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【Go言語】浮動小数点
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Tomoki Ota
July 20, 2024
Programming
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58
【Go言語】浮動小数点
Go言語の浮動小数点について、解説しています。
【Qiita】
【Go言語】浮動小数点
Tomoki Ota
July 20, 2024
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Transcript
Tomoki Ota ʲGoݴޠʳුಈখ
f loat32 f loat64 Goͷුಈখܕ 2
Goͷුಈখܕ 3
Goͷුಈখܕ 1.0001 * 1.0001 = 1.00020001 ؙΊޡࠩͰग़ྗ݁Ռ1.0002ʹͳΔ 4
খ : ແݶݸଘࡏ͢Δ f loat64 : ༗ݶɻ64bit Goͷුಈখܕ 5
ූ߸s, ԾF, ࢦeͷͱ͖ͷ10ਐЋ Goͷුಈখܕ α = (−1)s × F ×
2e 6
Goͷුಈখܕ 1.0001 = 1 × 1.000100016593933 × 20 ූ߸s, ԾF,
ࢦeͷͱ͖ͷ10ਐЋ 7
୯ਫ਼ුಈখ( f loat32) : ࢦ8ϏοτɺԾ23Ϗοτ ഒਫ਼ුಈখܕ( f loat64) : ࢦ11ϏοτɺԾ52Ϗοτ
Goͷුಈখܕ 8
Goͷුಈখܕ ූ߸ ࢦ(8bit) Ծ(23bit) 0 1111111 00000000000001101000111 9
ൺֱ ϓϩηοαʹґଘ͢Δ ಛघͳුಈখ ޡࠩͷੵ ۙࣅΛ͏͜ͱʹΑΔฐ 10
ۙࣅΛ͏ͱɺ==Λ༻ͨ͠ൺֱ͕ෆਖ਼֬ʹͳΔ߹ ͕͋Δɻ goͷςετϥΠϒϥϦtestify ʹൺֱ͍ͯ͠Δ͕Ўͷ ൣғͰ͋Δ͜ͱΛݕࠪ͢ΔͨΊͷInDelta͕ଘࡏ͢Δɻ ൺֱ 11
ϓϩηοαʹɺුಈখԋࢉΛॲཧ͢Δුಈখԋࢉ Ϣχοτ(Floating Point Unit, FPU)͕͋Δɻ ॲཧ݁ՌFPUʹґଘ͢ΔͷͰɺFPU͕ҟͳΔผͷϚγϯͰ ಉ݁͡ՌʹͳΔอূͳ͍ɻ ͪ͜Β 𝛿 Λߟ͑Δ͜ͱͰղܾ͢Δɻ
ϓϩηοαʹґଘ͢Δ 12
ϓϩηοαʹɺුಈখԋࢉΛॲཧ͢Δුಈখԋࢉ Ϣχοτ(Floating Point Unit, FPU)͕͋Δɻ ॲཧ݁ՌFPUʹґଘ͢ΔͷͰɺFPU͕ҟͳΔผͷϚγϯͰ ಉ݁͡ՌʹͳΔอূͳ͍ɻ ͪ͜Β 𝛿 Λߟ͑Δ͜ͱͰղܾ͢Δɻ
ಛघͳුಈখ 13
• ਖ਼ͷແݶେ • ෛͷແݶେ •NaN(Not-a-Number) ಛघͳුಈখ 14
NaNf != fΛຬͨ͢།Ұͷුಈখ ಛघͳුಈখ 15
ಛघͳුಈখ 16
ಛघͳුಈখ ͜ΕΒ3ͭͷුಈখʹ͍ͭͯͷൺֱɺ math.IsInf(ແݶ)Ͱɺmath.IsNan(NaN)ͰൺֱͰ͖ Δɻ 17
ޡࠩͷੵ(Ճࢉɾݮࢉ) 10000ʹ1.0001ΛnճՃࢉ͢ΔϓϩάϥϜ 18
ޡࠩͷੵ(Ճࢉɾݮࢉ) 1.0001ΛnճՃࢉͯ͠ɺ࠷ޙʹ10000ΛՃࢉ͢ΔϓϩάϥϜ 19
ޡࠩͷੵ(Ճࢉɾݮࢉ) n ਖ਼֬ͳ f1 f2 10 10010.001 10010.001 10010.001 1K
11000.1 11000.0999999993 11000.1 1M 1.0101E+06 1.01009999997614E+06 1.01009999997668E+06 ՃࢉݮࢉΛ࿈ଓͯ͠ߦ͏߹ɺେ͖͞ͷ͍ۙΛ·ͱΊͯܭࢉ͔ͯ͠Β େ͖ͳΛՃࢉɾݮࢉ͢Δͱɺޡ͕ࠩখ͘͞ͳΔɻ 20
ޡࠩͷੵ(ࢉɾআࢉ) a × (b + c) a × b +
a × c v.s. 21
ޡࠩͷੵ(ࢉɾআࢉ) a × (b + c) a × b +
a × c v.s. 22
ޡࠩͷੵ(ࢉɾআࢉ) a × b + a × c ͷํ͕ޡ͕ࠩগͳ͍ ՃࢉɾݮࢉΑΓࢉɾՃࢉΛઌʹߦ͏ͱ
ޡࠩΛখ͘͢͞Δ͜ͱ͕Ͱ͖Δ 23
Goͷ f loat32, f loat64ۙࣅΛͱΔͷͰɺޡ͕ࠩൃੜ͢Δ Ճࢉɾݮࢉಉܻ͡ͷԋࢉΛ·ͱΊͯߦ͏͜ͱͰɺਫ਼্͕͕Δ ࢛ଇԋࢉ͕ࠞ߹͢Δ߹ɺࢉͱআࢉΛઌʹߦ͏͜ͱͰɺਫ਼্͕͕Δ ·ͱΊ 24