Separate Printing Mantissa and Exponent of a Floating Point

[Era Scarecrow via Digitalmars-d-learn]

On Wednesday, 13 August 2014 at 07:51:30 UTC, Nordlöw wrote:
> Could someone briefly outline the algorithm that converts the 
> fraction part of FloatRep into a string in base 10?

  Walter Bright broke down the Floating point to explain how it 
works and why as i recall..

  http://dlang.org/d-floating-point.html
  http://en.wikipedia.org/wiki/Floating_point
  
http://en.wikipedia.org/wiki/Single-precision_floating-point_format

  As for the fraction part to floating point... You kinda have to 
think in reverse. If we have say a 4 bit floating point. So...

  1000 +0.5
  0100 +0.25
  0010 +0.125
  0001 +0.0625

  With this in mind you might be better off using hex, but it 
depends on the application.

On Wednesday, 13 August 2014 at 07:58:40 UTC, Nordlöw wrote:
> Can somebody shortly explain why it prints
>
> 3623111, 160, false
> 1945142772629504, 1056, false

Because they are raw int/uint types. But i'm sure that's not all 
that useful...
> x = 1.23e10;

  so 12300000000 or 12,300,000,000 or 2DD231B00

  they might make more sense in hex, but with the exponent really 
just shifting where the whole/fraction parts are separated. 
160-128 = it's shifted to 32/33 bits as it's starting point. and 
the 1056-1024 at the 32/33 bit starting point. Same place. The 
raw values they hold in hex are: 3748c7 & 0000d8000000

  Let's back up then. there is 23 bits of useful data we can use, 
and 34 bits present. So let's take our number and convert it to 
hex

  2DD231B00 and lower that until it fits in 23 bits. Or shift it 
about 11 to the right..

  And doing this I don't get very good results to feel like I'm 
helping much... I guess refer to the wiki on floating point is 
probably the best you can do...

  Although... I do recall seeing and having a hold of a formula 
for manually printing a floating point when I was looking at raw 
data before.. That formula was (don't ask where from, I don't 
remember.. might be on the wiki. This is from an AHK script):

HexToFloat(d) {
       Return (1-2*(d>>31)) * (2**((d>>23 & 255)-127)) * (1+(d & 
8388607)/8388608) ; 2**23
}