Brian Kessler 1643d4f33a math/big: implement Lehmer's GCD algorithm ...

Updates #15833

Lehmer's GCD algorithm uses single precision calculations
to simulate several steps of multiple precision calculations
in Euclid's GCD algorithm which leads to a considerable
speed up.  This implementation uses Collins' simplified
testing condition on the single digit cosequences which
requires only one quotient and avoids any possibility of
overflow.

name                          old time/op  new time/op  delta
GCD10x10/WithoutXY-4          1.82µs ±24%  0.28µs ± 6%  -84.40%  (p=0.008 n=5+5)
GCD10x10/WithXY-4             1.69µs ± 6%  1.71µs ± 6%     ~     (p=0.595 n=5+5)
GCD10x100/WithoutXY-4         1.87µs ± 2%  0.56µs ± 4%  -70.13%  (p=0.008 n=5+5)
GCD10x100/WithXY-4            2.61µs ± 2%  2.65µs ± 4%     ~     (p=0.635 n=5+5)
GCD10x1000/WithoutXY-4        2.75µs ± 2%  1.48µs ± 1%  -46.06%  (p=0.008 n=5+5)
GCD10x1000/WithXY-4           5.29µs ± 2%  5.25µs ± 2%     ~     (p=0.548 n=5+5)
GCD10x10000/WithoutXY-4       10.7µs ± 2%  10.3µs ± 0%   -4.38%  (p=0.008 n=5+5)
GCD10x10000/WithXY-4          22.3µs ± 6%  22.1µs ± 1%     ~     (p=1.000 n=5+5)
GCD10x100000/WithoutXY-4      93.7µs ± 2%  99.4µs ± 2%   +6.09%  (p=0.008 n=5+5)
GCD10x100000/WithXY-4          196µs ± 2%   199µs ± 2%     ~     (p=0.222 n=5+5)
GCD100x100/WithoutXY-4        10.1µs ± 2%   2.5µs ± 2%  -74.84%  (p=0.008 n=5+5)
GCD100x100/WithXY-4           21.4µs ± 2%  21.3µs ± 7%     ~     (p=0.548 n=5+5)
GCD100x1000/WithoutXY-4       11.3µs ± 2%   4.4µs ± 4%  -60.87%  (p=0.008 n=5+5)
GCD100x1000/WithXY-4          24.7µs ± 3%  23.9µs ± 1%     ~     (p=0.056 n=5+5)
GCD100x10000/WithoutXY-4      26.6µs ± 1%  20.0µs ± 2%  -24.82%  (p=0.008 n=5+5)
GCD100x10000/WithXY-4         78.7µs ± 2%  78.2µs ± 2%     ~     (p=0.690 n=5+5)
GCD100x100000/WithoutXY-4      174µs ± 2%   171µs ± 1%     ~     (p=0.056 n=5+5)
GCD100x100000/WithXY-4         563µs ± 4%   561µs ± 2%     ~     (p=1.000 n=5+5)
GCD1000x1000/WithoutXY-4       120µs ± 5%    29µs ± 3%  -75.71%  (p=0.008 n=5+5)
GCD1000x1000/WithXY-4          355µs ± 4%   358µs ± 2%     ~     (p=0.841 n=5+5)
GCD1000x10000/WithoutXY-4      140µs ± 2%    49µs ± 2%  -65.07%  (p=0.008 n=5+5)
GCD1000x10000/WithXY-4         626µs ± 3%   628µs ± 9%     ~     (p=0.690 n=5+5)
GCD1000x100000/WithoutXY-4     340µs ± 4%   259µs ± 6%  -23.79%  (p=0.008 n=5+5)
GCD1000x100000/WithXY-4       3.76ms ± 4%  3.82ms ± 5%     ~     (p=0.310 n=5+5)
GCD10000x10000/WithoutXY-4    3.11ms ± 3%  0.54ms ± 2%  -82.74%  (p=0.008 n=5+5)
GCD10000x10000/WithXY-4       7.96ms ± 3%  7.69ms ± 3%     ~     (p=0.151 n=5+5)
GCD10000x100000/WithoutXY-4   3.88ms ± 1%  1.27ms ± 2%  -67.21%  (p=0.008 n=5+5)
GCD10000x100000/WithXY-4      38.1ms ± 2%  38.8ms ± 1%     ~     (p=0.095 n=5+5)
GCD100000x100000/WithoutXY-4   208ms ± 1%    25ms ± 4%  -88.07%  (p=0.008 n=5+5)
GCD100000x100000/WithXY-4      533ms ± 5%   525ms ± 4%     ~     (p=0.548 n=5+5)

Change-Id: Ic1e007eb807b93e75f4752e968e98c1f0cb90e43
Reviewed-on: https://go-review.googlesource.com/59450
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>

2017-10-24 22:42:43 +00:00

..

big

math/big: implement Lehmer's GCD algorithm

2017-10-24 22:42:43 +00:00

bits

math/bits: complete examples

2017-10-06 16:58:03 +00:00

cmplx

math/cmplx: prevent infinite loop in tanSeries

2016-10-25 18:32:22 +00:00

rand

math/rand: fix comment for Shuffle

2017-09-14 03:41:35 +00:00

abs.go

cmd/compile,math: improve code generation for math.Abs

2017-08-25 19:15:01 +00:00

acos_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

acosh_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

acosh.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

all_test.go

math: add RoundToEven function

2017-10-24 22:33:09 +00:00

arith_s390x_test.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

arith_s390x.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

asin_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

asin_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

asin_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

asin_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

asin_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

asin.go

…

asinh_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

asinh_stub.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

asinh.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

atan2_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan2_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan2_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan2_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan2_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

atan2.go

…

atan_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

atan_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

atan.go

…

atanh_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

atanh.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

bits.go

math: add RoundToEven function

2017-10-24 22:33:09 +00:00

cbrt_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

cbrt_stub.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

cbrt.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

const.go

math: change oeis.org urls to https

2017-08-08 08:56:40 +00:00

copysign.go

…

cosh_s390x.s

cmd/asm, cmd/internal/obj/s390x, math: add LGDR and LDGR instructions

2017-04-17 16:33:51 +00:00

dim_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

dim_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

dim_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

dim_arm64.s

math: add some assembly implementations on ARM64

2016-09-27 23:52:12 +00:00

dim_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

dim_s390x.s

math: add functions and stubs for s390x

2016-04-06 23:35:56 +00:00

dim.go

…

erf_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

erf_stub.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

erf.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

erfc_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

erfinv.go

math: implement the erfcinv function

2017-08-22 13:13:20 +00:00

example_test.go

math: add examples for trig functions

2017-08-25 20:26:19 +00:00

exp2_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp2_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp2_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp2_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp_386.s

math: use portable Exp instead of 387 instructions on 386

2016-10-05 03:53:11 +00:00

exp_amd64.s

math: implement fast path for Exp

2017-09-20 21:43:00 +00:00

exp_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

exp_asm.go

math: implement fast path for Exp

2017-09-20 21:43:00 +00:00

exp_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

exp.go

math: fix inaccurate result of Exp(1)

2017-08-17 09:01:27 +00:00

expm1_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

expm1_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

expm1_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

expm1_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

expm1_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

expm1.go

all: unindent some big chunks of code

2017-08-18 06:59:48 +00:00

export_s390x_test.go

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

export_test.go

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

floor_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

floor_amd64.s

internal/cpu: new package to detect cpu features

2017-05-10 17:02:21 +00:00

floor_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

floor_arm64.s

math: add some assembly implementations on ARM64

2016-09-27 23:52:12 +00:00

floor_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

floor_asm.go

internal/cpu: new package to detect cpu features

2017-05-10 17:02:21 +00:00

floor_ppc64x.s

math, cmd/internal/obj/ppc64: improve floor, ceil, trunc with asm

2016-09-23 13:03:08 +00:00

floor_s390x.s

math: optimize Ceil, Floor and Trunc on s390x

2016-08-26 17:27:13 +00:00

floor.go

math: add RoundToEven function

2017-10-24 22:33:09 +00:00

frexp_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

frexp_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

frexp_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

frexp_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

frexp.go

…

gamma.go

math: speed up Gamma(+Inf)

2016-10-18 22:12:03 +00:00

hypot_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

hypot_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

hypot_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

hypot_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

hypot.go

…

j0.go

math: speed up bessel functions on AMD64

2016-08-31 14:45:29 +00:00

j1.go

math: speed up bessel functions on AMD64

2016-08-31 14:45:29 +00:00

jn.go

math: fix typos in Bessel function docs

2017-02-16 22:41:34 +00:00

ldexp_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

ldexp_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

ldexp_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

ldexp_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

ldexp.go

…

lgamma.go

all: single space after period.

2016-03-02 00:13:47 +00:00

log1p_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log1p_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log1p_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log1p_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log1p_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

log1p.go

math,math/cmplx: fix linter issues

2016-10-24 23:25:46 +00:00

log10_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log10_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log10_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log10_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log10_s390x.s

cmd/asm, cmd/internal/obj/s390x, math: add LGDR and LDGR instructions

2017-04-17 16:33:51 +00:00

log10.go

math: fix Log2 test failures on ppc64 (and s390)

2015-07-15 05:35:22 +00:00

log_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log_amd64.s

math: speed up Log on amd64

2017-03-29 20:36:29 +00:00

log_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

log_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

log.go

all: single space after period.

2016-03-02 00:13:47 +00:00

logb.go

…

mod_386.s

…

mod_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

mod_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

mod_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

mod.go

…

modf_386.s

all: fix assembly vet issues

2016-08-25 18:52:31 +00:00

modf_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

modf_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

modf_arm64.s

all: minor vet fixes

2016-10-24 17:27:37 +00:00

modf_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

modf.go

all: single space after period.

2016-03-02 00:13:47 +00:00

nextafter.go

math: change Nextafter64 to Nextafter in the description of Nextafter

2015-02-17 14:29:18 +00:00

pow10.go

math: speed up and improve accuracy of Pow10

2017-02-22 19:17:04 +00:00

pow_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

pow_stub.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

pow.go

math: eliminate overflow in Pow(x,y) for large y

2017-08-16 09:10:10 +00:00

remainder_386.s

…

remainder_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

remainder_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

remainder_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

remainder.go

all: single space after period.

2016-03-02 00:13:47 +00:00

signbit.go

…

sin_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sin_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sin_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sin_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sin_s390x.s

cmd/asm, cmd/internal/obj/s390x, math: add LGDR and LDGR instructions

2017-04-17 16:33:51 +00:00

sin.go

math,math/cmplx: fix linter issues

2016-10-24 23:25:46 +00:00

sincos_386.go

math: remove asm version of sincos everywhere, except 386

2017-04-24 15:09:18 +00:00

sincos_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sincos.go

math: remove asm version of sincos everywhere, except 386

2017-04-24 15:09:18 +00:00

sinh_s390x.s

cmd/asm, cmd/internal/obj/s390x, math: add LGDR and LDGR instructions

2017-04-17 16:33:51 +00:00

sinh_stub.s

math: use SIMD to accelerate some scalar math functions on s390x

2016-11-11 20:20:23 +00:00

sinh.go

math: use SIMD to accelerate some scalar math functions on s390x

2016-11-11 20:20:23 +00:00

sqrt_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sqrt_amd64.s

math: make sqrt smaller on AMD64

2016-09-29 15:56:52 +00:00

sqrt_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sqrt_arm64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sqrt_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

sqrt_mipsx.s

math, math/big: add support for GOARCH=mips{,le}

2016-11-03 22:55:06 +00:00

sqrt_ppc64x.s

all: make copyright headers consistent with one space after period

2016-05-02 13:43:18 +00:00

sqrt_s390x.s

math: add functions and stubs for s390x

2016-04-06 23:35:56 +00:00

sqrt.go

math: delete unused function sqrtC

2016-03-03 02:29:09 +00:00

stubs_arm64.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

stubs_mips64x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

stubs_mipsx.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

stubs_ppc64x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

stubs_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

tan_386.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

tan_amd64.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

tan_amd64p32.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

tan_arm.s

all: make copyright headers consistent with one space after period

2016-03-01 23:34:33 +00:00

tan_s390x.s

math: use SIMD to accelerate additional scalar math functions on s390x

2017-05-08 19:52:30 +00:00

tan.go

math,math/cmplx: fix linter issues

2016-10-24 23:25:46 +00:00

tanh_s390x.s

cmd/asm, cmd/internal/obj/s390x, math: add LGDR and LDGR instructions

2017-04-17 16:33:51 +00:00

tanh.go

math: use SIMD to accelerate some scalar math functions on s390x

2016-11-11 20:20:23 +00:00

unsafe.go

…