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Decimal64 floating-point format: Difference between revisions

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{{Short description|64-bit computer number format}}
{{lowercase title}}
{{Use dmy dates|date=July 2020|cs1-dates=y}}
{{floating-point}}
In [[computing]], '''decimal64''' is a [[decimal floating point|decimal floating-point]] [[computer numberingnumber format]] that occupies 8 bytes (64 bits) in computer memory.
 
Decimal64 is a decimal floating-point format, formally introduced in the [[IEEE 754-2008 revision|2008 versionrevision]]<ref name="IEEE-754_2008">{{cite book |title=IEEE Standard for Floating-Point Arithmetic |author=IEEE Computer Society |date=2008-08-29 |publisher=[[IEEE]] |id=IEEE Std 754-2008 |doi=10.1109/IEEESTD.2008.4610935 |ref=CITEREFIEEE_7542008 |isbn=978-0-7381-5753-5 |url=https://ieeexplore.ieee.org/document/4610935 |access-date=2016-02-08}}</ref> of the [[IEEE 754]] asstandard, wellalso known as with [[ISO/IEC/IEEE 60559:2011]].<ref name="ISO-60559_2011">{{citeCite journalbook |last=ISO/IEC JTC 1/SC 25|title=ISO/IEC/IEEE 60559:2011 — Information technology — Microprocessor Systems — Floating-Point arithmetic |url=httphttps://www.iso.org/isostandard/iso_catalogue/catalogue_tc/catalogue_detail57469.htm?csnumberhtml |publisher=57469ISO |datepages=20111–58 |access-date=2016-02-08June 2011}}</ref>
 
== Format ==
Decimal64 supports 'normal' values whichthat can have 16 digit precision from {{gaps|±1.000|000|000|000|000|e=-383}} to {{gaps|±9.999|999|999|999|999|e=384}}, plus 'denormal' values with ramp-down relative precision down to ±1.×10<sup>−398</sup>, [[signed zero]]s, -/+signed infinities and [[NaN]] (Not a Number). TheThis encodingformat insupports [[exponent]] and [[significand]] (other - deprechated - name: mantissa) using a 'combination field',two different significand encoding (BID or DPD) and different understanding of significand and 'exponent bias' is somewhat complex, see belowencodings.
 
The corresponding '''binary''' format, which isof the mostsame commonly used type in actual IT,size supports a range from denormal-min {{gaps|±5|||||e=-324|}}, over normal-min with full 53-bit precision {{gaps|±2.225|073|858|507|201|e=-308|4}} to max {{gaps|±1.797|693|134|862|315|e=+308|7}}.
 
Because the significand for decimalxxxthe [[IEEE 754]] decimal datatypesformats is not normalized, most values with less than 16 [[significant digits]] have multiple possible representations; 1000000 × 10<sup>-2−2</sup>=100000 × 10<sup>-1−1</sup>=10000 × 10<sup>0</sup>=1000 × 10<sup>1</sup> all have the value 10 00010000. These sets of representations for a same value are called ''[[Cohort (floating point)|cohorts]],'', the different members can be used to denote how many digits of the value are known precisely. ZeroEach signed zero has 768 possible representations (1536 iffor both [[signed zero]]s areall includedzeros, in two different cohorts).
 
== Encoding of decimal64 values ==
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| colspan="16" |combination field not! starting with '11', bits ab = 00, 01 or 10
|-
| style="font-family:monospace; background:#cedff2;" | '''a''' || style="font-family:monospace; background:#cedff2;" | '''b''' || style="font-family:monospace; background:#cedff2;" | '''c''' || style="font-family:monospace; background:#cedff2;" | '''d''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cef2e0;" | '''e''' || style="font-family:monospace; background:#cef2e0;" |'''f''' || style="font-family:monospace; background:#cef2e0;" |'''g'''
| || style="font-family:monospace; background:#cedff2;" | '''abcdmmmmmm''' || style="background:#cef2e0;" | {{mono|(0)'''efgtttttttttttttttttttttttttttttttttttttttttttttttttt''' }}
Finite number with small first digit of significand (0&nbsp;..&nbsp;7).
|-
| colspan="16" |combination field starting with '11', but not 1111, bits ab = 11, bits cd = 00, 01 or 10
|-
| 1 || 1 || style="font-family:monospace; background:#cedff2;" | '''c'''|| style="font-family:monospace; background:#cedff2;" | '''d''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''e''' || style="font-family:monospace; background:#cedff2;" | '''f''' || style="font-family:monospace; background:#cef2e0;" | '''g'''
| || style="font-family:monospace; background:#cedff2;" | '''cdmmmmmmef''' || style="background:#cef2e0;" | {{mono|'''100gtttttttttttttttttttttttttttttttttttttttttttttttttt''' }}
Finite number with big first digit of significand (8 or 9).
|-
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| colspan="16" |combination field not! starting with '11', bits ab = 00, 01 or 10
|-
| style="font-family:monospace; background:#cedff2;" | '''a''' || style="font-family:monospace; background:#cedff2;" | '''b''' || style="font-family:monospace; background:#cef2e0;" | '''c''' || style="font-family:monospace; background:#cef2e0;" | '''d''' || style="font-family:monospace; background:#cef2e0;" | '''e''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m'''
| || style="font-family:monospace; background:#cedff2;" | '''abmmmmmmmm'''|| style="background:#cef2e0;" | {{nowrap|{{mono|(0)'''cde tttttttttt tttttttttt tttttttttt tttttttttt tttttttttt''' }}}}
Finite number with small first digit of significand (0&nbsp;…&nbsp;7).
|-
| colspan="16" |combination field starting with '11', but not 1111, bits ab = 11, bits cd = 00, 01 or 10
|-
| 1 || 1 || style="font-family:monospace; background:#cedff2;" | '''c''' || style="font-family:monospace; background:#cedff2;" | '''d''' || style="font-family:monospace; background:#cef2e0;" | '''e''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m''' || style="font-family:monospace; background:#cedff2;" | '''m'''
| || style="font-family:monospace; background:#cedff2;" | '''cdmmmmmmmm'''|| style="background:#cef2e0;" | {{nowrap|{{mono|'''100e tttttttttt tttttttttt tttttttttt tttttttttt tttttttttt''' }}}}
Finite number with big first digit of significand (8 or 9).
|-
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|signaling NaN (with payload in significand)
|}
 
 
The DPD/3BCD transcoding for the declets is given by the following table. b9...b0 are the bits of the DPD, and d2...d0 are the three BCD digits.
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