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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 number 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 revision]]<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]] standard, also known as 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 that 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). This format supports two different encodings.
 
The binary format of the same 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 the [[IEEE 754]] decimal formats 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 10000. 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. Each [[signed zero]] has 768 possible representations (1536 for all zeros, 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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