How To Convert double To float

L. Spiro · 2018-01-16T22:21:08

The reason the title surprised you is the same as the reason I can’t get proper results on Google: You’re thinking about a cast, and no matter what search terms I use I keep getting results talking about casts. I enjoy super-low-level programming and I have both a personal interest in and a need for creating a manual cast from a double to a floating-point type given customizable properties (number of exponent bits, number of mantissa bits, is there a sign bit?, is there an implied mantissa bit?, etc.) I’ve already written something that could be called a prototype and it correctly handles all “normal” conversions from a 64-bit double into any other type of floating-point format based on however many bits you want. So as an example, let’s say I have PI as a double constant “3.1415926535897931”. I manually cast it to a 32-bit float by specifying SIGNBIT=TRUE, EXP=8, MANT=24, IMPLICITMAN=TRUE and I get this result: Actual [1,8,24,TRUE]FLOAT Result = 3.1415927410125732 Sign = 0 Exp = 0x0000000000000080 Man = 0x0000000000490fdb So it manually gives the exact same result as a regular cast from double to float, and can round or truncate (here, rounding up was performed). Casting manually seems useless, right? But I want to support arbitrary floating-point types that are not present in C. How about an example from a 16-bit float? Actual [1,5,11,TRUE]FLOAT Result = 3.1406250000000000 Sign = 0 Exp = 0x0000000000000010 Man = 0x0000000000000248 I also want to study arbitrary floating-point formats. For example, the smallest non-0 number a 32-bit float can be is 1.4012984643248171e-45 and the max is 3.4028234663852886e+38. How about for a 16-bit float? [1,5,11,TRUE]FLOAT Smallest non-0: 5.9604644775390625e-08 Max: 65504.000000000000. How about this random format? [1,7,31,TRUE]FLOAT Smallest non-0: 2.0194839173657902e-28 Max: 1.8446744065119617e+19 So a lot of my converter is already working. If you are still wondering what the point is, you can understand that a graphics programmer who has to work with 16-bit and 32-bit shader precision, F16 and F32 textures, D24 depth textures, and R11G11B10 float textures can really find something like this useful. There are many floating-point formats out there but not really any tools to investigate those float formats. Now to the Question There are special cases for denormalized numbers that I am not currently handling, and I am temporarily making assumptions about sign bits etc. Anyone have a good link to a break-down of casting from a floating-point value to another type of floating-point value manually? Going over IEEE doesn’t provide example implementations nor does it really dig into the details. The details I often find cover mostly what I have already implemented, which is from a normalized number converted to another normalized number. I don’t really see guides on the best way to implement the cases where either the source or the destination is denormalized. I can implement it “my way” but I definitely want to look at what has been done or at the very least go over specifications to ensure my way fully complies. L. Spiro

General and Gameplay Programming Programming

Started by L. Spiro January 11, 2018 03:55 AM

10 comments, last by DragonJoker 6 years, 8 months ago

DragonJoker

231

January 16, 2018 10:21 PM

Thanks.

I'll try to implement this tomorrow, but my guess is that I won't be able to use this guy's solution, since I need to keep track of overflow, non representibility, precision loss (it's for a deep flow analysis tool), and extended precision too (80 bits at least...).

Hence I'll try implementing your solution.

Thanks for the details!

If you can't find anything, look for something else.