From: jzakiya@... Date: 2017-02-20T05:04:11+00:00 Subject: [ruby-core:79619] [Ruby trunk Feature#13219] bug in Math.sqrt(n).to_i, to compute integer squareroot, new word to accurately fix it Issue #13219 has been updated by Jabari Zakiya. ``` class Integer def irootn(n) return nil if self < 0 && n.even? raise "root n is < 2 or not an Integer" unless n.is_a?(Integer) && n > 1 num = self.abs bits_shift = (num.bit_length)/n + 2 root, bitn_mask = 0, (1 << bits_shift) until (bitn_mask >>= 1) == 0 root |= bitn_mask root ^= bitn_mask if root**n > num end root *= (self < 0 ? -1 : 1) end def iroot2; irootn(2) end end require "bigdecimal" require "benchmark/ips" Benchmark.ips do |x| n = 10**35 puts "integer squareroot tests for n = #{n}" x.report("iroot2" ) { n.iroot2 } x.report("irootn(2)" ) { n.irootn(2) } x.report("BigDecimal(n).sqrt(5 ).to_i") { BigDecimal(n).sqrt(5 ).to_i } x.report("BigDecimal(n).sqrt(10).to_i") { BigDecimal(n).sqrt(10).to_i } x.report("BigDecimal(n).sqrt(20).to_i") { BigDecimal(n).sqrt(20).to_i } x.compare! end ``` Yes, its much slower, even to the highlevel Ruby versions. ``` 2.4.0 :201 > load 'irootstest.rb' integer squareroot tests for n = 100000000000000000000000000000000000 Warming up -------------------------------------- iroot2 5.681k i/100ms irootn(2) 5.714k i/100ms BigDecimal(n).sqrt(5 ).to_i 3.021k i/100ms BigDecimal(n).sqrt(10).to_i 2.953k i/100ms BigDecimal(n).sqrt(20).to_i 2.616k i/100ms Calculating ------------------------------------- iroot2 57.825k (�� 3.3%) i/s - 289.731k in 5.016021s irootn(2) 57.462k (�� 3.7%) i/s - 291.414k in 5.078940s BigDecimal(n).sqrt(5 ).to_i 30.543k (�� 2.8%) i/s - 154.071k in 5.048265s BigDecimal(n).sqrt(10).to_i 30.709k (�� 3.1%) i/s - 153.556k in 5.005239s BigDecimal(n).sqrt(20).to_i 26.725k (�� 3.0%) i/s - 136.032k in 5.094723s Comparison: iroot2: 57825.2 i/s irootn(2): 57461.9 i/s - same-ish: difference falls within error BigDecimal(n).sqrt(10).to_i: 30708.9 i/s - 1.88x slower BigDecimal(n).sqrt(5 ).to_i: 30543.4 i/s - 1.89x slower BigDecimal(n).sqrt(20).to_i: 26725.0 i/s - 2.16x slower => true 2.4.0 :202 ``` And you need to know beforehand the needed correct precision to display the correct results. ``` 2.4.0 :214 > n = 10**35; puts n, n.iroot2, BigDecimal(n).sqrt(5).to_i, BigDecimal(n).sqrt(10).to_i,BigDecimal(n).sqrt(20).to_i 100000000000000000000000000000000000 316227766016837933 316227766016837933 316227766016837933 316227766016837933 => nil 2.4.0 :215 > n = 10**45; puts n, n.iroot2, BigDecimal(n).sqrt(5).to_i, BigDecimal(n).sqrt(10).to_i,BigDecimal(n).sqrt(20).to_i 1000000000000000000000000000000000000000000000 31622776601683793319988 31622776601683666666666 31622776601683666666666 31622776601683793319988 => nil 2.4.0 :216 > n = 10**55; puts n, n.iroot2, BigDecimal(n).sqrt(5).to_i, BigDecimal(n).sqrt(10).to_i,BigDecimal(n).sqrt(20).to_i 10000000000000000000000000000000000000000000000000000000 3162277660168379331998893544 3162277660168379331499021527 3162277660168379331499021527 3162277660168379331998893544 => nil 2.4.0 :217 > n = 10**65; puts n, n.iroot2, BigDecimal(n).sqrt(5).to_i, BigDecimal(n).sqrt(10).to_i,BigDecimal(n).sqrt(20).to_i 100000000000000000000000000000000000000000000000000000000000000000 316227766016837933199889354443271 316227766016837466536394723986322 316227766016837466536394723986322 316227766016837933199889000000000 => nil 2.4.0 :218 > ``` ---------------------------------------- Feature #13219: bug in Math.sqrt(n).to_i, to compute integer squareroot, new word to accurately fix it https://bugs.ruby-lang.org/issues/13219#change-63041 * Author: Jabari Zakiya * Status: Open * Priority: Normal * Assignee: * Target version: ---------------------------------------- In doing a math application using **Math.sqrt(n).to_i** to compute integer squareroots of integers I started noticing errors for numbers > 10**28. I coded an algorithm that accurately computes the integer squareroot for arbirary sized numbers but its significantly slower than the math library written in C. Thus, I request a new method **Math.intsqrt(n)** be created, that is coded in C and part of the core library, that will compute the integer squareroots of integers accurately and fast. Here is working highlevel code to accurately compute the integer squareroot. ``` def intsqrt(n) bits_shift = (n.to_s(2).size)/2 + 1 bitn_mask = root = 1 << bits_shift while true root ^= bitn_mask if (root * root) > n bitn_mask >>= 1 return root if bitn_mask == 0 root |= bitn_mask end end def intsqrt1(n) return n if n | 1 == 1 # if n is 0 or 1 bits_shift = (Math.log2(n).ceil)/2 + 1 bitn_mask = root = 1 << bits_shift while true root ^= bitn_mask if (root * root) > n bitn_mask >>= 1 return root if bitn_mask == 0 root |= bitn_mask end end require "benchmark/ips" Benchmark.ips do |x| n = 10**40 puts "integer squareroot tests for n = #{n}" x.report("intsqrt(n)" ) { intsqrt(n) } x.report("intsqrt1(n)" ) { intsqrt1(n) } x.report("Math.sqrt(n).to_i") { Math.sqrt(n).to_i } x.compare! end ``` Here's why it needs to be done in C. ``` 2.4.0 :178 > load 'intsqrttest.rb' integer squareroot tests for n = 10000000000000000000000000000000000000000 Warming up -------------------------------------- intsqrt(n) 5.318k i/100ms intsqrt1(n) 5.445k i/100ms Math.sqrt(n).to_i 268.281k i/100ms Calculating ------------------------------------- intsqrt(n) 54.219k (�� 5.5%) i/s - 271.218k in 5.017552s intsqrt1(n) 55.872k (�� 5.4%) i/s - 283.140k in 5.082953s Math.sqrt(n).to_i 5.278M (�� 6.1%) i/s - 26.560M in 5.050707s Comparison: Math.sqrt(n).to_i: 5278477.8 i/s intsqrt1(n): 55871.7 i/s - 94.47x slower intsqrt(n): 54219.4 i/s - 97.35x slower => true 2.4.0 :179 > ``` Here are examples of math errors using **Math.sqrt(n).to_i** run on Ruby-2.4.0. ``` 2.4.0 :101 > n = 10**27; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 1000000000000000000000000000 31622776601683 999999999999949826038432489 31622776601683 999999999999949826038432489 31622776601683 999999999999949826038432489 => nil 2.4.0 :102 > n = 10**28; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 10000000000000000000000000000 100000000000000 10000000000000000000000000000 100000000000000 10000000000000000000000000000 100000000000000 10000000000000000000000000000 => nil 2.4.0 :103 > n = 10**29; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 100000000000000000000000000000 316227766016837 99999999999999409792567484569 316227766016837 99999999999999409792567484569 316227766016837 99999999999999409792567484569 => nil 2.4.0 :104 > n = 10**30; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 1000000000000000000000000000000 1000000000000000 1000000000000000000000000000000 1000000000000000 1000000000000000000000000000000 1000000000000000 1000000000000000000000000000000 => nil 2.4.0 :105 > n = 10**31; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 10000000000000000000000000000000 3162277660168379 9999999999999997900254631487641 3162277660168379 9999999999999997900254631487641 3162277660168379 9999999999999997900254631487641 => nil 2.4.0 :106 > n = 10**32; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 100000000000000000000000000000000 10000000000000000 100000000000000000000000000000000 10000000000000000 100000000000000000000000000000000 10000000000000000 100000000000000000000000000000000 => nil 2.4.0 :107 > n = 10**33; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 1000000000000000000000000000000000 31622776601683793 999999999999999979762122758866849 31622776601683793 999999999999999979762122758866849 31622776601683792 999999999999999916516569555499264 => nil 2.4.0 :108 > n = 10**34; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 10000000000000000000000000000000000 100000000000000000 10000000000000000000000000000000000 100000000000000000 10000000000000000000000000000000000 100000000000000000 10000000000000000000000000000000000 => nil 2.4.0 :109 > n = 10**35; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 100000000000000000000000000000000000 316227766016837933 99999999999999999873578871987712489 316227766016837933 99999999999999999873578871987712489 316227766016837952 100000000000000011890233980627554304 => nil 2.4.0 :110 > n = 10**36; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 1000000000000000000000000000000000000 1000000000000000000 1000000000000000000000000000000000000 1000000000000000000 1000000000000000000000000000000000000 1000000000000000000 1000000000000000000000000000000000000 => nil 2.4.0 :111 > n = 10**37; puts n, (a = intsqrt(n)), a*a, (b = intsqrt1(n)), b*b, (c = Math.sqrt(n).to_i), c*c 10000000000000000000000000000000000000 3162277660168379331 9999999999999999993682442519108007561 3162277660168379331 9999999999999999993682442519108007561 3162277660168379392 10000000000000000379480317059650289664 => nil 2.4.0 :112 > ``` -- https://bugs.ruby-lang.org/ Unsubscribe: