± 4% -1.06% (p=0.000 n=69+96)
AddVW/10000-8 8.64µs ± 1% 8.53µs ± 4% -1.25% (p=0.000 n=67+99)
AddVW/100000-8 84.3µs ± 2% 85.4µs ± 4% +1.22% (p=0.000 n=89+99)
name old time/op new time/op delta
SubVW/1-8 4.28ns ± 2% 3.82ns ± 3% -10.63% (p=0.000 n=91+89)
SubVW/2-8 4.61ns ± 1% 4.48ns ± 3% -2.67% (p=0.000 n=94+96)
SubVW/3-8 5.54ns ± 1% 5.81ns ± 4% +4.87% (p=0.000 n=92+97)
SubVW/4-8 6.20ns ± 1% 6.08ns ± 2% -1.99% (p=0.000 n=71+88)
SubVW/5-8 6.91ns ± 3% 6.64ns ± 1% -3.90% (p=0.000 n=97+70)
SubVW/10-8 9.85ns ± 2% 9.62ns ± 0% -2.31% (p=0.000 n=82+62)
SubVW/100-8 91.1ns ± 1% 90.9ns ± 3% -0.14% (p=0.010 n=71+93)
SubVW/1000-8 859ns ± 3% 867ns ± 1% +0.98% (p=0.000 n=99+78)
SubVW/10000-8 8.54µs ± 5% 8.57µs ± 2% +0.38% (p=0.007 n=98+92)
SubVW/100000-8 84.5µs ± 3% 84.6µs ± 3% ~ (p=0.334 n=95+94)
name old time/op new time/op delta
AddMulVVW/1-8 5.43ns ± 3% 4.36ns ± 2% -19.67% (p=0.000 n=95+94)
AddMulVVW/2-8 6.56ns ± 4% 6.11ns ± 1% -6.90% (p=0.000 n=91+91)
AddMulVVW/3-8 8.00ns ± 1% 7.80ns ± 4% -2.52% (p=0.000 n=83+95)
AddMulVVW/4-8 9.81ns ± 2% 9.53ns ± 1% -2.86% (p=0.000 n=77+64)
AddMulVVW/5-8 11.4ns ± 3% 11.3ns ± 5% -0.89% (p=0.000 n=95+97)
AddMulVVW/10-8 18.9ns ± 5% 19.1ns ± 5% +0.89% (p=0.000 n=91+94)
AddMulVVW/100-8 165ns ± 5% 165ns ± 4% ~ (p=0.427 n=97+98)
AddMulVVW/1000-8 1.56µs ± 3% 1.56µs ± 4% ~ (p=0.167 n=98+96)
AddMulVVW/10000-8 15.7µs ± 5% 15.6µs ± 5% -0.31% (p=0.044 n=95+97)
AddMulVVW/100000-8 156µs ± 3% 157µs ± 8% ~ (p=0.373 n=72+99)
Change-Id: Ibc720785d5b95f6a797103b1363843205f4d56bf
Reviewed-on: https://go-review.googlesource.com/c/go/+/164966
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
Reviewed-by: Robert Griesemer <gri@golang.org>
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Robert Griesemer
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129c6e4496 |
math/big: support new octal prefixes 0o and 0O
This CL extends the various SetString and Parse methods for Ints, Rats, and Floats to accept the new octal prefixes. The main change is in natconv.go, all other changes are documentation and test updates. Finally, this CL also fixes TestRatSetString which silently dropped certain failures. Updates #12711. Change-Id: I5ee5879e25013ba1e6eda93ff280915f25ab5d55 Reviewed-on: https://go-review.googlesource.com/c/go/+/165898 Reviewed-by: Emmanuel Odeke <emm.odeke@gmail.com> |
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Josh Bleecher Snyder
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d5edbcac98 |
math/big: rewrite pure Go implementations to use math/bits
While we're here, delete addWW_g and subWW_g, per the TODO. They are now obsolete. Benchmarks on amd64 with -tags=math_big_pure_go. name old time/op new time/op delta AddVV/1-8 5.24ns ± 2% 5.12ns ± 1% -2.11% (p=0.000 n=82+87) AddVV/2-8 6.44ns ± 1% 6.33ns ± 2% -1.82% (p=0.000 n=77+82) AddVV/3-8 7.89ns ± 8% 6.97ns ± 4% -11.71% (p=0.000 n=100+96) AddVV/4-8 8.60ns ± 0% 7.72ns ± 4% -10.24% (p=0.000 n=90+96) AddVV/5-8 10.3ns ± 4% 8.5ns ± 1% -17.02% (p=0.000 n=96+91) AddVV/10-8 16.2ns ± 5% 12.8ns ± 1% -21.11% (p=0.000 n=97+86) AddVV/100-8 148ns ± 1% 117ns ± 5% -21.07% (p=0.000 n=66+98) AddVV/1000-8 1.41µs ± 4% 1.13µs ± 3% -19.90% (p=0.000 n=97+97) AddVV/10000-8 14.2µs ± 5% 11.2µs ± 1% -20.82% (p=0.000 n=99+84) AddVV/100000-8 142µs ± 4% 113µs ± 4% -20.40% (p=0.000 n=91+92) SubVV/1-8 5.29ns ± 1% 5.11ns ± 0% -3.30% (p=0.000 n=87+88) SubVV/2-8 6.36ns ± 4% 6.33ns ± 2% -0.56% (p=0.002 n=98+73) SubVV/3-8 7.58ns ± 5% 6.98ns ± 4% -8.01% (p=0.000 n=97+91) SubVV/4-8 8.61ns ± 3% 7.98ns ± 2% -7.31% (p=0.000 n=95+83) SubVV/5-8 10.6ns ± 2% 8.5ns ± 1% -19.56% (p=0.000 n=79+89) SubVV/10-8 16.3ns ± 4% 12.7ns ± 1% -21.97% (p=0.000 n=98+82) SubVV/100-8 124ns ± 1% 118ns ± 1% -4.83% (p=0.000 n=85+81) SubVV/1000-8 1.14µs ± 5% 1.12µs ± 2% -1.17% (p=0.000 n=97+81) SubVV/10000-8 11.6µs ±10% 11.2µs ± 1% -3.39% (p=0.000 n=100+84) SubVV/100000-8 114µs ± 6% 114µs ± 5% ~ (p=0.396 n=83+94) AddVW/1-8 4.04ns ± 4% 4.34ns ± 4% +7.57% (p=0.000 n=96+98) AddVW/2-8 4.34ns ± 5% 4.40ns ± 5% +1.40% (p=0.000 n=99+98) AddVW/3-8 5.43ns ± 0% 5.54ns ± 2% +1.97% (p=0.000 n=85+94) AddVW/4-8 6.23ns ± 1% 6.18ns ± 2% -0.66% (p=0.000 n=77+78) AddVW/5-8 6.78ns ± 2% 6.90ns ± 4% +1.77% (p=0.000 n=80+99) AddVW/10-8 10.5ns ± 4% 9.9ns ± 1% -5.77% (p=0.000 n=97+69) AddVW/100-8 114ns ± 3% 91ns ± 0% -20.38% (p=0.000 n=98+77) AddVW/1000-8 1.12µs ± 1% 0.87µs ± 1% -22.80% (p=0.000 n=82+68) AddVW/10000-8 11.2µs ± 2% 8.5µs ± 5% -23.85% (p=0.000 n=85+100) AddVW/100000-8 112µs ± 2% 85µs ± 5% -24.22% (p=0.000 n=71+96) SubVW/1-8 4.09ns ± 2% 4.18ns ± 4% +2.32% (p=0.000 n=78+96) SubVW/2-8 4.59ns ± 5% 4.52ns ± 7% -1.54% (p=0.000 n=98+94) SubVW/3-8 5.41ns ±10% 5.55ns ± 1% +2.48% (p=0.000 n=100+89) SubVW/4-8 6.51ns ± 2% 6.19ns ± 0% -4.85% (p=0.000 n=97+81) SubVW/5-8 7.25ns ± 3% 6.90ns ± 4% -4.93% (p=0.000 n=97+96) SubVW/10-8 10.6ns ± 4% 9.8ns ± 2% -7.32% (p=0.000 n=95+96) SubVW/100-8 90.4ns ± 0% 90.8ns ± 0% +0.43% (p=0.000 n=83+78) SubVW/1000-8 853ns ± 4% 857ns ± 2% +0.42% (p=0.000 n=100+98) SubVW/10000-8 8.52µs ± 4% 8.53µs ± 2% ~ (p=0.061 n=99+97) SubVW/100000-8 84.8µs ± 5% 84.2µs ± 2% -0.78% (p=0.000 n=99+93) AddMulVVW/1-8 8.73ns ± 0% 5.33ns ± 3% -38.91% (p=0.000 n=91+96) AddMulVVW/2-8 14.8ns ± 3% 6.5ns ± 2% -56.33% (p=0.000 n=100+79) AddMulVVW/3-8 18.6ns ± 2% 7.8ns ± 5% -57.84% (p=0.000 n=89+96) AddMulVVW/4-8 24.0ns ± 2% 9.8ns ± 0% -59.09% (p=0.000 n=95+67) AddMulVVW/5-8 29.0ns ± 2% 11.5ns ± 5% -60.44% (p=0.000 n=90+97) AddMulVVW/10-8 54.1ns ± 0% 18.8ns ± 1% -65.37% (p=0.000 n=82+84) AddMulVVW/100-8 508ns ± 2% 165ns ± 4% -67.62% (p=0.000 n=72+98) AddMulVVW/1000-8 4.96µs ± 3% 1.55µs ± 1% -68.86% (p=0.000 n=99+91) AddMulVVW/10000-8 50.0µs ± 4% 15.5µs ± 4% -68.95% (p=0.000 n=97+97) AddMulVVW/100000-8 491µs ± 1% 156µs ± 8% -68.22% (p=0.000 n=79+95) Change-Id: I4c6ae0b4065f371aea8103f6a85d9e9274bf01d0 Reviewed-on: https://go-review.googlesource.com/c/go/+/164965 Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Josh Bleecher Snyder
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87cc56718a |
math/big: optimize shlVU_g and shrVU_g
Special case shifts by zero. Provide hints to the compiler that shifts are bounded. There are no existing benchmarks for shifts, but the Float implementation uses shifts, so we can use those. Benchmarks on amd64 with -tags=math_big_pure_go. name old time/op new time/op delta FloatString/100-8 869ns ± 3% 872ns ± 4% +0.40% (p=0.001 n=94+83) FloatString/1000-8 26.5µs ± 1% 26.4µs ± 1% -0.46% (p=0.000 n=87+96) FloatString/10000-8 2.18ms ± 2% 2.18ms ± 2% ~ (p=0.687 n=90+89) FloatString/100000-8 200ms ± 7% 197ms ± 5% -1.47% (p=0.000 n=100+90) FloatAdd/10-8 65.9ns ± 4% 64.0ns ± 4% -2.94% (p=0.000 n=92+93) FloatAdd/100-8 71.3ns ± 4% 67.4ns ± 4% -5.51% (p=0.000 n=96+93) FloatAdd/1000-8 128ns ± 1% 121ns ± 0% -5.69% (p=0.000 n=91+80) FloatAdd/10000-8 718ns ± 4% 626ns ± 4% -12.83% (p=0.000 n=99+99) FloatAdd/100000-8 6.43µs ± 3% 5.50µs ± 1% -14.50% (p=0.000 n=98+83) FloatSub/10-8 57.7ns ± 2% 57.0ns ± 4% -1.20% (p=0.000 n=89+96) FloatSub/100-8 59.9ns ± 3% 58.7ns ± 4% -2.10% (p=0.000 n=100+98) FloatSub/1000-8 94.5ns ± 1% 88.6ns ± 0% -6.16% (p=0.000 n=74+70) FloatSub/10000-8 456ns ± 1% 416ns ± 5% -8.83% (p=0.000 n=87+95) FloatSub/100000-8 4.00µs ± 1% 3.57µs ± 1% -10.87% (p=0.000 n=68+85) FloatSqrt/64-8 585ns ± 1% 579ns ± 1% -0.99% (p=0.000 n=92+90) FloatSqrt/128-8 1.26µs ± 1% 1.23µs ± 2% -2.42% (p=0.000 n=91+81) FloatSqrt/256-8 1.45µs ± 3% 1.40µs ± 1% -3.61% (p=0.000 n=96+90) FloatSqrt/1000-8 4.03µs ± 1% 3.91µs ± 1% -3.05% (p=0.000 n=90+93) FloatSqrt/10000-8 48.0µs ± 0% 47.3µs ± 1% -1.55% (p=0.000 n=90+90) FloatSqrt/100000-8 1.23ms ± 3% 1.22ms ± 4% -1.00% (p=0.000 n=99+99) FloatSqrt/1000000-8 96.7ms ± 4% 98.0ms ±10% ~ (p=0.322 n=89+99) Change-Id: I0f941c05b7c324256d7f0674559b6ba906e92ba8 Reviewed-on: https://go-review.googlesource.com/c/go/+/164967 Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Juraj Sukop
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1d992f2e36 |
math/big: better initial guess for nat.sqrt
The proposed change introduces a better initial guess which is closer to the final value and therefore converges in fewer steps. Consider for example sqrt(8): previously the guess was 8, whereas now it is 4 (and the result is 2). All this change does is it computes the division by two more accurately while it keeps the guess ≥ √x.
Change-Id: I917248d734a7b0488d14a647a063f674e56c4e30
GitHub-Last-Rev:
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Brian Kessler
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a73abca37b |
math/big: handle alias of cofactor inputs in GCD
If the variables passed in to the cofactor arguments of GCD (x, y) aliased the input arguments (a, b), the previous implementation would result in incorrect results for y. This change reorganizes the calculation so that the only case that need to be handled is when y aliases b, which can be handled with a simple check. Tests were added for all of the alias cases for input arguments and and and irrelevant test case for a previous binary GCD calculation was dropped. Fixes #30217 Change-Id: Ibe6137f09b3e1ae3c29e3c97aba85b67f33dc169 Reviewed-on: https://go-review.googlesource.com/c/162517 Run-TryBot: Robert Griesemer <gri@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
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Russ Cox
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d6311ff1e4 |
math/big: add %#b and %O integer formats
Matching fmt, %#b now prints an 0b prefix, and %O prints octal with an 0o prefix. See golang.org/design/19308-number-literals for background. For #19308. For #12711. Change-Id: I139c5a9a1dfae15415621601edfa13c6a5f19cfc Reviewed-on: https://go-review.googlesource.com/c/160250 Reviewed-by: Rob Pike <r@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Russ Cox
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675503c507 |
math/big: add %x float format
big.Float already had %p for printing hex format, but that format normalizes differently from fmt's %x and ignores precision entirely. This CL adds %x to big.Float, matching fmt's behavior: the verb is spelled 'x' not 'p', the mantissa is normalized to [1, 2), and precision is respected. See golang.org/design/19308-number-literals for background. For #29008. Change-Id: I9c1b9612107094856797e5b0b584c556c1914895 Reviewed-on: https://go-review.googlesource.com/c/160249 Reviewed-by: Robert Griesemer <gri@golang.org> |
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Russ Cox
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e2d87f2ca5 |
strconv: format hex floats
This CL updates FormatFloat to format standard hexadecimal floating-point constants, using the 'x' and 'X' verbs. See golang.org/design/19308-number-literals for background. For #29008. Change-Id: I540b8f71d492cfdb7c58af533d357a564591f28b Reviewed-on: https://go-review.googlesource.com/c/160242 Run-TryBot: Russ Cox <rsc@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Robert Griesemer <gri@golang.org> |
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Robert Griesemer
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7bc2aa670f |
math/big: permit upper-case 'P' binary exponent (not just 'p')
The current implementation accepted binary exponents but restricted them to 'p'. This change permits both 'p' and 'P'. R=Go1.13 Updates #29008. Change-Id: I7a89ccb86af4438f17b0422be7cb630ffcf43272 Reviewed-on: https://go-review.googlesource.com/c/159297 Reviewed-by: Russ Cox <rsc@golang.org> Reviewed-by: Emmanuel Odeke <emm.odeke@gmail.com> |
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Robert Griesemer
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33caf3be83 |
math/big: document that Rat.SetString accepts _decimal_ float representations
Updates #29799. Change-Id: I267c2c3ba3964e96903954affc248d0c52c4916c Reviewed-on: https://go-review.googlesource.com/c/158397 Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> |
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Will Beason
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bfaf11c158 |
math/big: fix incorrect comment variable reference
Fix comment as w&1 is the parity of 'x', not of 'n'.
Change-Id: Ia0e448f7e5896412ff9b164459ce15561ab624cc
GitHub-Last-Rev:
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Josh Bleecher Snyder
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bfc54bb6f3 |
math/big: allocate less for single-Word nats
For many uses of math/big, most numbers are small in practice. Prior to this change, big.NewInt allocated a minimum of five Words: one to hold the value, and four as extra capacity. In most cases, this extra capacity is waste. Worse, allocating a single Word uses a fast malloc path for tiny allocs; allocating five Words is more expensive in CPU as well as memory. This change is a simple fix: Treat a request for one Word at its word. I experimented with more complicated fixes and did not find anything that outperformed this easy fix. On some real world programs, this is a clear win. The compiler: name old alloc/op new alloc/op delta Template 37.1MB ± 0% 37.0MB ± 0% -0.23% (p=0.008 n=5+5) Unicode 29.2MB ± 0% 28.5MB ± 0% -2.48% (p=0.008 n=5+5) GoTypes 133MB ± 0% 133MB ± 0% -0.05% (p=0.008 n=5+5) Compiler 628MB ± 0% 628MB ± 0% -0.06% (p=0.008 n=5+5) SSA 2.04GB ± 0% 2.03GB ± 0% -0.14% (p=0.008 n=5+5) Flate 24.7MB ± 0% 24.6MB ± 0% -0.23% (p=0.008 n=5+5) GoParser 29.6MB ± 0% 29.6MB ± 0% -0.07% (p=0.008 n=5+5) Reflect 82.3MB ± 0% 82.2MB ± 0% -0.05% (p=0.008 n=5+5) Tar 36.2MB ± 0% 36.2MB ± 0% -0.12% (p=0.008 n=5+5) XML 49.5MB ± 0% 49.4MB ± 0% -0.23% (p=0.008 n=5+5) [Geo mean] 85.1MB 84.8MB -0.37% name old allocs/op new allocs/op delta Template 364k ± 0% 364k ± 0% ~ (p=0.476 n=5+5) Unicode 341k ± 0% 341k ± 0% ~ (p=0.690 n=5+5) GoTypes 1.37M ± 0% 1.37M ± 0% ~ (p=0.444 n=5+5) Compiler 5.50M ± 0% 5.50M ± 0% +0.02% (p=0.008 n=5+5) SSA 16.0M ± 0% 16.0M ± 0% +0.01% (p=0.008 n=5+5) Flate 238k ± 0% 238k ± 0% ~ (p=0.222 n=5+5) GoParser 305k ± 0% 305k ± 0% ~ (p=0.841 n=5+5) Reflect 976k ± 0% 976k ± 0% ~ (p=0.222 n=5+5) Tar 354k ± 0% 354k ± 0% ~ (p=0.103 n=5+5) XML 450k ± 0% 450k ± 0% ~ (p=0.151 n=5+5) [Geo mean] 837k 837k +0.01% go.skylark.net (at ea6d2813de75ded8d157b9540bc3d3ad0b688623): name old alloc/op new alloc/op delta Hashtable-8 456kB ± 0% 299kB ± 0% -34.33% (p=0.000 n=9+9) /bench_builtin_method-8 220kB ± 0% 190kB ± 0% -13.55% (p=0.000 n=9+10) name old allocs/op new allocs/op delta Hashtable-8 7.84k ± 0% 7.84k ± 0% ~ (all equal) /bench_builtin_method-8 7.49k ± 0% 7.49k ± 0% ~ (all equal) The math/big benchmarks are messy, which is predictable, since they naturally exercise the bigger-than-one-word code more. Also worth noting is that many of the benchmarks have very high variance. I've omitted the opVV and opVW benchmarks, as they are unrelated. name old time/op new time/op delta DecimalConversion-8 92.5µs ± 1% 90.6µs ± 0% -2.12% (p=0.000 n=17+19) FloatString/100-8 867ns ± 0% 871ns ± 0% +0.50% (p=0.000 n=18+18) FloatString/1000-8 26.4µs ± 1% 26.5µs ± 1% ~ (p=0.396 n=20+19) FloatString/10000-8 2.15ms ± 2% 2.16ms ± 2% ~ (p=0.089 n=19+20) FloatString/100000-8 209ms ± 1% 209ms ± 1% ~ (p=0.583 n=19+19) FloatAdd/10-8 63.5ns ± 2% 64.1ns ± 6% ~ (p=0.389 n=19+19) FloatAdd/100-8 66.0ns ± 2% 65.8ns ± 2% ~ (p=0.825 n=20+20) FloatAdd/1000-8 93.9ns ± 1% 94.3ns ± 1% ~ (p=0.273 n=19+20) FloatAdd/10000-8 347ns ± 2% 342ns ± 1% -1.50% (p=0.000 n=18+18) FloatAdd/100000-8 2.78µs ± 1% 2.78µs ± 2% ~ (p=0.961 n=20+19) FloatSub/10-8 56.9ns ± 2% 57.8ns ± 3% +1.59% (p=0.001 n=19+19) FloatSub/100-8 58.2ns ± 2% 58.9ns ± 2% +1.25% (p=0.004 n=20+20) FloatSub/1000-8 74.9ns ± 1% 74.4ns ± 1% -0.76% (p=0.000 n=19+20) FloatSub/10000-8 223ns ± 1% 220ns ± 2% -1.29% (p=0.000 n=16+20) FloatSub/100000-8 1.66µs ± 1% 1.66µs ± 2% ~ (p=0.147 n=20+20) ParseFloatSmallExp-8 8.38µs ± 0% 8.59µs ± 0% +2.48% (p=0.000 n=19+19) ParseFloatLargeExp-8 31.1µs ± 0% 32.0µs ± 0% +3.04% (p=0.000 n=16+17) GCD10x10/WithoutXY-8 115ns ± 1% 99ns ± 3% -14.07% (p=0.000 n=20+20) GCD10x10/WithXY-8 322ns ± 0% 312ns ± 0% -3.11% (p=0.000 n=18+13) GCD10x100/WithoutXY-8 233ns ± 1% 219ns ± 1% -5.73% (p=0.000 n=19+17) GCD10x100/WithXY-8 709ns ± 0% 759ns ± 0% +7.04% (p=0.000 n=19+19) GCD10x1000/WithoutXY-8 653ns ± 1% 642ns ± 1% -1.69% (p=0.000 n=17+20) GCD10x1000/WithXY-8 1.35µs ± 0% 1.35µs ± 1% ~ (p=0.255 n=20+16) GCD10x10000/WithoutXY-8 4.57µs ± 1% 4.61µs ± 1% +0.95% (p=0.000 n=18+17) GCD10x10000/WithXY-8 6.82µs ± 0% 6.84µs ± 0% +0.27% (p=0.000 n=16+17) GCD10x100000/WithoutXY-8 43.9µs ± 1% 44.0µs ± 1% +0.28% (p=0.000 n=18+17) GCD10x100000/WithXY-8 60.6µs ± 0% 60.6µs ± 0% ~ (p=0.907 n=18+18) GCD100x100/WithoutXY-8 1.13µs ± 0% 1.21µs ± 0% +6.39% (p=0.000 n=19+19) GCD100x100/WithXY-8 1.82µs ± 0% 1.92µs ± 0% +5.24% (p=0.000 n=19+17) GCD100x1000/WithoutXY-8 2.00µs ± 0% 2.03µs ± 1% +1.61% (p=0.000 n=18+16) GCD100x1000/WithXY-8 3.22µs ± 0% 3.20µs ± 1% -0.83% (p=0.000 n=19+19) GCD100x10000/WithoutXY-8 9.28µs ± 1% 9.17µs ± 1% -1.25% (p=0.000 n=18+19) GCD100x10000/WithXY-8 13.5µs ± 0% 13.3µs ± 0% -1.12% (p=0.000 n=18+19) GCD100x100000/WithoutXY-8 80.4µs ± 0% 78.6µs ± 0% -2.25% (p=0.000 n=19+19) GCD100x100000/WithXY-8 114µs ± 0% 112µs ± 0% -1.46% (p=0.000 n=19+17) GCD1000x1000/WithoutXY-8 12.9µs ± 1% 12.9µs ± 2% -0.50% (p=0.014 n=20+19) GCD1000x1000/WithXY-8 19.6µs ± 1% 19.6µs ± 2% -0.28% (p=0.040 n=17+18) GCD1000x10000/WithoutXY-8 22.4µs ± 0% 22.4µs ± 2% ~ (p=0.220 n=19+19) GCD1000x10000/WithXY-8 57.0µs ± 0% 56.5µs ± 0% -0.87% (p=0.000 n=20+20) GCD1000x100000/WithoutXY-8 116µs ± 0% 115µs ± 0% -0.49% (p=0.000 n=18+19) GCD1000x100000/WithXY-8 410µs ± 0% 411µs ± 0% ~ (p=0.052 n=19+19) GCD10000x10000/WithoutXY-8 247µs ± 1% 244µs ± 1% -0.92% (p=0.000 n=19+19) GCD10000x10000/WithXY-8 476µs ± 1% 473µs ± 1% -0.48% (p=0.009 n=19+19) GCD10000x100000/WithoutXY-8 573µs ± 1% 571µs ± 1% -0.45% (p=0.012 n=20+20) GCD10000x100000/WithXY-8 3.35ms ± 1% 3.35ms ± 1% ~ (p=0.444 n=20+19) GCD100000x100000/WithoutXY-8 12.0ms ± 2% 11.9ms ± 2% ~ (p=0.276 n=18+20) GCD100000x100000/WithXY-8 27.3ms ± 1% 27.3ms ± 1% ~ (p=0.792 n=20+19) Hilbert-8 672µs ± 0% 611µs ± 0% -9.02% (p=0.000 n=19+19) Binomial-8 1.40µs ± 0% 1.18µs ± 0% -15.69% (p=0.000 n=16+14) QuoRem-8 2.20µs ± 1% 2.17µs ± 1% -1.13% (p=0.000 n=19+19) Exp-8 4.10ms ± 1% 4.11ms ± 1% ~ (p=0.296 n=20+19) Exp2-8 4.11ms ± 1% 4.12ms ± 1% ~ (p=0.429 n=20+20) Bitset-8 8.67ns ± 6% 8.74ns ± 4% ~ (p=0.139 n=19+17) BitsetNeg-8 43.6ns ± 1% 43.8ns ± 2% +0.61% (p=0.036 n=20+20) BitsetOrig-8 77.5ns ± 1% 68.4ns ± 1% -11.77% (p=0.000 n=19+20) BitsetNegOrig-8 145ns ± 1% 141ns ± 1% -2.87% (p=0.000 n=19+20) ModSqrt225_Tonelli-8 324µs ± 1% 324µs ± 1% ~ (p=0.409 n=18+20) ModSqrt225_3Mod4-8 98.9µs ± 1% 99.1µs ± 1% ~ (p=0.298 n=19+18) ModSqrt231_Tonelli-8 337µs ± 1% 337µs ± 1% ~ (p=0.718 n=20+18) ModSqrt231_5Mod8-8 115µs ± 1% 114µs ± 1% -0.22% (p=0.050 n=20+20) ModInverse-8 895ns ± 0% 869ns ± 1% -2.83% (p=0.000 n=17+17) Sqrt-8 28.1µs ± 1% 28.1µs ± 0% -0.28% (p=0.000 n=16+20) IntSqr/1-8 10.8ns ± 3% 10.5ns ± 3% -2.51% (p=0.000 n=19+17) IntSqr/2-8 30.5ns ± 2% 30.3ns ± 4% -0.71% (p=0.035 n=18+18) IntSqr/3-8 40.1ns ± 1% 40.1ns ± 1% ~ (p=0.710 n=20+17) IntSqr/5-8 65.3ns ± 1% 65.4ns ± 2% ~ (p=0.744 n=19+19) IntSqr/8-8 101ns ± 1% 102ns ± 0% ~ (p=0.234 n=19+20) IntSqr/10-8 138ns ± 0% 138ns ± 2% ~ (p=0.827 n=18+18) IntSqr/20-8 378ns ± 1% 378ns ± 1% ~ (p=0.479 n=18+18) IntSqr/30-8 637ns ± 0% 638ns ± 1% ~ (p=0.051 n=18+20) IntSqr/50-8 1.34µs ± 2% 1.34µs ± 1% ~ (p=0.970 n=18+19) IntSqr/80-8 2.78µs ± 0% 2.78µs ± 1% -0.18% (p=0.006 n=19+17) IntSqr/100-8 3.98µs ± 0% 3.98µs ± 0% ~ (p=0.057 n=17+19) IntSqr/200-8 13.5µs ± 0% 13.5µs ± 1% -0.33% (p=0.000 n=19+17) IntSqr/300-8 25.3µs ± 1% 25.3µs ± 1% ~ (p=0.361 n=19+20) IntSqr/500-8 62.9µs ± 0% 62.9µs ± 1% ~ (p=0.899 n=17+17) IntSqr/800-8 128µs ± 1% 127µs ± 1% -0.32% (p=0.016 n=18+20) IntSqr/1000-8 192µs ± 0% 192µs ± 1% ~ (p=0.916 n=17+18) Div/20/10-8 34.9ns ± 2% 35.6ns ± 1% +2.01% (p=0.000 n=20+20) Div/200/100-8 218ns ± 1% 215ns ± 2% -1.43% (p=0.000 n=18+18) Div/2000/1000-8 1.16µs ± 1% 1.15µs ± 1% -1.04% (p=0.000 n=19+20) Div/20000/10000-8 35.7µs ± 1% 35.4µs ± 1% -0.69% (p=0.000 n=19+18) Div/200000/100000-8 2.89ms ± 1% 2.88ms ± 1% -0.62% (p=0.007 n=19+20) Mul-8 9.28ms ± 1% 9.27ms ± 1% ~ (p=0.563 n=18+18) ZeroShifts/Shl-8 712ns ± 6% 716ns ± 7% ~ (p=0.597 n=20+20) ZeroShifts/ShlSame-8 4.00ns ± 1% 4.06ns ± 5% ~ (p=0.162 n=18+20) ZeroShifts/Shr-8 714ns ±10% 1285ns ±156% ~ (p=0.250 n=20+20) ZeroShifts/ShrSame-8 4.00ns ± 1% 4.09ns ±10% +2.34% (p=0.048 n=16+19) Exp3Power/0x10-8 154ns ± 0% 159ns ±13% ~ (p=0.197 n=14+20) Exp3Power/0x40-8 171ns ± 1% 175ns ± 8% ~ (p=0.058 n=16+19) Exp3Power/0x100-8 287ns ± 0% 316ns ± 4% +10.03% (p=0.000 n=17+19) Exp3Power/0x400-8 698ns ± 1% 801ns ± 6% +14.75% (p=0.000 n=19+20) Exp3Power/0x1000-8 2.87µs ± 0% 3.65µs ± 6% +27.24% (p=0.000 n=18+18) Exp3Power/0x4000-8 21.9µs ± 1% 28.7µs ± 8% +31.09% (p=0.000 n=18+20) Exp3Power/0x10000-8 204µs ± 0% 267µs ± 9% +30.81% (p=0.000 n=20+20) Exp3Power/0x40000-8 1.86ms ± 0% 2.26ms ± 5% +21.68% (p=0.000 n=18+19) Exp3Power/0x100000-8 17.5ms ± 1% 20.7ms ± 7% +18.39% (p=0.000 n=19+20) Exp3Power/0x400000-8 156ms ± 0% 172ms ± 6% +10.54% (p=0.000 n=19+20) Fibo-8 26.9ms ± 1% 27.5ms ± 3% +2.32% (p=0.000 n=19+19) NatSqr/1-8 31.0ns ± 4% 39.5ns ±29% +27.25% (p=0.000 n=20+19) NatSqr/2-8 54.1ns ± 1% 69.0ns ±28% +27.52% (p=0.000 n=20+20) NatSqr/3-8 66.6ns ± 1% 83.0ns ±25% +24.59% (p=0.000 n=20+20) NatSqr/5-8 97.1ns ± 1% 119.9ns ±12% +23.50% (p=0.000 n=16+20) NatSqr/8-8 138ns ± 1% 171ns ± 9% +24.20% (p=0.000 n=19+20) NatSqr/10-8 182ns ± 0% 225ns ± 9% +23.50% (p=0.000 n=16+20) NatSqr/20-8 447ns ± 1% 624ns ± 6% +39.64% (p=0.000 n=19+19) NatSqr/30-8 736ns ± 2% 986ns ± 9% +33.94% (p=0.000 n=19+20) NatSqr/50-8 1.51µs ± 2% 1.97µs ± 9% +30.42% (p=0.000 n=20+20) NatSqr/80-8 3.03µs ± 1% 3.67µs ± 7% +21.08% (p=0.000 n=20+20) NatSqr/100-8 4.31µs ± 1% 5.20µs ± 7% +20.52% (p=0.000 n=19+20) NatSqr/200-8 14.2µs ± 0% 16.3µs ± 4% +14.92% (p=0.000 n=19+20) NatSqr/300-8 27.8µs ± 1% 33.2µs ± 7% +19.28% (p=0.000 n=20+18) NatSqr/500-8 66.6µs ± 1% 74.5µs ± 3% +11.87% (p=0.000 n=18+18) NatSqr/800-8 135µs ± 1% 165µs ± 7% +22.33% (p=0.000 n=20+20) NatSqr/1000-8 200µs ± 0% 228µs ± 3% +14.39% (p=0.000 n=19+20) NatSetBytes/8-8 8.87ns ± 4% 8.77ns ± 2% -1.17% (p=0.020 n=20+16) NatSetBytes/24-8 38.6ns ± 3% 49.5ns ±29% +28.32% (p=0.000 n=18+19) NatSetBytes/128-8 75.2ns ± 1% 120.7ns ±29% +60.60% (p=0.000 n=17+20) NatSetBytes/7-8 16.2ns ± 2% 16.5ns ± 2% +1.76% (p=0.000 n=20+20) NatSetBytes/23-8 46.5ns ± 1% 60.2ns ±24% +29.59% (p=0.000 n=20+20) NatSetBytes/127-8 83.1ns ± 1% 118.2ns ±20% +42.33% (p=0.000 n=18+20) ScanPi-8 89.1µs ± 1% 117.4µs ±12% +31.75% (p=0.000 n=18+20) StringPiParallel-8 35.1µs ± 9% 40.2µs ±12% +14.53% (p=0.000 n=20+20) Scan/10/Base2-8 410ns ±14% 429ns ±10% +4.47% (p=0.018 n=19+20) Scan/100/Base2-8 3.05µs ±20% 2.97µs ±14% ~ (p=0.449 n=20+20) Scan/1000/Base2-8 29.3µs ± 8% 30.1µs ±23% ~ (p=0.355 n=20+20) Scan/10000/Base2-8 402µs ±13% 395µs ±14% ~ (p=0.355 n=20+20) Scan/100000/Base2-8 11.8ms ±10% 11.6ms ± 1% ~ (p=0.245 n=17+18) Scan/10/Base8-8 194ns ± 6% 196ns ±12% ~ (p=0.829 n=20+19) Scan/100/Base8-8 1.11µs ±15% 1.11µs ±12% ~ (p=0.743 n=20+20) Scan/1000/Base8-8 11.7µs ±10% 11.7µs ±12% ~ (p=0.904 n=20+20) Scan/10000/Base8-8 209µs ± 7% 210µs ± 8% ~ (p=0.478 n=20+20) Scan/100000/Base8-8 10.6ms ± 7% 10.4ms ± 6% ~ (p=0.112 n=20+18) Scan/10/Base10-8 182ns ±12% 188ns ±11% +3.52% (p=0.044 n=20+20) Scan/100/Base10-8 1.01µs ± 8% 1.00µs ±13% ~ (p=0.588 n=20+20) Scan/1000/Base10-8 10.7µs ±20% 10.6µs ±14% ~ (p=0.560 n=20+20) Scan/10000/Base10-8 195µs ±10% 194µs ± 9% ~ (p=0.883 n=20+20) Scan/100000/Base10-8 10.6ms ± 2% 10.6ms ± 2% ~ (p=0.495 n=20+20) Scan/10/Base16-8 166ns ±10% 174ns ±17% ~ (p=0.072 n=20+20) Scan/100/Base16-8 836ns ±10% 826ns ±12% ~ (p=0.562 n=20+17) Scan/1000/Base16-8 8.96µs ±13% 8.65µs ± 9% ~ (p=0.203 n=20+18) Scan/10000/Base16-8 198µs ± 3% 198µs ± 5% ~ (p=0.718 n=20+20) Scan/100000/Base16-8 11.1ms ± 3% 11.0ms ± 4% ~ (p=0.512 n=20+20) String/10/Base2-8 88.1ns ± 7% 94.1ns ±11% +6.80% (p=0.000 n=19+20) String/100/Base2-8 577ns ± 4% 598ns ± 5% +3.72% (p=0.000 n=20+20) String/1000/Base2-8 5.25µs ± 2% 5.62µs ± 5% +7.04% (p=0.000 n=19+20) String/10000/Base2-8 55.6µs ± 1% 60.1µs ± 2% +8.12% (p=0.000 n=19+19) String/100000/Base2-8 519µs ± 2% 560µs ± 2% +7.91% (p=0.000 n=18+17) String/10/Base8-8 52.2ns ± 8% 53.3ns ±12% ~ (p=0.188 n=20+18) String/100/Base8-8 218ns ± 3% 232ns ±10% +6.66% (p=0.000 n=20+20) String/1000/Base8-8 1.84µs ± 3% 1.94µs ± 4% +5.07% (p=0.000 n=20+18) String/10000/Base8-8 18.1µs ± 2% 19.1µs ± 3% +5.84% (p=0.000 n=20+19) String/100000/Base8-8 184µs ± 2% 197µs ± 1% +7.15% (p=0.000 n=19+19) String/10/Base10-8 158ns ± 7% 146ns ± 6% -7.65% (p=0.000 n=20+19) String/100/Base10-8 807ns ± 2% 845ns ± 4% +4.79% (p=0.000 n=20+19) String/1000/Base10-8 3.99µs ± 3% 3.99µs ± 7% ~ (p=0.920 n=20+20) String/10000/Base10-8 20.8µs ± 6% 22.1µs ±10% +6.11% (p=0.000 n=19+20) String/100000/Base10-8 5.60ms ± 2% 5.59ms ± 2% ~ (p=0.749 n=20+19) String/10/Base16-8 49.0ns ±13% 49.3ns ±16% ~ (p=0.581 n=19+20) String/100/Base16-8 173ns ± 5% 185ns ± 6% +6.63% (p=0.000 n=20+18) String/1000/Base16-8 1.38µs ± 3% 1.49µs ±10% +8.27% (p=0.000 n=19+20) String/10000/Base16-8 13.5µs ± 2% 14.5µs ± 3% +7.08% (p=0.000 n=20+20) String/100000/Base16-8 138µs ± 4% 148µs ± 4% +7.57% (p=0.000 n=19+20) LeafSize/0-8 2.74ms ± 1% 2.79ms ± 2% +2.00% (p=0.000 n=19+19) LeafSize/1-8 24.8µs ± 4% 26.1µs ± 8% +5.33% (p=0.000 n=18+19) LeafSize/2-8 24.9µs ± 7% 25.0µs ± 8% ~ (p=0.989 n=20+19) LeafSize/3-8 97.6µs ± 3% 100.2µs ± 5% +2.66% (p=0.001 n=20+19) LeafSize/4-8 25.2µs ± 5% 25.4µs ± 5% ~ (p=0.173 n=19+20) LeafSize/5-8 118µs ± 2% 119µs ± 5% ~ (p=0.478 n=20+20) LeafSize/6-8 97.6µs ± 3% 100.1µs ± 8% +2.65% (p=0.021 n=20+19) LeafSize/7-8 65.6µs ± 5% 67.5µs ± 6% +2.92% (p=0.003 n=20+19) LeafSize/8-8 25.5µs ± 5% 25.6µs ± 6% ~ (p=0.461 n=19+20) LeafSize/9-8 134µs ± 4% 136µs ± 5% ~ (p=0.194 n=19+20) LeafSize/10-8 119µs ± 3% 122µs ± 3% +2.52% (p=0.000 n=20+19) LeafSize/11-8 115µs ± 5% 116µs ± 5% ~ (p=0.158 n=20+19) LeafSize/12-8 97.4µs ± 4% 100.3µs ± 5% +2.91% (p=0.003 n=19+20) LeafSize/13-8 93.1µs ± 4% 93.0µs ± 6% ~ (p=0.698 n=20+20) LeafSize/14-8 67.0µs ± 3% 69.7µs ± 6% +4.10% (p=0.000 n=20+20) LeafSize/15-8 48.3µs ± 2% 49.3µs ± 6% +1.91% (p=0.014 n=19+20) LeafSize/16-8 25.6µs ± 5% 25.6µs ± 6% ~ (p=0.947 n=20+20) LeafSize/32-8 30.1µs ± 4% 30.3µs ± 5% ~ (p=0.685 n=18+19) LeafSize/64-8 53.4µs ± 2% 54.0µs ± 3% ~ (p=0.053 n=19+19) ProbablyPrime/n=0-8 3.59ms ± 1% 3.55ms ± 1% -1.12% (p=0.000 n=20+18) ProbablyPrime/n=1-8 4.21ms ± 2% 4.17ms ± 2% -0.73% (p=0.018 n=20+19) ProbablyPrime/n=5-8 6.74ms ± 1% 6.72ms ± 1% ~ (p=0.102 n=20+20) ProbablyPrime/n=10-8 9.91ms ± 1% 9.89ms ± 2% ~ (p=0.322 n=19+20) ProbablyPrime/n=20-8 16.2ms ± 1% 16.1ms ± 2% -0.52% (p=0.006 n=19+19) ProbablyPrime/Lucas-8 2.94ms ± 1% 2.95ms ± 1% +0.52% (p=0.002 n=18+19) ProbablyPrime/MillerRabinBase2-8 641µs ± 2% 640µs ± 2% ~ (p=0.607 n=19+20) FloatSqrt/64-8 653ns ± 5% 704ns ± 5% +7.82% (p=0.000 n=19+20) FloatSqrt/128-8 1.32µs ± 3% 1.42µs ± 5% +7.29% (p=0.000 n=18+20) FloatSqrt/256-8 1.44µs ± 2% 1.45µs ± 4% ~ (p=0.089 n=19+19) FloatSqrt/1000-8 3.36µs ± 3% 3.42µs ± 5% +1.82% (p=0.012 n=20+20) FloatSqrt/10000-8 25.5µs ± 2% 27.5µs ± 7% +7.91% (p=0.000 n=18+19) FloatSqrt/100000-8 629µs ± 6% 663µs ± 9% +5.32% (p=0.000 n=18+20) FloatSqrt/1000000-8 46.4ms ± 2% 46.6ms ± 5% ~ (p=0.351 n=20+19) [Geo mean] 9.60µs 10.01µs +4.28% name old alloc/op new alloc/op delta DecimalConversion-8 54.0kB ± 0% 43.6kB ± 0% -19.40% (p=0.000 n=20+20) FloatString/100-8 400B ± 0% 400B ± 0% ~ (all equal) FloatString/1000-8 3.10kB ± 0% 3.10kB ± 0% ~ (all equal) FloatString/10000-8 52.1kB ± 0% 52.1kB ± 0% ~ (p=0.153 n=20+20) FloatString/100000-8 582kB ± 0% 582kB ± 0% ~ (all equal) FloatAdd/10-8 0.00B 0.00B ~ (all equal) FloatAdd/100-8 0.00B 0.00B ~ (all equal) FloatAdd/1000-8 0.00B 0.00B ~ (all equal) FloatAdd/10000-8 0.00B 0.00B ~ (all equal) FloatAdd/100000-8 0.00B 0.00B ~ (all equal) FloatSub/10-8 0.00B 0.00B ~ (all equal) FloatSub/100-8 0.00B 0.00B ~ (all equal) FloatSub/1000-8 0.00B 0.00B ~ (all equal) FloatSub/10000-8 0.00B 0.00B ~ (all equal) FloatSub/100000-8 0.00B 0.00B ~ (all equal) ParseFloatSmallExp-8 4.18kB ± 0% 3.60kB ± 0% -13.79% (p=0.000 n=20+20) ParseFloatLargeExp-8 18.9kB ± 0% 19.3kB ± 0% +2.25% (p=0.000 n=20+20) GCD10x10/WithoutXY-8 96.0B ± 0% 16.0B ± 0% -83.33% (p=0.000 n=20+20) GCD10x10/WithXY-8 240B ± 0% 88B ± 0% -63.33% (p=0.000 n=20+20) GCD10x100/WithoutXY-8 192B ± 0% 112B ± 0% -41.67% (p=0.000 n=20+20) GCD10x100/WithXY-8 464B ± 0% 424B ± 0% -8.62% (p=0.000 n=20+20) GCD10x1000/WithoutXY-8 416B ± 0% 336B ± 0% -19.23% (p=0.000 n=20+20) GCD10x1000/WithXY-8 1.25kB ± 0% 1.10kB ± 0% -12.18% (p=0.000 n=20+20) GCD10x10000/WithoutXY-8 2.91kB ± 0% 2.83kB ± 0% -2.75% (p=0.000 n=20+20) GCD10x10000/WithXY-8 8.70kB ± 0% 8.55kB ± 0% -1.76% (p=0.000 n=16+16) GCD10x100000/WithoutXY-8 27.2kB ± 0% 27.2kB ± 0% -0.29% (p=0.000 n=20+20) GCD10x100000/WithXY-8 82.4kB ± 0% 82.3kB ± 0% -0.17% (p=0.000 n=20+19) GCD100x100/WithoutXY-8 288B ± 0% 384B ± 0% +33.33% (p=0.000 n=20+20) GCD100x100/WithXY-8 464B ± 0% 576B ± 0% +24.14% (p=0.000 n=20+20) GCD100x1000/WithoutXY-8 640B ± 0% 688B ± 0% +7.50% (p=0.000 n=20+20) GCD100x1000/WithXY-8 1.52kB ± 0% 1.46kB ± 0% -3.68% (p=0.000 n=20+20) GCD100x10000/WithoutXY-8 4.24kB ± 0% 4.29kB ± 0% +1.13% (p=0.000 n=20+20) GCD100x10000/WithXY-8 11.1kB ± 0% 11.0kB ± 0% -0.51% (p=0.000 n=15+20) GCD100x100000/WithoutXY-8 40.9kB ± 0% 40.9kB ± 0% +0.12% (p=0.000 n=20+19) GCD100x100000/WithXY-8 110kB ± 0% 109kB ± 0% -0.08% (p=0.000 n=20+20) GCD1000x1000/WithoutXY-8 1.22kB ± 0% 1.06kB ± 0% -13.16% (p=0.000 n=20+20) GCD1000x1000/WithXY-8 2.37kB ± 0% 2.11kB ± 0% -10.83% (p=0.000 n=20+20) GCD1000x10000/WithoutXY-8 4.71kB ± 0% 4.63kB ± 0% -1.70% (p=0.000 n=20+19) GCD1000x10000/WithXY-8 28.2kB ± 0% 28.0kB ± 0% -0.43% (p=0.000 n=20+15) GCD1000x100000/WithoutXY-8 41.3kB ± 0% 41.2kB ± 0% -0.20% (p=0.000 n=20+16) GCD1000x100000/WithXY-8 301kB ± 0% 301kB ± 0% -0.13% (p=0.000 n=20+20) GCD10000x10000/WithoutXY-8 8.64kB ± 0% 8.48kB ± 0% -1.85% (p=0.000 n=20+20) GCD10000x10000/WithXY-8 57.2kB ± 0% 57.7kB ± 0% +0.80% (p=0.000 n=20+20) GCD10000x100000/WithoutXY-8 43.8kB ± 0% 43.7kB ± 0% -0.19% (p=0.000 n=20+18) GCD10000x100000/WithXY-8 2.08MB ± 0% 2.08MB ± 0% -0.02% (p=0.000 n=15+19) GCD100000x100000/WithoutXY-8 81.6kB ± 0% 81.4kB ± 0% -0.20% (p=0.000 n=20+20) GCD100000x100000/WithXY-8 4.32MB ± 0% 4.33MB ± 0% +0.12% (p=0.000 n=20+20) Hilbert-8 653kB ± 0% 313kB ± 0% -52.13% (p=0.000 n=19+20) Binomial-8 1.82kB ± 0% 1.02kB ± 0% -43.86% (p=0.000 n=20+20) QuoRem-8 0.00B 0.00B ~ (all equal) Exp-8 11.1kB ± 0% 11.0kB ± 0% -0.34% (p=0.000 n=19+20) Exp2-8 11.3kB ± 0% 11.3kB ± 0% -0.35% (p=0.000 n=19+20) Bitset-8 0.00B 0.00B ~ (all equal) BitsetNeg-8 0.00B 0.00B ~ (all equal) BitsetOrig-8 103B ± 0% 63B ± 0% -38.83% (p=0.000 n=20+20) BitsetNegOrig-8 215B ± 0% 175B ± 0% -18.60% (p=0.000 n=20+20) ModSqrt225_Tonelli-8 11.3kB ± 0% 11.0kB ± 0% -2.76% (p=0.000 n=20+17) ModSqrt225_3Mod4-8 3.57kB ± 0% 3.53kB ± 0% -1.12% (p=0.000 n=20+20) ModSqrt231_Tonelli-8 11.0kB ± 0% 10.7kB ± 0% -2.55% (p=0.000 n=20+20) ModSqrt231_5Mod8-8 4.21kB ± 0% 4.09kB ± 0% -2.85% (p=0.000 n=16+20) ModInverse-8 1.44kB ± 0% 1.28kB ± 0% -11.11% (p=0.000 n=20+20) Sqrt-8 6.00kB ± 0% 6.00kB ± 0% ~ (all equal) IntSqr/1-8 0.00B 0.00B ~ (all equal) IntSqr/2-8 0.00B 0.00B ~ (all equal) IntSqr/3-8 0.00B 0.00B ~ (all equal) IntSqr/5-8 0.00B 0.00B ~ (all equal) IntSqr/8-8 0.00B 0.00B ~ (all equal) IntSqr/10-8 0.00B 0.00B ~ (all equal) IntSqr/20-8 320B ± 0% 320B ± 0% ~ (all equal) IntSqr/30-8 480B ± 0% 480B ± 0% ~ (all equal) IntSqr/50-8 896B ± 0% 896B ± 0% ~ (all equal) IntSqr/80-8 1.28kB ± 0% 1.28kB ± 0% ~ (all equal) IntSqr/100-8 1.79kB ± 0% 1.79kB ± 0% ~ (all equal) IntSqr/200-8 3.20kB ± 0% 3.20kB ± 0% ~ (all equal) IntSqr/300-8 8.06kB ± 0% 8.06kB ± 0% ~ (all equal) IntSqr/500-8 12.3kB ± 0% 12.3kB ± 0% ~ (all equal) IntSqr/800-8 28.8kB ± 0% 28.8kB ± 0% ~ (all equal) IntSqr/1000-8 36.9kB ± 0% 36.9kB ± 0% ~ (all equal) Div/20/10-8 0.00B 0.00B ~ (all equal) Div/200/100-8 0.00B 0.00B ~ (all equal) Div/2000/1000-8 0.00B 0.00B ~ (all equal) Div/20000/10000-8 0.00B 0.00B ~ (all equal) Div/200000/100000-8 690B ± 0% 690B ± 0% ~ (all equal) Mul-8 565kB ± 0% 565kB ± 0% ~ (all equal) ZeroShifts/Shl-8 6.53kB ± 0% 6.53kB ± 0% ~ (all equal) ZeroShifts/ShlSame-8 0.00B 0.00B ~ (all equal) ZeroShifts/Shr-8 6.53kB ± 0% 6.53kB ± 0% ~ (all equal) ZeroShifts/ShrSame-8 0.00B 0.00B ~ (all equal) Exp3Power/0x10-8 192B ± 0% 112B ± 0% -41.67% (p=0.000 n=20+20) Exp3Power/0x40-8 192B ± 0% 112B ± 0% -41.67% (p=0.000 n=20+20) Exp3Power/0x100-8 288B ± 0% 208B ± 0% -27.78% (p=0.000 n=20+20) Exp3Power/0x400-8 672B ± 0% 592B ± 0% -11.90% (p=0.000 n=20+20) Exp3Power/0x1000-8 3.33kB ± 0% 3.25kB ± 0% -2.40% (p=0.000 n=20+20) Exp3Power/0x4000-8 13.8kB ± 0% 13.7kB ± 0% -0.58% (p=0.000 n=20+20) Exp3Power/0x10000-8 117kB ± 0% 117kB ± 0% -0.07% (p=0.000 n=20+20) Exp3Power/0x40000-8 755kB ± 0% 755kB ± 0% -0.01% (p=0.000 n=19+20) Exp3Power/0x100000-8 5.22MB ± 0% 5.22MB ± 0% -0.00% (p=0.000 n=20+20) Exp3Power/0x400000-8 39.8MB ± 0% 39.8MB ± 0% -0.00% (p=0.000 n=20+19) Fibo-8 3.09MB ± 0% 3.08MB ± 0% -0.28% (p=0.000 n=20+16) NatSqr/1-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) NatSqr/2-8 64.0B ± 0% 64.0B ± 0% ~ (all equal) NatSqr/3-8 80.0B ± 0% 80.0B ± 0% ~ (all equal) NatSqr/5-8 112B ± 0% 112B ± 0% ~ (all equal) NatSqr/8-8 160B ± 0% 160B ± 0% ~ (all equal) NatSqr/10-8 192B ± 0% 192B ± 0% ~ (all equal) NatSqr/20-8 672B ± 0% 672B ± 0% ~ (all equal) NatSqr/30-8 992B ± 0% 992B ± 0% ~ (all equal) NatSqr/50-8 1.79kB ± 0% 1.79kB ± 0% ~ (all equal) NatSqr/80-8 2.69kB ± 0% 2.69kB ± 0% ~ (all equal) NatSqr/100-8 3.58kB ± 0% 3.58kB ± 0% ~ (all equal) NatSqr/200-8 6.66kB ± 0% 6.66kB ± 0% ~ (all equal) NatSqr/300-8 24.4kB ± 0% 24.4kB ± 0% ~ (all equal) NatSqr/500-8 36.9kB ± 0% 36.9kB ± 0% ~ (all equal) NatSqr/800-8 69.8kB ± 0% 69.8kB ± 0% ~ (all equal) NatSqr/1000-8 86.0kB ± 0% 86.0kB ± 0% ~ (all equal) NatSetBytes/8-8 0.00B 0.00B ~ (all equal) NatSetBytes/24-8 64.0B ± 0% 64.0B ± 0% ~ (all equal) NatSetBytes/128-8 160B ± 0% 160B ± 0% ~ (all equal) NatSetBytes/7-8 0.00B 0.00B ~ (all equal) NatSetBytes/23-8 64.0B ± 0% 64.0B ± 0% ~ (all equal) NatSetBytes/127-8 160B ± 0% 160B ± 0% ~ (all equal) ScanPi-8 75.4kB ± 0% 75.7kB ± 0% +0.41% (p=0.000 n=20+20) StringPiParallel-8 20.4kB ± 0% 20.4kB ± 0% ~ (p=0.223 n=20+20) Scan/10/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/1000/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10000/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100000/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10/Base8-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100/Base8-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/1000/Base8-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10000/Base8-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100000/Base8-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10/Base10-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100/Base10-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/1000/Base10-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10000/Base10-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100000/Base10-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10/Base16-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100/Base16-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/1000/Base16-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/10000/Base16-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) Scan/100000/Base16-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) String/10/Base2-8 48.0B ± 0% 48.0B ± 0% ~ (all equal) String/100/Base2-8 352B ± 0% 352B ± 0% ~ (all equal) String/1000/Base2-8 3.46kB ± 0% 3.46kB ± 0% ~ (all equal) String/10000/Base2-8 41.0kB ± 0% 41.0kB ± 0% ~ (all equal) String/100000/Base2-8 336kB ± 0% 336kB ± 0% ~ (all equal) String/10/Base8-8 16.0B ± 0% 16.0B ± 0% ~ (all equal) String/100/Base8-8 112B ± 0% 112B ± 0% ~ (all equal) String/1000/Base8-8 1.15kB ± 0% 1.15kB ± 0% ~ (all equal) String/10000/Base8-8 12.3kB ± 0% 12.3kB ± 0% ~ (all equal) String/100000/Base8-8 115kB ± 0% 115kB ± 0% ~ (all equal) String/10/Base10-8 64.0B ± 0% 24.0B ± 0% -62.50% (p=0.000 n=20+20) String/100/Base10-8 192B ± 0% 192B ± 0% ~ (all equal) String/1000/Base10-8 1.95kB ± 0% 1.95kB ± 0% ~ (all equal) String/10000/Base10-8 20.0kB ± 0% 20.0kB ± 0% ~ (p=0.983 n=19+20) String/100000/Base10-8 210kB ± 1% 211kB ± 1% +0.82% (p=0.000 n=19+20) String/10/Base16-8 16.0B ± 0% 16.0B ± 0% ~ (all equal) String/100/Base16-8 96.0B ± 0% 96.0B ± 0% ~ (all equal) String/1000/Base16-8 896B ± 0% 896B ± 0% ~ (all equal) String/10000/Base16-8 9.47kB ± 0% 9.47kB ± 0% ~ (all equal) String/100000/Base16-8 90.1kB ± 0% 90.1kB ± 0% ~ (all equal) LeafSize/0-8 16.9kB ± 0% 16.8kB ± 0% -0.44% (p=0.000 n=20+20) LeafSize/1-8 22.4kB ± 0% 22.3kB ± 0% -0.34% (p=0.000 n=20+19) LeafSize/2-8 22.4kB ± 0% 22.3kB ± 0% -0.34% (p=0.000 n=20+19) LeafSize/3-8 22.4kB ± 0% 22.3kB ± 0% -0.34% (p=0.000 n=20+17) LeafSize/4-8 22.4kB ± 0% 22.3kB ± 0% -0.34% (p=0.000 n=20+19) LeafSize/5-8 22.4kB ± 0% 22.3kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/6-8 22.3kB ± 0% 22.2kB ± 0% -0.34% (p=0.000 n=20+20) LeafSize/7-8 22.3kB ± 0% 22.2kB ± 0% -0.35% (p=0.000 n=20+20) LeafSize/8-8 22.3kB ± 0% 22.2kB ± 0% -0.34% (p=0.000 n=16+20) LeafSize/9-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/10-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/11-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/12-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/13-8 22.3kB ± 0% 22.2kB ± 0% -0.34% (p=0.000 n=20+15) LeafSize/14-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/15-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=20+20) LeafSize/16-8 22.3kB ± 0% 22.2kB ± 0% -0.33% (p=0.000 n=19+20) LeafSize/32-8 22.3kB ± 0% 22.2kB ± 0% -0.32% (p=0.000 n=20+20) LeafSize/64-8 21.8kB ± 0% 21.7kB ± 0% -0.33% (p=0.000 n=18+19) ProbablyPrime/n=0-8 15.3kB ± 0% 14.9kB ± 0% -2.35% (p=0.000 n=20+20) ProbablyPrime/n=1-8 21.0kB ± 0% 20.7kB ± 0% -1.71% (p=0.000 n=20+20) ProbablyPrime/n=5-8 43.4kB ± 0% 42.9kB ± 0% -1.20% (p=0.000 n=20+20) ProbablyPrime/n=10-8 71.5kB ± 0% 70.7kB ± 0% -1.01% (p=0.000 n=19+20) ProbablyPrime/n=20-8 127kB ± 0% 126kB ± 0% -0.88% (p=0.000 n=20+20) ProbablyPrime/Lucas-8 3.07kB ± 0% 2.79kB ± 0% -9.12% (p=0.000 n=20+20) ProbablyPrime/MillerRabinBase2-8 12.1kB ± 0% 12.0kB ± 0% -0.66% (p=0.000 n=20+20) FloatSqrt/64-8 416B ± 0% 360B ± 0% -13.46% (p=0.000 n=20+20) FloatSqrt/128-8 640B ± 0% 584B ± 0% -8.75% (p=0.000 n=20+20) FloatSqrt/256-8 512B ± 0% 472B ± 0% -7.81% (p=0.000 n=20+20) FloatSqrt/1000-8 1.47kB ± 0% 1.43kB ± 0% -2.72% (p=0.000 n=20+20) FloatSqrt/10000-8 18.2kB ± 0% 18.1kB ± 0% -0.22% (p=0.000 n=20+20) FloatSqrt/100000-8 204kB ± 0% 204kB ± 0% -0.02% (p=0.000 n=20+20) FloatSqrt/1000000-8 6.37MB ± 0% 6.37MB ± 0% -0.00% (p=0.000 n=19+20) [Geo mean] 3.42kB 3.24kB -5.33% name old allocs/op new allocs/op delta DecimalConversion-8 1.65k ± 0% 1.65k ± 0% ~ (all equal) FloatString/100-8 8.00 ± 0% 8.00 ± 0% ~ (all equal) FloatString/1000-8 9.00 ± 0% 9.00 ± 0% ~ (all equal) FloatString/10000-8 22.0 ± 0% 22.0 ± 0% ~ (all equal) FloatString/100000-8 136 ± 0% 136 ± 0% ~ (all equal) FloatAdd/10-8 0.00 0.00 ~ (all equal) FloatAdd/100-8 0.00 0.00 ~ (all equal) FloatAdd/1000-8 0.00 0.00 ~ (all equal) FloatAdd/10000-8 0.00 0.00 ~ (all equal) FloatAdd/100000-8 0.00 0.00 ~ (all equal) FloatSub/10-8 0.00 0.00 ~ (all equal) FloatSub/100-8 0.00 0.00 ~ (all equal) FloatSub/1000-8 0.00 0.00 ~ (all equal) FloatSub/10000-8 0.00 0.00 ~ (all equal) FloatSub/100000-8 0.00 0.00 ~ (all equal) ParseFloatSmallExp-8 110 ± 0% 130 ± 0% +18.18% (p=0.000 n=20+20) ParseFloatLargeExp-8 319 ± 0% 371 ± 0% +16.30% (p=0.000 n=20+20) GCD10x10/WithoutXY-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) GCD10x10/WithXY-8 5.00 ± 0% 6.00 ± 0% +20.00% (p=0.000 n=20+20) GCD10x100/WithoutXY-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) GCD10x100/WithXY-8 9.00 ± 0% 12.00 ± 0% +33.33% (p=0.000 n=20+20) GCD10x1000/WithoutXY-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) GCD10x1000/WithXY-8 11.0 ± 0% 12.0 ± 0% +9.09% (p=0.000 n=20+20) GCD10x10000/WithoutXY-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) GCD10x10000/WithXY-8 11.0 ± 0% 12.0 ± 0% +9.09% (p=0.000 n=20+20) GCD10x100000/WithoutXY-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) GCD10x100000/WithXY-8 11.0 ± 0% 12.0 ± 0% +9.09% (p=0.000 n=20+20) GCD100x100/WithoutXY-8 6.00 ± 0% 10.00 ± 0% +66.67% (p=0.000 n=20+20) GCD100x100/WithXY-8 9.00 ± 0% 15.00 ± 0% +66.67% (p=0.000 n=20+20) GCD100x1000/WithoutXY-8 6.00 ± 0% 8.00 ± 0% +33.33% (p=0.000 n=20+20) GCD100x1000/WithXY-8 12.0 ± 0% 13.0 ± 0% +8.33% (p=0.000 n=20+20) GCD100x10000/WithoutXY-8 6.00 ± 0% 8.00 ± 0% +33.33% (p=0.000 n=20+20) GCD100x10000/WithXY-8 12.0 ± 0% 13.0 ± 0% +8.33% (p=0.000 n=20+20) GCD100x100000/WithoutXY-8 6.00 ± 0% 8.00 ± 0% +33.33% (p=0.000 n=20+20) GCD100x100000/WithXY-8 12.0 ± 0% 13.0 ± 0% +8.33% (p=0.000 n=20+20) GCD1000x1000/WithoutXY-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) GCD1000x1000/WithXY-8 19.0 ± 0% 20.0 ± 0% +5.26% (p=0.000 n=20+20) GCD1000x10000/WithoutXY-8 8.00 ± 0% 8.00 ± 0% ~ (all equal) GCD1000x10000/WithXY-8 26.0 ± 0% 26.0 ± 0% ~ (all equal) GCD1000x100000/WithoutXY-8 8.00 ± 0% 8.00 ± 0% ~ (all equal) GCD1000x100000/WithXY-8 27.0 ± 0% 27.0 ± 0% ~ (all equal) GCD10000x10000/WithoutXY-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) GCD10000x10000/WithXY-8 76.0 ± 0% 78.0 ± 0% +2.63% (p=0.000 n=20+20) GCD10000x100000/WithoutXY-8 8.00 ± 0% 8.00 ± 0% ~ (all equal) GCD10000x100000/WithXY-8 174 ± 0% 174 ± 0% ~ (all equal) GCD100000x100000/WithoutXY-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) GCD100000x100000/WithXY-8 645 ± 0% 647 ± 0% +0.31% (p=0.000 n=20+20) Hilbert-8 14.1k ± 0% 14.3k ± 0% +0.92% (p=0.000 n=20+20) Binomial-8 38.0 ± 0% 38.0 ± 0% ~ (all equal) QuoRem-8 0.00 0.00 ~ (all equal) Exp-8 21.0 ± 0% 21.0 ± 0% ~ (all equal) Exp2-8 22.0 ± 0% 22.0 ± 0% ~ (all equal) Bitset-8 0.00 0.00 ~ (all equal) BitsetNeg-8 0.00 0.00 ~ (all equal) BitsetOrig-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) BitsetNegOrig-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) ModSqrt225_Tonelli-8 85.0 ± 0% 86.0 ± 0% +1.18% (p=0.000 n=20+20) ModSqrt225_3Mod4-8 25.0 ± 0% 25.0 ± 0% ~ (all equal) ModSqrt231_Tonelli-8 80.0 ± 0% 80.0 ± 0% ~ (all equal) ModSqrt231_5Mod8-8 32.0 ± 0% 32.0 ± 0% ~ (all equal) ModInverse-8 11.0 ± 0% 11.0 ± 0% ~ (all equal) Sqrt-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) IntSqr/1-8 0.00 0.00 ~ (all equal) IntSqr/2-8 0.00 0.00 ~ (all equal) IntSqr/3-8 0.00 0.00 ~ (all equal) IntSqr/5-8 0.00 0.00 ~ (all equal) IntSqr/8-8 0.00 0.00 ~ (all equal) IntSqr/10-8 0.00 0.00 ~ (all equal) IntSqr/20-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/30-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/50-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/80-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/100-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/200-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) IntSqr/300-8 3.00 ± 0% 3.00 ± 0% ~ (all equal) IntSqr/500-8 3.00 ± 0% 3.00 ± 0% ~ (all equal) IntSqr/800-8 9.00 ± 0% 9.00 ± 0% ~ (all equal) IntSqr/1000-8 9.00 ± 0% 9.00 ± 0% ~ (all equal) Div/20/10-8 0.00 0.00 ~ (all equal) Div/200/100-8 0.00 0.00 ~ (all equal) Div/2000/1000-8 0.00 0.00 ~ (all equal) Div/20000/10000-8 0.00 0.00 ~ (all equal) Div/200000/100000-8 0.00 0.00 ~ (all equal) Mul-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) ZeroShifts/Shl-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) ZeroShifts/ShlSame-8 0.00 0.00 ~ (all equal) ZeroShifts/Shr-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) ZeroShifts/ShrSame-8 0.00 0.00 ~ (all equal) Exp3Power/0x10-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) Exp3Power/0x40-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) Exp3Power/0x100-8 5.00 ± 0% 5.00 ± 0% ~ (all equal) Exp3Power/0x400-8 7.00 ± 0% 7.00 ± 0% ~ (all equal) Exp3Power/0x1000-8 11.0 ± 0% 11.0 ± 0% ~ (all equal) Exp3Power/0x4000-8 15.0 ± 0% 15.0 ± 0% ~ (all equal) Exp3Power/0x10000-8 29.0 ± 0% 29.0 ± 0% ~ (all equal) Exp3Power/0x40000-8 140 ± 0% 140 ± 0% ~ (all equal) Exp3Power/0x100000-8 1.12k ± 0% 1.12k ± 0% ~ (all equal) Exp3Power/0x400000-8 9.88k ± 0% 9.88k ± 0% ~ (p=0.747 n=17+19) Fibo-8 739 ± 0% 743 ± 0% +0.54% (p=0.000 n=20+20) NatSqr/1-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/3-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/5-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSqr/20-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/30-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/50-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/80-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/100-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/200-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) NatSqr/300-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) NatSqr/500-8 4.00 ± 0% 4.00 ± 0% ~ (all equal) NatSqr/800-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) NatSqr/1000-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) NatSetBytes/8-8 0.00 0.00 ~ (all equal) NatSetBytes/24-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSetBytes/128-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSetBytes/7-8 0.00 0.00 ~ (all equal) NatSetBytes/23-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) NatSetBytes/127-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) ScanPi-8 60.0 ± 0% 61.0 ± 0% +1.67% (p=0.000 n=20+20) StringPiParallel-8 24.0 ± 0% 24.0 ± 0% ~ (all equal) Scan/10/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/1000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/1000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10/Base10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100/Base10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/1000/Base10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10000/Base10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100000/Base10-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/1000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/10000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) Scan/100000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/1000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100000/Base2-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/1000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100000/Base8-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10/Base10-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) String/100/Base10-8 2.00 ± 0% 2.00 ± 0% ~ (all equal) String/1000/Base10-8 3.00 ± 0% 3.00 ± 0% ~ (all equal) String/10000/Base10-8 3.00 ± 0% 3.00 ± 0% ~ (all equal) String/100000/Base10-8 3.00 ± 0% 3.00 ± 0% ~ (all equal) String/10/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/1000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/10000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) String/100000/Base16-8 1.00 ± 0% 1.00 ± 0% ~ (all equal) LeafSize/0-8 10.0 ± 0% 10.0 ± 0% ~ (all equal) LeafSize/1-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) LeafSize/2-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) LeafSize/3-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) LeafSize/4-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) LeafSize/5-8 13.0 ± 0% 13.0 ± 0% ~ (all equal) LeafSize/6-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/7-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/8-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/9-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/10-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/11-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/12-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/13-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/14-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/15-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/16-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/32-8 12.0 ± 0% 12.0 ± 0% ~ (all equal) LeafSize/64-8 11.0 ± 0% 11.0 ± 0% ~ (all equal) ProbablyPrime/n=0-8 52.0 ± 0% 52.0 ± 0% ~ (all equal) ProbablyPrime/n=1-8 73.0 ± 0% 73.0 ± 0% ~ (all equal) ProbablyPrime/n=5-8 157 ± 0% 157 ± 0% ~ (all equal) ProbablyPrime/n=10-8 262 ± 0% 262 ± 0% ~ (all equal) ProbablyPrime/n=20-8 472 ± 0% 472 ± 0% ~ (all equal) ProbablyPrime/Lucas-8 22.0 ± 0% 22.0 ± 0% ~ (all equal) ProbablyPrime/MillerRabinBase2-8 29.0 ± 0% 29.0 ± 0% ~ (all equal) FloatSqrt/64-8 9.00 ± 0% 10.00 ± 0% +11.11% (p=0.000 n=20+20) FloatSqrt/128-8 12.0 ± 0% 13.0 ± 0% +8.33% (p=0.000 n=20+20) FloatSqrt/256-8 8.00 ± 0% 8.00 ± 0% ~ (all equal) FloatSqrt/1000-8 9.00 ± 0% 9.00 ± 0% ~ (all equal) FloatSqrt/10000-8 14.0 ± 0% 14.0 ± 0% ~ (all equal) FloatSqrt/100000-8 33.0 ± 0% 33.0 ± 0% ~ (all equal) FloatSqrt/1000000-8 1.16k ± 0% 1.16k ± 0% ~ (all equal) [Geo mean] 6.62 6.76 +2.09% Change-Id: Id9df4157cac1e07721e35cff7fcdefe60703873a Reviewed-on: https://go-review.googlesource.com/c/150999 Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com> Reviewed-by: Alan Donovan <adonovan@google.com> Reviewed-by: Robert Griesemer <gri@golang.org> |
|
|
Brad Fitzpatrick
|
3813edf26e |
all: use "reports whether" consistently in the few places that didn't
Go documentation style for boolean funcs is to say:
// Foo reports whether ...
func Foo() bool
(rather than "returns true if")
This CL also replaces 4 uses of "iff" with the same "reports whether"
wording, which doesn't lose any meaning, and will prevent people from
sending typo fixes when they don't realize it's "if and only if". In
the past I think we've had the typo CLs updated to just say "reports
whether". So do them all at once.
(Inspired by the addition of another "returns true if" in CL 146938
in fd_plan9.go)
Created with:
$ perl -i -npe 's/returns true if/reports whether/' $(git grep -l "returns true iff" | grep -v vendor)
$ perl -i -npe 's/returns true if/reports whether/' $(git grep -l "returns true if" | grep -v vendor)
Change-Id: Ided502237f5ab0d25cb625dbab12529c361a8b9f
Reviewed-on: https://go-review.googlesource.com/c/147037
Reviewed-by: Ian Lance Taylor <iant@golang.org>
|
|
|
Robert Griesemer
|
c86d464734 |
math/big: shallow copies of Int/Rat/Float are not supported (documentation)
Fixes #28423. Change-Id: Ie57ade565d0407a4bffaa86fb4475ff083168e79 Reviewed-on: https://go-review.googlesource.com/c/145537 Reviewed-by: Ian Lance Taylor <iant@golang.org> |
|
hearot
|
f28191340e |
math/big: fix a formula used as documentation
The function documentation was wrong, it was using a wrong parameter. This change replaces it with the right parameter. The wrong formula was: q = (u1<<_W + u0 - r)/y The function has got a parameter "v" (of type Word), not a parameter "y". So, the right formula is: q = (u1<<_W + u0 - r)/v Fixes #28444 Change-Id: I82e57ba014735a9fdb6262874ddf498754d30d33 Reviewed-on: https://go-review.googlesource.com/c/145280 Reviewed-by: Robert Griesemer <gri@golang.org> |
|
Igor Zhilianin
|
f90e89e675 |
all: fix a bunch of misspellings
Change-Id: If2954bdfc551515403706b2cd0dde94e45936e08
GitHub-Last-Rev:
|
|
Zhou Peng
|
b8ac64a581 |
all: this big patch remove whitespace from assembly files
Don't worry, this patch just remove trailing whitespace from assembly files, and does not touch any logical changes. Change-Id: Ia724ac0b1abf8bc1e41454bdc79289ef317c165d Reviewed-on: https://go-review.googlesource.com/c/113595 Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org> Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org> |
|
|
Brian Kessler
|
a3381faf81 |
math/big: streamline divLarge initialization
The divLarge code contained "todo"s about avoiding alias and clear calls in the initialization of variables. By rearranging the order of initialization and always using an auxiliary variable for the shifted divisor, all of these calls can be safely avoided. On average, normalizing the divisor (shift>0) is required 31/32 or 63/64 of the time. If one always performs the shift into an auxiliary variable first, this avoids the need to check for aliasing of vIn in the output variables u and z. The remainder u is initialized via a left shift of uIn and thus needs no alias check against uIn. Since uIn and vIn were both used, z needs no alias checks except against u which is used for storage of the remainder. This change has a minimal impact on performance (see below), but cleans up the initialization code and eliminates the "todo"s. name old time/op new time/op delta Div/20/10-4 86.7ns ± 6% 85.7ns ± 5% ~ (p=0.841 n=5+5) Div/200/100-4 523ns ± 5% 502ns ± 3% -4.13% (p=0.024 n=5+5) Div/2000/1000-4 2.55µs ± 3% 2.59µs ± 5% ~ (p=0.548 n=5+5) Div/20000/10000-4 80.4µs ± 4% 80.0µs ± 2% ~ (p=1.000 n=5+5) Div/200000/100000-4 6.43ms ± 6% 6.35ms ± 4% ~ (p=0.548 n=5+5) Fixes #22928 Change-Id: I30d8498ef1cf8b69b0f827165c517bc25a5c32d7 Reviewed-on: https://go-review.googlesource.com/130775 Reviewed-by: Robert Griesemer <gri@golang.org> |