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Tomoki Ota ʲGoݴޠʳුಈখ਺఺

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f loat32 f loat64 Goͷුಈখ਺఺ܕ 2

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Goͷුಈখ਺఺ܕ 3

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Goͷුಈখ਺఺ܕ 1.0001 * 1.0001 = 1.00020001 ؙΊޡࠩͰग़ྗ݁Ռ͸1.0002ʹͳΔ 4

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খ਺ : ແݶݸଘࡏ͢Δ f loat64 : ༗ݶɻ64bit Goͷුಈখ਺఺ܕ 5

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ූ߸s, Ծ਺F, ࢦ਺eͷͱ͖ͷ10ਐ਺Ћ Goͷුಈখ਺఺ܕ α = (−1)s × F × 2e 6

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Goͷුಈখ਺఺ܕ 1.0001 = 1 × 1.000100016593933 × 20 ූ߸s, Ծ਺F, ࢦ਺eͷͱ͖ͷ10ਐ਺Ћ 7

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୯ਫ਼౓ුಈখ਺఺( f loat32) : ࢦ਺8ϏοτɺԾ਺23Ϗοτ ഒਫ਼౓ුಈখ਺఺ܕ( f loat64) : ࢦ਺11ϏοτɺԾ਺52Ϗοτ Goͷුಈখ਺఺ܕ 8

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Goͷුಈখ਺఺ܕ ූ߸ ࢦ਺(8bit) Ծ਺(23bit) 0 1111111 00000000000001101000111 9

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ൺֱ ϓϩηοαʹґଘ͢Δ ಛघͳුಈখ਺఺ ޡࠩͷ஝ੵ ۙࣅ஋Λ࢖͏͜ͱʹΑΔฐ֐ 10

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ۙࣅ஋Λ࢖͏ͱɺ==Λ࢖༻ͨ͠ൺֱ͕ෆਖ਼֬ʹͳΔ৔߹ ͕͋Δɻ goͷςετϥΠϒϥϦtestify ʹ͸ൺֱ͍ͯ͠Δ஋͕Ўͷ ൣғ಺Ͱ͋Δ͜ͱΛݕࠪ͢ΔͨΊͷInDelta͕ଘࡏ͢Δɻ ൺֱ 11

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ϓϩηοαʹ͸ɺුಈখ਺఺ԋࢉΛॲཧ͢Δුಈখ਺఺ԋࢉ Ϣχοτ(Floating Point Unit, FPU)͕͋Δɻ ॲཧ݁Ռ͸FPUʹґଘ͢ΔͷͰɺFPU͕ҟͳΔผͷϚγϯͰ ಉ݁͡ՌʹͳΔอূ͸ͳ͍ɻ ͪ͜Β΋ 𝛿 Λߟ͑Δ͜ͱͰղܾ͢Δɻ ϓϩηοαʹґଘ͢Δ 12

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ϓϩηοαʹ͸ɺුಈখ਺఺ԋࢉΛॲཧ͢Δුಈখ਺఺ԋࢉ Ϣχοτ(Floating Point Unit, FPU)͕͋Δɻ ॲཧ݁Ռ͸FPUʹґଘ͢ΔͷͰɺFPU͕ҟͳΔผͷϚγϯͰ ಉ݁͡ՌʹͳΔอূ͸ͳ͍ɻ ͪ͜Β΋ 𝛿 Λߟ͑Δ͜ͱͰղܾ͢Δɻ ಛघͳුಈখ਺఺਺ 13

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• ਖ਼ͷແݶେ • ෛͷແݶେ •NaN(Not-a-Number) ಛघͳුಈখ਺఺਺ 14

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NaN͸f != fΛຬͨ͢།Ұͷුಈখ਺఺਺ ಛघͳුಈখ਺఺਺ 15

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ಛघͳුಈখ਺఺਺ 16

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ಛघͳුಈখ਺఺਺ ͜ΕΒ3ͭͷුಈখ਺఺਺ʹ͍ͭͯͷൺֱ͸ɺ math.IsInf(ແݶ)Ͱɺmath.IsNan(NaN)ͰൺֱͰ͖ Δɻ 17

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ޡࠩͷ஝ੵ(Ճࢉɾݮࢉ) 10000ʹ1.0001ΛnճՃࢉ͢ΔϓϩάϥϜ 18

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ޡࠩͷ஝ੵ(Ճࢉɾݮࢉ) 1.0001ΛnճՃࢉͯ͠ɺ࠷ޙʹ10000ΛՃࢉ͢ΔϓϩάϥϜ 19

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ޡࠩͷ஝ੵ(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 Ճࢉ΍ݮࢉΛ࿈ଓͯ͠ߦ͏৔߹͸ɺେ͖͞ͷ͍ۙ஋Λ·ͱΊͯܭࢉ͔ͯ͠Β େ͖ͳ஋ΛՃࢉɾݮࢉ͢Δͱɺޡ͕ࠩখ͘͞ͳΔɻ 20

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ޡࠩͷ஝ੵ(৐ࢉɾআࢉ) a × (b + c) a × b + a × c v.s. 21

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ޡࠩͷ஝ੵ(৐ࢉɾআࢉ) a × (b + c) a × b + a × c v.s. 22

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ޡࠩͷ஝ੵ(৐ࢉɾআࢉ) a × b + a × c ͷํ͕ޡ͕ࠩগͳ͍ ՃࢉɾݮࢉΑΓ৐ࢉɾՃࢉΛઌʹߦ͏ͱ ޡࠩΛখ͘͢͞Δ͜ͱ͕Ͱ͖Δ 23

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Goͷ f loat32, f loat64͸ۙࣅ஋ΛͱΔͷͰɺޡ͕ࠩൃੜ͢Δ Ճࢉɾݮࢉ͸ಉܻ͡਺ͷԋࢉΛ·ͱΊͯߦ͏͜ͱͰɺਫ਼౓্͕͕Δ ࢛ଇԋࢉ͕ࠞ߹͢Δ৔߹ɺ৐ࢉͱআࢉΛઌʹߦ͏͜ͱͰɺਫ਼౓্͕͕Δ ·ͱΊ 24