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cl:functions:ash [2019/09/14 05:00] |
cl:functions:ash [2020/02/27 17:00] (current) |
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+ | ====== Function ASH ====== | ||

+ | |||

+ | ====Syntax==== | ||

+ | * **ash** //integer count// → //shifted-integer// | ||

+ | |||

+ | ====Arguments and Values==== | ||

+ | * //integer// - an //[[CL:Glossary:integer]]//. | ||

+ | * //count// - an //[[CL:Glossary:integer]]//. | ||

+ | * //shifted-integer// - an //[[CL:Glossary:integer]]//. | ||

+ | |||

+ | ====Description==== | ||

+ | **ash** performs the arithmetic shift operation on the binary representation of //integer//, which is treated as if it were binary. | ||

+ | |||

+ | **ash** shifts //integer// arithmetically left by //count// bit positions if //count// is positive, or right //count// bit positions if //count// is negative. The shifted value of the same sign as //integer// is returned. | ||

+ | |||

+ | Mathematically speaking, **ash** performs the computation ''floor(integer * 2<sup>//count//</sup>)''. | ||

+ | |||

+ | Logically, **ash** moves all of the bits in //integer// to the left, adding zero-bits at the right, or moves them to the right, discarding bits. | ||

+ | |||

+ | **ash** is defined to behave as if //integer// were represented in two's complement form, regardless of how //[[CL:Glossary:integers]]// are represented internally. | ||

+ | |||

+ | ====Examples==== | ||

+ | <blockquote> | ||

+ | (ash 16 1) <r>32 </r> | ||

+ | (ash 16 0) <r>16 </r> | ||

+ | (ash 16 -1) <r>8 </r> | ||

+ | (ash -100000000000000000000000000000000 -100) <r>-79 </r> | ||

+ | </blockquote> | ||

+ | |||

+ | ====Affected By==== | ||

+ | None. | ||

+ | |||

+ | ====Exceptional Situations==== | ||

+ | Should signal an error of type type-error if //integer// is not an //[[CL:Glossary:integer]]//. Should signal an error of type type-error if //count// is not an //[[CL:Glossary:integer]]//. Might signal **[[CL:Types:arithmetic-error]]**. | ||

+ | |||

+ | ====See Also==== | ||

+ | None. | ||

+ | |||

+ | ====Notes==== | ||

+ | <blockquote> | ||

+ | ([[CL:Functions:logbitp]] //j// (ash //n// //k//)) | ||

+ | ≡ ([[CL:Macros:and]] ([[CL:Macros:not-less|>=]] //j// //k//) | ||

+ | ([[CL:Functions:logbitp]] (- //j// //k//) //n//)) | ||

+ | </blockquote> | ||

+ | |||