Tag
4 posts
precision
8 min read
Fast-math deleted our emulated-double multiply on Apple GPUs, and every float-side guard — including hardware FMA — died with it. So we rebuilt twoSum and twoProd in u32 bit arithmetic: same pair format, same compositions, exact by construction. The device that zeroed every float variant returned the golden answer.
precision
6 min read
I shipped four in-shader fixes for the df64 multiply collapsing to zero on an Apple GPU. Every one failed on-device. Then the research settled it: Metal's default fast-math deletes the error term by construction, no opaque-guard trick reliably survives, and the durable answer is to restructure the math so the high-precision multiply never happens — which is why deck.gl deprecated emulated fp64.
precision
7 min read
The emulated-double add and multiply are the same algorithm family, but on an Apple GPU add read 0.5 and multiply read exactly 0. The bug was not in either — it was a renormalization step the textbook multiply omits and the battle-tested one keeps.
precision
9 min read
The same df64 value—1e8+0.5—minus 1e8. Computed on the GPU it reads 0.5; loaded from a uniform it reads 0.0, with the fast-math guard bound in both. To a reassociating compiler a loaded low word and a computed one are not the same number, and the fix is to launder one into the other.
