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#渋谷java : Java の数学関数を計算速度的に極めたい
KOMIYA Atsushi
April 23, 2016
Programming
7
950
#渋谷java : Java の数学関数を計算速度的に極めたい
第十五回 #渋谷java
http://shibuya-java.connpass.com/event/29113/
での発表資料です。
KOMIYA Atsushi
April 23, 2016
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Transcript
Java ͷֶؔΛ ܭࢉతʹۃΊ͍ͨ ौ୩ Java 15th, 2016-04-23 KOMIYA Atsushi
͓·͑ͩΕΑ
KOMIYA Atsushi @komiya_atsushi
None
Spark ຊΛॻ͖·ͨ͠ͷͰ ΑΖ͚͠Εͥͻ͝ߪೖ͍ͩ͘͞ʂ
ࠓͷτϐοΫ
Java ͷֶؔ
java.lang.Math ͔Β࢝Ίͯ Java ͷֶؔͷܭࢉΛ ٻ͍͖ͯ͠·͢
Implementations of Math functions in JDK
java.lang.Math & java.lang.StrictMath
JDK ඪ४ͷֶؔ • ֶؔͷ࣮ͱͯ͠ java.lang.Math ͱ java.lang.StrictMath ͕ఏڙ͞Ε͍ͯΔ • ͦΕͧΕԿ͕ҧ͏ͷ͔ʁ
java.lang.StrictMath • https://docs.oracle.com/javase/jp/8/docs/api/java/lang/ StrictMath.html ΑΓ • ʮJavaϓϩάϥϜͷҠ২ੑΛอͭͨΊʹɺ͜ͷύοέʔδʹ͋ΔҰ ෦ͷؔͷఆٛɺطଘͷΞϧΰϦζϜͱಉҰͷܭࢉ݁ՌΛग़ ͢͜ͱ͕ٻΊΒΕ͍ͯ·͢ɻ͜͏ͨ͠ΞϧΰϦζϜɺ༗໊ͳωο τϫʔΫɾϥΠϒϥϦͰ͋Δnetlib͔ΒʮFreely
Distributable Math Libraryʯ(fdlibm)ύοέʔδͱͯ͠ೖखՄೳͰ͢ɻ͜ΕΒͷΞϧΰ ϦζϜCݴޠͰهड़͞Ε͓ͯΓɺͯ͢ͷුಈখԋࢉ͕Java ͷුಈখԋࢉϧʔϧʹै࣮ͬͯߦ͞ΕΔͷͱݟͳ͞Ε· ͢ɻʯ
java.lang.StrictMath • ҟͳΔϓϥοτϑΥʔϜ (OS, CPU ͳͲ) ʹ ͓͍ͯɺϏοτύλʔϯͷϨϕϧͰಉ݁͡Ռ ͕ฦ͞ΕΔ͜ͱ (࠶ݱੑ)
͕อূ͞Ε͍ͯΔ • ੑೳೋͷ࣍
java.lang.Math • https://docs.oracle.com/javase/jp/8/docs/api/ java/lang/Math.html ΑΓ • ʮStrictMathΫϥεͷҰ෦ͷϝιουͱҟͳ ΓɺMathΫϥεͷՁؔͷͯ͢ͷ࣮ɺ ϏοτରϏοτͷಉ݁͡ՌΛฦ͢Α͏ʹఆٛ͞Ε ͍ͯ·ͤΜɻ͜ͷΏΔ͔͞ʹΑͬͯɺݫີͳ࠶ݱ
ੑ͕ཁٻ͞Εͳ͍࣮ʹ͓͍ͯύϑΥʔϚϯεͷ ্͕ՄೳʹͳΓ·͢ɻʯ
java.lang.Math • CPU ʹґଘ໋ͨ͠ྩͳͲར༻͠ͳ͕Βɺ ΑΓΑ͍ੑೳΛఏڙ͢Δ • ͨͩ͠ʮਖ਼֬͞ʯΛ٘ਜ਼ʹ͢ΔΘ͚Ͱͳ͍ • ࣮༷తʹʮਖ਼֬͞ʯʮ୯ௐੑʯ͕ཁٻ ͞Ε͍ͯΔ
Alternatives of java.lang.Math
commons-math3 org.apache.commons:commons-math3:3.6.1
commons-math3 • FastMath Ϋϥε͕ఏڙ͞Ε͍ͯΔ • java.lang.Math ͱಉ͡ϝιουߏ • ΑΓ͘ɺ͔ͭਫ਼͕ߴ͍͜ͱΛᨳ͍ͬͯΔ •
JIT ʹΑΔ࠷దԽΛલఏͱ͠ɺ·ͨେ͖Ίͷ ϧοΫΞοϓςʔϒϧΛར༻ͯ͠ߴԽΛਤͬ ͍ͯΔ
jafama net.jafama:jafama:2.1.0
jafama • ͪ͜Β FastMath Ϋϥε͕ఏڙ͞Ε͍ͯΔ • 1e-15 (0.000000000000001) ͷਫ਼Β͍͠ •
JIT ʹΑΔ࠷దԽΛલఏͱ͍ͯ͠Δ • ਫ਼Λ٘ਜ਼ʹͨ͠ɺֶؔͷߴ࣮ఏڙ͞ Ε͍ͯΔ • xxxQuick() ͷΑ͏ʹɺ”Quick” ͷαϑΟοΫε͕ ͍͍ͯΔ
Comparison: performance
ܭࢉͷൺֱ • java.lang.Math ͱ commons-math3, jafama ͱΛൺֱ͢Δ • jmh ͰεϧʔϓοτΛܭଌ͢Δ
• ࣍ͷֶؔͦΕͧΕʹ͍ͭͯܭଌ͢Δ • log, log1p, exp, tanh, pow, sqrt • ػցֶशͷ࣮ʹͯΑ͘ར༻͢Δؔ܈Ͱ͢ • ֶؔʹɺεέʔϧͷҟͳΔҾΛෳ༻ҙ͢Δ • ಛఆͷ (۠ؒ) ʹରԠͨ͠࠷దԽ࣮͕͞Ε͍ͯΔ߹ ͕͋ΔͨΊ
ϕϯνϚʔΫϓϩάϥϜ https://github.com/komiya-atsushi/ java-playground/tree/master/math- functions
log
log • commons-math3 ͕಄ͻͱͭൈ͖Μग़͍ͯΔ • 1.234 ͷҾΛ༩͑ͨͱ͖ͷੑೳ͕ҟৗత ʹඈͼൈ͚͍ͯΔ͚Ͳɺ͜ΕΘΓͱී௨ Ͱ͢ •
jafama ͱ jdk ΄΅ಉ͡ੑೳ
log1p
log1p • log ͱҟͳΓɺjafama ͕ѹతʹΑ͍ • jdk ͱ commons-math3 େࠩͳ͍͕ɺ
jdk > commons-math3 Ͱ͋Δ • commons-math3 ͷ log ͷ݁ՌԿͩͬͨ ͷ͔…
exp
exp • commons-math3, jafama ͱʹɺҾ͕େ͖ ͘ͳΔʹͭΕͯੑೳ͕ߴ·Δ • ಛʹ jafama શൠతʹੑೳ͕Α͍
• ҰํͰ jdk …
tanh
tanh • ͍ͣΕͷ࣮ɺҾͷεέʔϧ͕େ͖͘ͳ Δͱɺੑೳ͕Α͘ͳΔ • jafama > commons-math3 > jdk
sqrt
sqrt • େࠩͳ͍ • ͲΕΛͬͯ΄ͱΜͲಉ͡
pow
pow • jafama ϐʔΩʔͰ͋Δ͕ɺશମతʹ༏Ε͍ͯ Δ • jdk ϐʔΩʔա͗Δ • power
͕খ͍͞߹ commons-math3 ΑΓ Α͍ੑೳͰ͋Δ • commons-math3 ຌ༱
Comparison: accuracy
ܭࢉਫ਼ͷൺֱ • java.lang.StrictMath ʹ͓͚Δ࣮ͷΓͱൺֱ͢Δ • (StrictMath ͷ͕ਖ਼͍͠Θ͚Ͱͳ͍ͷ͕ͩ…) • Γಉ࢜ͷࠩʹର͠ɺStrictMath ଆͷΓΛ
ͱׂͯ͠߹Λܭࢉ͢Δ • ͦͷׂ߹ͷฏۉઈରͱ࠷େͰਫ਼ΛݟͯΈΔ • Ҿͷݻఆͤͣɺཚੜͨ͠ͷΛ༩͑Δ
Result: average DPNNPOTNBUI KBGBNB MPH & & MPHQ & &
FYQ & & UBOI & & TRSU & &
Result: maximum DPNNPOTNBUI KBGBNB MPH & & MPHQ & &
FYQ & & UBOI & & TRSU & &
Result • ͍ͣΕʹ͓͍ͯɺେ͖ͳࠩҟ͕͋ΔΘ͚Ͱ ͳ͍ • 1e-15 ͷਫ਼อূͰ͖ͦ͏ • jafama ʹ͍ͭͯɺStrictMath
ͷΓͱҟ ͳΔ͜ͱ͕ଟ͍ʹ͋Γͦ͏
Conclusion
·ͱΊ • ʮۜͷؙଘࡏ͠ͳ͔ͬͨʯ • “FastMath” ͱ໊͍ͬͯͯɺͯ͢ͷֶؔ ͷ࣮ʹ͓͍ͯ JDK ͷ࣮ΑΓ༏Ε͍ͯΔɺͱ ͍͏Θ͚Ͱͳ͍
• ·ͨɺֶؔʹ༩͑ΔҾ࣍ୈͰੑೳ͕େ͖͘ҟΔ ͜ͱ͋Γ͏Δ • ϢʔεέʔεʹԠͯ͡ɺ֤छ࣮Λ͍͚Δ͜ͱ͕ ඞཁ
Thank you!