2021年12月16日 星期四

split Floating-Point Arithmetic IEEE 754 IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic.

 split
Floating-Point Arithmetic IEEE 754 IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic. 


    32-bit floating point  32-bit Single precision
    64-bit Double precision
    80-bit Extended precision


32-bit floating point  
Sign    Exponent    (Fraction)Mantissa
1    +8    +23    Bits
sign 1=negative 0= positive

[-/+]*[2^ exp]*[frac bin]

General Double Precision  IEEE 754-1985 64 bits
values   Fraction
     Sign    Exponent    Fraction   
    1    +11    +52     Bits
    Sign bit: 1 bit
    Exponent: 11 bits
    Significand precision: 53 bits (52 explicitly stored) fraction

https://en.wikipedia.org/wiki/Single-precision_floating-point_format
https://en.wikipedia.org/wiki/Double-precision_floating-point_format
https://en.wikipedia.org/wiki/Microsoft_Binary_Format#64-bit_MBF
https://en.wikipedia.org/wiki/Exponent_bias

Operations on special numbers are well-defined by IEEE. In the simplest case, any operation with a NaN yields a NaN result.
Encodings of qNaN and sNaN
https://en.wikipedia.org/wiki/NaN#Encoding

http://steve.hollasch.net/cgindex/coding/ieeefloat.html
IEEE Standard 754 Floating Point Numbers
Steve Hollasch  •  Last update 2018-08-24 


https://stackoverflow.com/questions/50975653/convert-extended-80-bit-to-string
https://docwiki.embarcadero.com/Libraries/Tokyo/en/System.SysUtils.FloatToStr
https://docwiki.embarcadero.com/Libraries/Tokyo/en/System.SysUtils.FloatToStrF
https://docwiki.embarcadero.com/Libraries/Tokyo/en/System.SysUtils.FloatToText
https://docwiki.embarcadero.com/Libraries/Tokyo/en/System.SysUtils.FloatToDecimal

https://github.com/JackTrapper/Exact-Float-to-String-Routines
ID: 19421, ExactFloatToStr_JH0 -- Exact Float to String Routines
https://cc.embarcadero.com/Item.aspx?id=19421


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