I have a highly optimized CUDA kernel performing intensive 256-bit modular field arithmetic on RTX 4090 (sm_89). The kernel does repeated modular multiplications, subtractions, and inversions on 4×u64 limb representations, followed by some additional per-element computation. After extensive optimiza…

I finally got a monolithic implementation of nj_umul256wide() to work. I tested it with a bit of extra care as it is easy to introduce subtle bugs when writing hundreds of lines of code in assembly language. If you plan to use this in production code, you might want to subject it to industrial-stren…

Some general remarks: (1) I am generally suspicious of the use of asm volatile. By my understanding, leaving off the volatile gives the compiler greater wiggle room for valid code transformations. The backend compiler ptxas likely has hardware knowledge built into it that is not available to the ge…

[image] Mr.Steiner: // 256×256 → 512-bit schoolbook multiplication using 4 × UMult The comment says you are using a 256x256->512 bit multiplication (mul.wide), but the code in UMult is actually just a 256x256->256 multiplication. Which operation is actually being used? With the sm_35 archite…

[image] njuffa: Some years ago, I posted code for various wide multiplies (I think up to 128x128->256 bits) optimized for various older GPU architecture in these forums. Is this what you had in mind Norbert?

Thanks. Yes, I am 99% sure that the code at the link you provided is what I had in mind. It has been such a long time that I have to spend some time to re-acquaint myself with the possible variants.

[image] njuffa: Assuming your code uses the full 256 x 256 → 512 bit multiply, how many instructions does that resolve to? Thanks njuffa, this is incredibly helpful. On asm volatile: You’re right — I’m using asm volatile with "memory" clobber on every single arithmetic macro. That’s inherite…

FWIW, I am not yet convinced that carry propagation is the problem in this code. I first worked on long-integer arithmetic for cryptography in the early 1990s and seem to revisit the topic about once per decade, so I am not really acquainted with the state of the art at this point. I vaguely recall …

[image] njuffa: FWIW, I am not yet convinced that carry propagation is the problem in this code. I first worked on long-integer arithmetic for cryptography in the early 1990s and seem to revisit the topic about once per decade, so I am not really acquainted with the state of the art at this poin…

[image] njuffa: (1) I am generally suspicious of the use of asm volatile. By my understanding, leaving off the volatile gives the compiler greater wiggle room for valid code transformations. The backend compiler ptxas likely has hardware knowledge built into it that is not available to the gener…

Perhaps you could compare the 6% faster version and correct it again by hand? If could be worth looking into Nsight Compute Warp State to see what is preventing warps from doing more compute. And at which locations in the program. Are there alternative ways to compute multiplications? Using floati…

[image] Mr.Steiner: The frontend compiler reorders carry-chain instructions (add.cc/addc.cc) since it doesn’t see the CC dependency in the operand constraints. As I said, you would need to use a single asm block for the multiplication code to get the correct dependencies through the carry fla…

Squeezing the last 17.5% out of a compute-bound 256-bit modular arithmetic kernel (sm_89, 82.5% SM throughput)

Accelerated Computing CUDA CUDA Programming and Performance

rs277 April 25, 2026, 4:41am 4

Is this what you had in mind Norbert?

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Squeezing the last 17.5% out of a compute-bound 256-bit modular arithmetic kernel (sm_89, 82.5% SM throughput)

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