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I think the implication is that GPU rendering ends up using lower-precision floating point numbers than are available on modern CPUs, which leads to more roundi

by wtracy 6y ago

I think the implication is that GPU rendering ends up using lower-precision floating point numbers than are available on modern CPUs, which leads to more rounding errors.

gmueckl 6y ago
No, CPU renderers also use IEEE single precision floats for performance. Unless you do something really absurd[0], single precision has more than enough range and resolution to not lead to any noticable inaccuracies in the result. [0] like trying to render an insect eye to scale while having everything shifted 1000km from the origin.
- fxtentacle 6y ago
  While that is in general correct, most GPUs do not fully adhere to IEEE or they do not calculate at full resolution. It's a well-documented fact that the same floating point operations on a GPU will have less precision than on CPU, despite both using the same IEEE storage format. https://developer.nvidia.com/sites/default/files/akamai/cuda/files/NVIDIA-CUDA-Floating-Point.pdf https://developer.nvidia.com/sites/default/files/akamai/cuda...
  - dahart 6y ago
    That paper does not say what you claim it does, it is not showing that GPUs are computing at lower resolution, nor that CUDA is failing to adhere to the IEEE 754 standard. In at least two cases, it says the opposite of what you just claimed: FMA on the GPU was a way to achieve higher float precision than you could with CPU math, in 2011 when the paper was written. That is changing now with CPU adoption of fma, but that doesn't change the claims of the paper. The GPU's strict adherence to IEEE 754 is mentioned multiple times. "The same inputs will give the same results for individual IEEE 754 operations to a given precision on the CPU and GPU. As we have explained, there are many reasons why the same sequence of operations may not be performed on the CPU and GPU. The GPU has fused multiply-add while the CPU does not. Parallelizing algorithms may rearrange operations, yielding different numeric results. The CPU may be computing results in a precision higher than expected. Finally, many common mathematical functions are not required by the IEEE 754 standard to be correctly rounded so should not be expected to yield identical results between implementations."

by wtracy 6y ago

I think the implication is that GPU rendering ends up using lower-precision floating point numbers than are available on modern CPUs, which leads to more rounding errors.

gmueckl 6y ago

No, CPU renderers also use IEEE single precision floats for performance. Unless you do something really absurd[0], single precision has more than enough range and resolution to not lead to any noticable inaccuracies in the result. [0] like trying to render an insect eye to scale while having everything shifted 1000km from the origin.

fxtentacle 6y ago
While that is in general correct, most GPUs do not fully adhere to IEEE or they do not calculate at full resolution. It's a well-documented fact that the same floating point operations on a GPU will have less precision than on CPU, despite both using the same IEEE storage format. https://developer.nvidia.com/sites/default/files/akamai/cuda/files/NVIDIA-CUDA-Floating-Point.pdf https://developer.nvidia.com/sites/default/files/akamai/cuda...
- dahart 6y ago
  That paper does not say what you claim it does, it is not showing that GPUs are computing at lower resolution, nor that CUDA is failing to adhere to the IEEE 754 standard. In at least two cases, it says the opposite of what you just claimed: FMA on the GPU was a way to achieve higher float precision than you could with CPU math, in 2011 when the paper was written. That is changing now with CPU adoption of fma, but that doesn't change the claims of the paper. The GPU's strict adherence to IEEE 754 is mentioned multiple times. "The same inputs will give the same results for individual IEEE 754 operations to a given precision on the CPU and GPU. As we have explained, there are many reasons why the same sequence of operations may not be performed on the CPU and GPU. The GPU has fused multiply-add while the CPU does not. Parallelizing algorithms may rearrange operations, yielding different numeric results. The CPU may be computing results in a precision higher than expected. Finally, many common mathematical functions are not required by the IEEE 754 standard to be correctly rounded so should not be expected to yield identical results between implementations."