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小数の丸め誤差の話
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circled9
July 26, 2024
Programming
0
150
小数の丸め誤差の話
Niigata5分Tech #10の発表資料です。
https://niigata-5min-tech.connpass.com/event/324842/
circled9
July 26, 2024
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Transcript
খͷؙΊޡࠩͷ Niigata 5min Tech #10 @circled9 1
ࣗݾհ @circled9 দҪɹਖ਼ࢤ / Matsui Masashi גࣜձࣾϞχΫϧ جຊใٕज़ऀͷࢿ֨͋Γ·͕͢ هԱ͋Γ·ͤΜ 2
ࠓখͷؙΊޡࠩͷΛ͠·͢ 3
Node.js 4
Ͳ͏ͯ͠ʁ • ଟ͘ͷϓϩάϥϛϯάݴޠɺ෦తʹΛೋਐͰѻ͍ͬͯΔ • ेਐͷখΛೋਐʹม͢Δͱޡ͕ࠩੜ͡Δ߹͕͋Δ • Ή͠Ζޡ͕ࠩग़ͳ͍ํ͕গͳ͍ͷͰ...? 5
ेਐͷখΛೋਐͰද͢ͷ͍͠ • ೋਐͷͷNܻ2ͷN-1ͷ 1 1 1 1 = 15 8
4 2 1 • ҰํɺೋਐͷখͷNܻ2ͷϚΠφεN-1ͷ 0. 1 1 1 = 0.5 + 0.25 + 0.125 = 0.875 1 1/2 1/4 1/8 • 2ͷϚΠφεNͷΈ߹ΘͤͰਖ਼֬ʹදݱͰ͖Δʹݶք͕͋Δ 6
Node.js 7
Ͳ͏͢ΕޡࠩΛ͛Δ͔ • খͷܭࢉΛͯ͠େৎͳܕͳͲΛ͏ • খͰͳ͘ͷܭࢉʹ͢Δ 8
খͷܭࢉΛͯ͠େৎͳܕͳͲΛ͏ • C#ͷ߹decimalܕ͕͋Δ • Pythonͷ߹decimalϞδϡʔϧ͕͋Δ • JavaScriptͷ߹big.jsͳͲͷϥΠϒϥϦ͕͋Δ 9
Python 10
খͰͳ͘ͷܭࢉʹ͢Δ • ܭࢉ͢Δલʹʹͯ͠ɺܭࢉޙʹখʹ͢ • ྫ͑100Λ͔͚ͯɺ࠷ޙʹ100ͰׂΔ • ((0.1 * 100) +
(0.2 * 100)) / 100 • ͜ͷ߹ɺܭࢉରͷͷܻΛؾʹ͢Δඞཁ͕͋Δ 11
Node.js 12
·ͱΊ • ଟ͘ͷϓϩάϥϛϯάݴޠͰɺখͷܭࢉͰޡ͕ࠩൃੜ͢Δ • ޡࠩΛग़͞ͳ͍Α͏ʹ͢ΔʹదͳରԠΛ͢Δඞཁ͕͋Δ 13
ଟ͘ͷϓϩάϥϛϯάݴޠʁ 14
খͷܭࢉͰޡࠩͷग़ͳ͍ϓϩάϥϛϯάݴޠ • COBOL • Ada • MSX-BASIC • etc... දݱʹBCDΛ͏ͷ͕ϙΠϯτͬΆ͍
15
BCD • Binary-Coded DecimalɺೋਐԽेਐ • ೋਐ4ܻ͋Ε0͔Β15·ͰͷΛදͤΔͷͰɺ0͔Β9Λͬ ͯेਐͷҰܻΛදݱ͢Δ • ྫ͑ेਐͷ26ɺBCDͰ 0010
0110 ʹͳΔ • BCDجຊใٕज़ऀࢼݧͷࢼݧൣғʹؚ·Ε͍ͯΔ 16
BCDجຊใٕज़ऀࢼݧͷ ࢼݧൣғʹؚ·Ε͍ͯΔ 17
શʹΕͯͨͱ͍͏͔ ֮͑ͨهԱ͢Βͳ͍😇 18
Goݴޠ 19
20
https://go.dev/ref/spec#Constant_expressions υΩϡϝϯτᐌ͘ ఆࣜৗʹਖ਼֬ʹධՁ͞Ε·͢ Constant expressions are always evaluated exactly; 21
22
͓͠·͍ 23
ࢀߟࢿྉ • খΛѻ͏ͳΒBCDΛ࠾༻͍ͯ͠Δݴޠ͕ѹత • https://qiita.com/ma2shita/items/d8aeec9e2921dc3536f4 24