ืื ื’ืœื™ืชืฆืจืคืชื™ืชืกืคืจื“ื™

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ืกืžืœ OnWorks

bc - ืžืงื•ื•ืŸ ื‘ืขื ืŸ

ื”ืคืขืœ bc ื‘ืกืคืง ืื™ืจื•ื— ื‘ื—ื™ื ื ืฉืœ OnWorks ืขืœ ืื•ื‘ื•ื ื˜ื• ืžืงื•ื•ืŸ, ืคื“ื•ืจื” ืžืงื•ื•ืŸ, ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ Windows ืื• ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ MAC OS

ื–ื•ื”ื™ ื”ืคืงื•ื“ื” bc ืฉื ื™ืชืŸ ืœื”ืคืขื™ืœ ื‘ืกืคืง ื”ืื™ืจื•ื— ื”ื—ื™ื ืžื™ ืฉืœ OnWorks ื‘ืืžืฆืขื•ืช ืื—ืช ืžืชื—ื ื•ืช ื”ืขื‘ื•ื“ื” ื”ืžืงื•ื•ื ื•ืช ื”ืžืจื•ื‘ื•ืช ืฉืœื ื•, ื›ื’ื•ืŸ Ubuntu Online, Fedora Online, ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ Windows ืื• ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ MAC OS

ืชึธื›ึฐื ึดื™ืช:

ืฉืึตื


bc - ืฉืคืช ืžื—ืฉื‘ื•ืŸ ื“ื™ื•ืง ืฉืจื™ืจื•ืชื™

ืชื—ื‘ื™ืจ


bc [ -hlwsqv ] [ืืคืฉืจื•ื™ื•ืช ืืจื•ื›ื•ืช] [ ืคื™ืœื” ... ]

ืชื™ืื•ืจ


bc ื”ื™ื ืฉืคื” ื”ืชื•ืžื›ืช ื‘ืžืกืคืจื™ ื“ื™ื•ืง ืฉืจื™ืจื•ืชื™ื™ื ืขื ื‘ื™ืฆื•ืข ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ ืฉืœ
ื”ืฆื”ืจื•ืช. ื™ืฉ ื›ืžื” ืงื•ื•ื™ ื“ืžื™ื•ืŸ ื‘ืชื—ื‘ื™ืจ ืœืฉืคืช ื”ืชื›ื ื•ืช C. ื
ืกืคืจื™ื™ืช ืžืชืžื˜ื™ืงื” ืจื’ื™ืœื” ื–ืžื™ื ื” ื‘ืืžืฆืขื•ืช ืืคืฉืจื•ืช ืฉื•ืจืช ื”ืคืงื•ื“ื”. ืื ืชืชื‘ืงืฉ, ืกืคืจื™ื™ืช ื”ืžืชืžื˜ื™ืงื”
ืžื•ื’ื“ืจ ืœืคื ื™ ืขื™ื‘ื•ื“ ืงื‘ืฆื™ื ื›ืœืฉื”ื. bc ืžืชื—ื™ืœ ื‘ืขื™ื‘ื•ื“ ืงื•ื“ ืžื›ืœ ื”ืงื‘ืฆื™ื
ืจืฉื•ื ื‘ืฉื•ืจืช ื”ืคืงื•ื“ื” ื‘ืกื“ืจ ื”ืจืฉื•ื. ืœืื—ืจ ืขื™ื‘ื•ื“ ื›ืœ ื”ืงื‘ืฆื™ื, bc
ืงื•ืจื ืžื”ืงืœื˜ ื”ืกื˜ื ื“ืจื˜ื™. ื›ืœ ื”ืงื•ื“ ืžื‘ื•ืฆืข ืชื•ืš ื›ื“ื™ ืงืจื™ืืชื•. (ืื ืงื•ื‘ืฅ ืžื›ื™ืœ ื
ืคืงื•ื“ื” ืœืขืฆื•ืจ ืืช ื”ืžืขื‘ื“, bc ืœืขื•ืœื ืœื ื™ืงืจื ืžื”ืงืœื˜ ื”ืกื˜ื ื“ืจื˜ื™.)

ื’ืจืกื” ื–ื• ืฉืœ bc ืžื›ื™ืœ ืžืกืคืจ ื”ืจื—ื‘ื•ืช ืžืขื‘ืจ ืœืžืกื•ืจืชื™ bc ื™ื™ืฉื•ืžื™ื ื•
ืชืงืŸ ื˜ื™ื•ื˜ืช POSIX. ืืคืฉืจื•ื™ื•ืช ืฉื•ืจืช ื”ืคืงื•ื“ื” ื™ื›ื•ืœื•ืช ืœื’ืจื•ื ืœื”ืจื—ื‘ื•ืช ืืœื” ืœื”ื“ืคื™ืก ื
ืื–ื”ืจื” ืื• ืœื”ื™ื“ื—ื•ืช. ืžืกืžืš ื–ื” ืžืชืืจ ืืช ื”ืฉืคื” ื”ืžืงื•ื‘ืœืช ืขืœ ื™ื“ื™ ื–ื”
ืžืขื‘ื“. ื”ืจื—ื‘ื•ืช ื™ื–ื•ื”ื• ื›ื›ืืœื”.

ืืคืฉืจื•ื™ื•ืช
-ื—, --ืขื–ืจื”
ื”ื“ืคืก ืืช ื”ืฉื™ืžื•ืฉ ื•ืฆื.

-i, --ืื™ื ื˜ืจืืงื˜ื™ื‘ื™
ื›ืคื” ืžืฆื‘ ืื™ื ื˜ืจืืงื˜ื™ื‘ื™.

-ืœ, -ืžืชืœื™ื‘
ื”ื’ื“ืจ ืืช ืกืคืจื™ื™ืช ื”ืžืชืžื˜ื™ืงื” ื”ืกื˜ื ื“ืจื˜ื™ืช.

-w, --ื”ื–ื”ื™ืจ
ืชืŸ ืื–ื”ืจื•ืช ืขืœ ื”ืจื—ื‘ื•ืช ืœ-POSIX bc.

-s, --ืกื˜ื ื“ืจื˜ื™
ืขื‘ื“ ื‘ื“ื™ื•ืง ืืช ื”-POSIX bc ืฉืคื”.

-ืฉ, -ืฉืงื˜
ืืœ ืชื“ืคื™ืก ืืช ื”ื‘ืจื›ื” ื”ืจื’ื™ืœื” ืฉืœ GNU bc.

-v, --ื’ืจืกื”
ื”ื“ืคืก ืืช ืžืกืคืจ ื”ื’ืจืกื” ื•ื–ื›ื•ื™ื•ืช ื”ื™ื•ืฆืจื™ื ื•ืฆื.

ืžืกืคืจื™ื
ื”ืืœืžื ื˜ ื”ื‘ืกื™ืกื™ ื‘ื™ื•ืชืจ ื‘ bc ื”ื•ื ื”ืžืกืคืจ. ืžืกืคืจื™ื ื”ื ืžืกืคืจื™ื ื“ื™ื•ืง ืฉืจื™ืจื•ืชื™ื™ื.
ื“ื™ื•ืง ื–ื” ื ืžืฆื ื’ื ื‘ื—ืœืง ื”ืฉืœื ื•ื’ื ื‘ื—ืœืง ื”ืฉื‘ืจ. ื›ืœ ื”ืžืกืคืจื™ื ื”ื
ืžื™ื•ืฆื’ ืคื ื™ืžื™ ื‘ืขืฉืจื•ื ื™ ื•ื›ืœ ื”ื—ื™ืฉื•ื‘ ื ืขืฉื” ื‘ืขืฉืจื•ื ื™. (ื’ืจืกื” ื–ื•
ื—ื•ืชืš ืชื•ืฆืื•ืช ืžืคืขื•ืœื•ืช ื—ืœื•ืงื” ื•ื›ืคืœ.) ื™ืฉื ืŸ ืฉืชื™ ืชื›ื•ื ื•ืช ืฉืœ
ืžืกืคืจื™ื, ื”ืื•ืจืš ื•ื”ืงื ื” ืžื™ื“ื”. ื”ืื•ืจืš ื”ื•ื ื”ืžืกืคืจ ื”ื›ื•ืœืœ ืฉืœ ืขืฉืจื•ื ื™ื•ืช ืžืฉืžืขื•ืชื™ื•ืช
ืกืคืจื•ืช ื‘ืžืกืคืจ ื•ื”ืกืงืืœื” ื”ื™ื ื”ืžืกืคืจ ื”ื›ื•ืœืœ ืฉืœ ื”ืกืคืจื•ืช ื”ืขืฉืจื•ื ื™ื•ืช ืื—ืจื™ ื”ืขืฉืจื•ื ื™
ื ึฐืงื•ึผื“ึธื”. ืœื“ื•ื’ืžื”:
ืœ-.000001 ื™ืฉ ืื•ืจืš ืฉืœ 6 ื•ืกื•ืœื ืฉืœ 6.
ืœ-1935.000 ื™ืฉ ืื•ืจืš ืฉืœ 7 ื•ืกื•ืœื ืฉืœ 3.

ื•ืจื™ืืฆื™ื•ืช
ืžืกืคืจื™ื ืžืื•ื—ืกื ื™ื ื‘ืฉื ื™ ืกื•ื’ื™ื ืฉืœ ืžืฉืชื ื™ื, ืžืฉืชื ื™ื ืคืฉื•ื˜ื™ื ื•ืžืขืจื›ื™ื. ืฉื ื™ื”ื ืคืฉื•ื˜ื™ื
ืžืฉืชื ื™ื ื•ืžืฉืชื ื™ ืžืขืจืš ืžืงื‘ืœื™ื ืฉืžื•ืช. ืฉืžื•ืช ืžืชื—ื™ืœื™ื ื‘ืื•ืช ื•ืื—ืจื™ื” ื›ืœ ืžืกืคืจ
ืฉืœ ืื•ืชื™ื•ืช, ืกืคืจื•ืช ื•ืงื•ื•ื™ื ืชื—ืชื•ื ื™ื. ื›ืœ ื”ืื•ืชื™ื•ืช ื—ื™ื™ื‘ื•ืช ืœื”ื™ื•ืช ืงื˜ื ื•ืช. (ืืœืคื-ื ื•ืžืจื™ ืžืœื
ืฉืžื•ืช ื”ื ื”ืจื—ื‘ื”. ื‘-POSIX bc ื›ืœ ื”ืฉืžื•ืช ื”ื ืื•ืช ืงื˜ื ื” ืื—ืช.) ื”ืกื•ื’
ืฉืœ ื”ืžืฉืชื ื” ื‘ืจื•ืจ ืขืœ ื™ื“ื™ ื”ื”ืงืฉืจ ืžื›ื™ื•ื•ืŸ ืฉื›ืœ ืฉืžื•ืช ืžืฉืชื ื™ ื”ืžืขืจืš ื™ื‘ื•ืื• ืื—ืจื™ื”ื
ืกื•ื’ืจื™ื™ื ([]).

ื™ืฉื ื ืืจื‘ืขื” ืžืฉืชื ื™ื ืžื™ื•ื—ื“ื™ื, ืกื•ึผืœึธื, ibase, obase, ื• ืื—ืจื•ืŸ. ืกื•ืœื ืžื’ื“ื™ืจ ื›ืžื”
ืคืขื•ืœื•ืช ืžืฉืชืžืฉื•ืช ื‘ืกืคืจื•ืช ืื—ืจื™ ื”ื ืงื•ื“ื” ื”ืขืฉืจื•ื ื™ืช. ืขืจืš ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ืฉืœ ืกื•ืœื ื”ื•ื 0. ื‘ืกื™ืก ืž
ื• ื‘ึผื•ึนืก ืœื”ื’ื“ื™ืจ ืืช ื‘ืกื™ืก ื”ื”ืžืจื” ืœืžืกืคืจื™ ืงืœื˜ ื•ืคืœื˜. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ืขื‘ื•ืจ ืฉื ื™ื”ื
ืงืœื˜ ื•ืคืœื˜ ื”ื ื‘ืกื™ืก 10. ืื—ืจื•ืŸ (ื”ืจื—ื‘ื”) ื”ื•ื ืžืฉืชื ื” ื‘ืขืœ ื”ืขืจืš ืฉืœ
ื”ืžืกืคืจ ื”ืื—ืจื•ืŸ ืฉื”ื•ื“ืคืก. ืืœื” ื™ื™ื“ื•ื ื• ื‘ืคื™ืจื•ื˜ ื ื•ืกืฃ ื‘ืžื™ื“ืช ื”ืฆื•ืจืš. ื›ืœ
ืœืžืฉืชื ื™ื ืืœื” ืขืฉื•ื™ื™ื ืœื”ื™ื•ืช ืžื•ืงืฆื™ื ืœื”ื ืขืจื›ื™ื ื•ื›ืŸ ื‘ืฉื™ืžื•ืฉ ื‘ื‘ื™ื˜ื•ื™ื™ื.

ืชื’ื•ื‘ื•ืช
ื”ืขืจื•ืช ื‘ bc ืœื”ืชื—ื™ืœ ืขื ื”ื“ืžื•ื™ื•ืช /* ื•ืœืกื™ื™ื ื‘ื“ืžื•ื™ื•ืช */. ื”ืขืจื•ืช ืขืฉื•ื™ื•ืช
ืœื”ืชื—ื™ืœ ื‘ื›ืœ ืžืงื•ื ื•ืœื”ื•ืคื™ืข ื›ืจื•ื•ื— ื‘ื•ื“ื“ ื‘ืงืœื˜. (ื–ื” ื’ื•ืจื ืœื”ืขืจื•ืช
ืœืชื—ื•ื ืคืจื™ื˜ื™ ืงืœื˜ ืื—ืจื™ื. ืœื“ื•ื’ืžื”, ื”ืขืจื” ืœื ื ื™ืชืŸ ืœืžืฆื•ื ื‘ืืžืฆืข ื
ืฉื ืžืฉืชื ื”.) ื”ืขืจื•ืช ื›ื•ืœืœื•ืช ืฉื•ืจื•ืช ื—ื“ืฉื•ืช (ืกื•ืฃ ืฉื•ืจื”) ื‘ื™ืŸ ื”ื”ืชื—ืœื” ืœืกื•ืฃ
ืฉืœ ื”ื”ืขืจื”.

ื›ื“ื™ ืœืชืžื•ืš ื‘ืฉื™ืžื•ืฉ ื‘ืกืงืจื™ืคื˜ื™ื ืขื‘ื•ืจ bc, ื”ืขืจื” ื‘ืฉื•ืจื” ืื—ืช ื ื•ืกืคื” ื‘ืชื•ืจ
ืกื™ื•ืžืช. ื”ืขืจื” ื‘ืฉื•ืจื” ืื—ืช ืžืชื—ื™ืœื” ื‘-a # ืชื• ื•ืžืžืฉื™ืš ืœืกื•ืฃ ื”ื‘ื ืฉืœ
ื”ืฉื•ืจื”. ืชื• ืกื•ืฃ ื”ืฉื•ืจื” ืื™ื ื• ื—ืœืง ืžื”ื”ืขืจื” ื•ืžืขื•ื‘ื“ ื›ืจื’ื™ืœ.

ื‘ื™ื˜ื•ื™ื™ื
ื”ืžืกืคืจื™ื ืขื•ื‘ืจื™ื ืžื ื™ืคื•ืœืฆื™ื•ืช ืขืœ ื™ื“ื™ ื‘ื™ื˜ื•ื™ื™ื ื•ื”ืฆื”ืจื•ืช. ืžืื– ื”ืฉืคื” ื”ื™ื™ืชื”
ืชื•ื›ื ืŸ ืœื”ื™ื•ืช ืื™ื ื˜ืจืืงื˜ื™ื‘ื™, ื”ืฆื”ืจื•ืช ื•ื‘ื™ื˜ื•ื™ื™ื ืžื‘ื•ืฆืขื™ื ื‘ื”ืงื“ื ื”ืืคืฉืจื™.
ืื™ืŸ ืชื•ื›ื ื™ืช "ืจืืฉื™ืช". ื‘ืžืงื•ื ื–ืืช, ื”ืงื•ื“ ืžื‘ื•ืฆืข ืชื•ืš ื›ื“ื™ ืฉื”ื•ื ื ืชืงืœ. (ืคื•ื ืงืฆื™ื•ืช,
ื ื“ื•ืŸ ื‘ืคื™ืจื•ื˜ ืžืื•ื—ืจ ื™ื•ืชืจ, ืžื•ื’ื“ืจื™ื ื›ืืฉืจ ื ืชืงืœื™ื ื‘ื”ื.)

ื‘ื™ื˜ื•ื™ ืคืฉื•ื˜ ื”ื•ื ืจืง ืงื‘ื•ืข. bc ืžืžื™ืจื” ืงื‘ื•ืขื™ื ืœืขืฉืจื•ื ื™ื ืคื ื™ืžื™ื™ื
ืžืกืคืจื™ื ื‘ืืžืฆืขื•ืช ื‘ืกื™ืก ื”ืงืœื˜ ื”ื ื•ื›ื—ื™, ื”ืžืฆื•ื™ืŸ ืขืœ ื™ื“ื™ ื”ืžืฉืชื ื” ื‘ืกื™ืก ืž. (ื™ืฉ
ื—ืจื™ื’ ื‘ืคื•ื ืงืฆื™ื•ืช.) ื”ืขืจื›ื™ื ื”ืžืฉืคื˜ื™ื™ื ืฉืœ ื‘ืกื™ืก ืž ื”ื 2 ืขื“ 16. ื”ืงืฆืืช ืขืจืš
ืžื—ื•ืฅ ืœื˜ื•ื•ื— ื”ื–ื” ืœ ื‘ืกื™ืก ืž ื™ื‘ื™ื ืœืขืจืš ืฉืœ 2 ืื• 16. ืžืกืคืจื™ ืงืœื˜ ืขืฉื•ื™ื™ื ืœื”ื›ื™ืœ
ื”ืชื•ื•ื™ื 0โ€“9 ื•-Aโ€“F. (ื”ืขืจื”: ื”ืŸ ื—ื™ื™ื‘ื•ืช ืœื”ื™ื•ืช ืจื™ืฉื™ื•ืช. ืื•ืชื™ื•ืช ืงื˜ื ื•ืช ืžืฉืชื ื•ืช
ืฉืžื•ืช.) ืœืžืกืคืจื™ื ื—ื“ ืกืคืจืชื™ื™ื ื™ืฉ ืชืžื™ื“ ืืช ื”ืขืจืš ืฉืœ ื”ืกืคืจื” ืœืœื ืงืฉืจ ืœืขืจืš
of ื‘ืกื™ืก ืž. (ื›ืœื•ืžืจ A = 10.) ืขื‘ื•ืจ ืžืกืคืจื™ื ืจื‘ ืกืคืจืชื™ื™ื, bc ืžืฉื ื” ืืช ื›ืœ ืกืคืจื•ืช ื”ืงืœื˜ ื’ื“ื•ืœ ื™ื•ืชืจ ืื•
ืฉื•ื•ื” ืœ-ibase ืœืขืจืš ืฉืœ ื‘ืกื™ืก ืž-1. ื–ื” ื”ื•ืคืš ืืช ื”ืžืกืคืจ FFF ืชืžื™ื“ ืœื”ื™ื•ืช ื”ื’ื“ื•ืœ 3
ืžืกืคืจ ืกืคืจื•ืช ืฉืœ ื‘ืกื™ืก ื”ืงืœื˜.

ื‘ื™ื˜ื•ื™ื™ื ืžืœืื™ื ื“ื•ืžื™ื ืœืฉืคื•ืช ืจื‘ื•ืช ืื—ืจื•ืช ื‘ืจืžื” ื’ื‘ื•ื”ื”. ื›ื™ ื™ืฉ ืจืง ืื—ื“
ืกื•ื’ ืฉืœ ืžืกืคืจ, ืื™ืŸ ื›ืœืœื™ื ืœืขืจื‘ื•ื‘ ืกื•ื’ื™ื. ื‘ืžืงื•ื ื–ืืช, ื™ืฉื ื ื›ืœืœื™ื ื‘ื ื•ืฉื
ืกื•ืœื ื‘ื™ื˜ื•ื™ื™ื. ืœื›ืœ ื‘ื™ื˜ื•ื™ ื™ืฉ ืงื ื” ืžื™ื“ื”. ื–ื” ื ื’ื–ืจ ืžืกื•ืœื ืฉืœ
ืžืกืคืจื™ื ืžืงื•ืจื™ื™ื, ื”ืคืขื•ืœื” ืฉื‘ื•ืฆืขื” ื•ื‘ืžืงืจื™ื ืจื‘ื™ื, ืขืจืš ื”ืžืฉืชื ื”
ืกื•ืœื. ืขืจื›ื™ื ืžืฉืคื˜ื™ื™ื ืฉืœ ื”ืžืฉืชื ื” ืกื•ืœื ื”ื 0 ืœืžืกืคืจ ื”ืžืจื‘ื™ ื”ืžื™ื•ืฆื’ ืขืœ ื™ื“ื™ C
ืžืกืคืจ ืฉืœื.

ื‘ืชื™ืื•ืจื™ื ื”ื‘ืื™ื ืฉืœ ื‘ื™ื˜ื•ื™ื™ื ืžืฉืคื˜ื™ื™ื, "expr" ืžืชื™ื™ื—ืก ืœื‘ื™ื˜ื•ื™ ืฉืœื
ื•-"var" ืžืชื™ื™ื—ืก ืœืžืฉืชื ื” ืคืฉื•ื˜ ืื• ืฉืœ ืžืขืจืš. ืžืฉืชื ื” ืคืฉื•ื˜ ื”ื•ื ืจืง ื
ืฉื
ื•ืžืฉืชื ื” ืžืขืจืš ืžืฆื•ื™ืŸ ื›
ืฉื[ื‘ื™ื˜ื•ื™]
ืืœื ืื ื›ืŸ ืฆื•ื™ืŸ ื‘ืžืคื•ืจืฉ, ืกื•ืœื ื”ืชื•ืฆืื” ื”ื•ื ื”ืกื•ืœื ื”ืžืงืกื™ืžืœื™ ืฉืœ
ื‘ื™ื˜ื•ื™ื™ื ืžืขื•ืจื‘ื™ื.

- expr ื”ืชื•ืฆืื” ื”ื™ื ืฉืœื™ืœืช ื”ื‘ื™ื˜ื•ื™.

++ var ื”ืžืฉืชื ื” ืžื•ื’ื“ืœ ื‘ืื—ื“ ื•ื”ืขืจืš ื”ื—ื“ืฉ ื”ื•ื ื”ืชื•ืฆืื” ืฉืœ ื”-
ื‘ื™ื˜ื•ื™.

-- var ื”ืžืฉืชื ื” ืžื•ืคื—ืช ื‘ืื—ื“ ื•ื”ืขืจืš ื”ื—ื“ืฉ ื”ื•ื ื”ืชื•ืฆืื” ืฉืœ ื”-
ื‘ื™ื˜ื•ื™.

var ++
ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื”ืขืจืš ืฉืœ ื”ืžืฉืชื ื” ื•ืื– ื”ืžืฉืชื ื” ื”ื•ื
ื’ื“ืœ ื‘ืื—ื“.

var -- ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื”ืขืจืš ืฉืœ ื”ืžืฉืชื ื” ื•ืื– ื”ืžืฉืชื ื” ื”ื•ื
ื™ืจื“ ื‘ืื—ื“.

expr + expr
ืชื•ืฆืืช ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ืกื›ื•ื ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื.

expr - expr
ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื”ื”ื‘ื“ืœ ื‘ื™ืŸ ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื.

expr * expr
ืชื•ืฆืืช ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ืชื•ืฆืจ ืฉืœ ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื.

expr / expr
ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื”ืžื ื” ืฉืœ ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื. ืงื ื” ื”ืžื™ื“ื” ืฉืœ
ื”ืชื•ืฆืื” ื”ื™ื ื”ืขืจืš ืฉืœ ื”ืžืฉืชื ื” ืกื•ืœื.

expr % expr
ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื”"ืฉืืจื™ืช" ื•ื”ื™ื ืžื—ื•ืฉื‘ืช ื‘ื”ืžืฉืš
ื“ึถืจึถืš. ื›ื“ื™ ืœื—ืฉื‘ ืืช a%b, ื”ืจืืฉื•ืŸ a/b ืžื—ื•ืฉื‘ ืœืคื™ ืกื•ืœื ืกืคืจื•ืช. ื”ืชื•ืฆืื” ื”ื–ื• ืžืฉืžืฉืช
ืœื—ืฉื‘ ืืช a-(a/b)*b ื‘ืกื•ืœื ื”ืžืงืกื™ืžื•ื ืฉืœ ืกื•ืœื+ืกืงืืœื”(ื‘) ื•ืกื•ืœื(ื).
If ืกื•ืœื ืžื•ื’ื“ืจ ืœืืคืก ื•ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื ื”ื ืžืกืคืจื™ื ืฉืœืžื™ื ื”ื‘ื™ื˜ื•ื™ ื”ื–ื” ื”ื•ื
ืคื•ื ืงืฆื™ื™ืช ืฉืืจื™ืช ืžืกืคืจ ืฉืœื.

expr ^ expr
ื”ืชื•ืฆืื” ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ืขืจื›ื• ืฉืœ ื”ืจืืฉื•ืŸ ืฉื”ื•ืขืœื” ืœืฉื ื™. ื”
ื”ื‘ื™ื˜ื•ื™ ื”ืฉื ื™ ื—ื™ื™ื‘ ืœื”ื™ื•ืช ืžืกืคืจ ืฉืœื. (ืื ื”ื‘ื™ื˜ื•ื™ ื”ืฉื ื™ ืื™ื ื• ืžืกืคืจ ืฉืœื,
ื ื•ืฆืจืช ืื–ื”ืจื” ื•ื”ื‘ื™ื˜ื•ื™ ื ื—ืชืš ื›ื“ื™ ืœืงื‘ืœ ืขืจืš ืฉืœ ืžืกืคืจ ืฉืœื.)
ืงื ื” ื”ืžื™ื“ื” ืฉืœ ื”ืชื•ืฆืื” ื”ื•ื ืกื•ืœื ืื ื”ืžืขืจื™ืš ืฉืœื™ืœื™. ืื ื”ืžืขืจื™ืš ื”ื•ื
ื—ื™ื•ื‘ื™ ืงื ื” ื”ืžื™ื“ื” ืฉืœ ื”ืชื•ืฆืื” ื”ื•ื ื”ืžื™ื ื™ืžื•ื ืฉืœ ืงื ื” ื”ืžื™ื“ื” ืฉืœ ื”ืจืืฉื•ืŸ
ื”ื‘ื™ื˜ื•ื™ ื›ืคื•ืœ ื”ืขืจืš ืฉืœ ื”ืžืขืจื™ืš ื•ื”ืžืงืกื™ืžื•ื ืฉืœ ืกื•ืœื ื•ืืช ื”ืกื•ืœื
ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื”ืจืืฉื•ืŸ. (ืœืžืฉืœ scale(a^b) = min(scale(a)*b, max( ืกื•ึผืœึธื,
scale(a))).) ื™ืฉ ืœืฆื™ื™ืŸ ืฉ-exr^0 ืชืžื™ื“ ื™ื—ื–ื™ืจ ืืช ื”ืขืจืš ืฉืœ 1.

( expr )
ื–ื” ืžืฉื ื” ืืช ื”ืขื“ื™ืคื•ืช ื”ืกื˜ื ื“ืจื˜ื™ืช ื›ื“ื™ ืœืืœืฅ ืืช ื”ืขืจื›ืช ื”ื‘ื™ื˜ื•ื™.

var = expr
ืœืžืฉืชื ื” ืžื•ืงืฆื” ืขืจืš ื”ื‘ื™ื˜ื•ื™.

var = expr
ื–ื” ืฉื•ื•ื” ืขืจืš ืœ-"var = var expr" ืœืžืขื˜ ื”ื—ืœืง "var".
ืžื•ืขืจืš ืคืขื ืื—ืช ื‘ืœื‘ื“. ื–ื” ื™ื›ื•ืœ ืœืขืฉื•ืช ื”ื‘ื“ืœ ืื "var" ื”ื•ื ืžืขืจืš.

ื‘ื™ื˜ื•ื™ื™ื ื™ื—ืกื™ื™ื ื”ื ืกื•ื’ ืžื™ื•ื—ื“ ืฉืœ ื‘ื™ื˜ื•ื™ ืฉืชืžื™ื“ ืžื•ืขืจืš ืœ-0 ืื• 1, 0
ืื ื”ื™ื—ืก ืฉืงืจื™ ื•-1 ืื ื”ื™ื—ืก ื ื›ื•ืŸ. ืืœื” ืขืฉื•ื™ื™ื ืœื”ื•ืคื™ืข ื‘ื›ืœ ื—ื•ืงื™ื
ื‘ื™ื˜ื•ื™. (POSIX bc ืžื—ื™ื™ื‘ ืฉื™ืžื•ืฉ ื‘ื‘ื™ื˜ื•ื™ื™ื ื™ื—ืกื™ื™ื ืจืง ืื, ื‘ืขื•ื“,
ื•ืขืœ ืืžื™ืจื•ืช ื•ืฉืืคืฉืจ ืœืขืฉื•ืช ื‘ื”ืŸ ืจืง ืžื‘ื—ืŸ ื™ื—ืกื™ ืื—ื“.) ื”ื”ืชื™ื™ื—ืกื•ืช
ืžืคืขื™ืœื™ื ื”ื

expr1 < expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ืงื˜ืŸ ื‘ื”ื—ืœื˜ ืž-exr2.

expr1 <= expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ืงื˜ืŸ ืื• ืฉื•ื•ื” ืœ- expr2.

expr1 > expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ื’ื“ื•ืœ ื‘ื”ื—ืœื˜ ืž-exr2.

expr1 >= expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ื’ื“ื•ืœ ืื• ืฉื•ื•ื” ืœ- expr2.

expr1 == expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ืฉื•ื•ื” ืœ-exr2.

expr1 != expr2
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr1 ืื™ื ื• ืฉื•ื•ื” ืœ-exr2.

ืคืขื•ืœื•ืช ื‘ื•ืœื™ืื ื™ื•ืช ื”ืŸ ื’ื ื—ื•ืงื™ื•ืช. (POSIX bc ืื™ืŸ ืคืขื•ืœื•ืช ื‘ื•ืœื™ืื ื™ื•ืช). ื”
ื”ืชื•ืฆืื” ืฉืœ ื›ืœ ื”ืคืขื•ืœื•ืช ื”ื‘ื•ืœื™ืื ื™ื•ืช ื”ืŸ 0 ื•-1 (ืขื‘ื•ืจ ืฉืงืจ ื•ืืžื™ืชื™) ื›ืžื• ื‘ื™ื—ืกื™ื
ื‘ื™ื˜ื•ื™ื™ื. ื”ืื•ืคืจื˜ื•ืจื™ื ื”ื‘ื•ืœื™ืื ื™ื™ื ื”ื:

!expr ื”ืชื•ืฆืื” ื”ื™ื 1 ืื expr ื”ื•ื 0.

expr && expr
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื ืฉื ื™ ื”ื‘ื™ื˜ื•ื™ื™ื ืื™ื ื ืืคืก.

expr || expr
ื”ืชื•ืฆืื” ื”ื™ื 1 ืื ืื—ื“ ืžื”ื‘ื™ื˜ื•ื™ื™ื ืื™ื ื• ืืคืก.

ืขื“ื™ืคื•ืช ื”ื‘ื™ื˜ื•ื™ ื”ื™ื ื›ื“ืœืงืžืŸ: (ื”ื ืžื•ืš ื‘ื™ื•ืชืจ ืœื’ื‘ื•ื”)
|| ืžืคืขื™ืœ, ืืกื•ืฆื™ืื˜ื™ื‘ื™ ืฉืžืืœ
ืžืคืขื™ืœ &&, ืฉืžืืœ ืืกื•ืฆื™ืื˜ื™ื‘ื™
! ืžืคืขื™ืœ, ืœื ืืกื•ืฆื™ืื˜ื™ื‘ื™
ืžืคืขื™ืœื™ ื™ื—ืกื™ื, ืฉืžืืœ ืืกื•ืฆื™ืื˜ื™ื‘ื™ื™ื
ืžืคืขื™ืœ ืžืฉื™ืžื”, ืืกื•ืฆื™ืื˜ื™ื‘ื™ ืžื™ืžื™ืŸ
+ ื•- ืื•ืคืจื˜ื•ืจื™ื, ืฉืžืืœ ืืกื•ืฆื™ืื˜ื™ื‘ื™
ืื•ืคืจื˜ื•ืจื™ื *, / ื•-%, ืžืฉืžืืœ ืืกื•ืฆื™ืื˜ื™ื‘ื™
^ ืžืคืขื™ืœ, ืืกื•ืฆื™ืื˜ื™ื‘ื™ ืžื™ืžื™ืŸ
unary - ืื•ืคืจื˜ื•ืจ, ืœื ืืกื•ืฆื™ืื˜ื™ื‘ื™
++ ื•- ืื•ืคืจื˜ื•ืจื™ื, ืœื ืืกื•ืฆื™ืื˜ื™ื‘ื™ื™ื

ืขื“ื™ืคื•ืช ื–ื• ื ื‘ื—ืจื” ื›ืš ืฉืชืชืื™ื ืœ-POSIX bc ืชื•ื›ื ื™ื•ืช ื™ืคืขืœื• ื›ื”ืœื›ื”. ื–ึถื”
ื™ื’ืจื•ื ืœืฉื™ืžื•ืฉ ื‘ืื•ืคืจื˜ื•ืจื™ื ื”ื™ื—ืกื™ื™ื ื•ื”ืœื•ื’ื™ื™ื ืœื”ืชื ื”ื’ื•ืช ื—ืจื™ื’ื” ื›ืœืฉื”ื™
ื‘ืฉื™ืžื•ืฉ ืขื ื‘ื™ื˜ื•ื™ื™ ื”ืงืฆืื”. ืฉืงื•ืœ ืืช ื”ื‘ื™ื˜ื•ื™:
a = 3 < 5

ืจื•ื‘ ืžืชื›ื ืชื™ C ื”ื™ื• ืžื ื™ื—ื™ื ืฉื–ื” ื™ืงืฆื” ืืช ื”ืชื•ืฆืื” ืฉืœ "3 < 5" (ื”ืขืจืš 1) ืœ
ื”ืžืฉืชื ื” "a". ืžื” ื–ื” ืขื•ืฉื” ื‘ bc ื”ื•ื ืœื”ืงืฆื•ืช ืืช ื”ืขืจืš 3 ืœืžืฉืชื ื” "a" ื•ืœืื—ืจ ืžื›ืŸ
ื”ืฉื•ื•ื” ื‘ื™ืŸ 3 ืœ-5. ืขื“ื™ืฃ ืœื”ืฉืชืžืฉ ื‘ืกื•ื’ืจื™ื™ื ื‘ืขืช ืฉื™ืžื•ืฉ ื‘ืื•ืคืจื˜ื•ืจื™ื ื™ื—ืกื™ื™ื ื•ืœื•ื’ื™ื™ื
ืขื ืžืคืขื™ืœื™ ื”ื”ืงืฆืื”.

ื™ืฉ ืขื•ื“ ื›ืžื” ื‘ื™ื˜ื•ื™ื™ื ืžื™ื•ื—ื“ื™ื ืฉืžืกื•ืคืงื™ื ื‘ bc. ืืœื” ืงืฉื•ืจื™ื
ืคื•ื ืงืฆื™ื•ืช ืžื•ื’ื“ืจื•ืช ืขืœ ื™ื“ื™ ืžืฉืชืžืฉ ื•ืคื•ื ืงืฆื™ื•ืช ืกื˜ื ื“ืจื˜ื™ื•ืช. ื›ื•ืœื ืžื•ืคื™ืขื™ื ื›"ืฉื(ืคืจืžื˜ืจื™ื)".
ืขื™ื™ืŸ ื‘ืกืขื™ืฃ ืขืœ ืคื•ื ืงืฆื™ื•ืช ืขื‘ื•ืจ ืคื•ื ืงืฆื™ื•ืช ื”ืžื•ื’ื“ืจื•ืช ืขืœ ื™ื“ื™ ื”ืžืฉืชืžืฉ. ื”ืคื•ื ืงืฆื™ื•ืช ื”ืกื˜ื ื“ืจื˜ื™ื•ืช ื”ืŸ:

ืื•ืจืš (ื‘ื™ื˜ื•ื™)
ื”ืขืจืš ืฉืœ ืคื•ื ืงืฆื™ื™ืช ื”ืื•ืจืš ื”ื•ื ืžืกืคืจ ื”ืกืคืจื•ืช ื”ืžืฉืžืขื•ืชื™ื•ืช ื‘-
ื‘ื™ื˜ื•ื™.

ืœืงืจื•ื ( )
ืคื•ื ืงืฆื™ื™ืช ื”ืงืจื™ืื” (ื”ืจื—ื‘ื”) ืชืงืจื ืžืกืคืจ ืžื”ืงืœื˜ ื”ืกื˜ื ื“ืจื˜ื™,
ืœืœื ืงืฉืจ ืœืžืงื•ื ืฉื‘ื• ื”ืคื•ื ืงืฆื™ื” ืžืชืจื—ืฉืช. ื”ื™ื–ื”ืจ, ื–ื” ื™ื›ื•ืœ ืœื’ืจื•ื ืœื‘ืขื™ื•ืช ืขื
ืขืจื‘ื•ื‘ ืฉืœ ื ืชื•ื ื™ื ื•ืชื•ื›ื ื™ืช ื‘ืงืœื˜ ื”ืกื˜ื ื“ืจื˜ื™. ื”ืฉื™ืžื•ืฉ ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืขื‘ื•ืจ ืคื•ื ืงืฆื™ื” ื–ื•
ื ืžืฆื ื‘ืชื•ื›ื ื™ืช ืฉื ื›ืชื‘ื” ื‘ืขื‘ืจ ืฉืฆืจื™ื›ื” ืงืœื˜ ืžื”ืžืฉืชืžืฉ, ืืš ืœืขื•ืœื ืœื ืžืืคืฉืจืช
ืงื•ื“ ื”ืชื•ื›ื ื™ืช ืฉื™ืฉ ืœื”ื–ื™ืŸ ืžื”ืžืฉืชืžืฉ. ื”ืขืจืš ืฉืœ ืคื•ื ืงืฆื™ื™ืช ื”ืงืจื™ืื” ื”ื•ื
ืžืกืคืจ ืฉื ืงืจื ืžื”ืงืœื˜ ื”ืกื˜ื ื“ืจื˜ื™ ื‘ืืžืฆืขื•ืช ื”ืขืจืš ื”ื ื•ื›ื—ื™ ืฉืœ ื”ืžืฉืชื ื” ื‘ืกื™ืก ืž
ืขื‘ื•ืจ ื‘ืกื™ืก ื”ื”ืžืจื”.

ืกื•ืœื (ื‘ื™ื˜ื•ื™)
ื”ืขืจืš ืฉืœ ืคื•ื ืงืฆื™ื™ืช ื”ืกื•ืœื ื”ื•ื ืžืกืคืจ ื”ืกืคืจื•ืช ืื—ืจื™ ื”ื ืงื•ื“ื” ื”ืขืฉืจื•ื ื™ืช ื‘
ื”ื‘ื™ื˜ื•ื™.

sqrt (ื‘ื™ื˜ื•ื™)
ื”ืขืจืš ืฉืœ ื”ืคื•ื ืงืฆื™ื” sqrt ื”ื•ื ื”ืฉื•ืจืฉ ื”ืจื™ื‘ื•ืขื™ ืฉืœ ื”ื‘ื™ื˜ื•ื™. ืื ื”
ื”ื‘ื™ื˜ื•ื™ ืฉืœื™ืœื™, ื ื•ืฆืจืช ืฉื’ื™ืืช ื–ืžืŸ ืจื™ืฆื”.

ื”ืฆื”ืจื•ืช
ื”ืฆื”ืจื•ืช (ื›ืžื• ื‘ืจื•ื‘ ื”ืฉืคื•ืช ื”ืืœื’ื‘ืจื™ื•ืช) ืžืกืคืงื•ืช ืืช ืจืฆืฃ ื”ื‘ื™ื˜ื•ื™
ื”ึทืขึฒืจึธื›ึธื”. ื‘ bc ื”ืฆื”ืจื•ืช ืžื‘ื•ืฆืขื•ืช "ื‘ื”ืงื“ื ื”ืืคืฉืจื™". ื‘ื™ืฆื•ืข ืžืชืจื—ืฉ ื›ืืฉืจ
ื ืชืงืœืชื™ ื‘ืฉื•ืจื” ื—ื“ืฉื” ื•ื™ืฉ ื”ืฆื”ืจื” ืฉืœืžื” ืื—ืช ืื• ื™ื•ืชืจ. ื‘ืขืงื‘ื•ืช ื–ืืช
ื‘ื™ืฆื•ืข ืžื™ื™ื“ื™, ืฉื•ืจื•ืช ื—ื“ืฉื•ืช ื—ืฉื•ื‘ื•ืช ืžืื•ื“ ื‘ bc. ืœืžืขืฉื”, ื’ื ื ืงื•ื“ื”-ืคืกื™ืง ื•ื’ื ื
ืฉื•ืจื” ื—ื“ืฉื” ืžืฉืžืฉื™ื ื›ืžืคืจื™ื“ื™ ื”ืฆื”ืจื•ืช. ืงื• ื—ื“ืฉ ืžืžื•ืงื ื‘ืฆื•ืจื” ืœื ื ื›ื•ื ื” ื™ื’ืจื•ื ืœ-
ืฉื’ื™ืืช ืชื—ื‘ื™ืจ. ืžื›ื™ื•ื•ืŸ ืฉืฉื•ืจื•ืช ื—ื“ืฉื•ืช ื”ืŸ ืžืคืจื™ื“ื™ ื”ืฆื”ืจื•ืช, ื ื™ืชืŸ ืœื”ืกืชื™ืจ ืฉื•ืจื” ื—ื“ืฉื”
ื‘ืืžืฆืขื•ืช ืชื• ื”ื ื˜ื•ื™ ื”ืื—ื•ืจื™. ื”ืจืฆืฃ "\ ", ืื™ืคื” ื”ืื ื”ืฉื•ืจื” ื”ื—ื“ืฉื” ืžื•ืคื™ืขื”
ืœ bc ื›ืจื•ื•ื— ืœื‘ืŸ ื‘ืžืงื•ื ืฉื•ืจื” ื—ื“ืฉื”. ืจืฉื™ืžืช ื”ืฆื”ืจื•ืช ื”ื™ื ืกื“ืจื” ืฉืœ ื”ืฆื”ืจื•ืช
ืžื•ืคืจื“ื™ื ืขืœ ื™ื“ื™ ื ืงื•ื“ื•ืช ืคืกื™ืง ื•ืงื•ื•ื™ื ื—ื“ืฉื™ื. ืœื”ืœืŸ ืจืฉื™ืžื” ืฉืœ bc ืืžื™ืจื•ืช ื•ืžื”
ื”ื ืขื•ืฉื™ื ื–ืืช: (ื“ื‘ืจื™ื ื”ืžื•ืงืคื™ื ื‘ืกื•ื’ืจื™ื™ื ([]) ื”ื ื—ืœืงื™ื ืื•ืคืฆื™ื•ื ืœื™ื™ื ืฉืœ ื”ื”ืฆื”ืจื”.)

ื‘ื™ื˜ื•ื™
ื”ื”ืฆื”ืจื” ื”ื–ื• ืขื•ืฉื” ืื—ื“ ืžืฉื ื™ ื“ื‘ืจื™ื. ืื ื”ื‘ื™ื˜ื•ื™ ืžืชื—ื™ืœ ื‘"
...", ื–ื” ื ื—ืฉื‘ ื›ื”ืฆื”ืจืช ืžืฉื™ืžื”. ืื ื”
ื‘ื™ื˜ื•ื™ ืื™ื ื• ื”ืฆื”ืจืช ืžืฉื™ืžื”, ื”ื‘ื™ื˜ื•ื™ ืžื•ืขืจืš ื•ืžื•ื“ืคืก
ืœืคืœื˜. ืœืื—ืจ ื”ื“ืคืกืช ื”ืžืกืคืจ, ืžื•ื“ืคืกืช ืฉื•ืจื” ื—ื“ืฉื”. ืœื“ื•ื’ืžื”,
"a=1" ื”ื•ื ื”ืฆื”ืจืช ื”ืงืฆืื” ื•-"(a=1)" ื”ื•ื ื‘ื™ื˜ื•ื™ ืฉื™ืฉ ืœื• ืžื•ื˜ื‘ืข
ืžึฐืฉืึดื™ืžึธื”. ื›ืœ ื”ืžืกืคืจื™ื ื”ืžื•ื“ืคืกื™ื ืžื•ื“ืคืกื™ื ื‘ื‘ืกื™ืก ื”ืžืฆื•ื™ืŸ ืขืœ ื™ื“ื™ ื”
ืžืฉืชื ื” ื‘ึผื•ึนืก. ื”ืขืจื›ื™ื ื”ืžืฉืคื˜ื™ื™ื ืขื‘ื•ืจ ื‘ึผื•ึนืก ื”ื 2 ืขื“ BC_BASE_MAX. (ืจืื” ืืช
ืกืขื™ืฃ LIMITS.) ืขื‘ื•ืจ ื‘ืกื™ืกื™ื 2 ืขื“ 16, ื”ืฉื™ื˜ื” ื”ืจื’ื™ืœื” ืœื›ืชื™ื‘ืช ืžืกืคืจื™ื ื”ื™ื
ื‘ืฉื™ืžื•ืฉ. ืขื‘ื•ืจ ื‘ืกื™ืกื™ื ื’ื“ื•ืœื™ื ืž-16, bc ืžืฉืชืžืฉ ื‘ืฉื™ื˜ืช ืกืคืจื•ืช ืžืจื•ื‘ื•ืช ืชื•ื•ื™ื ืฉืœ
ื”ื“ืคืกืช ื”ืžืกืคืจื™ื ืฉื‘ื”ื ื›ืœ ืกืคืจืช ื‘ืกื™ืก ื’ื‘ื•ื”ื” ื™ื•ืชืจ ืžื•ื“ืคืกืช ื›ืžืกืคืจ ื‘ืกื™ืก 10.
ื”ืกืคืจื•ืช ืžืจื•ื‘ื•ืช ื”ืชื•ื•ื™ื ืžื•ืคืจื“ื•ืช ืขืœ ื™ื“ื™ ืจื•ื•ื—ื™ื. ื›ืœ ืกืคืจื” ืžื›ื™ืœื” ืืช ื”ืžืกืคืจ
ืฉืœ ืชื•ื•ื™ื ื”ื ื“ืจืฉื™ื ื›ื“ื™ ืœื™ื™ืฆื’ ืืช ืขืจืš ื”ื‘ืกื™ืก ืขืฉืจ ืฉืœ "obase-1". ืžืื– ืžืกืคืจื™ื
ื”ื ื‘ืขืœื™ ื“ื™ื•ืง ืฉืจื™ืจื•ืชื™, ื™ื™ืชื›ืŸ ืฉืžืกืคืจื™ื ืžืกื•ื™ืžื™ื ืœื ื ื™ืชื ื™ื ืœื”ื“ืคืกื” ืขืœ ืคืœื˜ ื‘ื•ื“ื“
ืงึทื•. ื”ืžืกืคืจื™ื ื”ืืจื•ื›ื™ื ื”ืœืœื• ื™ื—ื•ืœืงื• ืขืœ ืคื ื™ ืงื•ื•ื™ื ืชื•ืš ืฉื™ืžื•ืฉ ื‘-"\" ื‘ืชื•ืจ ื”ืื—ืจื•ืŸ
ืชื• ืขืœ ืฉื•ืจื”. ื”ืžืกืคืจ ื”ืžืจื‘ื™ ืฉืœ ืชื•ื•ื™ื ืžื•ื“ืคืกื™ื ื‘ืฉื•ืจื” ื”ื•ื 70. ื‘ืฉืœ
ืœืื•ืคื™ ื”ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ ืฉืœ bc, ื”ื“ืคืกืช ืžืกืคืจ ื’ื•ืจืžืช ืœืชื•ืคืขืช ื”ืœื•ื•ืื™ ืฉืœ
ื”ืงืฆืืช ื”ืขืจืš ื”ืžื•ื“ืคืก ืœืžืฉืชื ื” ื”ืžื™ื•ื—ื“ ืื—ืจื•ืŸ. ื–ื” ืžืืคืฉืจ ืœืžืฉืชืžืฉ
ืฉื—ื–ืจ ืืช ื”ืขืจืš ื”ืื—ืจื•ืŸ ืฉื”ื•ื“ืคืก ืœืœื ืฆื•ืจืš ืœื”ืงืœื™ื“ ืžื—ื“ืฉ ืืช ื”ื‘ื™ื˜ื•ื™ ืฉื”ื•ื“ืคืก
ื”ืžืกืคืจ. ืžืงืฆื” ืœ ืื—ืจื•ืŸ ื”ื•ื ื—ื•ืงื™ ื•ื™ื—ืœื™ืฃ ืืช ื”ืขืจืš ื”ืžื•ื“ืคืก ื”ืื—ืจื•ืŸ
ืขื ื”ืขืจืš ืฉื”ื•ืงืฆื”. ื”ืขืจืš ื”ื—ื“ืฉ ืฉื”ื•ืงืฆื” ื™ื™ืฉืืจ ืขื“ ื”ืขืจืš ื”ื‘ื
ืžืกืคืจ ืžื•ื“ืคืก ืื• ืžื•ืงืฆื” ืขืจืš ืื—ืจ ืื—ืจื•ืŸ. (ื™ื™ืชื›ื ื• ื”ืชืงื ื•ืช ืžืกื•ื™ืžื•ืช
ืœืืคืฉืจ ืฉื™ืžื•ืฉ ื‘ื ืงื•ื“ื” ืื—ืช (.) ืฉืื™ื ื” ื—ืœืง ืžืžืกืคืจ ื›ืžื—ื•ื’ ืงืฆืจ
ืกื™ืžื•ืŸ ืขื‘ื•ืจ ืขื‘ื•ืจ ืื—ืจื•ืŸ.)

string ื”ืžื—ืจื•ื–ืช ืžื•ื“ืคืกืช ืœืคืœื˜. ืžื—ืจื•ื–ื•ืช ืžืชื—ื™ืœื•ืช ื‘ืื•ืช ืžืจื›ืื” ื›ืคื•ืœื”
ื•ืœื”ื›ื™ืœ ืืช ื›ืœ ื”ืชื•ื•ื™ื ืขื“ ืœืชื• ื”ืžื™ืจื›ืื” ื”ื›ืคื•ืœื” ื”ื‘ืื”. ื›ืœ ื”ื“ืžื•ื™ื•ืช
ื”ื ืœื•ืงื—ื™ื ืคืฉื•ื˜ื• ื›ืžืฉืžืขื•, ื›ื•ืœืœ ื›ืœ ืงื• ื—ื“ืฉ. ืฉื•ื ืชื• ื—ื“ืฉ ืœื ืžื•ื“ืคืก ืื—ืจื™
ื”ืžื™ืชืจ.

ื”ื“ืคืกื” ืจืฉื™ืžื”
ื”ืฆื”ืจืช ื”ื”ื“ืคืกื” (ื”ืจื—ื‘ื”) ืžืกืคืงืช ืฉื™ื˜ืช ืคืœื˜ ื ื•ืกืคืช. ื”ืจืฉื™ืžื”"
ื”ื™ื ืจืฉื™ืžื” ืฉืœ ืžื—ืจื•ื–ื•ืช ื•ื‘ื™ื˜ื•ื™ื™ื ื”ืžื•ืคืจื“ื™ื ื‘ืคืกื™ืงื™ื. ื›ืœ ืžื—ืจื•ื–ืช ืื•
ื”ื‘ื™ื˜ื•ื™ ืžื•ื“ืคืก ืœืคื™ ืกื“ืจ ื”ืจืฉื™ืžื”. ืœื ืžื•ื“ืคืกืช ืฉื•ืจื” ื—ื“ืฉื” ืฉืžืกื™ื™ืžืช.
ื‘ื™ื˜ื•ื™ื™ื ืžื•ืขืจื›ื™ื ื•ืขืจื›ื ืžื•ื“ืคืก ื•ืžื•ืงืฆื” ืœืžืฉืชื ื”
ืื—ืจื•ืŸ. ืžื—ืจื•ื–ื•ืช ื‘ื”ืฆื”ืจืช ื”ื”ื“ืคืกื” ืžื•ื“ืคืกื•ืช ืœืคืœื˜ ื•ืขืฉื•ื™ื•ืช ืœื”ื›ื™ืœ
ืชื•ื•ื™ื ืžื™ื•ื—ื“ื™ื. ืชื•ื•ื™ื ืžื™ื•ื—ื“ื™ื ืžืชื—ื™ืœื™ื ื‘ืชื• ื”ื ื˜ื•ื™ ื”ืื—ื•ืจื™ (\).
ื”ืชื•ื•ื™ื ื”ืžื™ื•ื—ื“ื™ื ื”ืžื•ื›ืจื™ื ืขืœ ื™ื“ื™ bc ื”ื "a" (ื”ืชืจืื” ืื• ืคืขืžื•ืŸ), "b" (backspace),
"f" (ื”ื–ื ืช ื˜ื•ืคืก), "n" (ืฉื•ืจื” ื—ื“ืฉื”), "r" (ื”ื—ื–ืจืช ื›ืจื›ืจื”), "q" (ืžืจื›ืื•ืช ื›ืคื•ืœื•ืช), "t"
(ื˜ืื‘), ื•-"\" (ืงื• ื ื˜ื•ื™ ืื—ื•ืจื™). ื›ืœ ื“ืžื•ืช ืื—ืจืช ืฉืื—ืจื™ื” ืœืื—ื•ืจ ืชื”ื™ื”
ื”ืชืขืœื.

{ statement_list }
ื–ื• ื”ื”ืฆื”ืจื” ื”ืžื•ืจื›ื‘ืช. ื–ื” ืžืืคืฉืจ ืœืงื‘ืฅ ื”ืฆื”ืจื•ืช ืžืจื•ื‘ื•ืช
ื™ื—ื“ ืœื‘ื™ืฆื•ืข.

if ( ื‘ื™ื˜ื•ื™ ) ืžืฉืคื˜1 [ืื—ืจ ื”ืฆื”ืจื” 2]
ืžืฉืคื˜ if ืžืขืจื™ืš ืืช ื”ื‘ื™ื˜ื•ื™ ื•ืžื‘ืฆืข ืžืฉืคื˜1 ืื• ืžืฉืคื˜2
ื‘ื”ืชืื ืœืขืจืš ื”ื‘ื™ื˜ื•ื™. ืื ื”ื‘ื™ื˜ื•ื™ ืื™ื ื• ืืคืก,
ืžืฉืคื˜1 ืžื‘ื•ืฆืข. ืื ืงื™ื™ื ืžืฉืคื˜2 ื•ื”ืขืจืš ืฉืœ ื”ื‘ื™ื˜ื•ื™
ื”ื•ื 0, ื•ืื– ืžืฉืคื˜2 ืžื‘ื•ืฆืข. (ื”ืกืขื™ืฃ ื”ืื—ืจ ื”ื•ื ื”ืจื—ื‘ื”.)

ื‘ื–ืžืŸ (ื‘ื™ื˜ื•ื™) ืืžื™ืจื”
ื”ืžืฉืคื˜ while ื™ื‘ืฆืข ืืช ื”ื”ืฆื”ืจื” ื‘ื–ืžืŸ ืฉื”ื‘ื™ื˜ื•ื™ ืื™ื ื• ืืคืก.
ื”ื•ื ืžืขืจื™ืš ืืช ื”ื‘ื™ื˜ื•ื™ ืœืคื ื™ ื›ืœ ื‘ื™ืฆื•ืข ืฉืœ ื”ื”ืฆื”ืจื”. ืกื™ื•ื
ืฉืœ ื”ืœื•ืœืื” ื ื’ืจืžืช ืขืœ ื™ื“ื™ ืขืจืš ื‘ื™ื˜ื•ื™ ืืคืก ืื• ื‘ื™ืฆื•ืข ืฉืœ ื”ืคืกืงื”
ื”ืฆื”ืจื”.

ืœ ( [ื‘ื™ื˜ื•ื™1] ; [ื‘ื™ื˜ื•ื™2] ; [ื‘ื™ื˜ื•ื™3] ) ืžืฉืคื˜
ื”ื”ืฆื”ืจื” for ืฉื•ืœื˜ืช ื‘ื‘ื™ืฆื•ืข ื—ื•ื–ืจ ืฉืœ ื”ื”ืฆื”ืจื”. ื‘ื™ื˜ื•ื™1 ื”ื•ื
ืžื•ืขืจืš ืœืคื ื™ ื”ืœื•ืœืื”. Expression2 ืžื•ืขืจืš ืœืคื ื™ ื›ืœ ื‘ื™ืฆื•ืข ืฉืœ ื”-
ื”ึทืฆื”ึธืจึธื”. ืื ื”ื•ื ืื™ื ื• ืืคืก, ื”ื”ืฆื”ืจื” ืžื•ืขืจื›ืช. ืื ื”ื•ื ืืคืก, ื”ืœื•ืœืื”
ืžื•ืคืกืง. ืœืื—ืจ ื›ืœ ื‘ื™ืฆื•ืข ืฉืœ ื”ื”ืฆื”ืจื”, expression3 ืžื•ืขืจืš
ืœืคื ื™ ื”ื”ืขืจื›ื” ืžื—ื“ืฉ ืฉืœ ื‘ื™ื˜ื•ื™2. ืื ื‘ื™ื˜ื•ื™1 ืื• ื‘ื™ื˜ื•ื™3 ื—ืกืจื™ื,
ืฉื•ื ื“ื‘ืจ ืœื ืžื•ืขืจืš ื‘ื ืงื•ื“ื” ืฉื‘ื” ื”ื ื™ื•ืขืจื›ื•. ืื ื‘ื™ื˜ื•ื™2 ื”ื•ื
ื—ืกืจ, ื–ื” ื–ื”ื” ืœื”ื—ืœืคืช ื”ืขืจืš 1 ืขื‘ื•ืจ expression2. (ื”ืื•ืคืฆื™ื•ื ืœื™
ื‘ื™ื˜ื•ื™ื™ื ื”ื ื”ืจื—ื‘ื”. POSIX bc ื“ื•ืจืฉ ืืช ื›ืœ ืฉืœื•ืฉืช ื”ื‘ื™ื˜ื•ื™ื™ื.) ื”
ืœื”ืœืŸ ืงื•ื“ ืฉื•ื•ื” ืขืจืš ืœื”ืฆื”ืจืช for:
ื‘ื™ื˜ื•ื™1;
while (ื‘ื™ื˜ื•ื™2) {
ื”ึทืฆื”ึธืจึธื”;
ื‘ื™ื˜ื•ื™3;
}

ืœืฉื‘ื•ืจ ื”ืฆื”ืจื” ื–ื• ื’ื•ืจืžืช ืœื™ืฆื™ืื” ืžืื•ืœืฆืช ืฉืœ ื”-enclosing while statement ืื•
ืœื”ืฆื”ืจื”.

ืœื”ืžืฉื™ืš
ื”ืฆื”ืจืช ื”ื”ืžืฉืš (ื”ืจื—ื‘ื”) ื’ื•ืจืžืช ืœื”ืงื™ืฃ ื”ืื—ืจื•ืŸ ืขื‘ื•ืจ
ื”ืฆื”ืจื” ื›ื“ื™ ืœื”ืชื—ื™ืœ ืืช ื”ืื™ื˜ืจืฆื™ื” ื”ื‘ืื”.

ืœึทืขึฒืฆื•ึนืจ ื”ืฆื”ืจืช halt (ื”ืจื—ื‘ื”) ื”ื™ื ืžืฉืคื˜ ืžื‘ื•ืฆืข ืฉื’ื•ืจื ืœ- bc
ืžืขื‘ื“ ืœื”ืคืกื™ืง ืจืง ื›ืืฉืจ ื”ื•ื ืžื‘ื•ืฆืข. ืœื“ื•ื’ืžื”, "ืื (0 == 1) ืขืฆื•ืจ" ื™ื™ืขืฆืจ
ืœื ืœื’ืจื•ื bc ืœื”ืคืกื™ืง ื‘ื’ืœืœ ืฉื”ืขืฆื™ืจื” ืœื ืžื‘ื•ืฆืขืช.

ืœึทื—ึฒื–ื•ึนืจ ื”ื—ื–ืจ ืืช ื”ืขืจืš 0 ืžืคื•ื ืงืฆื™ื”. (ืจืื” ืกืขื™ืฃ ืขืœ ืคื•ื ืงืฆื™ื•ืช.)

ืœึทื—ึฒื–ื•ึนืจ ( ื‘ื™ื˜ื•ื™ )
ื”ื—ื–ืจ ืืช ื”ืขืจืš ืฉืœ ื”ื‘ื™ื˜ื•ื™ ืžืคื•ื ืงืฆื™ื”. (ืจืื” ืกืขื™ืฃ ื‘ื ื•ืฉื
ืคื•ื ืงืฆื™ื•ืช.) ื›ื”ืจื—ื‘ื”, ืื™ืŸ ืฆื•ืจืš ื‘ืกื•ื’ืจื™ื™ื.

ืžื“ื•ืžื” ื”ืฆื”ืจื•ืช
ื”ืฆื”ืจื•ืช ืืœื• ืื™ื ืŸ ื”ืฆื”ืจื•ืช ื‘ืžื•ื‘ืŸ ื”ืžืกื•ืจืชื™. ื”ื ืœื ืžื•ืฆืื™ื ืœื”ื•ืจื’
ื”ืฆื”ืจื•ืช. ืชืคืงื™ื“ื ืžื‘ื•ืฆืข ื‘ื–ืžืŸ "ืงื•ืžืคื™ืœืฆื™ื”".

ื’ื‘ื•ืœื•ืช ื”ื“ืคืก ืืช ื”ืžื’ื‘ืœื•ืช ื”ืžืงื•ืžื™ื•ืช ืฉื ืื›ืคื•ืช ืขืœ ื™ื“ื™ ื”ื’ืจืกื” ื”ืžืงื•ืžื™ืช ืฉืœ bc. ื–ื•ื”ื™ ื”ืจื—ื‘ื”.

ืœื”ืคืกื™ืง ื›ืืฉืจ ื”ืฆื”ืจืช ื”ื™ืฆื™ืื” ื ืงืจืืช, ื” bc ื”ืžืขื‘ื“ ืžื•ืคืกืง, ืœืœื ืงืฉืจ ืœ
ื”ื™ื›ืŸ ื ืžืฆื ื”ืฆื”ืจืช ื”ื™ืฆื™ืื”. ืœื“ื•ื’ืžื”, "ืื (0 == 1) ื™ืฆื™ืื”" ื™ื’ืจื•ื bc
ืœื—ืกืœ.

ืึทื—ึฒืจึธื™ื•ึผืช
ื”ื“ืคืก ื”ื•ื“ืขืช ืื—ืจื™ื•ืช ืืจื•ื›ื” ื™ื•ืชืจ. ื–ื•ื”ื™ ื”ืจื—ื‘ื”.

ืคื•ื ืงืฆื™ื•ืช
ืคื•ื ืงืฆื™ื•ืช ืžืกืคืงื•ืช ืฉื™ื˜ื” ืœื”ื’ื“ืจืช ื—ื™ืฉื•ื‘ ืฉื ื™ืชืŸ ืœื‘ืฆืข ืžืื•ื—ืจ ื™ื•ืชืจ.
ืคื•ื ืงืฆื™ื•ืช ื‘ bc ืชืžื™ื“ ืœื—ืฉื‘ ืขืจืš ื•ืœื”ื—ื–ื™ืจ ืื•ืชื• ืœืžืชืงืฉืจ. ื”ื’ื“ืจื•ืช ืคื•ื ืงืฆื™ื”
ื”ื "ื“ื™ื ืžื™ื™ื" ื‘ืžื•ื‘ืŸ ืฉืคื•ื ืงืฆื™ื” ืื™ื ื” ืžื•ื’ื“ืจืช ืขื“ ืฉื ืชืงืœืช ื‘ื”ื’ื“ืจื”
ื‘ืงืœื˜. ืœืื—ืจ ืžื›ืŸ ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ื”ื’ื“ืจื” ื–ื• ืขื“ ืœืคื•ื ืงืฆื™ื™ืช ื”ื’ื“ืจื” ื ื•ืกืคืช ืขื‘ื•ืจ ืื•ืชื”
ืฉื ื”ื•ื ื ืชืงืœ. ื”ื”ื’ื“ืจื” ื”ื—ื“ืฉื” ืžื—ืœื™ืคื” ืื– ืืช ื”ื”ื’ื“ืจื” ื”ื™ืฉื ื” ื™ื•ืชืจ. ืชืคืงื•ื“
ืžื•ื’ื“ืจ ื›ื“ืœืงืžืŸ:
ืœึฐื”ึทื’ื“ึดื™ืจ ืฉื ( ืคืจืžื˜ืจื™ื ) { ืฉื•ืจื” ื—ื“ืฉื”
auto_list statement_list }
ืงืจื™ืื” ืœืคื•ื ืงืฆื™ื” ื”ื™ื ืจืง ื‘ื™ื˜ื•ื™ ืฉืœ ื”ืฆื•ืจื” "ืฉื(ืคืจืžื˜ืจื™ื)".

ืคืจืžื˜ืจื™ื ื”ื ืžืกืคืจื™ื ืื• ืžืขืจื›ื™ื (ื”ืจื—ื‘ื”). ื‘ื”ื’ื“ืจืช ื”ืคื•ื ืงืฆื™ื”, ืืคืก ืื• ื™ื•ืชืจ
ืคืจืžื˜ืจื™ื ืžื•ื’ื“ืจื™ื ืขืœ ื™ื“ื™ ืจื™ืฉื•ื ืฉืžื•ืชื™ื”ื ืžื•ืคืจื“ื™ื ื‘ืคืกื™ืงื™ื. ื›ืœ ื”ืคืจืžื˜ืจื™ื ื”ื
ืงืจื™ืื” ืœืคื™ ืคืจืžื˜ืจื™ื ืฉืœ ืขืจืš. ืžืขืจื›ื™ื ืžืฆื•ื™ื ื™ื ื‘ื”ื’ื“ืจืช ื”ืคืจืžื˜ืจ ืขืœ ื™ื“ื™ ื”-
ืกื™ืžื•ืŸ"ืฉื[]". ื‘ืงืจื™ืื” ืœืคื•ื ืงืฆื™ื”, ืคืจืžื˜ืจื™ื ื‘ืคื•ืขืœ ื”ื ื‘ื™ื˜ื•ื™ื™ื ืžืœืื™ื ืขื‘ื•ืจ
ืคืจืžื˜ืจื™ื ืฉืœ ืžืกืคืจ. ืื•ืชื• ืกื™ืžื•ืŸ ืžืฉืžืฉ ืœื”ืขื‘ืจืช ืžืขืจื›ื™ื ื›ืžื• ืœื”ื’ื“ืจืช ืžืขืจืš
ืคืจืžื˜ืจื™ื. ื”ืžืขืจืš ื‘ืขืœ ื”ืฉื ืžื•ืขื‘ืจ ืœืคื™ ืขืจืš ืœืคื•ื ืงืฆื™ื”. ืžืื– ื”ืคื•ื ืงืฆื™ื”
ื”ื”ื’ื“ืจื•ืช ื”ืŸ ื“ื™ื ืžื™ื•ืช, ืžืกืคืจื™ ืคืจืžื˜ืจื™ื ื•ืกื•ื’ื™ื ื ื‘ื“ืงื™ื ื›ืืฉืจ ืคื•ื ืงืฆื™ื” ื”ื™ื
ืฉืงื•ืจืื™ื ืœื•. ื›ืœ ื—ื•ืกืจ ื”ืชืืžื” ื‘ืžืกืคืจ ืื• ื‘ืกื•ื’ื™ ื”ืคืจืžื˜ืจื™ื ื™ื’ืจื•ื ืœืฉื’ื™ืืช ื–ืžืŸ ืจื™ืฆื”. ื
ืฉื’ื™ืืช ื–ืžืŸ ืจื™ืฆื” ืชืชืจื—ืฉ ื’ื ืขื‘ื•ืจ ื”ืงืจื™ืื” ืœืคื•ื ืงืฆื™ื” ืœื ืžื•ื’ื“ืจืช.

ื”ืฉืžื™ื™ื auto_list ื”ื™ื ืจืฉื™ืžื” ืื•ืคืฆื™ื•ื ืœื™ืช ืฉืœ ืžืฉืชื ื™ื ื”ืžื™ื•ืขื“ื™ื ืœืฉื™ืžื•ืฉ "ืžืงื•ืžื™". ื”ืชื—ื‘ื™ืจ ืฉืœ
ื”ืจืฉื™ืžื” ื”ืื•ื˜ื•ืžื˜ื™ืช (ืื ืงื™ื™ืžืช) ื”ื™ื "ื”ืžื›ื•ื ื™ืช ืฉื, ... ;". (ื”ื ืงื•ื“ื”-ืคืกื™ืง ื”ื™ื ืื•ืคืฆื™ื•ื ืœื™ืช.) ื›ืœ ืื—ื“ ืฉื
ื”ื•ื ืฉื ืฉืœ ืžืฉืชื ื” ืื•ื˜ื•ืžื˜ื™. ื ื™ืชืŸ ืœืฆื™ื™ืŸ ืžืขืจื›ื™ื ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘ืื•ืชื• ืกื™ืžื•ืŸ ื›ืžื•
ืžืฉืžืฉ ื‘ืคืจืžื˜ืจื™ื. ืœืžืฉืชื ื™ื ืืœื” ื”ืขืจื›ื™ื ืฉืœื”ื ื ื“ื—ืคื™ื ืœืขืจื™ืžื” ื‘ืชื—ื™ืœืช
ื”ืคื•ื ืงืฆื™ื”. ืœืื—ืจ ืžื›ืŸ, ื”ืžืฉืชื ื™ื ืžืื•ืชื—ืœื™ื ืœืืคืก ื•ืžืฉืžืฉื™ื ืœืื•ืจืš ื›ืœ ื”ื–ืžืŸ
ื‘ื™ืฆื•ืข ื”ืคื•ื ืงืฆื™ื”. ื‘ื™ืฆื™ืื” ืžื”ืคื•ื ืงืฆื™ื”, ืžืฉืชื ื™ื ืืœื” ืžื•ืงืคืฆื™ื ื›ืš ืฉื”
ื”ืขืจืš ื”ืžืงื•ืจื™ (ื‘ื–ืžืŸ ื”ืงืจื™ืื” ืœืคื•ื ืงืฆื™ื”) ืฉืœ ืžืฉืชื ื™ื ืืœื” ืžืฉื•ื—ื–ืจื™ื. ื”
ืคืจืžื˜ืจื™ื ื”ื ื‘ืืžืช ืžืฉืชื ื™ื ืื•ื˜ื•ืžื˜ื™ื™ื ืฉืžืื•ื—ืœื™ื ืœืขืจืš ื”ืžืกื•ืคืง ื‘-
ืงืจื™ืืช ืคื•ื ืงืฆื™ื”. ืžืฉืชื ื™ื ืื•ื˜ื•ืžื˜ื™ื™ื ืฉื•ื ื™ื ืžืžืฉืชื ื™ื ืžืงื•ืžื™ื™ื ืžืกื•ืจืชื™ื™ื ื›ื™ ืื
ืคื•ื ืงืฆื™ื” A ืงื•ืจืืช ืœืคื•ื ืงืฆื™ื” B, B ืขืฉื•ื™ื” ืœื’ืฉืช ืœืžืฉืชื ื™ื ื”ืื•ื˜ื•ืžื˜ื™ื™ื ืฉืœ ืคื•ื ืงืฆื™ื” A ืจืง ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘-
ืื•ืชื• ืฉื, ืืœื ืื ื›ืŸ ืคื•ื ืงืฆื™ื” B ืงืจืื” ืœื”ื ืžืฉืชื ื™ื ืื•ื˜ื•ืžื˜ื™ื™ื. ื‘ืฉืœ ื”ืขื•ื‘ื“ื” ืฉืื•ื˜ื•
ืžืฉืชื ื™ื ื•ืคืจืžื˜ืจื™ื ื ื“ื—ืคื™ื ืœืขืจื™ืžื”, bc ืชื•ืžืš ื‘ืคื•ื ืงืฆื™ื•ืช ืจืงื•ืจืกื™ื‘ื™ื•ืช.

ื’ื•ืฃ ื”ืคื•ื ืงืฆื™ื” ื”ื•ื ืจืฉื™ืžื” ืฉืœ bc ื”ืฆื”ืจื•ืช. ืฉื•ื‘, ื”ืฆื”ืจื•ืช ืžื•ืคืจื“ื•ืช ืขืœ ื™ื“ื™
ื ืงื•ื“ื•ืช ืคืกื™ืง ืื• ืฉื•ืจื•ืช ื—ื“ืฉื•ืช. ื”ืฆื”ืจื•ืช ื”ื—ื–ืจื” ื’ื•ืจืžื•ืช ืœืกื™ื•ื ืฉืœ ืคื•ื ืงืฆื™ื” ื•ื”-
ื”ื—ื–ืจืช ืขืจืš. ื™ืฉื ืŸ ืฉืชื™ ื’ืจืกืื•ืช ืฉืœ ื”ืฆื”ืจืช ื”ื—ื–ืจื”. ื”ืฆื•ืจื” ื”ืจืืฉื•ื ื”,
"ืœึทื—ึฒื–ื•ึนืจ", ืžื—ื–ื™ืจ ืืช ื”ืขืจืš 0 ืœื‘ื™ื˜ื•ื™ ื”ืงื•ืจื. ื”ืฆื•ืจื” ื”ืฉื ื™ื™ื”, "ืœึทื—ึฒื–ื•ึนืจ (
ื‘ื™ื˜ื•ื™ )", ืžื—ืฉื‘ ืืช ื”ืขืจืš ืฉืœ ื”ื‘ื™ื˜ื•ื™ ื•ืžื—ื–ื™ืจ ืืช ื”ืขืจืš ื”ื–ื” ืœืงืจื™ืื”
ื‘ื™ื˜ื•ื™. ื™ืฉ ืžืฉืžืข "ืœึทื—ึฒื–ื•ึนืจ (0)" ื‘ืกื•ืฃ ื›ืœ ืคื•ื ืงืฆื™ื”. ื–ื” ืžืืคืฉืจ ื
ืคื•ื ืงืฆื™ื” ืœืกื™ื™ื ื•ืœื”ื—ื–ื™ืจ 0 ืœืœื ื”ืฆื”ืจืช ื”ื—ื–ืจื” ืžืคื•ืจืฉืช.

ืคื•ื ืงืฆื™ื•ืช ื’ื ืžืฉื ื•ืช ืืช ื”ืฉื™ืžื•ืฉ ื‘ืžืฉืชื ื” ื‘ืกื™ืก ืž. ื›ืœ ื”ืงื‘ื•ืขื™ื ื‘ื’ื•ืฃ ื”ืคื•ื ืงืฆื™ื”
ื™ื•ืžืจ ื‘ืืžืฆืขื•ืช ื”ืขืจืš ืฉืœ ื‘ืกื™ืก ืž ื‘ื–ืžืŸ ืงืจื™ืืช ื”ืคื•ื ืงืฆื™ื”. ืฉื™ื ื•ื™ื™ื ืฉืœ
ื‘ืกื™ืก ืž ืชืชืขืœื ื‘ืžื”ืœืš ื‘ื™ืฆื•ืข ื”ืคื•ื ืงืฆื™ื” ืœืžืขื˜ ื”ืชืงืŸ
ืคื•ื ืงืฆื™ื” ืœืงืจื•ื, ืฉืชืžื™ื“ ื™ืฉืชืžืฉ ื‘ืขืจืš ื”ื ื•ื›ื—ื™ ืฉืœ ื‘ืกื™ืก ืž ืœื”ืžืจื” ืฉืœ ืžืกืคืจื™ื.

ืœืคื•ื ืงืฆื™ื•ืช ื ื•ืกืคื• ืžืกืคืจ ื”ืจื—ื‘ื•ืช. ืจืืฉื™ืช, ื™ืฉ ืœืคื•ืจืžื˜ ืฉืœ ื”ื”ื’ื“ืจื”
ื”ื™ื” ืจื’ื•ืข ืžืขื˜. ื”ืชืงืŸ ื“ื•ืจืฉ ืฉืกื“ ื”ืคืชื™ื—ื” ื™ื”ื™ื” ื‘ืื•ืชื• ืงื• ื›ืžื• ื”-
ืœึฐื”ึทื’ื“ึดื™ืจ ืžื™ืœืช ื”ืžืคืชื— ื•ื›ืœ ื”ื—ืœืงื™ื ื”ืื—ืจื™ื ื—ื™ื™ื‘ื™ื ืœื”ื™ื•ืช ื‘ืฉื•ืจื•ืช ื”ื‘ืื•ืช. ื’ืจืกื” ื–ื• ืฉืœ bc ื™ืฆื˜ืจืš
ืืคืฉืจ ื›ืœ ืžืกืคืจ ืฉืœ ืฉื•ืจื•ืช ื—ื“ืฉื•ืช ืœืคื ื™ ื•ืื—ืจื™ ืกื“ ื”ืคืชื™ื—ื” ืฉืœ ื”ืคื•ื ืงืฆื™ื”. ืœ
ืœื“ื•ื’ืžื”, ื”ื”ื’ื“ืจื•ืช ื”ื‘ืื•ืช ื”ืŸ ื—ื•ืงื™ื•ืช.
define d (n) { return (2*n); }
ื”ื’ื“ืจ ื“ (n)
{ return (2*n); }

ื ื™ืชืŸ ืœื”ื’ื“ื™ืจ ืคื•ื ืงืฆื™ื•ืช ื› ืœื‘ื˜ืœ ืืช. ืคื•ื ืงืฆื™ื” void ืœื ืžื—ื–ื™ืจื” ืขืจืš ื•ืœื›ืŸ ื™ื™ืชื›ืŸ ืฉืœื
ืžืฉืžืฉ ื‘ื›ืœ ืžืงื•ื ืฉืฆืจื™ืš ืขืจืš. ืคื•ื ืงืฆื™ื™ืช void ืื™ื ื” ืžื™ื™ืฆืจืช ืคืœื˜ ื›ืืฉืจ
ื ืงืจื ืžืขืฆืžื• ืขืœ ืงื• ืงืœื˜. ืžื™ืœืช ื”ืžืคืชื— ืœื‘ื˜ืœ ืืช ืžืžื•ืงื ื‘ื™ืŸ ืžื™ืœืช ื”ืžืคืชื—
ืœึฐื”ึทื’ื“ึดื™ืจ ื•ืืช ืฉื ื”ืคื•ื ืงืฆื™ื”. ืœื“ื•ื’ืžื”, ืฉืงื•ืœ ืืช ื”ืคื’ื™ืฉื” ื”ื‘ืื”.
define py (y) { print "--->", y, "<---", "\n"; }
ื”ื’ื“ืจ void px (x) { print "--->", x, "<---", "\n"; }
py(1)
--->1<---
0
px(1)
--->1<---
ื”ืฉืืœื” ื”ื™ื ืื™ืš? py ืื™ื ื• ืคื•ื ืงืฆื™ื” ื‘ื˜ืœ, ื”ืงืจื™ืื” ืฉืœ py(1) ืžื“ืคื™ืก ืืช ื”ืคืœื˜ ื”ืจืฆื•ื™ ื•ืœืื—ืจ ืžื›ืŸ
ืžื“ืคื™ืก ืฉื•ืจื” ืฉื ื™ื™ื” ืฉื”ื™ื ื”ืขืจืš ืฉืœ ื”ืคื•ื ืงืฆื™ื”. ืžืื– ื”ืขืจืš ืฉืœ ืคื•ื ืงืฆื™ื”
ืฉืœื ื ื™ืชืŸ ืžืฉืคื˜ ื”ื—ื–ืจื” ืžืคื•ืจืฉ ื”ื•ื ืืคืก, ื”ืืคืก ืžื•ื“ืคืก. ืœ px(1),
ืœื ืžื•ื“ืคืก ืืคืก ื›ื™ ื”ืคื•ื ืงืฆื™ื” ื”ื™ื ืคื•ื ืงืฆื™ื” ื‘ื˜ืœ.

ื›ืžื• ื›ืŸ, ื ื•ืกืคื” ืงืจื™ืื” ืœืคื™ ืžืฉืชื ื” ืขื‘ื•ืจ ืžืขืจื›ื™ื. ื›ื“ื™ ืœื”ื›ืจื™ื– ืขืœ ืงืจื™ืื” ืœืคื™ ืžืขืจืš ืžืฉืชื ื”, ื”-
ื”ืฆื”ืจืช ืคืจืžื˜ืจ ื”ืžืขืจืš ื‘ื”ื’ื“ืจืช ื”ืคื•ื ืงืฆื™ื” ื ืจืื™ืช ื›ืžื• "*ืฉืึตื[]". ื”
ื”ืงืจื™ืื” ืœืคื•ื ืงืฆื™ื” ื ืฉืืจืช ื–ื”ื” ืœืงืจื™ืื” ืœืคื™ ืžืขืจื›ื™ ืขืจืš.

MATH ืกึดืคึฐืจึดื™ึธื”
If bc ื”ื•ื ืžื•ืคืขืœ ืขื -l ืืคืฉืจื•ืช, ืกืคืจื™ื™ืช ืžืชืžื˜ื™ืงื” ื ื˜ืขื ืช ืžืจืืฉ ื•ืกื•ืœื ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื•ื
ืžื•ื’ื“ืจ ืœ-20. ื”ืคื•ื ืงืฆื™ื•ืช ื”ืžืชืžื˜ื™ื•ืช ื™ื—ืฉื‘ื• ืืช ืชื•ืฆืื•ืชื™ื”ืŸ ื‘ืกื•ืœื ืฉื ืงื‘ืข ื‘ืื•ืชื” ืขืช
ืžื”ืฉื™ื—ื” ืฉืœื”ื. ืกืคืจื™ื™ืช ื”ืžืชืžื˜ื™ืงื” ืžื’ื“ื™ืจื” ืืช ื”ืคื•ื ืงืฆื™ื•ืช ื”ื‘ืื•ืช:

ืฉืœ (x) ื”ืกื™ื ื•ืก ืฉืœ x, x ื”ื•ื ื‘ืจื“ื™ืื ื™ื.

ื’ (x) ื”ืงื•ืกื™ื ื•ืก ืฉืœ x, x ื”ื•ื ื‘ืจื“ื™ืื ื™ื.

ื• (x) ื”ืืจืงื˜ื ื’'ื ื˜ ืฉืœ x, arctangent ืžื—ื–ื™ืจ ืจื“ื™ืื ื™ื.

l (x) ื”ืœื•ื’ืจื™ืชื ื”ื˜ื‘ืขื™ ืฉืœ x.

ื•x) ื”ืคื•ื ืงืฆื™ื” ื”ืžืขืจื™ื›ื™ืช ืฉืœ ื”ืขืœืืช e ืœืขืจืš x.

j (n,x)
ื”ืคื•ื ืงืฆื™ื” Bessel ื‘ืกื“ืจ ืžืกืคืจ ืฉืœื n ืฉืœ x.

ื“ื•ื’ืžืื•ืช
In / Bin / sh, ื”ื“ื‘ืจื™ื ื”ื‘ืื™ื ื™ืงืฆื” ืืช ื”ืขืจืš ืฉืœ "pi" ืœืžืฉืชื ื” ื”ืžืขื˜ืคืช pi.
pi=$(echo "scale=10; 4*a(1)" | bc -l)

ืœื”ืœืŸ ื”ื”ื’ื“ืจื” ืฉืœ ื”ืคื•ื ืงืฆื™ื” ื”ืžืขืจื™ื›ื™ืช ื”ืžืฉืžืฉืช ื‘ืกืคืจื™ื™ืช ื”ืžืชืžื˜ื™ืงื”.
ืคื•ื ืงืฆื™ื” ื–ื• ื›ืชื•ื‘ื” ื‘-POSIX bc.
ืกื•ืœื = 20

/* ืžืฉืชืžืฉ ื‘ืขื•ื‘ื“ื” ืฉ-e^x = (e^(x/2))^2
ื›ืืฉืจ x ืงื˜ืŸ ืžืกืคื™ืง, ืื ื• ืžืฉืชืžืฉื™ื ื‘ืกื“ืจื”:
e^x = 1 + x + x^2/2! + x^3/3! +...
*/

ื”ื’ื“ืจืช e(x) {
auto a, d, e, f, i, m, v, z

/* ื‘ื“ื•ืง ืืช ื”ืกื™ืžืŸ ืฉืœ x. */
if (x<0) {
m = 1
x = -x
}

/* ืชื ืื™ ืžื•ืงื“ื x. */
z = ืกื•ืœื;
ืกื•ืœื = 4 + z + .44*x;
while (x > 1) {
f += 1;
x /= 2;
}

/* ืืชื—ื•ืœ ื”ืžืฉืชื ื™ื. */
v = 1+x
a = x
d = 1

ืขื‘ื•ืจ (i=2; 1; i++) {
e = (a *= x) / (d *= i)
if (e == 0) {
if (f>0) ื‘ืขื•ื“ (f--) v = v*v;
ืกื•ืœื = z
ืื (ืž) ืœื—ื–ื•ืจ (1/v);
ื—ื–ืจื” (v/1);
}
v += ื”
}
}

ืœื”ืœืŸ ืงื•ื“ ื”ืžืฉืชืžืฉ ื‘ืชื›ื•ื ื•ืช ื”ืžื•ืจื—ื‘ื•ืช ืฉืœ bc ืœื™ื™ืฉื ืชื•ื›ื ื™ืช ืคืฉื•ื˜ื”
ืœื—ื™ืฉื•ื‘ ื™ืชืจื•ืช ืคื ืงืก ื”ืฆ'ืงื™ื. ืชื•ื›ื ื™ืช ื–ื• ื ืฉืžืจืช ื‘ืฆื•ืจื” ื”ื˜ื•ื‘ื” ื‘ื™ื•ืชืจ ื‘ืงื•ื‘ืฅ ื›ืš ืฉืชื•ื›ืœ ืœื”ื™ื•ืช
ื‘ืฉื™ืžื•ืฉ ืคืขืžื™ื ืจื‘ื•ืช ืžื‘ืœื™ ืฆื•ืจืš ืœื”ืงืœื™ื“ ืื•ืชื• ื‘ื›ืœ ืฉื™ืžื•ืฉ.
ืกื•ืœื=2
ื”ื“ืคืก "\nืชื•ื›ื ื™ืช ื‘ื“ื•ืง!\n"
ื”ื“ืคืก "ื–ื›ื•ืจ, ื”ืคืงื“ื•ืช ื”ืŸ ืขืกืงืื•ืช ืฉืœื™ืœื™ื•ืช.\n"
ื”ื“ืคืก " ื™ืฆื™ืื” ืขืœ ื™ื“ื™ 0 ืขืกืงื”.\n\n"

ื”ื“ืคืก "ืื™ื–ื” ืจืืฉื•ื ื™ืช?"; bal = read()
bal /= 1
ื”ื“ืคืก "\n"
ื‘ืขื•ื“ (1) {
"ื™ืชืจื” ื ื•ื›ื—ื™ืช = "; bal
"ืขืกืงื”?"; trans = read()
if (trans == 0) break;
bal -= ื˜ืจื ืก
bal /= 1
}
ืœื”ืคืกื™ืง

ืœื”ืœืŸ ื”ื”ื’ื“ืจื” ืฉืœ ื”ืคื•ื ืงืฆื™ื” ื”ืคืงื˜ื•ืจื™ืืœื™ืช ื”ืจืงื•ืจืกื™ื‘ื™ืช.
ื”ื’ื“ืจืช f (x) {
if (x <= 1) return (1);
return (f(x-1) * x);
}

ืงืจื™ืืช ืฉื•ืจื” ื• LIBEDIT ืืคืฉืจื•ื™ื•ืช
ื’ื ื” bc ื ื™ืชืŸ ืœื”ืจื›ื™ื‘ (ื‘ืืžืฆืขื•ืช ืืคืฉืจื•ืช ืชืฆื•ืจื”) ืœืฉื™ืžื•ืฉ ื‘-GNU ืงืจื™ืืช ืฉื•ืจื” ืขื•ืจืš ืงืœื˜
ื”ืกืคืจื™ื™ื” ืื• ื”-BSD ืœื™ื‘ื“ื™ื˜ ืกึดืคึฐืจึดื™ึธื”. ื–ื” ืžืืคืฉืจ ืœืžืฉืชืžืฉ ืœื‘ืฆืข ืขืจื™ื›ื” ืฉืœ ืฉื•ืจื•ืช ืœืคื ื™ ื›ืŸ
ืœืฉืœื•ื— ืื•ืชื ืœ bc. ื–ื” ื’ื ืžืืคืฉืจ ื”ื™ืกื˜ื•ืจื™ื” ืฉืœ ืฉื•ืจื•ืช ืงื•ื“ืžื•ืช ืฉื”ื•ืงืœื“ื•. ื›ืฉื–ื”
ื”ืืคืฉืจื•ืช ื ื‘ื—ืจื”, bc ื™ืฉ ืขื•ื“ ืžืฉืชื ื” ืžื™ื•ื—ื“ ืื—ื“. ื”ืžืฉืชื ื” ื”ืžื™ื•ื—ื“ ื”ื–ื”, ื”ื™ืกื˜ื•ืจื™ื” is
ืžืกืคืจ ืฉื•ืจื•ืช ื”ื”ื™ืกื˜ื•ืจื™ื” ืฉื ืฉืžืจื•. ืœ ืงืจื™ืืช ืฉื•ืจื”, ืขืจืš ืฉืœ -1 ืื•ืžืจ ื›ื™ an
ืžืกืคืจ ื‘ืœืชื™ ืžื•ื’ื‘ืœ ืฉืœ ืฉื•ืจื•ืช ื”ื™ืกื˜ื•ืจื™ื” ื ืฉืžืจ. ื”ื’ื“ืจืช ื”ืขืจืš ืฉืœ ื”ื™ืกื˜ื•ืจื™ื” ื›ื“ื™
ืžืกืคืจ ื—ื™ื•ื‘ื™ ืžื’ื‘ื™ืœ ืืช ืžืกืคืจ ืฉื•ืจื•ืช ื”ื”ื™ืกื˜ื•ืจื™ื” ืœืžืกืคืจ ืฉื ื™ืชืŸ. ื”ืขืจืš ืฉืœ 0
ืžืฉื‘ื™ืช ืืช ืชื›ื•ื ืช ื”ื”ื™ืกื˜ื•ืจื™ื”. ืขืจืš ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื•ื 100. ืœืžื™ื“ืข ื ื•ืกืฃ, ืงืจื ืืช
ืžื“ืจื™ื›ื™ ืžืฉืชืžืฉ ืขื‘ื•ืจ GNU ืงืจื™ืืช ืฉื•ืจื”, ื”ื™ืกื˜ื•ืจื™ื” ื•-BSD ืœื™ื‘ื“ื™ื˜ ืกืคืจื™ื•ืช. ืœื ื ื™ืชืŸ ืœื”ืคืขื™ืœ
ืฉื ื™ื”ื ืงืจื™ืืช ืฉื•ืจื” ื• ืœื™ื‘ื“ื™ื˜ ื‘ืขืช ื•ื‘ืขื•ื ื” ืื—ืช.

ื”ื‘ื“ืœื™ื
ื’ืจืกื” ื–ื• ืฉืœ bc ื™ื•ืฉื ืžืชื•ืš ื˜ื™ื•ื˜ืช POSIX P1003.2/D11 ื•ืžื›ื™ืœ ื›ืžื”
ื”ื‘ื“ืœื™ื ื•ื”ืจื—ื‘ื•ืช ื‘ื™ื—ืก ืœื˜ื™ื•ื˜ื” ื•ืœื™ื™ืฉื•ืžื™ื ื”ืžืกื•ืจืชื™ื™ื. ื–ื”
ืœื ืžื™ื•ืฉื ื‘ื“ืจืš ื”ืžืกื•ืจืชื™ืช ื‘ืืžืฆืขื•ืช dc(1). ื’ืจืกื” ื–ื• ื”ื™ื ืชื”ืœื™ืš ื™ื—ื™ื“
ืฉืžื ืชื— ื•ืžืจื™ืฅ ืชืจื’ื•ื ืงื•ื“ ื‘ืชื™ื ืฉืœ ื”ืชื•ื›ื ื™ืช. ื™ืฉ "ืœื ืžืชื•ืขื“"
ืืคืฉืจื•ืช (-c) ืฉื’ื•ืจืžืช ืœืชื•ื›ื ื™ืช ืœื”ื•ืฆื™ื ืืช ืงื•ื“ ื”ื‘ืชื™ื ืœืคืœื˜ ื”ืกื˜ื ื“ืจื˜ื™ ื‘ืžืงื•ื ื–ืืช
ืฉืœ ื”ืคืขืœืชื•. ื”ื•ื ืฉื™ืžืฉ ื‘ืขื™ืงืจ ืœื ื™ืคื•ื™ ื‘ืื’ื™ื ื‘ืžื ืชื— ื•ื”ื›ื ืช ื”ืžืชืžื˜ื™ืงื”
ืกึดืคึฐืจึดื™ึธื”.

ืžืงื•ืจ ืขื™ืงืจื™ ืœื”ื‘ื“ืœื™ื ื”ื•ื ื”ืจื—ื‘ื•ืช, ืฉื‘ื”ืŸ ืชื›ื•ื ื” ืžื•ืจื—ื‘ืช ื›ื“ื™ ืœื”ื•ืกื™ืฃ ืขื•ื“
ืคื•ื ืงืฆื™ื•ื ืœื™ื•ืช ื•ืชื•ืกืคื•ืช, ืฉื‘ื”ืŸ ืชื›ื•ื ื•ืช ื—ื“ืฉื•ืช ืžืชื•ื•ืกืคื•ืช. ืœื”ืœืŸ ื”ืจืฉื™ืžื” ืฉืœ
ื”ื‘ื“ืœื™ื ื•ื”ืจื—ื‘ื•ืช.

ืกื‘ื™ื‘ืช LANG
ื’ืจืกื” ื–ื• ืื™ื ื” ืชื•ืืžืช ืืช ืชืงืŸ POSIX ื‘ืขื™ื‘ื•ื“ ื”-LANG
ืžืฉืชื ื” ืกื‘ื™ื‘ื” ื•ื›ืœ ืžืฉืชื ื™ ื”ืกื‘ื™ื‘ื” ื”ืžืชื—ื™ืœื™ื ื‘-LC_.

ืฉืžื•ืช Traditional ื•-POSIX bc ื™ืฉ ืฉืžื•ืช ืฉืœ ืื•ืชื™ื•ืช ื‘ื•ื“ื“ื•ืช ืขื‘ื•ืจ ืคื•ื ืงืฆื™ื•ืช, ืžืฉืชื ื™ื ื•
ืžืขืจื›ื™ื. ื”ื ื”ื•ืจื—ื‘ื• ืœืฉืžื•ืช ืžืจื•ื‘ื™ ืชื•ื•ื™ื ืฉืžืชื—ื™ืœื™ื ื‘ื
ืื•ืช ื•ืขืฉื•ื™ื” ืœื”ื›ื™ืœ ืื•ืชื™ื•ืช, ืžืกืคืจื™ื ื•ืืช ืชื• ื”ืงื• ื”ืชื—ืชื•ืŸ.

ืžื—ืจื•ื–ื•ืช
ืืกื•ืจ ืœืžื—ืจื•ื–ื•ืช ืœื”ื›ื™ืœ ืชื•ื•ื™ NUL. POSIX ืื•ืžืจ ืฉื›ืœ ื”ืชื•ื•ื™ื ื—ื™ื™ื‘ื™ื
ืœื”ื™ื›ืœืœ ื‘ืžื—ืจื•ื–ื•ืช.

POSIX ืื—ืจื•ืŸ bc ืื™ืŸ ืื—ืจื•ืŸ ืžึดืฉืึฐืชึทื ึถื”. ื›ืžื” ื™ื™ืฉื•ืžื™ื ืฉืœ bc ืœื”ืฉืชืžืฉ ื‘ืชืงื•ืคื”
(.) ื‘ื“ืจืš ื“ื•ืžื”.

ื”ืฉื•ื•ืื•ืช
POSIX bc ืžืืคืฉืจ ื”ืฉื•ื•ืื•ืช ืจืง ื‘ืžืฉืคื˜ if, ื‘ื”ืฆื”ืจืช while ื•ื‘ืžืฉืคื˜
ื‘ื™ื˜ื•ื™ ืฉื ื™ ืฉืœ ื”ืฆื”ืจืช for. ื›ืžื• ื›ืŸ, ืจืง ืคืขื•ืœื” ืจืœืฆื™ื•ื ื™ืช ืื—ืช ื”ื™ื
ืžื•ืชืจ ื‘ื›ืœ ืื—ืช ืžื”ื”ืฆื”ืจื•ืช ื”ืœืœื•.

ืื ื”ืฆื”ืจื”, ืกืขื™ืฃ ืื—ืจ
POSIX bc ืื™ืŸ ืกืขื™ืฃ ืื—ืจ.

ืœื”ืฆื”ืจื”
POSIX bc ื“ื•ืจืฉ ืฉื›ืœ ื”ื‘ื™ื˜ื•ื™ื™ื ื™ื”ื™ื• ื ื•ื›ื—ื™ื ื‘ื”ืฆื”ืจืช for.

&&, ||, !
POSIX bc ืื™ืŸ ืืช ื”ืื•ืคืจื˜ื•ืจื™ื ื”ืœื•ื’ื™ื™ื.

ืคื•ื ืงืฆื™ื™ืช ืงืจื™ืื”
POSIX bc ืื™ืŸ ืคื•ื ืงืฆื™ื™ืช ืงืจื™ืื”.

ืœื”ื“ืคื™ืก ื”ืฆื”ืจื”
POSIX bc ืื™ืŸ ื”ืฆื”ืจื” ืžื•ื“ืคืกืช.

ืœื”ืžืฉื™ืš ื‘ื”ืฆื”ืจื”
POSIX bc ืื™ืŸ ื”ืฆื”ืจืช ื”ืžืฉืš.

ื”ืฆื”ืจืช ื”ื—ื–ืจื”
POSIX bc ื“ื•ืจืฉ ืกื•ื’ืจื™ื™ื ืกื‘ื™ื‘ ื‘ื™ื˜ื•ื™ ื”ื”ื—ื–ืจื”.

ืคืจืžื˜ืจื™ื ืฉืœ ืžืขืจืš
POSIX bc ืื™ื ื• ืชื•ืžืš (ื›ืจื’ืข) ื‘ืคืจืžื˜ืจื™ื ืฉืœ ืžืขืจืš ื‘ืื•ืคืŸ ืžืœื. ื”ื“ืงื“ื•ืง ืฉืœ POSIX
ืžืืคืฉืจ ืžืขืจื›ื™ื ื‘ื”ื’ื“ืจื•ืช ืคื•ื ืงืฆื™ื•ืช, ืืš ืื™ื ื• ืžืกืคืง ืฉื™ื˜ื” ืœืฆื™ื•ืŸ
ืžืขืจืš ื›ืคืจืžื˜ืจ ื‘ืคื•ืขืœ. (ืกื‘ื™ืจ ืœื”ื ื™ื— ืฉื–ื• ื”ืฉื’ื—ื” ื‘-
ื“ืงื“ื•ืง.) ื™ื™ืฉื•ืžื™ื ืžืกื•ืจืชื™ื™ื ืฉืœ bc ื™ืฉ ืจืง ืงืจื™ืื” ืœืคื™ ืžืขืจืš ืขืจื›ื™ื
ืคืจืžื˜ืจื™ื.

ืคื•ืจืžื˜ ืคื•ื ืงืฆื™ื”
POSIX bc ื“ื•ืจืฉ ืืช ื”ืคืœื˜ื” ื”ืคืชื™ื—ื” ื‘ืื•ืชื• ืงื• ื›ืžื• ื”- ืœึฐื”ึทื’ื“ึดื™ืจ ืžื™ืœืช ืžืคืชื— ื•ืืช
ื”ืžื›ื•ื ื™ืช ื”ืฆื”ืจื” ื‘ืฉื•ืจื” ื”ื‘ืื”.

=+, =-, =*, =/, =%, =^
POSIX bc ืื™ื ื• ื“ื•ืจืฉ ื”ื’ื“ืจื” ืฉืœ ืื•ืคืจื˜ื•ืจื™ ื”ืงืฆืืช "ืกื’ื ื•ืŸ ื™ืฉืŸ" ืืœื•.
ื’ืจืกื” ื–ื• ืขืฉื•ื™ื” ืœืืคืฉืจ ืžื˜ืœื•ืช ืืœื” ื‘ืกื’ื ื•ืŸ "ื™ืฉืŸ". ื”ืฉืชืžืฉ ื‘ื”ืฆื”ืจืช ื”ื’ื‘ื•ืœื•ืช ื›ื“ื™
ื‘ื“ื•ืง ืื ื”ื’ืจืกื” ื”ืžื•ืชืงื ืช ืชื•ืžื›ืช ื‘ื”ื. ืื ื–ื” ื›ืŸ ืชื•ืžืš ื‘"ืกื’ื ื•ืŸ ื”ื™ืฉืŸ"
ืื•ืคืจื˜ื•ืจื™ ื”ืงืฆืื”, ื”ื”ืฆื”ืจื” "a =- 1" ืชืจื“ a ืœืคื™ 1 ื‘ืžืงื•ื
ื”ืฆื‘ื” a ืœืขืจืš -1.

ืจื•ื•ื—ื™ื ื‘ืžืกืคืจื™ื
ื™ื™ืฉื•ืžื™ื ืื—ืจื™ื ืฉืœ bc ืืคืฉืจ ืจื•ื•ื—ื™ื ื‘ืžืกืคืจื™ื. ืœื“ื•ื’ืžื”, "x=1 3" ื™ืขืฉื” ื–ืืช
ื”ืงืฆื” ืืช ื”ืขืจืš 13 ืœืžืฉืชื ื” x. ืื•ืชื” ืืžื™ืจื” ืชื’ืจื•ื ืœืชื—ื‘ื™ืจ
ืฉื’ื™ืื” ื‘ื’ืจืกื” ื–ื• ืฉืœ bc.

ืฉื’ื™ืื•ืช ื•ื‘ื™ืฆื•ืข
ื™ื™ืฉื•ื ื–ื” ืžืฉืชื ื” ืžื™ื™ืฉื•ืžื™ื ืื—ืจื™ื ืžื‘ื—ื™ื ืช ืžื” ื™ื”ื™ื” ื”ืงื•ื“
ืžื•ืคืขืœ ื›ืืฉืจ ื”ืชื—ื‘ื™ืจ ื•ืฉื’ื™ืื•ืช ืื—ืจื•ืช ื ืžืฆืื•ืช ื‘ืชื•ื›ื ื™ืช. ืื ืฉื’ื™ืืช ืชื—ื‘ื™ืจ
ื ืžืฆื ื‘ื”ื’ื“ืจืช ืคื•ื ืงืฆื™ื”, ืฉื—ื–ื•ืจ ืฉื’ื™ืื” ืžื ืกื” ืœืžืฆื•ื ืืช ื”ื”ืชื—ืœื” ืฉืœ a
ืžืฉืคื˜ ื•ื”ืžืฉืš ืœื ืชื— ืืช ื”ืคื•ื ืงืฆื™ื”. ื‘ืจื’ืข ืฉื ืžืฆืื” ืฉื’ื™ืืช ืชื—ื‘ื™ืจ ื‘-
ืคื•ื ืงืฆื™ื”, ื”ืคื•ื ืงืฆื™ื” ืœื ืชื”ื™ื” ื ื™ืชื ืช ืœื”ืงืจืื” ื•ืชื”ืคื•ืš ืœืœื ืžื•ื’ื“ืจืช. ืฉื’ื™ืื•ืช ืชื—ื‘ื™ืจ
ื‘ืงื•ื“ ื”ื‘ื™ืฆื•ืข ื”ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ ื™ื‘ื˜ืœ ืืช ืชื•ืงืฃ ื‘ืœื•ืง ื”ื‘ื™ืฆื•ืข ื”ื ื•ื›ื—ื™. ื”
ื‘ืœื•ืง ื‘ื™ืฆื•ืข ืžืกืชื™ื™ื ืขืœ ื™ื“ื™ ืกื•ืฃ ืฉื•ืจื” ืฉืžื•ืคื™ืข ืœืื—ืจ ื”ืฉืœืžื”
ืจืฆืฃ ืฉืœ ื”ืฆื”ืจื•ืช. ืœื“ื•ื’ืžื”,
= 1
b = 2
ื™ืฉ ืฉื ื™ ื‘ืœื•ืงื™ื ืœื‘ื™ืฆื•ืข ื•
{ a = 1
b = 2 }
ื™ืฉ ื‘ืœื•ืง ื‘ื™ืฆื•ืข ืื—ื“. ื›ืœ ืฉื’ื™ืืช ื–ืžืŸ ืจื™ืฆื” ืชืคืกื™ืง ืืช ื‘ื™ืฆื•ืข ื”ื–ืจื
ื‘ืœื•ืง ื‘ื™ืฆื•ืข. ืื–ื”ืจืช ื–ืžืŸ ืจื™ืฆื” ืœื ืชืกื™ื™ื ืืช ื‘ืœื•ืง ื”ื‘ื™ืฆื•ืข ื”ื ื•ื›ื—ื™.

ืžืคืจื™ืข
ื‘ืžื”ืœืš ื”ืคืขืœื” ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ืช, ืื•ืช SIGINT (ื‘ื“ืจืš ื›ืœืœ ื ื•ืฆืจ ืขืœ ื™ื“ื™ ื”ื‘ืงืจื”-
ืชื• C ืžื”ืžืกื•ืฃ) ื™ื’ืจื•ื ืœื‘ื™ืฆื•ืข ืฉืœ ื‘ืœื•ืง ื”ื‘ื™ืฆื•ืข ื”ื ื•ื›ื—ื™
ืœื”ืคืจื™ืข. ื–ื” ื™ืฆื™ื’ ืฉื’ื™ืืช "ื–ืžืŸ ืจื™ืฆื”" ื”ืžืฆื™ื™ื ืช ืื™ื–ื• ืคื•ื ืงืฆื™ื” ื”ื™ื™ืชื”
ืžื•ึผืคืจึธืข. ืœืื—ืจ ืฉื›ืœ ืžื‘ื ื™ ื–ืžืŸ ื”ืจื™ืฆื” ื ื•ืงื•, ืชื•ืคื™ืข ื”ื•ื“ืขื”
ืžื•ื“ืคืก ื›ื“ื™ ืœื”ื•ื“ื™ืข โ€‹โ€‹ืœืžืฉืชืžืฉ ืขืœ ื›ืš bc ืžื•ื›ืŸ ืœืงืœื˜ ื ื•ืกืฃ. ื”ื›ืœ ื”ื•ื’ื“ืจ ืงื•ื“ื ืœื›ืŸ
ื”ืคื•ื ืงืฆื™ื•ืช ื ืฉืืจื•ืช ืžื•ื’ื“ืจื•ืช ื•ื”ืขืจืš ืฉืœ ื›ืœ ื”ืžืฉืชื ื™ื ื”ืœื ืื•ื˜ื•ืžื˜ื™ื™ื ื”ื•ื ื”ืขืจืš ื‘
ื ืงื•ื“ืช ื”ื”ืคืจืขื”. ื›ืœ ื”ืžืฉืชื ื™ื ื”ืื•ื˜ื•ืžื˜ื™ื™ื ื•ืคืจืžื˜ืจื™ ื”ืคื•ื ืงืฆื™ื” ืžื•ืกืจื™ื
ื‘ืžื”ืœืš ืชื”ืœื™ืš ื”ื ื™ืงื•ื™. ื‘ืžื”ืœืš ื”ืคืขืœื” ืœื ืื™ื ื˜ืจืืงื˜ื™ื‘ื™ืช, ื”ืื•ืช SIGINT
ื™ืคืกื™ืง ืืช ื›ืœ ื”ื”ืจืฆื” ืฉืœ bc.

ื’ื‘ื•ืœื•ืช
ืœื”ืœืŸ ื”ืžื’ื‘ืœื•ืช ื”ืงื™ื™ืžื•ืช ื›ืขืช ืขื‘ื•ืจ ื–ื” bc ืžืขื‘ื“. ื™ื™ืชื›ืŸ ืฉื—ืœืง ืžื”ื
ืฉื•ื ื• ืขืœ ื™ื“ื™ ื”ืชืงื ื”. ื”ืฉืชืžืฉ ื‘ื”ืฆื”ืจืช ื”ื’ื‘ื•ืœื•ืช ื›ื“ื™ ืœืจืื•ืช ืืช ื”ืขืจื›ื™ื ื‘ืคื•ืขืœ.

BC_BASE_MAX
ื‘ืกื™ืก ื”ืคืœื˜ ื”ืžืจื‘ื™ ืžื•ื’ื“ืจ ื›ืขืช ืขืœ 999. ื‘ืกื™ืก ื”ืงืœื˜ ื”ืžืงืกื™ืžืœื™ ื”ื•ื 16.

BC_DIM_MAX
ื–ื•ื”ื™ ื›ื™ื•ื ืžื’ื‘ืœื” ืฉืจื™ืจื•ืชื™ืช ืฉืœ 65535 ื›ืคื™ ืฉื”ืคืฆื”. ื”ื”ืชืงื ื” ืฉืœืš
ื™ื›ื•ืœ ืœื”ื™ื•ืช ืฉื•ื ื”.

BC_SCALE_MAX
ืžืกืคืจ ื”ืกืคืจื•ืช ืื—ืจื™ ื”ื ืงื•ื“ื” ื”ืขืฉืจื•ื ื™ืช ืžื•ื’ื‘ืœ ืœ-INT_MAX ืกืคืจื•ืช. ื’ึทื,
ืžืกืคืจ ื”ืกืคืจื•ืช ืœืคื ื™ ื”ื ืงื•ื“ื” ื”ืขืฉืจื•ื ื™ืช ืžื•ื’ื‘ืœ ืœ-INT_MAX ืกืคืจื•ืช.

BC_STRING_MAX
ื”ืžื’ื‘ืœื” ืขืœ ืžืกืคืจ ื”ืชื•ื•ื™ื ื‘ืžื—ืจื•ื–ืช ื”ื™ื INT_MAX ืชื•ื•ื™ื.

ืžึทืขึฒืจึดื™ืš
ื”ืขืจืš ืฉืœ ื”ืžืขืจื™ืš ื‘ืคืขื•ืœืช ื”ืขืœืื” (^) ืžื•ื’ื‘ืœ ืœ-LONG_MAX.

ืฉืžื•ืช ืžืฉืชื ื™ื
ื”ืžื’ื‘ืœื” ื”ื ื•ื›ื—ื™ืช ืขืœ ืžืกืคืจ ื”ืฉืžื•ืช ื”ื™ื™ื—ื•ื“ื™ื™ื ื”ื™ื 32767 ืœื›ืœ ืื—ื“ ืžื”ืฉืžื•ืช ื”ืคืฉื•ื˜ื™ื
ืžืฉืชื ื™ื, ืžืขืจื›ื™ื ื•ืคื•ื ืงืฆื™ื•ืช.

ื”ืกื‘ื™ื‘ื” ื•ืจื™ืืฆื™ื•ืช


ืžืฉืชื ื™ ื”ืกื‘ื™ื‘ื” ื”ื‘ืื™ื ืžืขื•ื‘ื“ื™ื ืขืœ ื™ื“ื™ bc:

POSIXLY_CORRECT
ื–ื” ื–ื”ื” ืœ- -s ืื•ึนืคึผึฐืฆึดื™ึธื”.

BC_ENV_ARGS
ื–ื” ืขื•ื“ ืžื ื’ื ื•ืŸ ืœื”ื’ื™ืข ืืœื™ื• ื˜ื™ืขื•ื ื™ื bc. ื”ืคื•ืจืžื˜ ื–ื”ื” ืœ-
ืืจื’ื•ืžื ื˜ื™ื ืฉืœ ืฉื•ืจืช ื”ืคืงื•ื“ื”. ืืจื’ื•ืžื ื˜ื™ื ืืœื” ืžืขื•ื‘ื“ื™ื ืชื—ื™ืœื”, ื•ืœื›ืŸ ื›ืœ ื”ืงื‘ืฆื™ื ื”ืจืฉื•ืžื™ื
ื‘ืกื‘ื™ื‘ื” ื”ืืจื’ื•ืžื ื˜ื™ื ืžืขื•ื‘ื“ื™ื ืœืคื ื™ ื›ืœ ืงื‘ืฆื™ ื”ืืจื’ื•ืžื ื˜ื™ื ืฉืœ ืฉื•ืจืช ื”ืคืงื•ื“ื”.
ื–ื” ืžืืคืฉืจ ืœืžืฉืชืžืฉ ืœื”ื’ื“ื™ืจ ืืคืฉืจื•ื™ื•ืช "ืกื˜ื ื“ืจื˜ื™ื•ืช" ื•ืงื‘ืฆื™ื ืœืขื™ื‘ื•ื“
ื›ืœ ืงืจื™ืื” ืฉืœ bc. ื”ืงื‘ืฆื™ื ื‘ืžืฉืชื ื™ ื”ืกื‘ื™ื‘ื” ื”ื™ื• ื‘ื“ืจืš ื›ืœืœ
ืžื›ื™ืœ ื”ื’ื“ืจื•ืช ืคื•ื ืงืฆื™ื•ืช ืขื‘ื•ืจ ืคื•ื ืงืฆื™ื•ืช ืฉื”ืžืฉืชืžืฉ ืจื•ืฆื” ืœื”ื’ื“ื™ืจ ื‘ื›ืœ ืคืขื bc is
ืœึธืจื•ึผืฅ.

BC_LINE_LENGTH
ื–ื” ืฆืจื™ืš ืœื”ื™ื•ืช ืžืกืคืจ ืฉืœื ื”ืžืฆื™ื™ืŸ ืืช ืžืกืคืจ ื”ืชื•ื•ื™ื ื‘ืฉื•ืจืช ืคืœื˜ ืขื‘ื•ืจ
ืžืกืคืจื™ื. ื–ื” ื›ื•ืœืœ ืืช ื”ืชื•ื•ื™ื ื”ืื—ื•ืจื™ื™ื ื•ื”ืงื• ื”ื—ื“ืฉ ืขื‘ื•ืจ ืžืกืคืจื™ื ืืจื•ื›ื™ื. ื›ืคื™ ืฉ
ื”ืจื—ื‘ื”, ื”ืขืจืš ืฉืœ ืืคืก ืžืฉื‘ื™ืช ืืช ื”ืชื›ื•ื ื” ืžืจื•ื‘ืช ืฉื•ืจื•ืช. ื›ืœ ืขืจืš ืื—ืจ
ืฉืœ ืžืฉืชื ื” ื–ื” ืฉื”ื•ื ืคื—ื•ืช ืž-3 ืžื’ื“ื™ืจ ืืช ืื•ืจืš ื”ืฉื•ืจื” ืœ-70.

ื“ื™ืื’ื ื•ืกื˜ื™ืงื”


ืื ืœื ื ื™ืชืŸ ืœืคืชื•ื— ืงื•ื‘ืฅ ื›ืœืฉื”ื• ื‘ืฉื•ืจืช ื”ืคืงื•ื“ื”, bc ื™ื“ื•ื•ื— ืฉื”ืงื•ื‘ืฅ ื”ื•ื
ืœื ื–ืžื™ืŸ ื•ืžืกืชื™ื™ื. ื›ืžื• ื›ืŸ, ื™ืฉ ืื‘ื—ื•ืŸ ื–ืžืŸ ืงื•ืžืคื™ืœืฆื™ื” ื•ื”ืจืฆื” ืฉืฆืจื™ืš
ืœื”ื™ื•ืช ืžื•ื‘ืŸ ืžืืœื™ื•.

ื”ืฉืชืžืฉ ื‘-BC ื‘ืื™ื ื˜ืจื ื˜ ื‘ืืžืฆืขื•ืช ืฉื™ืจื•ืชื™ onworks.net


ืฉืจืชื™ื ื•ืชื—ื ื•ืช ืขื‘ื•ื“ื” ื‘ื—ื™ื ื

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  • 5
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  • 6
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