4 ms·

how many levels are you talking about? I agree the worse floating point precision of GPUs puts them at a disadvantage but they still do better for massively pa

how many levels are you talking about? I agree the worse floating point precision of GPUs puts them at a disadvantage but they still do better for massively parallel problems like fractal renders. (http://www.bealto.com/mp-mandelbrot_benchmarks.html http://www.bealto.com/mp-mandelbrot_benchmarks.html)

ctdonath 11y ago
The more interesting zooms magnify something like 10^256 times.
brucedawson 11y ago
GPUs are happiest when doing float precision, which is 24 bits. Most GPUs can, at reduced speed, do double precision, which is 53 bits. The maximum precision for this zoom movie is 960 bits. So, unless you write code to compose high-precision math operations out of double-precision math then the GPU cannot even participate. And once you do that you will find that the GPU's speed advantage is mostly or entirely lost.
- Houshalter 11y ago
  CPUs can't do 960 bit operations either.
  - rincebrain 11y ago
    Yes, but we have a lot more experience and existing code for solving this on more monolithic systems, whereas the massively parallel architecture of a GPU stops having so many advantages when you have heavy dependencies between operations on different "cores" (e.g. needing to compose arbitrary-precision math out of smaller operations), and thereby end up needing to synchronize rather than letting the threads compute in parallel.
  - brucedawson 11y ago
    - CPUs can do 64x64 multiplies that give 128-bit results. GPUs cannot. - CPUs can do add-with-carry. GPUs cannot. That means that GPUs are not very good at doing high-precision math. They lose a lot more efficiency implementing high-precision math than CPUs do. And GPUs are also worse at doing parallel calculations that end up following different paths, which inevitably happens when one pixel diverges before another. My back-of-the-envelope estimates show that GPUs are not worth it for this use-case. I will change my mind when I see a GPU-based deep zoom fractal program.
    - WheretIB 11y ago
      While AMD GPU can't do 64x64 multiplies that give 128-bit results, they still can do a 32x32 multiply with a 64-bit result. (MULHI_INT and MULLO_INT instructions). And you can do add-with-carry manually on the AMD GPU using two instructions: ADDC_UINT to get the carry flag from an addition followed by ADD_PREV to add it.
      - brucedawson 11y ago
        Good to know. I was not aware of those instructions. It would be interesting to see how well a GPU can do compared to a CPU. Doing 64-bit math gives an automatic four-to-one advantage (it takes four 32x32 multiplies to replicate a single 64x64 multiply) so the GPU would be starting out at a disadvantage, plus GPUs run at lower clock rates and have other disadvantages, but perhaps their many many cores would be enough to overcome this.

ctdonath 11y ago

The more interesting zooms magnify something like 10^256 times.

brucedawson 11y ago

GPUs are happiest when doing float precision, which is 24 bits. Most GPUs can, at reduced speed, do double precision, which is 53 bits. The maximum precision for this zoom movie is 960 bits. So, unless you write code to compose high-precision math operations out of double-precision math then the GPU cannot even participate. And once you do that you will find that the GPU's speed advantage is mostly or entirely lost.

Houshalter 11y ago
CPUs can't do 960 bit operations either.
- rincebrain 11y ago
  Yes, but we have a lot more experience and existing code for solving this on more monolithic systems, whereas the massively parallel architecture of a GPU stops having so many advantages when you have heavy dependencies between operations on different "cores" (e.g. needing to compose arbitrary-precision math out of smaller operations), and thereby end up needing to synchronize rather than letting the threads compute in parallel.
- brucedawson 11y ago
  - CPUs can do 64x64 multiplies that give 128-bit results. GPUs cannot. - CPUs can do add-with-carry. GPUs cannot. That means that GPUs are not very good at doing high-precision math. They lose a lot more efficiency implementing high-precision math than CPUs do. And GPUs are also worse at doing parallel calculations that end up following different paths, which inevitably happens when one pixel diverges before another. My back-of-the-envelope estimates show that GPUs are not worth it for this use-case. I will change my mind when I see a GPU-based deep zoom fractal program.
  - WheretIB 11y ago
    While AMD GPU can't do 64x64 multiplies that give 128-bit results, they still can do a 32x32 multiply with a 64-bit result. (MULHI_INT and MULLO_INT instructions). And you can do add-with-carry manually on the AMD GPU using two instructions: ADDC_UINT to get the carry flag from an addition followed by ADD_PREV to add it.
    - brucedawson 11y ago
      Good to know. I was not aware of those instructions. It would be interesting to see how well a GPU can do compared to a CPU. Doing 64-bit math gives an automatic four-to-one advantage (it takes four 32x32 multiplies to replicate a single 64x64 multiply) so the GPU would be starting out at a disadvantage, plus GPUs run at lower clock rates and have other disadvantages, but perhaps their many many cores would be enough to overcome this.