forge-sort 0.2.3

GPU radix sort for Apple Silicon — 4,800+ Mkeys/s, 6 data types, zero-copy
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#include <metal_stdlib>
using namespace metal;

// ═══════════════════════════════════════════════════════════════════
// forge-sort: MSD+fused-inner radix sort (4 dispatches)
//
// Extracted from exp17 Investigation W.
// Architecture: 1 MSD scatter (bits 24:31) → 256 buckets
// → 3 inner LSD passes per bucket at SLC speed.
// Single encoder, 4 dispatches, zero CPU readback.
// ═══════════════════════════════════════════════════════════════════

#define SORT_NUM_BINS  256u
#define SORT_TILE_SIZE 4096u
#define SORT_ELEMS     16u
#define SORT_THREADS   256u
#define SORT_NUM_SGS   8u
#define SORT_MAX_TPB   17u

// 64-bit: half the elements per thread (registers are 2x wider)
#define SORT_ELEMS_64     8u
#define SORT_TILE_64   2048u

struct SortParams {
    uint element_count;
    uint num_tiles;
    uint shift;
    uint pass;
};

struct BucketDesc {
    uint offset;
    uint count;
    uint tile_count;
    uint tile_base;
};

struct InnerParams {
    uint start_shift;
    uint pass_count;
    uint batch_start;
};

// ═══════════════════════════════════════════════════════════════════
// Function constants — specialized at PSO creation time
// Defaults ensure existing kernels are unaffected when unset.
// ═══════════════════════════════════════════════════════════════════

constant bool HAS_VALUES [[function_constant(0)]];
constant bool IS_64BIT   [[function_constant(1)]];
constant uint TRANSFORM_MODE [[function_constant(2)]];
constant bool has_values = is_function_constant_defined(HAS_VALUES) ? HAS_VALUES : false;
constant bool is_64bit   = is_function_constant_defined(IS_64BIT)   ? IS_64BIT   : false;
constant uint transform_mode = is_function_constant_defined(TRANSFORM_MODE) ? TRANSFORM_MODE : 0u;

// ═══════════════════════════════════════════════════════════════════
// Kernel 1: MSD Histogram — single-pass, bits[24:31]
//
// Reads ALL data once, computes 256-bin histogram for MSD byte only.
// Uses per-SG atomic histogram on TG memory.
// Output: global_hist[digit] = total count for digit 0..255
// ═══════════════════════════════════════════════════════════════════

kernel void sort_msd_histogram(
    device const uint*     src          [[buffer(0)]],
    device atomic_uint*    global_hist  [[buffer(1)]],
    constant SortParams&   params       [[buffer(2)]],
    uint lid [[thread_position_in_threadgroup]],
    uint gid [[threadgroup_position_in_grid]],
    uint simd_id   [[simdgroup_index_in_threadgroup]],
    uint simd_lane [[thread_index_in_simdgroup]])
{
    uint n = params.element_count;
    uint shift = params.shift;

    // Per-SG accumulator in shared memory
    threadgroup atomic_uint sg_counts[SORT_NUM_SGS * SORT_NUM_BINS]; // 8 KB

    // Zero sg_counts (all 256 threads cooperate)
    for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
        atomic_store_explicit(&sg_counts[i], 0u, memory_order_relaxed);
    }
    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (is_64bit) {
        // ── 64-bit path: 8 elements/thread, 2048-element tiles ──
        uint base = gid * SORT_TILE_64;
        device const ulong* src64 = reinterpret_cast<device const ulong*>(src);

        ulong keys64[SORT_ELEMS_64];
        bool valid[SORT_ELEMS_64];
        for (uint e = 0u; e < SORT_ELEMS_64; e++) {
            uint idx = base + e * SORT_THREADS + lid;
            valid[e] = idx < n;
            keys64[e] = valid[e] ? src64[idx] : 0ul;
        }

        for (uint e = 0u; e < SORT_ELEMS_64; e++) {
            if (valid[e]) {
                uint digit = (uint)(keys64[e] >> shift) & 0xFFu;
                atomic_fetch_add_explicit(
                    &sg_counts[simd_id * SORT_NUM_BINS + digit],
                    1u, memory_order_relaxed);
            }
        }
    } else {
        // ── 32-bit path: 16 elements/thread, 4096-element tiles ──
        uint base = gid * SORT_TILE_SIZE;

        uint keys[SORT_ELEMS];
        bool valid[SORT_ELEMS];
        for (uint e = 0u; e < SORT_ELEMS; e++) {
            uint idx = base + e * SORT_THREADS + lid;
            valid[e] = idx < n;
            keys[e] = valid[e] ? src[idx] : 0u;
        }

        for (uint e = 0u; e < SORT_ELEMS; e++) {
            if (valid[e]) {
                uint digit = (keys[e] >> shift) & 0xFFu;
                atomic_fetch_add_explicit(
                    &sg_counts[simd_id * SORT_NUM_BINS + digit],
                    1u, memory_order_relaxed);
            }
        }
    }
    threadgroup_barrier(mem_flags::mem_threadgroup);

    // Reduce across SGs: 256 threads handle one bin each
    {
        uint total = 0u;
        for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
            total += atomic_load_explicit(
                &sg_counts[sg * SORT_NUM_BINS + lid],
                memory_order_relaxed);
        }
        if (total > 0u) {
            atomic_fetch_add_explicit(&global_hist[lid],
                                      total, memory_order_relaxed);
        }
    }
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 2: MSD Prep — combined prefix sum + bucket descs
//
// Single dispatch, 1 TG, 256 threads.
// Input:  global_hist[256] = per-digit counts
// Output: counters[256]    = exclusive prefix (for atomic scatter)
//         bucket_descs[256] = offset/count/tile_count for inner sort
// ═══════════════════════════════════════════════════════════════════

kernel void sort_msd_prep(
    device const uint*     global_hist  [[buffer(0)]],
    device uint*           counters     [[buffer(1)]],
    device BucketDesc*     bucket_descs [[buffer(2)]],
    constant uint&         tile_size    [[buffer(3)]],
    uint lid [[thread_position_in_threadgroup]])
{
    // Thread 0 does serial prefix sum (256 values — trivial)
    threadgroup uint prefix[SORT_NUM_BINS];
    threadgroup uint running_offset;

    if (lid == 0u) {
        uint sum = 0u;
        for (uint i = 0u; i < SORT_NUM_BINS; i++) {
            prefix[i] = sum;
            sum += global_hist[i];
        }
        running_offset = sum;  // total element count (sanity)
    }
    threadgroup_barrier(mem_flags::mem_threadgroup);

    // All 256 threads write counters and bucket_descs in parallel
    uint count = global_hist[lid];
    uint offset = prefix[lid];
    counters[lid] = offset;  // non-atomic write (used as initial value)

    uint tc = (count + tile_size - 1u) / tile_size;
    bucket_descs[lid] = BucketDesc{offset, count, tc, 0u};
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 3: Atomic MSD Scatter — replaces decoupled lookback
//
// Uses atomic_fetch_add on global counters initialized to
// exclusive_prefix[d]. Each tile's atomic returns its exact
// global position — zero spin-waiting.
//
// TG Memory: 18 KB
// ═══════════════════════════════════════════════════════════════════

kernel void sort_msd_atomic_scatter(
    device const uint*     src       [[buffer(0)]],
    device uint*           dst       [[buffer(1)]],
    device atomic_uint*    counters  [[buffer(2)]],
    constant SortParams&   params    [[buffer(3)]],
    device const uint*     src_vals  [[buffer(4)]],
    device uint*           dst_vals  [[buffer(5)]],
    uint lid [[thread_position_in_threadgroup]],
    uint gid [[threadgroup_position_in_grid]],
    uint simd_lane [[thread_index_in_simdgroup]],
    uint simd_id   [[simdgroup_index_in_threadgroup]])
{
    uint n     = params.element_count;
    uint shift = params.shift;

    // ── TG Memory (18 KB) ────────────────────────────────────────
    threadgroup atomic_uint sg_hist_or_rank[SORT_NUM_SGS * SORT_NUM_BINS]; // 8 KB
    threadgroup uint sg_prefix[SORT_NUM_SGS * SORT_NUM_BINS];             // 8 KB
    threadgroup uint tile_hist[SORT_NUM_BINS];                              // 1 KB
    threadgroup uint tile_base[SORT_NUM_BINS];                              // 1 KB

    // ── Phase 2: Per-SG atomic histogram (zero first) ────────────
    for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
        atomic_store_explicit(&sg_hist_or_rank[i], 0u, memory_order_relaxed);
    }
    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (is_64bit) {
        // ═══ 64-bit path: 8 elements/thread, 2048-element tiles ═══
        uint base = gid * SORT_TILE_64;
        device const ulong* src64 = reinterpret_cast<device const ulong*>(src);
        device ulong* dst64 = reinterpret_cast<device ulong*>(dst);

        // ── Phase 1: Load 8 ulong elements ───────────────────────
        ulong mk64[SORT_ELEMS_64];
        uint md[SORT_ELEMS_64];
        bool mv[SORT_ELEMS_64];
        uint mv_vals[SORT_ELEMS_64];
        for (uint e = 0u; e < SORT_ELEMS_64; e++) {
            uint idx = base + e * SORT_THREADS + lid;
            mv[e] = idx < n;
            mk64[e] = mv[e] ? src64[idx] : 0xFFFFFFFFFFFFFFFFul;
            md[e] = mv[e] ? (uint)((mk64[e] >> shift) & 0xFFu) : 0xFFu;
            if (has_values) {
                mv_vals[e] = mv[e] ? src_vals[idx] : 0u;
            }
        }

        // ── Phase 2: Per-SG atomic histogram ─────────────────────
        for (uint e = 0u; e < SORT_ELEMS_64; e++) {
            if (mv[e]) {
                atomic_fetch_add_explicit(
                    &sg_hist_or_rank[simd_id * SORT_NUM_BINS + md[e]],
                    1u, memory_order_relaxed);
            }
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 2b: Tile histogram + cross-SG prefix ───────────
        {
            uint total = 0u;
            for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                uint c = atomic_load_explicit(
                    &sg_hist_or_rank[sg * SORT_NUM_BINS + lid],
                    memory_order_relaxed);
                sg_prefix[sg * SORT_NUM_BINS + lid] = total;
                total += c;
            }
            tile_hist[lid] = total;
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 3: Atomic fetch-add on global counters ─────────
        {
            tile_base[lid] = atomic_fetch_add_explicit(
                &counters[lid], tile_hist[lid], memory_order_relaxed);
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 4: Per-SG ranking + scatter ────────────────────
        for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
            atomic_store_explicit(&sg_hist_or_rank[i], 0u, memory_order_relaxed);
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        for (uint e = 0u; e < SORT_ELEMS_64; e++) {
            if (mv[e]) {
                uint d = md[e];
                uint within_sg = atomic_fetch_add_explicit(
                    &sg_hist_or_rank[simd_id * SORT_NUM_BINS + d],
                    1u, memory_order_relaxed);
                uint gp = tile_base[d]
                         + sg_prefix[simd_id * SORT_NUM_BINS + d]
                         + within_sg;
                dst64[gp] = mk64[e];
                if (has_values) {
                    dst_vals[gp] = mv_vals[e];
                }
            }
        }
    } else {
        // ═══ 32-bit path: 16 elements/thread, 4096-element tiles ═══
        uint base = gid * SORT_TILE_SIZE;

        // ── Phase 1: Load 16 elements ────────────────────────────
        uint mk[SORT_ELEMS];
        uint md[SORT_ELEMS];
        bool mv[SORT_ELEMS];
        uint mv_vals[SORT_ELEMS];
        for (uint e = 0u; e < SORT_ELEMS; e++) {
            uint idx = base + e * SORT_THREADS + lid;
            mv[e] = idx < n;
            mk[e] = mv[e] ? src[idx] : 0xFFFFFFFFu;
            md[e] = mv[e] ? ((mk[e] >> shift) & 0xFFu) : 0xFFu;
            if (has_values) {
                mv_vals[e] = mv[e] ? src_vals[idx] : 0u;
            }
        }

        // ── Phase 2: Per-SG atomic histogram ─────────────────────
        for (uint e = 0u; e < SORT_ELEMS; e++) {
            if (mv[e]) {
                atomic_fetch_add_explicit(
                    &sg_hist_or_rank[simd_id * SORT_NUM_BINS + md[e]],
                    1u, memory_order_relaxed);
            }
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 2b: Tile histogram + cross-SG prefix ───────────
        {
            uint total = 0u;
            for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                uint c = atomic_load_explicit(
                    &sg_hist_or_rank[sg * SORT_NUM_BINS + lid],
                    memory_order_relaxed);
                sg_prefix[sg * SORT_NUM_BINS + lid] = total;
                total += c;
            }
            tile_hist[lid] = total;
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 3: Atomic fetch-add on global counters ─────────
        {
            tile_base[lid] = atomic_fetch_add_explicit(
                &counters[lid], tile_hist[lid], memory_order_relaxed);
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        // ── Phase 4: Per-SG ranking + scatter ────────────────────
        for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
            atomic_store_explicit(&sg_hist_or_rank[i], 0u, memory_order_relaxed);
        }
        threadgroup_barrier(mem_flags::mem_threadgroup);

        for (uint e = 0u; e < SORT_ELEMS; e++) {
            if (mv[e]) {
                uint d = md[e];
                uint within_sg = atomic_fetch_add_explicit(
                    &sg_hist_or_rank[simd_id * SORT_NUM_BINS + d],
                    1u, memory_order_relaxed);
                uint gp = tile_base[d]
                         + sg_prefix[simd_id * SORT_NUM_BINS + d]
                         + within_sg;
                dst[gp] = mk[e];
                if (has_values) {
                    dst_vals[gp] = mv_vals[e];
                }
            }
        }
    }
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 4: Fused Inner Sort — 3-pass LSD per bucket
//
// Self-contained: computes own histograms for all 3 inner passes
// during the first scan. No separate precompute dispatch needed.
// 4 dispatches total instead of 5.
//
// Extra TG memory: 2 × 256 atomic_uint = 2KB (pass 1 & 2 histograms)
// Total TG memory: ~22KB (within 32KB limit)
// ═══════════════════════════════════════════════════════════════════

kernel void sort_inner_fused(
    device uint*                buf_a         [[buffer(0)]],
    device uint*                buf_b         [[buffer(1)]],
    device const BucketDesc*    bucket_descs  [[buffer(2)]],
    constant InnerParams&       inner_params  [[buffer(3)]],
    device uint*                vals_a        [[buffer(4)]],
    device uint*                vals_b        [[buffer(5)]],
    uint lid       [[thread_position_in_threadgroup]],
    uint gid       [[threadgroup_position_in_grid]],
    uint simd_lane [[thread_index_in_simdgroup]],
    uint simd_id   [[simdgroup_index_in_threadgroup]])
{
    BucketDesc desc = bucket_descs[gid + inner_params.batch_start];
    if (desc.count == 0u) return;

    uint tile_count = desc.tile_count;

    // ═══ Shared memory (22 KB total) ═══
    threadgroup atomic_uint sg_ctr[SORT_NUM_SGS * SORT_NUM_BINS]; // 8 KB (scatter ranking)
    threadgroup uint sg_pfx[SORT_NUM_SGS * SORT_NUM_BINS];        // 8 KB (cross-SG prefix)
    threadgroup uint bkt_hist[SORT_NUM_BINS];                       // 1 KB (current pass histogram)
    threadgroup uint glb_pfx[SORT_NUM_BINS];                        // 1 KB (exclusive prefix sum)
    threadgroup uint run_pfx[SORT_NUM_BINS];                        // 1 KB (running tile prefix)
    threadgroup uint chk_tot[8];                                      // 32 B (prefix sum helper)
    // Self-computed histograms for passes 1 and 2 (accumulated during pass 0)
    threadgroup atomic_uint hist_p1[SORT_NUM_BINS];                  // 1 KB
    threadgroup atomic_uint hist_p2[SORT_NUM_BINS];                  // 1 KB

    // ═══ Zero all histogram accumulators ═══
    atomic_store_explicit(&hist_p1[lid], 0u, memory_order_relaxed);
    atomic_store_explicit(&hist_p2[lid], 0u, memory_order_relaxed);
    // Zero per-SG counters (used for pass 0 histogram accumulation)
    for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
        atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
    }
    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (is_64bit) {
        // ═══════════════════════════════════════════════════════════
        // 64-bit path: ulong keys, 8 elements/thread, 2048-element tiles
        // Uses inner_params.start_shift and pass_count for variable passes
        // ═══════════════════════════════════════════════════════════
        device ulong* buf_a_64 = reinterpret_cast<device ulong*>(buf_a);
        device ulong* buf_b_64 = reinterpret_cast<device ulong*>(buf_b);

        for (uint pass = 0u; pass < inner_params.pass_count; pass++) {
            uint shift = (inner_params.start_shift + pass) * 8u;

            // Alternate buffers: pass 0: b->a, pass 1: a->b, pass 2: b->a
            device ulong* src = (pass % 2u == 0u) ? buf_b_64 : buf_a_64;
            device ulong* dst = (pass % 2u == 0u) ? buf_a_64 : buf_b_64;

            // Values follow same ping-pong as keys (values are always uint)
            device uint* src_vals = (pass % 2u == 0u) ? vals_b : vals_a;
            device uint* dst_vals = (pass % 2u == 0u) ? vals_a : vals_b;

            // ═══ Load histogram ═══
            if (pass == 0u) {
                bkt_hist[lid] = 0u;
                threadgroup_barrier(mem_flags::mem_threadgroup);

                // First pass: read all tiles, compute histograms for up to 3 passes
                for (uint t = 0u; t < tile_count; t++) {
                    for (uint e = 0u; e < SORT_ELEMS_64; e++) {
                        uint local_idx = t * SORT_TILE_64
                                       + simd_id * (SORT_ELEMS_64 * 32u) + e * 32u + simd_lane;
                        if (local_idx < desc.count) {
                            ulong val = src[desc.offset + local_idx];
                            uint d0 = (uint)(val >> shift) & 0xFFu;
                            // Accumulate pass 0 histogram using per-SG accumulation
                            atomic_fetch_add_explicit(&sg_ctr[simd_id * SORT_NUM_BINS + d0],
                                                      1u, memory_order_relaxed);
                            // Pre-compute pass 1 & 2 histograms if they exist
                            if (inner_params.pass_count > 1u) {
                                uint d1 = (uint)(val >> (shift + 8u)) & 0xFFu;
                                atomic_fetch_add_explicit(&hist_p1[d1], 1u, memory_order_relaxed);
                            }
                            if (inner_params.pass_count > 2u) {
                                uint d2 = (uint)(val >> (shift + 16u)) & 0xFFu;
                                atomic_fetch_add_explicit(&hist_p2[d2], 1u, memory_order_relaxed);
                            }
                        }
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                // Reduce pass 0 per-SG histogram to per-bucket histogram
                {
                    uint total = 0u;
                    for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                        total += atomic_load_explicit(
                            &sg_ctr[sg * SORT_NUM_BINS + lid],
                            memory_order_relaxed);
                    }
                    bkt_hist[lid] = total;
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);
            } else if (pass == 1u) {
                bkt_hist[lid] = atomic_load_explicit(&hist_p1[lid], memory_order_relaxed);
                threadgroup_barrier(mem_flags::mem_threadgroup);
            } else {
                bkt_hist[lid] = atomic_load_explicit(&hist_p2[lid], memory_order_relaxed);
                threadgroup_barrier(mem_flags::mem_threadgroup);
            }

            // ═══ 256-bin exclusive prefix sum ═══
            {
                uint chunk = lid / 32u;
                uint lane = lid % 32u;
                uint val = bkt_hist[lid];
                uint prefix = simd_prefix_exclusive_sum(val);

                if (lane == 31u) chk_tot[chunk] = prefix + val;
                threadgroup_barrier(mem_flags::mem_threadgroup);

                if (lid == 0u) {
                    uint running = 0u;
                    for (uint c = 0u; c < 8u; c++) {
                        uint ct = chk_tot[c];
                        chk_tot[c] = running;
                        running += ct;
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                glb_pfx[lid] = prefix + chk_tot[chunk];
            }
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // ═══ Serial scatter with running cross-tile prefix ═══
            run_pfx[lid] = 0u;
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // Zero sg_ctr before scatter
            for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
            }
            threadgroup_barrier(mem_flags::mem_threadgroup);

            for (uint t = 0u; t < tile_count; t++) {
                uint tile_base_off = desc.offset + t * SORT_TILE_64;

                ulong keys64[SORT_ELEMS_64];
                uint v_vals[SORT_ELEMS_64];
                uint digits[SORT_ELEMS_64];
                bool valid[SORT_ELEMS_64];
                for (uint e = 0u; e < SORT_ELEMS_64; e++) {
                    uint local_idx = t * SORT_TILE_64
                                   + simd_id * (SORT_ELEMS_64 * 32u) + e * 32u + simd_lane;
                    valid[e] = local_idx < desc.count;
                    uint idx = tile_base_off + simd_id * (SORT_ELEMS_64 * 32u) + e * 32u + simd_lane;
                    keys64[e] = valid[e] ? src[idx] : 0xFFFFFFFFFFFFFFFFul;
                    digits[e] = valid[e] ? (uint)((keys64[e] >> shift) & 0xFFu) : 0xFFu;
                    if (has_values) {
                        v_vals[e] = valid[e] ? src_vals[idx] : 0u;
                    }
                }

                for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                    atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint e = 0u; e < SORT_ELEMS_64; e++) {
                    if (valid[e]) {
                        atomic_fetch_add_explicit(
                            &sg_ctr[simd_id * SORT_NUM_BINS + digits[e]],
                            1u, memory_order_relaxed);
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                uint tile_digit_count;
                {
                    uint total = 0u;
                    for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                        uint c = atomic_load_explicit(
                            &sg_ctr[sg * SORT_NUM_BINS + lid],
                            memory_order_relaxed);
                        sg_pfx[sg * SORT_NUM_BINS + lid] = total;
                        total += c;
                    }
                    tile_digit_count = total;
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                    atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint e = 0u; e < SORT_ELEMS_64; e++) {
                    if (valid[e]) {
                        uint d = digits[e];
                        uint within_sg = atomic_fetch_add_explicit(
                            &sg_ctr[simd_id * SORT_NUM_BINS + d],
                            1u, memory_order_relaxed);
                        uint dst_idx = desc.offset
                                     + glb_pfx[d]
                                     + run_pfx[d]
                                     + sg_pfx[simd_id * SORT_NUM_BINS + d]
                                     + within_sg;
                        dst[dst_idx] = keys64[e];
                        if (has_values) {
                            dst_vals[dst_idx] = v_vals[e];
                        }
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                run_pfx[lid] += tile_digit_count;
                threadgroup_barrier(mem_flags::mem_threadgroup);
            }

            // Device memory barrier: ensure scatter writes visible for next pass reads
            threadgroup_barrier(mem_flags::mem_device);
        }
    } else {
        // ═══════════════════════════════════════════════════════════
        // 32-bit path: uint keys, 16 elements/thread, 4096-element tiles
        // ═══════════════════════════════════════════════════════════
        for (uint pass = 0u; pass < inner_params.pass_count; pass++) {
            uint shift = (inner_params.start_shift + pass) * 8u;

            // Alternate buffers: pass 0: b->a, pass 1: a->b, pass 2: b->a
            device uint* src = (pass % 2u == 0u) ? buf_b : buf_a;
            device uint* dst = (pass % 2u == 0u) ? buf_a : buf_b;

            // Values follow same ping-pong as keys
            device uint* src_vals = (pass % 2u == 0u) ? vals_b : vals_a;
            device uint* dst_vals = (pass % 2u == 0u) ? vals_a : vals_b;

            // ═══ Load histogram ═══
            if (pass == 0u) {
                // Pass 0: compute histogram via first scan through data
                bkt_hist[lid] = 0u;
                threadgroup_barrier(mem_flags::mem_threadgroup);

                // First pass: read all tiles, compute histograms for ALL 3 passes
                for (uint t = 0u; t < tile_count; t++) {
                    for (uint e = 0u; e < SORT_ELEMS; e++) {
                        uint local_idx = t * SORT_TILE_SIZE
                                       + simd_id * (SORT_ELEMS * 32u) + e * 32u + simd_lane;
                        if (local_idx < desc.count) {
                            uint val = src[desc.offset + local_idx];
                            uint d0 = val & 0xFFu;
                            uint d1 = (val >> 8u) & 0xFFu;
                            uint d2 = (val >> 16u) & 0xFFu;
                            // Accumulate pass 0 histogram using per-SG accumulation
                            atomic_fetch_add_explicit(&sg_ctr[simd_id * SORT_NUM_BINS + d0],
                                                      1u, memory_order_relaxed);
                            // Pass 1 & 2: direct TG atomic (256 bins, avg 1 collision — fast)
                            atomic_fetch_add_explicit(&hist_p1[d1], 1u, memory_order_relaxed);
                            atomic_fetch_add_explicit(&hist_p2[d2], 1u, memory_order_relaxed);
                        }
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                // Reduce pass 0 per-SG histogram to per-bucket histogram
                {
                    uint total = 0u;
                    for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                        total += atomic_load_explicit(
                            &sg_ctr[sg * SORT_NUM_BINS + lid],
                            memory_order_relaxed);
                    }
                    bkt_hist[lid] = total;
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);
            } else if (pass == 1u) {
                bkt_hist[lid] = atomic_load_explicit(&hist_p1[lid], memory_order_relaxed);
                threadgroup_barrier(mem_flags::mem_threadgroup);
            } else {
                bkt_hist[lid] = atomic_load_explicit(&hist_p2[lid], memory_order_relaxed);
                threadgroup_barrier(mem_flags::mem_threadgroup);
            }

            // ═══ 256-bin exclusive prefix sum ═══
            {
                uint chunk = lid / 32u;
                uint lane = lid % 32u;
                uint val = bkt_hist[lid];
                uint prefix = simd_prefix_exclusive_sum(val);

                if (lane == 31u) chk_tot[chunk] = prefix + val;
                threadgroup_barrier(mem_flags::mem_threadgroup);

                if (lid == 0u) {
                    uint running = 0u;
                    for (uint c = 0u; c < 8u; c++) {
                        uint ct = chk_tot[c];
                        chk_tot[c] = running;
                        running += ct;
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                glb_pfx[lid] = prefix + chk_tot[chunk];
            }
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // ═══ Serial scatter with running cross-tile prefix ═══
            run_pfx[lid] = 0u;
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // Zero sg_ctr before scatter
            for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
            }
            threadgroup_barrier(mem_flags::mem_threadgroup);

            for (uint t = 0u; t < tile_count; t++) {
                uint tile_base = desc.offset + t * SORT_TILE_SIZE;

                uint keys[SORT_ELEMS];
                uint vals[SORT_ELEMS];
                uint digits[SORT_ELEMS];
                bool valid[SORT_ELEMS];
                for (uint e = 0u; e < SORT_ELEMS; e++) {
                    uint local_idx = t * SORT_TILE_SIZE
                                   + simd_id * (SORT_ELEMS * 32u) + e * 32u + simd_lane;
                    valid[e] = local_idx < desc.count;
                    uint idx = tile_base + simd_id * (SORT_ELEMS * 32u) + e * 32u + simd_lane;
                    keys[e] = valid[e] ? src[idx] : 0xFFFFFFFFu;
                    digits[e] = valid[e] ? ((keys[e] >> shift) & 0xFFu) : 0xFFu;
                    if (has_values) {
                        vals[e] = valid[e] ? src_vals[idx] : 0u;
                    }
                }

                for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                    atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint e = 0u; e < SORT_ELEMS; e++) {
                    if (valid[e]) {
                        atomic_fetch_add_explicit(
                            &sg_ctr[simd_id * SORT_NUM_BINS + digits[e]],
                            1u, memory_order_relaxed);
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                uint tile_digit_count;
                {
                    uint total = 0u;
                    for (uint sg = 0u; sg < SORT_NUM_SGS; sg++) {
                        uint c = atomic_load_explicit(
                            &sg_ctr[sg * SORT_NUM_BINS + lid],
                            memory_order_relaxed);
                        sg_pfx[sg * SORT_NUM_BINS + lid] = total;
                        total += c;
                    }
                    tile_digit_count = total;
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint i = lid; i < SORT_NUM_SGS * SORT_NUM_BINS; i += SORT_THREADS) {
                    atomic_store_explicit(&sg_ctr[i], 0u, memory_order_relaxed);
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                for (uint e = 0u; e < SORT_ELEMS; e++) {
                    if (valid[e]) {
                        uint d = digits[e];
                        uint within_sg = atomic_fetch_add_explicit(
                            &sg_ctr[simd_id * SORT_NUM_BINS + d],
                            1u, memory_order_relaxed);
                        uint dst_idx = desc.offset
                                     + glb_pfx[d]
                                     + run_pfx[d]
                                     + sg_pfx[simd_id * SORT_NUM_BINS + d]
                                     + within_sg;
                        dst[dst_idx] = keys[e];
                        if (has_values) {
                            dst_vals[dst_idx] = vals[e];
                        }
                    }
                }
                threadgroup_barrier(mem_flags::mem_threadgroup);

                run_pfx[lid] += tile_digit_count;
                threadgroup_barrier(mem_flags::mem_threadgroup);
            }

            // Device memory barrier: ensure scatter writes visible for next pass reads
            threadgroup_barrier(mem_flags::mem_device);
        }
    }
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 5: Index Initializer — fill indices[i] = i for argsort
//
// Simple 1D dispatch: 1 thread per element.
// ═══════════════════════════════════════════════════════════════════

kernel void sort_init_indices(
    device uint*   indices [[buffer(0)]],
    constant uint& count   [[buffer(1)]],
    uint gid [[thread_position_in_grid]])
{
    if (gid < count) indices[gid] = gid;
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 6: Gather Values — rearrange values by sorted index permutation
//
// gathered_vals[i] = original_vals[sorted_indices[i]]
// Simple 1D dispatch: 1 thread per element.
// ═══════════════════════════════════════════════════════════════════

kernel void sort_gather_values(
    device const uint* sorted_indices [[buffer(0)]],
    device const uint* original_vals  [[buffer(1)]],
    device uint*       gathered_vals  [[buffer(2)]],
    constant uint&     count          [[buffer(3)]],
    uint gid [[thread_position_in_grid]])
{
    if (gid < count) gathered_vals[gid] = original_vals[sorted_indices[gid]];
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 7: 32-bit Key Transform — pre/post sort bit manipulation
//
// mode 0: XOR 0x80000000 (i32 sign flip, self-inverse)
// mode 1: FloatFlip forward (map float order → unsigned order)
// mode 2: IFloatFlip inverse (map unsigned order → float order)
//
// Simple 1D dispatch: 1 thread per element.
// ═══════════════════════════════════════════════════════════════════

kernel void sort_transform_32(
    device uint*       data  [[buffer(0)]],
    constant uint&     count [[buffer(1)]],
    uint gid [[thread_position_in_grid]])
{
    if (gid >= count) return;
    uint v = data[gid];

    if (transform_mode == 0u) {
        // i32: flip sign bit (self-inverse)
        v ^= 0x80000000u;
    } else if (transform_mode == 1u) {
        // FloatFlip forward: negative (sign set) → flip all; positive → flip sign only
        v = (v & 0x80000000u) ? ~v : (v ^ 0x80000000u);
    } else if (transform_mode == 2u) {
        // IFloatFlip inverse: sign set (was positive) → flip sign; sign clear (was negative) → flip all
        v = (v & 0x80000000u) ? (v ^ 0x80000000u) : ~v;
    }

    data[gid] = v;
}

// ═══════════════════════════════════════════════════════════════════
// Kernel 8: 64-bit Key Transform — pre/post sort bit manipulation
//
// mode 1: FloatFlip64 forward (also works for i64 sign-XOR)
//         if sign bit set: flip all 64 bits (negative float/i64)
//         else: flip only sign bit (positive float/i64)
//         Mathematically: FloatFlip for f64, XOR 0x8000000000000000 for i64
// mode 2: IFloatFlip64 inverse
//         if sign bit set (was positive): flip only sign bit
//         else (was negative): flip all 64 bits
//
// Simple 1D dispatch: 1 thread per element.
// ═══════════════════════════════════════════════════════════════════

kernel void sort_transform_64(
    device ulong*      data  [[buffer(0)]],
    constant uint&     count [[buffer(1)]],
    uint gid [[thread_position_in_grid]])
{
    if (gid >= count) return;
    ulong v = data[gid];

    if (transform_mode == 0u) {
        // i64: flip sign bit (self-inverse)
        v ^= 0x8000000000000000UL;
    } else if (transform_mode == 1u) {
        // FloatFlip64 forward: negative (sign set) → flip all; positive → flip sign only
        v = (v & 0x8000000000000000UL) ? ~v : (v ^ 0x8000000000000000UL);
    } else if (transform_mode == 2u) {
        // IFloatFlip64 inverse: sign set (was positive) → flip sign; sign clear (was negative) → flip all
        v = (v & 0x8000000000000000UL) ? (v ^ 0x8000000000000000UL) : ~v;
    }

    data[gid] = v;
}