Strange performance difference? #8516
Description
In testing this code against 4 Ruby VMs there is a significant performance anomaly in JRuby (via rvm).
jruby 9.4.9.0 (3.1.4) 2024-11-04 547c6b150e Java HotSpot(TM) 64-Bit Server VM 15.0.2+7-27 on 15.0.2+7-27 +jit [x86_64-linux]
Test Code
module Primes
module Utils
# Miller-Rabin prime test in Ruby
# From: http://en.wikipedia.org/wiki/Miller-Rabin_primality_test
# Ruby Rosetta Code: http://rosettacode.org/wiki/Miller-Rabin_primality_test
# I modified the Rosetta Code, as shown below
def primemr2?(k=5) # increase k for more reliability
return self >= 2 if self <= 3
return false unless 6.gcd(self) == 1
neg_one_mod = n = d = self - 1 # these are even as self is always odd
s = 0
(d >>= 1; s += 1) while d.even?
k.times do
a = 2 + rand(self-4)
y = a.pow(d,self) # y = (a**d) mod self
next if y == 1 or y == neg_one_mod
(s-1).times do
y = y.pow(2, self) # y = (y**2) mod self
return false if y == 1
break if y == neg_one_mod
end
return false unless y == neg_one_mod
end
true # n is prime (with high probability)
end
def primemr3?(k=5) # increase k for more reliability
return self >= 2 if self <= 3
return false unless 6.gcd(self) == 1
neg_one_mod = n = d = self - 1 # these are even as self is always odd
d >>= 2 while (d & 0b11) == 0; d >>= (d & 1)^1 # make d odd number
k.times do
a = 2 + rand(self-4)
y = a.pow(d, self) # y = (a**d) mod self
next if y == 1 or y == self-1
until y == 1 || y == neg_one_mod || d == n
y = y.pow(2, self) # y = (y**2) mod self
d <<= 1
end
return false unless y == neg_one_mod
end
true # n is prime (with high probability)
end
# Returns true if +self+ is a prime number, else returns false.
def primemr?(k = 5)
wits = WITNESS_RANGES.find { |range, wits| range > self }
witnesses = wits ? wits[1] : k.times.map{ rand(self - 4) + 2 }
witnesses.each { |p| return false unless miller_rabin_test(p) }
true
end
def primemr1?(k = 5) # k is default number of random bases
return PRIMES.include? self if self <= PRIMES.last
return false if MODPN.gcd(self) != 1
#return true if self < PRIMES.last**2
neg_one_mod = n = d = self - 1 # these are even as self is always odd
d >>= 2 while (d & 0b11) == 0; d >>= (d & 1)^1 # make d odd number
# wits = [range, [wit_prms]] or nil
wits = WITNESS_RANGES.find { |range, wits| range > self }
witnesses = wits ? wits[1] : k.times.map{ rand(self - 4) + 2 }
witnesses.each do |b|
next if (b % self).zero? # **skip base if a multiple of input**
y = b.pow(d, self) # y = (b**d) mod self
s = d
until y == 1 || y == neg_one_mod || s == n
y = y.pow(2, self) # y = (y**2) mod self
s <<= 1
end
return false unless y == neg_one_mod || s.odd?
end
true
end
private
WITNESS_RANGES = {
341_531 => [9345883071009581737],
1_050_535_501 => [336781006125, 9639812373923155],
350_269_456_337 => [4230279247111683200, 14694767155120705706, 16641139526367750375],
55_245_642_489_451 => [2, 141889084524735, 1199124725622454117, 11096072698276303650],
7_999_252_175_582_851 => [2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805],
585_226_005_592_931_977 => [2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375],
18_446_744_073_709_551_615 => [2, 325, 9375, 28178, 450775, 9780504, 1795265022],
#318_665_857_834_031_151_167_461 => [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37],
#3_317_044_064_679_887_385_961_981 => [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
}
MODPN = 232862364358497360900063316880507363070 # 101# (101 primorial) is largest for u128
PRIMES = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103]
# Returns true if +self+ passes Miller-Rabin Test on +b+
def miller_rabin_test(b) # b is a witness to test with
return self >= 2 if self <= 3
return false unless 6.gcd(self) == 1
n = d = self - 1
d >>= 2 while (d & 0b11) == 0; d >>= (d & 1)^1 # make d odd number
return if (b % self).zero? # **skip base if a multiple of input**
y = b.pow(d, self) # y = (b**d) mod self
until y == 1 || y == n || d == n
y = y.pow(2, self) # x = (x**2) mod self
d <<= 1
end
y == n || d.odd?
end
end
end
class Integer; include Primes::Utils end
def tm; s=Time.now; yield; Time.now-s end
# Perform primality tests with Miler-Rabin methods
def primes_tests(n)
puts "test value #{n} is prime?: #{n.primemr1?}"
puts "time for n.primemr? is #{tm{ (10**4).times{ n.primemr? } } }"
puts "time for n.primemr1? is #{tm{ (10**4).times{ n.primemr1? } } }"
puts "time for n.primemr2? is #{tm{ (10**4).times{ n.primemr2? } } }"
puts "time for n.primemr3? is #{tm{ (10**4).times{ n.primemr3? } } }"
puts
end
For these tests:
n = 100000000000000000000000000000000000000000000000000000000000000000000000001309503
primes_tests(n)
n = 303_371_455_241 # lo prime pair for gap of 500
primes_tests(n)
n = 8446744073709551627
primes_tests(n)
n = 8446744073709551556
primes_tests(n)
n = 18446744073709551556
primes_tests(n)
n = 18446744073709551557 # largest 64-bit prime
primes_tests(n)
n = 18446744073709551615 # 2**64 - 1, largest 64-bits
primes_tests(n)
n = 18446744073709551629 # next prime > 64-bits
primes_tests(n)
n = 340282366920938463463374607431768211296 # 1 < largest 128-bit prime
primes_tests(n)
n = 340282366920938463463374607431768211297 # largest 128-bit prime
primes_tests(n)
n = 340282366920938463463374607431768211455 # 2**128 - 1, largest 128-bits
primes_tests(n)
JRuby results
est value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 0.873514
time for n.primemr1? is 0.754906
time for n.primemr2? is 0.733884
time for n.primemr3? is 0.692394
test value 303371455241 is prime?: true
time for n.primemr? is 8.858697000000001
time for n.primemr1? is 8.801776
time for n.primemr2? is 14.792952
time for n.primemr3? is 15.211563
test value 8446744073709551627 is prime?: false
time for n.primemr? is 4.929926
time for n.primemr1? is 4.843951000000001
time for n.primemr2? is 5.052339999999999
time for n.primemr3? is 5.02239
test value 8446744073709551556 is prime?: false
➜ miller-rabin ruby miller-rabintest1.rb
test value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 0.836465
time for n.primemr1? is 0.749006
time for n.primemr2? is 0.715312
time for n.primemr3? is 0.703027
test value 303371455241 is prime?: true
time for n.primemr? is 8.743595
time for n.primemr1? is 8.502458
time for n.primemr2? is 14.66437
time for n.primemr3? is 14.517415000000002
test value 8446744073709551627 is prime?: false
time for n.primemr? is 4.941791
time for n.primemr1? is 4.80778
time for n.primemr2? is 5.038014
time for n.primemr3? is 5.132918
test value 8446744073709551556 is prime?: false
time for n.primemr? is 0.016883000000000002
time for n.primemr1? is 0.009792
time for n.primemr2? is 0.005158
time for n.primemr3? is 0.002415
test value 18446744073709551556 is prime?: false
time for n.primemr? is 0.021440999999999998
time for n.primemr1? is 0.00723
time for n.primemr2? is 0.010395999999999999
time for n.primemr3? is 0.006878
test value 18446744073709551557 is prime?: true
time for n.primemr? is 0.164283
time for n.primemr1? is 0.106833
time for n.primemr2? is 0.091131
time for n.primemr3? is 0.076461
test value 18446744073709551615 is prime?: false
time for n.primemr? is 0.019133999999999998
time for n.primemr1? is 0.004553
time for n.primemr2? is 0.0025
time for n.primemr3? is 0.002422
test value 18446744073709551629 is prime?: true
time for n.primemr? is 0.117601
time for n.primemr1? is 0.11476800000000001
time for n.primemr2? is 0.098049
time for n.primemr3? is 0.09081299999999999
test value 340282366920938463463374607431768211296 is prime?: false
time for n.primemr? is 0.022298
time for n.primemr1? is 0.009453999999999999
time for n.primemr2? is 0.000998
time for n.primemr3? is 0.000956
test value 340282366920938463463374607431768211297 is prime?: true
time for n.primemr? is 0.260003
time for n.primemr1? is 0.258279
time for n.primemr2? is 0.24645899999999998
time for n.primemr3? is 0.205179
test value 340282366920938463463374607431768211455 is prime?: false
time for n.primemr? is 0.021006
time for n.primemr1? is 0.009675999999999999
time for n.primemr2? is 0.001349
time for n.primemr3? is 0.001433
The 2nd||3rd values (303371455241||8446744073709551627) are way slower, though smaller than others!?!
Compare the results on other Ruby VMs
TruffleRuby 24.1.1
test value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 2.037394
time for n.primemr1? is 2.044762
time for n.primemr2? is 2.023177
time for n.primemr3? is 2.030676
test value 303371455241 is prime?: true
time for n.primemr? is 0.130453
time for n.primemr1? is 0.083802
time for n.primemr2? is 0.13637000000000002
time for n.primemr3? is 0.10047499999999998
test value 8446744073709551627 is prime?: false
time for n.primemr? is 0.074172
time for n.primemr1? is 0.09076000000000001
time for n.primemr2? is 0.05860000000000001
time for n.primemr3? is 0.05164800000000001
test value 8446744073709551556 is prime?: false
time for n.primemr? is 0.03371
time for n.primemr1? is 0.008634
time for n.primemr2? is 0.002139
time for n.primemr3? is 0.002048
test value 18446744073709551556 is prime?: false
time for n.primemr? is 0.027187
time for n.primemr1? is 0.013865
time for n.primemr2? is 0.00269
time for n.primemr3? is 0.001435
test value 18446744073709551557 is prime?: true
time for n.primemr? is 0.268511
time for n.primemr1? is 0.27220300000000003
time for n.primemr2? is 0.207252
time for n.primemr3? is 0.204208
test value 18446744073709551615 is prime?: false
time for n.primemr? is 0.046696
time for n.primemr1? is 0.003036
time for n.primemr2? is 0.001324
time for n.primemr3? is 0.001558
test value 18446744073709551629 is prime?: true
time for n.primemr? is 0.34620700000000004
time for n.primemr1? is 0.2535529999999999
time for n.primemr2? is 0.190887
time for n.primemr3? is 0.256318
test value 340282366920938463463374607431768211296 is prime?: false
time for n.primemr? is 0.050591
time for n.primemr1? is 0.028317
time for n.primemr2? is 0.000678
time for n.primemr3? is 0.000937
test value 340282366920938463463374607431768211297 is prime?: true
time for n.primemr? is 0.678474
time for n.primemr1? is 0.63026
time for n.primemr2? is 0.5384709999999999
time for n.primemr3? is 0.534702
test value 340282366920938463463374607431768211455 is prime?: false
time for n.primemr? is 0.03755
time for n.primemr1? is 0.028116
time for n.primemr2? is 0.000501
time for n.primemr3? is 0.001292
Ruby 3.3.6
est value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 0.61845201
time for n.primemr1? is 0.600007099
time for n.primemr2? is 0.579011867
time for n.primemr3? is 0.579763807
test value 303371455241 is prime?: true
time for n.primemr? is 0.019405872
time for n.primemr1? is 0.018532674
time for n.primemr2? is 0.022467344
time for n.primemr3? is 0.017704992
test value 8446744073709551627 is prime?: false
time for n.primemr? is 0.023057941
time for n.primemr1? is 0.02498252
time for n.primemr2? is 0.013945913
time for n.primemr3? is 0.026167141
test value 8446744073709551556 is prime?: false
➜ miller-rabin ruby miller-rabintest1.rb
test value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 0.632514411
time for n.primemr1? is 0.617031376
time for n.primemr2? is 0.584806694
time for n.primemr3? is 0.591961562
test value 303371455241 is prime?: true
time for n.primemr? is 0.020221291
time for n.primemr1? is 0.018887651
time for n.primemr2? is 0.022730917
time for n.primemr3? is 0.017800883
test value 8446744073709551627 is prime?: false
time for n.primemr? is 0.023692471
time for n.primemr1? is 0.024016789
time for n.primemr2? is 0.013324277
time for n.primemr3? is 0.019741071
test value 8446744073709551556 is prime?: false
time for n.primemr? is 0.00981716
time for n.primemr1? is 0.002083217
time for n.primemr2? is 0.001528687
time for n.primemr3? is 0.001532383
test value 18446744073709551556 is prime?: false
time for n.primemr? is 0.009846595
time for n.primemr1? is 0.002255851
time for n.primemr2? is 0.001545298
time for n.primemr3? is 0.001540399
test value 18446744073709551557 is prime?: true
time for n.primemr? is 0.098092364
time for n.primemr1? is 0.074849837
time for n.primemr2? is 0.057987474
time for n.primemr3? is 0.050729434
test value 18446744073709551615 is prime?: false
time for n.primemr? is 0.032238006
time for n.primemr1? is 0.002349256
time for n.primemr2? is 0.001806658
time for n.primemr3? is 0.001847625
test value 18446744073709551629 is prime?: true
time for n.primemr? is 0.103820035
time for n.primemr1? is 0.085631054
time for n.primemr2? is 0.065799875
time for n.primemr3? is 0.062917339
test value 340282366920938463463374607431768211296 is prime?: false
time for n.primemr? is 0.034392627
time for n.primemr1? is 0.003315758
time for n.primemr2? is 0.001747036
time for n.primemr3? is 0.001703224
test value 340282366920938463463374607431768211297 is prime?: true
time for n.primemr? is 0.21347393
time for n.primemr1? is 0.191538654
time for n.primemr2? is 0.165191455
time for n.primemr3? is 0.130311444
test value 340282366920938463463374607431768211455 is prime?: false
time for n.primemr? is 0.034583705
time for n.primemr1? is 0.003264902
time for n.primemr2? is 0.001701821
time for n.primemr3? is 0.001677576
Ruby 3.4-preview1
est value 100000000000000000000000000000000000000000000000000000000000000000000000001309503 is prime?: true
time for n.primemr? is 0.635770087
time for n.primemr1? is 0.638503523
time for n.primemr2? is 0.595368691
time for n.primemr3? is 0.598772634
test value 303371455241 is prime?: true
time for n.primemr? is 0.020588841
time for n.primemr1? is 0.019819027
time for n.primemr2? is 0.022277577
time for n.primemr3? is 0.017595767
test value 8446744073709551627 is prime?: false
time for n.primemr? is 0.024912559
time for n.primemr1? is 0.027428728
time for n.primemr2? is 0.014424921
time for n.primemr3? is 0.025096815
test value 8446744073709551556 is prime?: false
time for n.primemr? is 0.011165799
time for n.primemr1? is 0.002304622
time for n.primemr2? is 0.001619867
time for n.primemr3? is 0.001628684
test value 18446744073709551556 is prime?: false
time for n.primemr? is 0.012746023
time for n.primemr1? is 0.003037716
time for n.primemr2? is 0.002829116
time for n.primemr3? is 0.001748089
test value 18446744073709551557 is prime?: true
time for n.primemr? is 0.099865469
time for n.primemr1? is 0.077873137
time for n.primemr2? is 0.059939405
time for n.primemr3? is 0.055619184
test value 18446744073709551615 is prime?: false
time for n.primemr? is 0.035954957
time for n.primemr1? is 0.002472667
time for n.primemr2? is 0.001887079
time for n.primemr3? is 0.001818871
test value 18446744073709551629 is prime?: true
time for n.primemr? is 0.104930787
time for n.primemr1? is 0.08522826
time for n.primemr2? is 0.068326143
time for n.primemr3? is 0.064138119
test value 340282366920938463463374607431768211296 is prime?: false
time for n.primemr? is 0.035416507
time for n.primemr1? is 0.003739953
time for n.primemr2? is 0.001777073
time for n.primemr3? is 0.00171192
test value 340282366920938463463374607431768211297 is prime?: true
time for n.primemr? is 0.21398621
time for n.primemr1? is 0.190769001
time for n.primemr2? is 0.171413123
time for n.primemr3? is 0.131613246
test value 340282366920938463463374607431768211455 is prime?: false
time for n.primemr? is 0.034755878
time for n.primemr1? is 0.003716379
time for n.primemr2? is 0.001799555
time for n.primemr3? is 0.001675553
My system
➜ ~ neofetch
ooooooooooooo jzakiya@jz1
ooooooooooooooooooooo -----------
oooooooooooooooooooooooooo OS: PCLinuxOS x86_64
oooooooo oooooooo Host: 83DH Legion Slim 5 16AHP9
oooooo oooooo Kernel: 6.6.58-pclos1
oooooo ooooo Uptime: 5 hours, 5 mins
ooooo pppppppp cccccccc ooooo Packages: 2660 (rpm)
oooo ppp pppp ccccccccc oooo Shell: zsh 5.8
ooooo ppp ppp ccccc ooooo Resolution: 2560x1600
ooooo ppp ppp cccc ooooo DE: Plasma 5.27.11
ooooo ppppppp ccccc ooooo WM: KWin
ooooo ppp cccccccc ooooo WM Theme: Breeze
ooooo ppp ccccccc ooooo Theme: [Plasma], Breeze [GTK3]
ooooo oooooo Icons: [Plasma], breeze [GTK2/3]
ooooo ooooooo Terminal: konsole
ooooooo ooooooo CPU: AMD Ryzen 7 8845HS w/ Radeon 780M Graphics (16) @ 3.800GHz
oooooooooooooooooooooooo GPU: AMD ATI 05:00.0 Device 1900
oooooooooooooooooo GPU: NVIDIA GeForce RTX 4070 Max-Q / Mobile
ooooooooo Memory: 2901MiB / 15306MiB