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nicer visualization of DPD encoding, WIP, pls. don't revert, only improve! |
improved and corrected description, WIP, pls. don't revert, if necessary improve! |
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== Format ==
Decimal64 supports 'normal' values which 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>, zero, -/+infinities and NaN (Not a Number). The encoding in [[exponent]] and [[significand]] (other - deprechated - name: mantissa) using a 'combination field', different significand encoding (BID or DPD) and different understanding of significand and 'exponent bias' is somewhat complex, see below.
The corresponding '''binary''' format, which is the most commonly used type in actual IT, 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 decimalxxx datatypes is not normalized, most values with less than 16 [[significant digits]] have multiple possible representations; 1000000 × 10<sup>-2</sup>=100000 × 10<sup>-1</sup>=10000 × 10<sup>0</sup>=1000 × 10<sup>1</sup> all have the value 10 000. 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. Zero has 768 possible representations (1536 if both [[signed zero]]s are included, in two different cohorts).
== Encoding of decimal64 values ==
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