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It's worth saying the original Playstation was entirely fixed point. You can go surprisingly far with it. https://en.wikipedia.org/wiki/Fixed-point_arithmetic#

It's worth saying the original Playstation was entirely fixed point. You can go surprisingly far with it. https://en.wikipedia.org/wiki/Fixed-point_arithmetic#Software_application_examples https://en.wikipedia.org/wiki/Fixed-point_arithmetic#Softwar... I spent so much of the early stage of my career doing early mobile stuff I practically still think in fixed point, and always have to adjust to floats, for example, fixed point results can be compared exactly while with floats that is not a great idea. TeX uses fixed point entirely because it was reproducible across machines in an era where floating point was not.

__s 2y ago
I think fixed point would be used a lot more with proper support in programming languages
- fidotron 2y ago
  What you would need is the language to track the expected range of the numbers. You often end up with multiple different multiply/divide implementations (shifting amounts before/after) based on if you can safely guarantee you are within an expected range or not.
- SideQuark 2y ago
  I doubt it. It fails for far too many useful programming situations that it would cause more problems than floating point. Cannot use it efficiently for nearly anything: finance software, science software, engineering software, high quality graphics software... 3d software, pretty much anything that has any range needed or ability to lower errors while doing accumulation of information. This is exactly why floating point was invented and standardized - fixed point is a failure for most any program, and only can work with much effort only for certain situations. (I've written tons of fixed point code, numerical libraries across the spectrum from high performance, high quality, tunable quality, arbitrary precision libs, posits and unums, IEEE half-float software implementations, and more, so I do know what I'm talking about).
  - jerf 2y ago
    Is there even any performance benefit on modern CPUs? I tried to consult some real tables but I'm not experienced enough to be sure I'm reading them correctly. If I'm reading something like [1] properly, it looks like it is not a clear win on modern hardware to use fixed point & integer operations. It would depend on the ratio of addition/subtraction/multiplication to division. (Obviously one must factor out a lot of local considerations, which modern CPUs are full unto overflowing with; I'm kind of looking at a very, very broad average performance question across code bases doing enough different math operations to average out, not whether one particular loop can run theoretically run faster or slower with one or the other.) [1]: https://stackoverflow.com/questions/2550281/floating-point-vs-integer-calculations-on-modern-hardware https://stackoverflow.com/questions/2550281/floating-point-v...
    - ooterness 2y ago
      It depends a lot on CPU architecture. Floating point units may be tied to each core, or they may be shared, so it may further depend on other concurrent workloads. There's also SIMD instructions. Modern CPUs have built-in instructions for handling multiple ints or floats as a vector. If you can get your fixed-point varies to for into 8-bit or 16-bit fields instead of 32, then the same sized vector units can handle more values per instruction.
    - taeric 2y ago
      My gut would be that you also get some benefit by some auxiliary choices. With a lot of precomputed constants, you can probably avoid a lot of known multiplications. That said, yeah, if you have to start doing a lot of fixed point multiplications, you could eat any savings you had.
    - ack_complete 2y ago
      Address calculations are a place where fixed point can still have an advantage -- it's often less latency and fewer ops to step a fixed-point accumulator and shift it into an address offset on the integer units than to step a floating point accumulator, convert it to integer, then move that over from the FP/vector units to the integer units.
hansvm 2y ago
> fixed point results can be compared exactly You gain the ability to get stable results across machines, but there still necessarily exists a loss of precision, and different implementations of the same algorithm will get different results. When would you want to compare fixed-point results bitwise though?

__s 2y ago

I think fixed point would be used a lot more with proper support in programming languages

fidotron 2y ago
What you would need is the language to track the expected range of the numbers. You often end up with multiple different multiply/divide implementations (shifting amounts before/after) based on if you can safely guarantee you are within an expected range or not.
SideQuark 2y ago
I doubt it. It fails for far too many useful programming situations that it would cause more problems than floating point. Cannot use it efficiently for nearly anything: finance software, science software, engineering software, high quality graphics software... 3d software, pretty much anything that has any range needed or ability to lower errors while doing accumulation of information. This is exactly why floating point was invented and standardized - fixed point is a failure for most any program, and only can work with much effort only for certain situations. (I've written tons of fixed point code, numerical libraries across the spectrum from high performance, high quality, tunable quality, arbitrary precision libs, posits and unums, IEEE half-float software implementations, and more, so I do know what I'm talking about).
- jerf 2y ago
  Is there even any performance benefit on modern CPUs? I tried to consult some real tables but I'm not experienced enough to be sure I'm reading them correctly. If I'm reading something like [1] properly, it looks like it is not a clear win on modern hardware to use fixed point & integer operations. It would depend on the ratio of addition/subtraction/multiplication to division. (Obviously one must factor out a lot of local considerations, which modern CPUs are full unto overflowing with; I'm kind of looking at a very, very broad average performance question across code bases doing enough different math operations to average out, not whether one particular loop can run theoretically run faster or slower with one or the other.) [1]: https://stackoverflow.com/questions/2550281/floating-point-vs-integer-calculations-on-modern-hardware https://stackoverflow.com/questions/2550281/floating-point-v...
  - ooterness 2y ago
    It depends a lot on CPU architecture. Floating point units may be tied to each core, or they may be shared, so it may further depend on other concurrent workloads. There's also SIMD instructions. Modern CPUs have built-in instructions for handling multiple ints or floats as a vector. If you can get your fixed-point varies to for into 8-bit or 16-bit fields instead of 32, then the same sized vector units can handle more values per instruction.
  - taeric 2y ago
    My gut would be that you also get some benefit by some auxiliary choices. With a lot of precomputed constants, you can probably avoid a lot of known multiplications. That said, yeah, if you have to start doing a lot of fixed point multiplications, you could eat any savings you had.
  - ack_complete 2y ago
    Address calculations are a place where fixed point can still have an advantage -- it's often less latency and fewer ops to step a fixed-point accumulator and shift it into an address offset on the integer units than to step a floating point accumulator, convert it to integer, then move that over from the FP/vector units to the integer units.

hansvm 2y ago

> fixed point results can be compared exactly You gain the ability to get stable results across machines, but there still necessarily exists a loss of precision, and different implementations of the same algorithm will get different results. When would you want to compare fixed-point results bitwise though?