54 lines
3.0 KiB
Markdown
54 lines
3.0 KiB
Markdown
For a value <span class="postcard-grammar binarysyntax">*V*</span>, we write <span
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class="postcard-grammar binarysyntax">«*V*»</span> for the binary encoding of <span
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class="postcard-grammar binarysyntax">*V*</span>.
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{:.postcard-grammar.binarysyntax}
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«`#f`» | = | `80`
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«`#t`» | = | `81`
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{:.postcard-grammar.binarysyntax}
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«`@`*W* *V*» | = | `85` «*W*» «*V*»
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«`#!`*V*» | = | `86` «*V*»
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{:.postcard-grammar.binarysyntax}
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«*V*» | = | `87``04` **binary32**(*V*) | if *V* ∈ Float
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«*V*» | = | `87``08` **binary64**(*V*) | if *V* ∈ Double
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{:.postcard-grammar.binarysyntax}
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«*V*» | = | `B0` **varint**(|**intbytes**(*V*)|) **intbytes**(*V*) | if *V* ∈ SignedInteger
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«*V*» | = | `B1` **varint**(|**utf8**(*V*)|) **utf8**(*V*) | if *V* ∈ String
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«*V*» | = | `B2` **varint**(|*V*|) *V* | if *V* ∈ ByteString
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«*V*» | = | `B3` **varint**(|**utf8**(*V*)|) **utf8**(*V*) | if *V* ∈ Symbol
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{:.postcard-grammar.binarysyntax}
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«`<`*L* *F*<sub>1</sub> ... *F*<sub>m</sub>`>`» | = | `B4` «*L*» «*F*<sub>1</sub>» ... «*F*<sub>m</sub>» `84`
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«`[`*X*<sub>1</sub> ... *X*<sub>m</sub>`]`» | = | `B5` «*X*<sub>1</sub>» ... «*X*<sub>m</sub>» `84`
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«`#{`*E*<sub>1</sub> ... *E*<sub>m</sub>`}`» | = | `B6` «*E*<sub>1</sub>» ... «*E*<sub>m</sub>» `84`
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«`{`*K*<sub>1</sub>`:`*V*<sub>1</sub> ... *K*<sub>m</sub>`:`*V*<sub>m</sub>`}`» | = | `B7` «*K*<sub>1</sub>» «*V*<sub>1</sub>» ... «*K*<sub>m</sub>» «*V*<sub>m</sub>» `84`
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{:.postcard-grammar.binarysyntax}
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**varint**(*n*) | = | <span class="outputish">*n*</span> | if *n* < 128
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| | <span class="outputish">(*n* & 127) | 128</span> **varint**(*n* >> 7) | if *n* ≥ 128
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{:.postcard-grammar.binarysyntax}
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**intbytes**(*n*) | = | <span class="roman">the empty sequence if</span> *n* = 0<span class="roman">, otherwise</span> **signedBigEndian**(*n*)
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{:.postcard-grammar.binarysyntax}
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**signedBigEndian**(*n*) | = | <span class="outputish">*n* & 255</span> | if −128 ≤ *n* ≤ 127
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| | **signedBigEndian**(*n* >> 8) <span class="outputish">*n* & 255</span> | otherwise
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The functions <span class="postcard-grammar binarysyntax">**binary32**(*F*)</span> and <span
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class="postcard-grammar binarysyntax">**binary64**(*D*)</span> yield big-endian 4- and 8-byte
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IEEE 754 binary representations of <span class="postcard-grammar binarysyntax">*F*</span> and
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<span class="postcard-grammar binarysyntax">*D*</span>, respectively.
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<!--
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Together, <span class="postcard-grammar binarysyntax">**div**</span> and <span
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class="postcard-grammar binarysyntax">**mod**</span> give [Euclidean
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division](https://en.wikipedia.org/wiki/Euclidean_division); that is, if
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<span class="postcard-grammar binarysyntax">*n* **div** *d* = *q*</span> and
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<span class="postcard-grammar binarysyntax">*n* **mod** *d* = *r*</span>, then
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<span class="postcard-grammar binarysyntax">*n* = *dq* + *r*</span> and
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<span class="postcard-grammar binarysyntax">0 ≤ *r* < |d|</span>.
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-->
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