Talk:Decimal64 floating-point format

Meaning of m x c?

I guess c is easiest, it is probably 1.c in decimal? Or 0.c ? however m and x are a mystery in this article. what is biasing? I guess there is 10^z , where z is somehow dependent on m and x, but tables do not explain this.

Quantum vs Exponent

I'm new to the encoding, but I suspect the range of floating point numbers is incorrect. At the moment the range is described as:

±0.000000000000000×10^⁻³⁸³ to ±9.999999999999999×10^³⁸⁴

According to the IEEE-754 2008 standard, the decimal bias is expressed in terms of the quantum (bias=E-q), unlike the binary bias being expressed in terms of the exponent (bias=E-e). As such, I believe the range is actually:

±0000000000000000×10^⁻³⁸³ to ±9999999999999999×10^³⁸⁴

(note the lack of decimal point)

I was hoping someone more familiar with the standard could clarify this?

Mabtjie (talk) 03:34, 19 February 2022 (UTC)

@Mabtjie: No, this is correct. The standard says that emax is 384, thus the maximum value is ±9.999999999999999×10^³⁸⁴. It also says that the bias E−q is 398. E is encoded on 10 bits and the first two cannot be 11; thus its maximum value is 1011111111 in binary, i.e. 3×256−1 = 767. Thus the maximum value of q is 767−398 = 369, so that the maximum decimal64 finite value is ±9999999999999999×10^³⁶⁹. This is consistent. — Vincent Lefèvre (talk) 10:31, 19 February 2022 (UTC)