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* turboquant_cuda_kernel.cu -- TQ3 (3-bit) KV Cache Quantization for CUDA
*
* Copyright (c) 2026 Elyan Labs. All rights reserved.
* Licensed under the MIT License.
*
* CUDA implementation of TurboQuant TQ3, matching the POWER8 VSX version
* in ggml-turboquant-vsx.h. 128-float blocks quantized to 56 bytes
* (9.1x compression vs FP32).
*
* Algorithm (quantize):
* 1. L2 norm of 128-float block, normalize to unit vector
* 2. Deterministic sign flips (xoshiro256** PRNG, seed-based)
* 3. Fast Walsh-Hadamard Transform (FWHT) -- 7 butterfly stages
* 4. Absmax of transformed vector, scale to [-1, +1]
* 5. Lloyd-Max codebook quantize (8 centroids, 3 bits)
* 6. Pack 128 x 3-bit indices into 48 bytes
* Store: norm (4B) + scale (4B) + packed (48B) = 56 bytes
*
* Dequantize is the exact reverse.
*
* Target GPUs: V100 (SM_70), RTX 5070 (SM_100), RTX 3060 (SM_86), M40 (SM_52)
*
* Build:
* nvcc -arch=sm_70 -O2 -o tq3_cuda_test turboquant_cuda_kernel.cu \
* -DTURBOQUANT_SELF_TEST
*/
#include <cstdio>
#include <cstdint>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <cuda_runtime.h>
/* ------------------------------------------------------------------ */
/* Constants */
/* ------------------------------------------------------------------ */
#define TQ3_BLOCK_SIZE 128
#define TQ3_PACKED_BYTES 48 /* 128 * 3 / 8 */
#define TQ3_FWHT_STAGES 7 /* log2(128) */
#define TQ3_NUM_CENTROIDS 8
/* ------------------------------------------------------------------ */
/* Block layout: 56 bytes per 128 floats */
/* ------------------------------------------------------------------ */
typedef struct {
float norm; /* 4 bytes */
float scale; /* 4 bytes */
unsigned char packed_indices[TQ3_PACKED_BYTES]; /* 48 bytes */
} block_tq3_t; /* 56 bytes */
/* ------------------------------------------------------------------ */
/* Constant memory: Lloyd-Max codebook and decision boundaries */
/* Matches ggml-turboquant-vsx.h exactly for bit-compatible output. */
/* ------------------------------------------------------------------ */
__constant__ float d_TQ3_CENTROIDS[TQ3_NUM_CENTROIDS] = {
-0.9816f, -0.6168f, -0.3479f, -0.1129f,
0.1129f, 0.3479f, 0.6168f, 0.9816f
};
__constant__ float d_TQ3_BOUNDARIES[7] = {
-0.79920f, -0.48235f, -0.23040f, 0.00000f,
0.23040f, 0.48235f, 0.79920f
};
/* Host-side centroids available if needed for CPU-side verification */
/* static const float h_TQ3_CENTROIDS[TQ3_NUM_CENTROIDS] = {
-0.9816f, -0.6168f, -0.3479f, -0.1129f,
0.1129f, 0.3479f, 0.6168f, 0.9816f
}; */
/* ------------------------------------------------------------------ */
/* xoshiro256** PRNG -- device side */
/* Used to generate deterministic sign-flip mask per seed. */
/* ------------------------------------------------------------------ */
__device__ __forceinline__
uint64_t tq3_rotl(uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
}
/*
* Generate next xoshiro256** value and advance state.
* Matches the VSX header implementation exactly.
*/
__device__ __forceinline__
uint64_t tq3_xoshiro_next(uint64_t s[4]) {
const uint64_t result = tq3_rotl(s[1] * 5, 7) * 9;
const uint64_t t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = tq3_rotl(s[3], 45);
return result;
}
/*
* Seed xoshiro256** state from a 64-bit seed via splitmix64.
* Identical to the VSX header so sign masks match bit-for-bit.
*/
__device__ __forceinline__
void tq3_xoshiro_seed(uint64_t s[4], uint64_t seed) {
for (int i = 0; i < 4; i++) {
seed += 0x9E3779B97F4A7C15ULL;
uint64_t z = seed;
z = (z ^ (z >> 30)) * 0xBF58476D1CE4E5B9ULL;
z = (z ^ (z >> 27)) * 0x94D049BB133111EBULL;
z = z ^ (z >> 31);
s[i] = z;
}
}
/* ================================================================== */
/* CUDA Kernels */
/* ================================================================== */
/*
* Shared memory layout per block (1 block = 1 TQ3 vector):
* [0..511] float work[128] -- 512 bytes, working buffer
* [512..639] int8_t signs[128] -- 128 bytes, +1/-1 as bytes
*
* Block size: 128 threads, one per vector coordinate.
*/
/* ------------------------------------------------------------------ */
/* tq3_quantize_kernel */
/* One CUDA block per 128-float TQ3 vector. */
/* ------------------------------------------------------------------ */
__global__ void tq3_quantize_kernel(
const float * __restrict__ src,
block_tq3_t * __restrict__ dst,
int n_vectors,
uint64_t seed)
{
const int vec_id = blockIdx.x;
if (vec_id >= n_vectors) return;
const int tid = threadIdx.x; /* 0..127 */
/* Shared memory: working buffer + sign mask */
__shared__ float s_work[TQ3_BLOCK_SIZE];
__shared__ int8_t s_sign[TQ3_BLOCK_SIZE];
/* ---- Step 0: Generate sign-flip mask (thread 0 only, tiny cost) ---- */
if (tid == 0) {
uint64_t rng[4];
tq3_xoshiro_seed(rng, seed);
for (int i = 0; i < TQ3_BLOCK_SIZE; i++) {
uint64_t r = tq3_xoshiro_next(rng);
s_sign[i] = (r & 1) ? -1 : 1;
}
}
__syncthreads();
/* ---- Step 1: Load source value ---- */
const float *block_src = src + (int64_t)vec_id * TQ3_BLOCK_SIZE;
float val = block_src[tid];
/* ---- Step 2: Compute L2 norm ---- */
/*
* Reduction order is part of the format here, not an implementation
* detail: `norm` scales the vector the codebook indices are derived
* from, so a last-bit disagreement changes the packed indices for a
* percent-scale fraction of blocks. A warp-shuffle tree sums in a
* different order than the 4-lane vec_madd loop in
* ggml-turboquant-vsx.h, which is why the two backends did not agree
* bit-for-bit. Mirror the VSX lane layout instead: accumulator j
* takes elements j, j+4, j+8, ... with a fused multiply-add, then the
* four accumulators are combined left to right.
*/
__shared__ float s_lane[4];
s_work[tid] = val; /* staged here; overwritten in Step 3 */
__syncthreads();
if (tid < 4) {
float acc = 0.0f;
for (int i = tid; i < TQ3_BLOCK_SIZE; i += 4) {
acc = fmaf(s_work[i], s_work[i], acc);
}
s_lane[tid] = acc;
}
__syncthreads();
__shared__ float s_norm;
__shared__ float s_inv_norm;
if (tid == 0) {
float total = s_lane[0] + s_lane[1] + s_lane[2] + s_lane[3];
s_norm = sqrtf(total);
s_inv_norm = (s_norm > 1e-12f) ? (1.0f / s_norm) : 0.0f;
}
__syncthreads();
float norm = s_norm;
/* Handle zero-norm block: write zeros and exit */
if (norm < 1e-12f) {
if (tid == 0) {
dst[vec_id].norm = 0.0f;
dst[vec_id].scale = 0.0f;
}
/* Each thread clears part of packed_indices (48 bytes / 128 threads) */
if (tid < TQ3_PACKED_BYTES) {
dst[vec_id].packed_indices[tid] = 0;
}
return;
}
/* ---- Step 3: Normalize to unit vector, then apply the sign flips ---- */
/*
* D of the randomized Hadamard transform H*D must be applied *before*
* H. Applied after the transform the flips are inert: absmax is
* invariant under a sign flip and the codebook is symmetric about zero,
* so the reconstruction is identical to using no flips at all.
*/
val *= s_inv_norm;
s_work[tid] = val * (float)s_sign[tid];
__syncthreads();
/* ---- Step 4: In-place FWHT (7 butterfly stages) ---- */
/*
* Each stage s: stride = 2^(s+1), half = 2^s
* Pair (base + j, base + j + half): a' = a + b, b' = a - b
* Each thread handles its own index based on butterfly pattern.
*/
for (int stage = 0; stage < TQ3_FWHT_STAGES; stage++) {
int half = 1 << stage;
int stride = half << 1;
/* Determine which pair this thread belongs to */
int group = tid / stride; /* which group of size 'stride' */
int within = tid % stride; /* position within group */
int base = group * stride;
if (within < half) {
/* This thread is in the 'a' position */
int idx_a = base + within;
int idx_b = base + within + half;
float a = s_work[idx_a];
float b = s_work[idx_b];
s_work[idx_a] = a + b;
s_work[idx_b] = a - b;
}
__syncthreads();
}
/* ---- Step 5: Compute absmax via warp reduction ---- */
/* absmax is order independent (fmaxf is associative and exact), so the
warp-shuffle tree here is safe to keep. */
__shared__ float s_partial[4];
float absval = fabsf(s_work[tid]);
for (int offset = 16; offset > 0; offset >>= 1) {
float other = __shfl_down_sync(0xFFFFFFFF, absval, offset);
absval = fmaxf(absval, other);
}
if ((tid & 31) == 0) {
s_partial[tid >> 5] = absval;
}
__syncthreads();
__shared__ float s_scale;
__shared__ float s_inv_scale;
if (tid == 0) {
float amax = fmaxf(fmaxf(s_partial[0], s_partial[1]),
fmaxf(s_partial[2], s_partial[3]));
s_scale = amax;
s_inv_scale = (amax > 1e-12f) ? (1.0f / amax) : 0.0f;
}
__syncthreads();
/* ---- Step 6: Normalize to [-1, +1] for codebook ---- */
float normalized = s_work[tid] * s_inv_scale;
/* ---- Step 7: Quantize to nearest Lloyd-Max centroid ---- */
/*
* Binary search through 7 boundaries for 8 centroids.
* Matches _tq3_quantize_scalar() in the VSX header exactly.
*/
uint8_t idx;
if (normalized < d_TQ3_BOUNDARIES[3]) {
if (normalized < d_TQ3_BOUNDARIES[1]) {
idx = (normalized < d_TQ3_BOUNDARIES[0]) ? 0 : 1;
} else {
idx = (normalized < d_TQ3_BOUNDARIES[2]) ? 2 : 3;
}
} else {
if (normalized < d_TQ3_BOUNDARIES[5]) {
idx = (normalized < d_TQ3_BOUNDARIES[4]) ? 4 : 5;
} else {
idx = (normalized < d_TQ3_BOUNDARIES[6]) ? 6 : 7;
}
}
/* ---- Step 8: Pack 128 x 3-bit indices into 48 bytes ---- */
/*
* Each thread owns one 3-bit index. We compute the byte position
* and bit offset, then use atomicOr to write without conflicts.
* This is safe because at most 2 threads share a byte, and their
* 3-bit fields never overlap on the same bits.
*
* For throughput we first zero the packed buffer, then OR in bits.
*/
unsigned char *packed = dst[vec_id].packed_indices;
/* Zero the packed buffer (48 bytes, use first 48 threads) */
if (tid < TQ3_PACKED_BYTES) {
packed[tid] = 0;
}
__syncthreads();
{
int bit_pos = tid * 3;
int byte_idx = bit_pos >> 3;
int bit_off = bit_pos & 7;
/* Low part always fits in one byte */
atomicOr((unsigned int *)(packed + (byte_idx & ~3)),
(unsigned int)((idx << bit_off) << ((byte_idx & 3) * 8)));
/* High part: if bit_off > 5, 3 bits spill into next byte */
if (bit_off > 5) {
int next_byte = byte_idx + 1;
atomicOr((unsigned int *)(packed + (next_byte & ~3)),
(unsigned int)(((idx >> (8 - bit_off)) & 0x07)
<< ((next_byte & 3) * 8)));
}
}
__syncthreads();
/* ---- Step 9: Write norm and scale (thread 0) ---- */
if (tid == 0) {
dst[vec_id].norm = norm;
dst[vec_id].scale = s_scale;
}
}
/* ------------------------------------------------------------------ */
/* tq3_dequantize_kernel */
/* One CUDA block per 128-float TQ3 vector. */
/* ------------------------------------------------------------------ */
__global__ void tq3_dequantize_kernel(
const block_tq3_t * __restrict__ src,
float * __restrict__ dst_out,
int n_vectors,
uint64_t seed)
{
const int vec_id = blockIdx.x;
if (vec_id >= n_vectors) return;
const int tid = threadIdx.x; /* 0..127 */
__shared__ float s_work[TQ3_BLOCK_SIZE];
__shared__ int8_t s_sign[TQ3_BLOCK_SIZE];
/* ---- Step 0: Generate sign-flip mask ---- */
if (tid == 0) {
uint64_t rng[4];
tq3_xoshiro_seed(rng, seed);
for (int i = 0; i < TQ3_BLOCK_SIZE; i++) {
uint64_t r = tq3_xoshiro_next(rng);
s_sign[i] = (r & 1) ? -1 : 1;
}
}
__syncthreads();
float norm = src[vec_id].norm;
float scale = src[vec_id].scale;
/* Handle zero-norm block */
if (norm < 1e-12f) {
dst_out[(int64_t)vec_id * TQ3_BLOCK_SIZE + tid] = 0.0f;
return;
}
/* ---- Step 1: Unpack this thread's 3-bit index ---- */
const unsigned char *packed = src[vec_id].packed_indices;
uint8_t idx;
{
int bit_pos = tid * 3;
int byte_idx = bit_pos >> 3;
int bit_off = bit_pos & 7;
uint16_t two_bytes = (uint16_t)packed[byte_idx];
if (byte_idx + 1 < TQ3_PACKED_BYTES) {
two_bytes |= ((uint16_t)packed[byte_idx + 1]) << 8;
}
idx = (uint8_t)((two_bytes >> bit_off) & 0x07);
}
/* ---- Step 2: Dequantize: centroid * absmax_scale ---- */
s_work[tid] = d_TQ3_CENTROIDS[idx] * scale;
__syncthreads();
/* ---- Step 3: Inverse FWHT (same as forward, then /N) ---- */
for (int stage = 0; stage < TQ3_FWHT_STAGES; stage++) {
int half = 1 << stage;
int stride = half << 1;
int group = tid / stride;
int within = tid % stride;
int base = group * stride;
if (within < half) {
int idx_a = base + within;
int idx_b = base + within + half;
float a = s_work[idx_a];
float b = s_work[idx_b];
s_work[idx_a] = a + b;
s_work[idx_b] = a - b;
}
__syncthreads();
}
/* Divide by N (= 128) */
float result = s_work[tid] * (1.0f / (float)TQ3_BLOCK_SIZE);
/* ---- Step 4: Undo sign flips (D is its own inverse) ---- */
result *= (float)s_sign[tid];
/* ---- Step 5: Rescale by original L2 norm ---- */
result *= norm;
/* ---- Write output ---- */
dst_out[(int64_t)vec_id * TQ3_BLOCK_SIZE + tid] = result;
}
/* ================================================================== */
/* Host Wrappers */
/* ================================================================== */
void tq3_cuda_quantize(
const float *d_src,
block_tq3_t *d_dst,
int n_vectors,
uint64_t seed,
cudaStream_t stream)
{
if (n_vectors <= 0) return;
dim3 grid(n_vectors);
dim3 block(TQ3_BLOCK_SIZE);
tq3_quantize_kernel<<<grid, block, 0, stream>>>(d_src, d_dst, n_vectors, seed);
}
void tq3_cuda_dequantize(
const block_tq3_t *d_src,
float *d_dst,
int n_vectors,
uint64_t seed,
cudaStream_t stream)
{
if (n_vectors <= 0) return;
dim3 grid(n_vectors);
dim3 block(TQ3_BLOCK_SIZE);
tq3_dequantize_kernel<<<grid, block, 0, stream>>>(d_src, d_dst, n_vectors, seed);
}
/* ================================================================== */
/* Self-Test */
/* ================================================================== */
#ifdef TURBOQUANT_SELF_TEST
#define CUDA_CHECK(call) \
do { \
cudaError_t err = (call); \
if (err != cudaSuccess) { \
fprintf(stderr, "CUDA error at %s:%d: %s\n", \
__FILE__, __LINE__, cudaGetErrorString(err)); \
exit(EXIT_FAILURE); \
} \
} while (0)
/*
* tq3_cuda_self_test -- round-trip accuracy test on GPU
*
* 1. Generate pseudo-Gaussian test data (central limit theorem, 12 uniforms)
* 2. Quantize on GPU
* 3. Dequantize on GPU
* 4. Copy back and check MSE + cosine similarity
*
* Returns 0 on PASS, 1 on FAIL.
*/
int tq3_cuda_self_test(void) {
const uint64_t seed = 0x456C79616E4C6162ULL; /* "ElyanLab" */
const int n_vectors = 64; /* test 64 blocks for good coverage */
const int n_floats = n_vectors * TQ3_BLOCK_SIZE;
/* ---- Allocate host memory ---- */
float *h_original = (float *)malloc(n_floats * sizeof(float));
float *h_recovered = (float *)malloc(n_floats * sizeof(float));
if (!h_original || !h_recovered) {
fprintf(stderr, "Host allocation failed\n");
return 1;
}
/* ---- Generate test data: pseudo-Gaussian via CLT ---- */
{
uint32_t lcg = 0xDEADBEEF;
for (int i = 0; i < n_floats; i++) {
float sum = 0.0f;
for (int j = 0; j < 12; j++) {
lcg = lcg * 1664525u + 1013904223u;
sum += (float)(lcg & 0xFFFF) / 65535.0f;
}
h_original[i] = (sum - 6.0f) * 0.5f; /* ~N(0, 0.25) */
}
}
/* ---- Allocate device memory ---- */
float *d_src = NULL;
float *d_dst = NULL;
block_tq3_t *d_blocks = NULL;
CUDA_CHECK(cudaMalloc(&d_src, n_floats * sizeof(float)));
CUDA_CHECK(cudaMalloc(&d_dst, n_floats * sizeof(float)));
CUDA_CHECK(cudaMalloc(&d_blocks, n_vectors * sizeof(block_tq3_t)));
/* ---- Upload source data ---- */
CUDA_CHECK(cudaMemcpy(d_src, h_original, n_floats * sizeof(float),
cudaMemcpyHostToDevice));
/* ---- Quantize on GPU ---- */
tq3_cuda_quantize(d_src, d_blocks, n_vectors, seed, 0);
CUDA_CHECK(cudaGetLastError());
/* ---- Dequantize on GPU ---- */
tq3_cuda_dequantize(d_blocks, d_dst, n_vectors, seed, 0);
CUDA_CHECK(cudaGetLastError());
/* ---- Copy results back ---- */
CUDA_CHECK(cudaMemcpy(h_recovered, d_dst, n_floats * sizeof(float),
cudaMemcpyDeviceToHost));
CUDA_CHECK(cudaDeviceSynchronize());
/* ---- Compute error metrics ---- */
double mse_total = 0.0;
double mean_total = 0.0;
double var_total = 0.0;
double dot_or = 0.0, dot_oo = 0.0, dot_rr = 0.0;
for (int i = 0; i < n_floats; i++) {
mean_total += (double)h_original[i];
}
mean_total /= (double)n_floats;
for (int i = 0; i < n_floats; i++) {
double diff = (double)h_recovered[i] - (double)h_original[i];
mse_total += diff * diff;
double dev = (double)h_original[i] - mean_total;
var_total += dev * dev;
dot_or += (double)h_original[i] * (double)h_recovered[i];
dot_oo += (double)h_original[i] * (double)h_original[i];
dot_rr += (double)h_recovered[i] * (double)h_recovered[i];
}
double mse = mse_total / (double)n_floats;
double var = var_total / (double)n_floats;
double nmse = (var > 1e-12) ? (mse / var) : 0.0;
double cos_sim = (dot_oo > 1e-12 && dot_rr > 1e-12)
? dot_or / (sqrt(dot_oo) * sqrt(dot_rr))
: 0.0;
/* ---- Also verify one block's packed data via host unpack ---- */
block_tq3_t h_block;
CUDA_CHECK(cudaMemcpy(&h_block, d_blocks, sizeof(block_tq3_t),
cudaMemcpyDeviceToHost));
int pack_ok = 1;
{
/* Unpack and verify each index is in range [0, 7] */
int bit_pos = 0;
for (int i = 0; i < TQ3_BLOCK_SIZE; i++) {
int byte_idx = bit_pos >> 3;
int bit_off = bit_pos & 7;
uint16_t two_bytes = (uint16_t)h_block.packed_indices[byte_idx];
if (byte_idx + 1 < TQ3_PACKED_BYTES) {
two_bytes |= ((uint16_t)h_block.packed_indices[byte_idx + 1]) << 8;
}
uint8_t idx = (uint8_t)((two_bytes >> bit_off) & 0x07);
if (idx > 7) {
pack_ok = 0;
break;
}
bit_pos += 3;
}
}
/* ---- Print GPU info ---- */
int device;
cudaDeviceProp prop;
cudaGetDevice(&device);
cudaGetDeviceProperties(&prop, device);
printf("TQ3 CUDA Self-Test (Elyan Labs TurboQuant)\n");
printf(" GPU: %s (SM_%d%d)\n", prop.name, prop.major, prop.minor);
printf(" Test vectors: %d (%d floats)\n", n_vectors, n_floats);
printf(" Block size: %d floats\n", TQ3_BLOCK_SIZE);
printf(" Packed size: %d bytes (%.1fx compression vs FP32)\n",
(int)sizeof(block_tq3_t),
(float)(TQ3_BLOCK_SIZE * sizeof(float)) / (float)sizeof(block_tq3_t));
printf(" Block[0] norm: %.6f\n", h_block.norm);
printf(" Block[0] scale: %.6f\n", h_block.scale);
printf(" MSE: %.8f\n", mse);
printf(" Variance: %.8f\n", var);
printf(" NMSE: %.6f (%.2f%%)\n", nmse, nmse * 100.0);
printf(" Cosine sim: %.6f\n", cos_sim);
printf(" Pack check: %s\n", pack_ok ? "PASS" : "FAIL");
/*
* Pass criteria (same as VSX header):
* - NMSE < 15%: TQ3 with Lloyd-Max achieves ~3-12% on typical activations.
* - Cosine similarity > 0.90: directional preservation is critical for
* KV cache -- attention depends on vector direction.
*/
int nmse_ok = (nmse < 0.15);
int cos_ok = (cos_sim > 0.90);
int pass = nmse_ok && cos_ok && pack_ok;
printf(" NMSE check: %s (%.2f%% < 15%%)\n",
nmse_ok ? "PASS" : "FAIL", nmse * 100.0);
printf(" Cosine check: %s (%.4f > 0.90)\n",
cos_ok ? "PASS" : "FAIL", cos_sim);
printf(" Result: %s\n", pass ? "PASS" : "FAIL");
/* ---- Cleanup ---- */
cudaFree(d_src);
cudaFree(d_dst);
cudaFree(d_blocks);
free(h_original);
free(h_recovered);
return pass ? 0 : 1;
}
int main(void) {
int device_count = 0;
CUDA_CHECK(cudaGetDeviceCount(&device_count));
if (device_count == 0) {
fprintf(stderr, "No CUDA devices found.\n");
return 1;
}
return tq3_cuda_self_test();
}
#endif /* TURBOQUANT_SELF_TEST */
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