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* CLICKHOUSE-4063: less manual html @ index.md * CLICKHOUSE-4063: recommend markdown="1" in README.md * CLICKHOUSE-4003: manually purge custom.css for now * CLICKHOUSE-4064: expand <details> before any print (including to pdf) * CLICKHOUSE-3927: rearrange interfaces/formats.md a bit * CLICKHOUSE-3306: add few http headers * Remove copy-paste introduced in #3392 * Hopefully better chinese fonts #3392 * get rid of tabs @ custom.css * Apply comments and patch from #3384 * Add jdbc.md to ToC and some translation, though it still looks badly incomplete * minor punctuation * Add some backlinks to official website from mirrors that just blindly take markdown sources * Do not make fonts extra light * find . -name '*.md' -type f | xargs -I{} perl -pi -e 's//g' {} * find . -name '*.md' -type f | xargs -I{} perl -pi -e 's/ sql/g' {} * Remove outdated stuff from roadmap.md * Not so light font on front page too * Refactor Chinese formats.md to match recent changes in other languages * Update some links on front page * Remove some outdated comment * Add twitter link to front page * More front page links tuning * Add Amsterdam meetup link * Smaller font to avoid second line * Add Amsterdam link to README.md * Proper docs nav translation * Back to 300 font-weight except Chinese * fix docs build * Update Amsterdam link * remove symlinks * more zh punctuation * apply lost comment by @zhang2014 * Apply comments by @zhang2014 from #3417 * Remove Beijing link * rm incorrect symlink * restore content of docs/zh/operations/table_engines/index.md * CLICKHOUSE-3751: stem terms while searching docs * CLICKHOUSE-3751: use English stemmer in non-English docs too * CLICKHOUSE-4135 fix * Remove past meetup link * Add blog link to top nav * Add ContentSquare article link * Add form link to front page + refactor some texts * couple markup fixes * minor * Introduce basic ODBC driver page in docs * More verbose 3rd party libs disclaimer * Put third-party stuff into a separate folder * Separate third-party stuff in ToC too * Update links * Move stuff that is not really (only) a client library into a separate page * Add clickhouse-hdfs-loader link * Some introduction for "interfaces" section * Rewrite tcp.md * http_interface.md -> http.md * fix link * Remove unconvenient error for now * try to guess anchor instead of failing * remove symlink * Remove outdated info from introduction * remove ru roadmap.md * replace ru roadmap.md with symlink * Update roadmap.md * lost file * Title case in toc_en.yml * Sync "Functions" ToC section with en * Remove reference to pretty old ClickHouse release from docs * couple lost symlinks in fa * Close quote in proper place * Rewrite en/getting_started/index.md * Sync en<>ru getting_started/index.md * minor changes * Some gui.md refactoring * Translate DataGrip section to ru * Translate DataGrip section to zh * Translate DataGrip section to fa * Translate DBeaver section to fa * Translate DBeaver section to zh * Split third-party GUI to open-source and commercial * Mention some RDBMS integrations + ad-hoc translation fixes * Add rel="external nofollow" to outgoing links from docs * Lost blank lines * Fix class name * More rel="external nofollow" * Apply suggestions by @sundy-li * Mobile version of front page improvements * test * test 2 * test 3 * Update LICENSE * minor docs fix * Highlight current article as suggested by @sundy-li * fix link destination * Introduce backup.md (only "en" for now) * Mention INSERT+SELECT in backup.md * Some improvements for replication.md * Add backup.md to toc * Mention clickhouse-backup tool * Mention LightHouse in third-party GUI list * Introduce interfaces/third-party/proxy.md * Add clickhouse-bulk to proxy.md * Major extension of integrations.md contents * fix link target * remove unneeded file * better toc item name * fix markdown * better ru punctuation * Add yet another possible backup approach * Simplify copying permalinks to headers * Support non-eng link anchors in docs + update some deps * Generate anchors for single-page mode automatically * Remove anchors to top of pages * Remove anchors that nobody links to * build fixes * fix few links * restore css * fix some links * restore gifs * fix lost words * more docs fixes * docs fixes * NULL anchor * update urllib3 dependency * more fixes
97 lines
3.6 KiB
Markdown
97 lines
3.6 KiB
Markdown
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# Decimal(P, S), Decimal32(S), Decimal64(S), Decimal128(S)
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有符号的定点数,可在加、减和乘法运算过程中保持精度。对于除法,最低有效数字会被丢弃(不舍入)。
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## 参数
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- P - 精度。有效范围:[1:38],决定可以有多少个十进制数字(包括分数)。
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- S - 规模。有效范围:[0:P],决定数字的小数部分中包含的小数位数。
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对于不同的 P 参数值 Decimal 表示,以下例子都是同义的:
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- P from [ 1 : 9 ] - for Decimal32(S)
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- P from [ 10 : 18 ] - for Decimal64(S)
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- P from [ 19 : 38 ] - for Decimal128(S)
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## 十进制值范围
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- Decimal32(S) - ( -1 * 10^(9 - S), 1 * 10^(9 - S) )
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- Decimal64(S) - ( -1 * 10^(18 - S), 1 * 10^(18 - S) )
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- Decimal128(S) - ( -1 * 10^(38 - S), 1 * 10^(38 - S) )
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例如,Decimal32(4) 可以表示 -99999.9999 至 99999.9999 的数值,步长为0.0001。
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## 内部表示方式
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数据采用与自身位宽相同的有符号整数存储。这个数在内存中实际范围会高于上述范围,从 String 转换到十进制数的时候会做对应的检查。
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由于现代CPU不支持128位数字,因此 Decimal128 上的操作由软件模拟。所以 Decimal128 的运算速度明显慢于 Decimal32/Decimal64。
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## 运算和结果类型
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对Decimal的二进制运算导致更宽的结果类型(无论参数的顺序如何)。
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- Decimal64(S1) <op> Decimal32(S2) -> Decimal64(S)
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- Decimal128(S1) <op> Decimal32(S2) -> Decimal128(S)
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- Decimal128(S1) <op> Decimal64(S2) -> Decimal128(S)
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精度变化的规则:
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- 加法,减法:S = max(S1, S2)。
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- 乘法:S = S1 + S2。
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- 除法:S = S1。
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对于 Decimal 和整数之间的类似操作,结果是与参数大小相同的十进制。
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未定义Decimal和Float32/Float64之间的函数。要执行此类操作,您可以使用:toDecimal32、toDecimal64、toDecimal128 或 toFloat32,toFloat64,需要显式地转换其中一个参数。注意,结果将失去精度,类型转换是昂贵的操作。
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Decimal上的一些函数返回结果为Float64(例如,var或stddev)。对于其中一些,中间计算发生在Decimal中。对于此类函数,尽管结果类型相同,但Float64和Decimal中相同数据的结果可能不同。
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## 溢出检查
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在对 Decimal 类型执行操作时,数值可能会发生溢出。分数中的过多数字被丢弃(不是舍入的)。整数中的过多数字将导致异常。
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```
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SELECT toDecimal32(2, 4) AS x, x / 3
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```
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```
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┌──────x─┬─divide(toDecimal32(2, 4), 3)─┐
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│ 2.0000 │ 0.6666 │
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└────────┴──────────────────────────────┘
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```
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```
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SELECT toDecimal32(4.2, 8) AS x, x * x
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```
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```
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DB::Exception: Scale is out of bounds.
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```
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```
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SELECT toDecimal32(4.2, 8) AS x, 6 * x
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```
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```
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DB::Exception: Decimal math overflow.
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```
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检查溢出会导致计算变慢。如果已知溢出不可能,则可以通过设置`decimal_check_overflow`来禁用溢出检查,在这种情况下,溢出将导致结果不正确:
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```
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SET decimal_check_overflow = 0;
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SELECT toDecimal32(4.2, 8) AS x, 6 * x
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```
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```
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┌──────────x─┬─multiply(6, toDecimal32(4.2, 8))─┐
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│ 4.20000000 │ -17.74967296 │
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└────────────┴──────────────────────────────────┘
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```
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溢出检查不仅发生在算术运算上,还发生在比较运算上:
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```
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SELECT toDecimal32(1, 8) < 100
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```
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```
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DB::Exception: Can't compare.
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```
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