submission 824829
div22 · python · License unknown
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solution_224.py
curl "https://kernelindex.com/api/v1/implementations/kernelbot-qr-v2-824829?include=source"interfacepython
Compatibility
measured onNVIDIA B200
declared hardwareNVIDIA B200
architecturessm_100
dtypesfp32
Benchmark evidence
1 measurement across 1 GPU, fastest first.
Operation / workload
Hardware
Latency
Rank
Observed
Reported · How evidence levels are derived →
Source and license
sourceavailable
revision digestsha256:0e72235aa1ca88e88091965e5c93bb74f445447dbeae00d7259ee52b3b9c9488
license declaredunknown
license concludedunknown
authorsdiv22
imported2026-08-26
Techniques
Extracted from the mirrored source by pattern, never inferred. Each row cites its line.
mbarrier
from triton.experimental.gluon.language.nvidia.hopper import tma, mbarrier, fence_async_sharedmma
W += tl.dot(tl.trans(V), C, input_precision=PREC)num-warps = 4
srb, srr, sri, srj, BLOCK_M=BM, NB=nb, num_warps=4)stages = 1
BLOCK_M=64, BLOCK_N=128, num_warps=4, num_stages=1)tile-m = 128
_TBM = 128tile-n = 32
return dict(pBM=32, pW=1, tBM=64, tBN=32, tW=2, tS=2)Kernel source
solution_224.py1499 lines
#!POPCORN leaderboard qr_v2
#!POPCORN gpu B200
import torch
import triton
import triton.language as tl
from triton.experimental import gluon
from triton.experimental.gluon import language as gl
from triton.experimental.gluon.nvidia.hopper import TensorDescriptor
from triton.experimental.gluon.language.nvidia.hopper import tma, mbarrier, fence_async_shared
from triton.experimental.gluon.language.nvidia.blackwell import (
TensorMemoryLayout, allocate_tensor_memory, get_tmem_reg_layout, tcgen05_mma, tcgen05_commit)
try:
TensorDescriptor.round_f32_to_tf32 = False
except Exception:
pass
@gluon.jit
def _g_formw(vh_desc, vl_desc, c_desc, th_desc, tlo_desc, o_desc, N, WN, kr, k,
NTM: gl.constexpr, NTN: gl.constexpr, BM: gl.constexpr, BN: gl.constexpr,
K: gl.constexpr, NBUF: gl.constexpr, VPRE: gl.constexpr,
C_BYTES: gl.constexpr, LC16: gl.constexpr,
PARTIAL: gl.constexpr, VALID: gl.constexpr, num_warps: gl.constexpr):
pid = gl.program_id(0)
f32: gl.constexpr = gl.float32
f16: gl.constexpr = gl.float16
base = pid * N + kr
cb = k + K
Vh = gl.allocate_shared_memory(f16, [NTM, BM, K], vh_desc.layout)
Vl = gl.allocate_shared_memory(f16, [NTM, BM, K], vl_desc.layout)
c_ring = gl.allocate_shared_memory(f32, [NBUF, BM, BN], c_desc.layout)
ch_s = gl.allocate_shared_memory(f16, [BM, BN], LC16)
cl_s = gl.allocate_shared_memory(f16, [BM, BN], LC16)
Th = gl.allocate_shared_memory(f16, [K, K], th_desc.layout)
Tlo = gl.allocate_shared_memory(f16, [K, K], tlo_desc.layout)
ah_s = gl.allocate_shared_memory(f16, [BN, K], o_desc.layout)
al_s = gl.allocate_shared_memory(f16, [BN, K], o_desc.layout)
c_bars = gl.allocate_shared_memory(gl.int64, [NBUF, 1], mbarrier.MBarrierLayout())
pre_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
mma_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
m2_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
for i in gl.static_range(NBUF):
mbarrier.init(c_bars.index(i), count=1)
mbarrier.init(pre_bar, count=1)
mbarrier.init(mma_bar, count=1)
mbarrier.init(m2_bar, count=1)
c_layout: gl.constexpr = TensorMemoryLayout([BM, BN], col_stride=1)
c_reg: gl.constexpr = get_tmem_reg_layout(f32, (BM, BN), c_layout, num_warps)
acc_layout: gl.constexpr = TensorMemoryLayout([BN, K], col_stride=1)
acc_reg: gl.constexpr = get_tmem_reg_layout(f32, (BN, K), acc_layout, num_warps)
acc_tmem = allocate_tensor_memory(f32, [BN, K], acc_layout)
wog_tmem = allocate_tensor_memory(f32, [BN, K], acc_layout)
mbarrier.expect(pre_bar, VPRE)
for mt in gl.static_range(NTM):
tma.async_copy_global_to_shared(vh_desc, [base + mt * BM, 0], pre_bar, Vh.index(mt))
tma.async_copy_global_to_shared(vl_desc, [base + mt * BM, 0], pre_bar, Vl.index(mt))
tma.async_copy_global_to_shared(th_desc, [pid * K, 0], pre_bar, Th)
tma.async_copy_global_to_shared(tlo_desc, [pid * K, 0], pre_bar, Tlo)
mbarrier.wait(pre_bar, phase=0)
mbarrier.invalidate(pre_bar)
NTILES: gl.constexpr = NTM * NTN
for ci in gl.static_range(NBUF - 1):
nt = ci // NTM
mt = ci % NTM
slot = ci % NBUF
mbarrier.expect(c_bars.index(slot), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mt * BM, cb + nt * BN], c_bars.index(slot), c_ring.index(slot))
for nt in gl.static_range(NTN):
for mt in gl.static_range(NTM):
i = nt * NTM + mt
ci = i + (NBUF - 1)
if ci < NTILES:
ntc = ci // NTM
mtc = ci % NTM
slotc = ci % NBUF
mbarrier.expect(c_bars.index(slotc), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mtc * BM, cb + ntc * BN], c_bars.index(slotc), c_ring.index(slotc))
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(c_reg)
if PARTIAL and (mt == NTM - 1):
rid = gl.arange(0, BM, layout=gl.SliceLayout(1, c_reg))
cval = gl.where(rid[:, None] < VALID, cval, 0.0)
chi = cval.to(f16)
clo = (cval - chi.to(f32)).to(f16)
ch_s.store(chi)
cl_s.store(clo)
fence_async_shared()
chp = ch_s.permute((1, 0))
clp = cl_s.permute((1, 0))
first = mt == 0
tcgen05_mma(chp, Vh.index(mt), acc_tmem, use_acc=(not first))
tcgen05_mma(chp, Vl.index(mt), acc_tmem, use_acc=True)
tcgen05_mma(clp, Vh.index(mt), acc_tmem, use_acc=True)
tcgen05_commit(mma_bar)
mbarrier.wait(mma_bar, i & 1)
accv = acc_tmem.load(acc_reg)
ahi = accv.to(f16)
alo = (accv - ahi.to(f32)).to(f16)
ah_s.store(ahi)
al_s.store(alo)
fence_async_shared()
tcgen05_mma(ah_s, Th, wog_tmem, use_acc=False)
tcgen05_mma(ah_s, Tlo, wog_tmem, use_acc=True)
tcgen05_mma(al_s, Th, wog_tmem, use_acc=True)
tcgen05_commit(m2_bar)
mbarrier.wait(m2_bar, nt & 1)
wogv = wog_tmem.load(acc_reg)
ah_s.store((-wogv).to(o_desc.dtype))
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [pid * WN + cb + nt * BN, 0], ah_s)
tma.store_wait(pendings=0)
for i in gl.static_range(NBUF):
mbarrier.invalidate(c_bars.index(i))
mbarrier.invalidate(mma_bar)
mbarrier.invalidate(m2_bar)
tma.store_wait(pendings=0)
@gluon.jit
def _g_formw_c1(vh_desc, vl_desc, c_desc, th_desc, tlo_desc, o_desc, N, WN, kr, k,
NTN_TOT: gl.constexpr, NTM: gl.constexpr, BM: gl.constexpr, BN: gl.constexpr,
K: gl.constexpr, NBUF: gl.constexpr, VPRE: gl.constexpr,
C_BYTES: gl.constexpr, V_BYTES: gl.constexpr, LC16: gl.constexpr,
PARTIAL: gl.constexpr, VALID: gl.constexpr, num_warps: gl.constexpr):
pid_b = gl.program_id(0)
pid_c = gl.program_id(1)
f32: gl.constexpr = gl.float32
f16: gl.constexpr = gl.float16
base = pid_b * N + kr
cb = k + K
nt = pid_c
vh_ring = gl.allocate_shared_memory(f16, [NBUF, BM, K], vh_desc.layout)
vl_ring = gl.allocate_shared_memory(f16, [NBUF, BM, K], vl_desc.layout)
c_ring = gl.allocate_shared_memory(f32, [NBUF, BM, BN], c_desc.layout)
ch_s = gl.allocate_shared_memory(f16, [BM, BN], LC16)
cl_s = gl.allocate_shared_memory(f16, [BM, BN], LC16)
Th = gl.allocate_shared_memory(f16, [K, K], th_desc.layout)
Tlo = gl.allocate_shared_memory(f16, [K, K], tlo_desc.layout)
ah_s = gl.allocate_shared_memory(f16, [BN, K], o_desc.layout)
al_s = gl.allocate_shared_memory(f16, [BN, K], o_desc.layout)
c_bars = gl.allocate_shared_memory(gl.int64, [NBUF, 1], mbarrier.MBarrierLayout())
pre_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
mma_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
m2_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
for i in gl.static_range(NBUF):
mbarrier.init(c_bars.index(i), count=1)
mbarrier.init(pre_bar, count=1)
mbarrier.init(mma_bar, count=1)
mbarrier.init(m2_bar, count=1)
c_layout: gl.constexpr = TensorMemoryLayout([BM, BN], col_stride=1)
c_reg: gl.constexpr = get_tmem_reg_layout(f32, (BM, BN), c_layout, num_warps)
acc_layout: gl.constexpr = TensorMemoryLayout([BN, K], col_stride=1)
acc_reg: gl.constexpr = get_tmem_reg_layout(f32, (BN, K), acc_layout, num_warps)
acc_tmem = allocate_tensor_memory(f32, [BN, K], acc_layout)
wog_tmem = allocate_tensor_memory(f32, [BN, K], acc_layout)
mbarrier.expect(pre_bar, VPRE)
tma.async_copy_global_to_shared(th_desc, [pid_b * K, 0], pre_bar, Th)
tma.async_copy_global_to_shared(tlo_desc, [pid_b * K, 0], pre_bar, Tlo)
mbarrier.wait(pre_bar, phase=0)
mbarrier.invalidate(pre_bar)
for ci in gl.static_range(NBUF - 1):
mt = ci
slot = ci % NBUF
mbarrier.expect(c_bars.index(slot), C_BYTES + V_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mt * BM, cb + nt * BN], c_bars.index(slot), c_ring.index(slot))
tma.async_copy_global_to_shared(vh_desc, [base + mt * BM, 0], c_bars.index(slot), vh_ring.index(slot))
tma.async_copy_global_to_shared(vl_desc, [base + mt * BM, 0], c_bars.index(slot), vl_ring.index(slot))
for mt in gl.static_range(NTM):
i = mt
ci = i + (NBUF - 1)
if ci < NTM:
mtc = ci
slotc = ci % NBUF
mbarrier.expect(c_bars.index(slotc), C_BYTES + V_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mtc * BM, cb + nt * BN], c_bars.index(slotc), c_ring.index(slotc))
tma.async_copy_global_to_shared(vh_desc, [base + mtc * BM, 0], c_bars.index(slotc), vh_ring.index(slotc))
tma.async_copy_global_to_shared(vl_desc, [base + mtc * BM, 0], c_bars.index(slotc), vl_ring.index(slotc))
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(c_reg)
if PARTIAL and (mt == NTM - 1):
rid = gl.arange(0, BM, layout=gl.SliceLayout(1, c_reg))
cval = gl.where(rid[:, None] < VALID, cval, 0.0)
chi = cval.to(f16)
clo = (cval - chi.to(f32)).to(f16)
ch_s.store(chi)
cl_s.store(clo)
fence_async_shared()
chp = ch_s.permute((1, 0))
clp = cl_s.permute((1, 0))
first = mt == 0
tcgen05_mma(chp, vh_ring.index(slotr), acc_tmem, use_acc=(not first))
tcgen05_mma(chp, vl_ring.index(slotr), acc_tmem, use_acc=True)
tcgen05_mma(clp, vh_ring.index(slotr), acc_tmem, use_acc=True)
tcgen05_commit(mma_bar)
mbarrier.wait(mma_bar, i & 1)
accv = acc_tmem.load(acc_reg)
ahi = accv.to(f16)
alo = (accv - ahi.to(f32)).to(f16)
ah_s.store(ahi)
al_s.store(alo)
fence_async_shared()
tcgen05_mma(ah_s, Th, wog_tmem, use_acc=False)
tcgen05_mma(ah_s, Tlo, wog_tmem, use_acc=True)
tcgen05_mma(al_s, Th, wog_tmem, use_acc=True)
tcgen05_commit(m2_bar)
mbarrier.wait(m2_bar, 0)
wogv = wog_tmem.load(acc_reg)
ah_s.store((-wogv).to(o_desc.dtype))
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [pid_b * WN + cb + nt * BN, 0], ah_s)
tma.store_wait(pendings=0)
for i in gl.static_range(NBUF):
mbarrier.invalidate(c_bars.index(i))
mbarrier.invalidate(mma_bar)
mbarrier.invalidate(m2_bar)
tma.store_wait(pendings=0)
@gluon.jit
def _g_apply(c_desc, v_desc, w_desc, o_desc, N, WN, kr, k,
M: gl.constexpr, NTM: gl.constexpr, NTN: gl.constexpr,
BM: gl.constexpr, BN: gl.constexpr, K: gl.constexpr,
NBUF: gl.constexpr, PRE_BYTES: gl.constexpr, C_BYTES: gl.constexpr, num_warps: gl.constexpr):
pid = gl.program_id(0)
f32: gl.constexpr = gl.float32
NTILES: gl.constexpr = NTM * NTN
base = pid * N + kr
cb = k + K
V_smem = gl.allocate_shared_memory(v_desc.dtype, [NTM, BM, K], v_desc.layout)
W_smem = gl.allocate_shared_memory(w_desc.dtype, [NTN, BN, K], w_desc.layout)
c_ring = gl.allocate_shared_memory(c_desc.dtype, [NBUF, BM, BN], c_desc.layout)
o_smem = gl.allocate_shared_memory(o_desc.dtype, [BM, BN], o_desc.layout)
c_bars = gl.allocate_shared_memory(gl.int64, [NBUF, 1], mbarrier.MBarrierLayout())
pre_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
mma_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
for i in gl.static_range(NBUF):
mbarrier.init(c_bars.index(i), count=1)
mbarrier.init(pre_bar, count=1)
mbarrier.init(mma_bar, count=1)
acc_layout: gl.constexpr = TensorMemoryLayout([BM, BN], col_stride=1)
acc_reg: gl.constexpr = get_tmem_reg_layout(f32, (BM, BN), acc_layout, num_warps)
acc_tmem = allocate_tensor_memory(f32, [BM, BN], acc_layout)
mbarrier.expect(pre_bar, PRE_BYTES)
for mt in gl.static_range(NTM):
tma.async_copy_global_to_shared(v_desc, [base + mt * BM, 0], pre_bar, V_smem.index(mt))
for nt in gl.static_range(NTN):
tma.async_copy_global_to_shared(w_desc, [pid * WN + cb + nt * BN, 0], pre_bar, W_smem.index(nt))
mbarrier.wait(pre_bar, phase=0)
mbarrier.invalidate(pre_bar)
for ci in gl.static_range(NBUF - 1):
mt = ci // NTN
nt = ci % NTN
slot = ci % NBUF
mbarrier.expect(c_bars.index(slot), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mt * BM, cb + nt * BN], c_bars.index(slot), c_ring.index(slot))
for i in gl.static_range(NTILES - (NBUF - 1)):
ci = i + (NBUF - 1)
mtc = ci // NTN
ntc = ci % NTN
slotc = ci % NBUF
mbarrier.expect(c_bars.index(slotc), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mtc * BM, cb + ntc * BN], c_bars.index(slotc), c_ring.index(slotc))
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(acc_reg)
acc_tmem.store(cval)
mtr = i // NTN
ntr = i % NTN
wperm = W_smem.index(ntr).permute((1, 0))
tcgen05_mma(V_smem.index(mtr), wperm, acc_tmem, use_acc=True, mbarriers=[mma_bar])
mbarrier.wait(mma_bar, i & 1)
out = acc_tmem.load(acc_reg)
tma.store_wait(pendings=0)
o_smem.store(out)
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [base + mtr * BM, cb + ntr * BN], o_smem)
for i in gl.static_range(NTILES - (NBUF - 1), NTILES):
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(acc_reg)
acc_tmem.store(cval)
mtr = i // NTN
ntr = i % NTN
wperm = W_smem.index(ntr).permute((1, 0))
tcgen05_mma(V_smem.index(mtr), wperm, acc_tmem, use_acc=True, mbarriers=[mma_bar])
mbarrier.wait(mma_bar, i & 1)
out = acc_tmem.load(acc_reg)
tma.store_wait(pendings=0)
o_smem.store(out)
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [base + mtr * BM, cb + ntr * BN], o_smem)
for i in gl.static_range(NBUF):
mbarrier.invalidate(c_bars.index(i))
mbarrier.invalidate(mma_bar)
tma.store_wait(pendings=0)
@gluon.jit
def _g_apply_cs(c_desc, v_desc, w_desc, o_desc, N, WN, kr, k,
M: gl.constexpr, NTM: gl.constexpr, CTPC: gl.constexpr,
BM: gl.constexpr, BN: gl.constexpr, K: gl.constexpr,
NBUF: gl.constexpr, PRE_BYTES: gl.constexpr, C_BYTES: gl.constexpr, num_warps: gl.constexpr):
pid = gl.program_id(0)
pid_c = gl.program_id(1)
ct0 = pid_c * CTPC
f32: gl.constexpr = gl.float32
NTILES: gl.constexpr = NTM * CTPC
base = pid * N + kr
cb = k + K
V_smem = gl.allocate_shared_memory(v_desc.dtype, [NTM, BM, K], v_desc.layout)
W_smem = gl.allocate_shared_memory(w_desc.dtype, [CTPC, BN, K], w_desc.layout)
c_ring = gl.allocate_shared_memory(c_desc.dtype, [NBUF, BM, BN], c_desc.layout)
o_smem = gl.allocate_shared_memory(o_desc.dtype, [BM, BN], o_desc.layout)
c_bars = gl.allocate_shared_memory(gl.int64, [NBUF, 1], mbarrier.MBarrierLayout())
pre_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
mma_bar = gl.allocate_shared_memory(gl.int64, [1], mbarrier.MBarrierLayout())
for i in gl.static_range(NBUF):
mbarrier.init(c_bars.index(i), count=1)
mbarrier.init(pre_bar, count=1)
mbarrier.init(mma_bar, count=1)
acc_layout: gl.constexpr = TensorMemoryLayout([BM, BN], col_stride=1)
acc_reg: gl.constexpr = get_tmem_reg_layout(f32, (BM, BN), acc_layout, num_warps)
acc_tmem = allocate_tensor_memory(f32, [BM, BN], acc_layout)
mbarrier.expect(pre_bar, PRE_BYTES)
for mt in gl.static_range(NTM):
tma.async_copy_global_to_shared(v_desc, [base + mt * BM, 0], pre_bar, V_smem.index(mt))
for ctl in gl.static_range(CTPC):
tma.async_copy_global_to_shared(w_desc, [pid * WN + cb + (ct0 + ctl) * BN, 0], pre_bar, W_smem.index(ctl))
mbarrier.wait(pre_bar, phase=0)
mbarrier.invalidate(pre_bar)
for ci in gl.static_range(NBUF - 1):
mtr = ci % NTM
ctl = ci // NTM
slot = ci % NBUF
mbarrier.expect(c_bars.index(slot), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mtr * BM, cb + (ct0 + ctl) * BN], c_bars.index(slot), c_ring.index(slot))
for i in gl.static_range(NTILES - (NBUF - 1)):
ci = i + (NBUF - 1)
mtc = ci % NTM
ctc = ci // NTM
slotc = ci % NBUF
mbarrier.expect(c_bars.index(slotc), C_BYTES)
tma.async_copy_global_to_shared(c_desc, [base + mtc * BM, cb + (ct0 + ctc) * BN], c_bars.index(slotc), c_ring.index(slotc))
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(acc_reg)
acc_tmem.store(cval)
mtr = i % NTM
ctr = i // NTM
wperm = W_smem.index(ctr).permute((1, 0))
tcgen05_mma(V_smem.index(mtr), wperm, acc_tmem, use_acc=True, mbarriers=[mma_bar])
mbarrier.wait(mma_bar, i & 1)
out = acc_tmem.load(acc_reg)
tma.store_wait(pendings=0)
o_smem.store(out)
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [base + mtr * BM, cb + (ct0 + ctr) * BN], o_smem)
for i in gl.static_range(NTILES - (NBUF - 1), NTILES):
slotr = i % NBUF
rphase = (i // NBUF) & 1
mbarrier.wait(c_bars.index(slotr), rphase)
cval = c_ring.index(slotr).load(acc_reg)
acc_tmem.store(cval)
mtr = i % NTM
ctr = i // NTM
wperm = W_smem.index(ctr).permute((1, 0))
tcgen05_mma(V_smem.index(mtr), wperm, acc_tmem, use_acc=True, mbarriers=[mma_bar])
mbarrier.wait(mma_bar, i & 1)
out = acc_tmem.load(acc_reg)
tma.store_wait(pendings=0)
o_smem.store(out)
fence_async_shared()
tma.async_copy_shared_to_global(o_desc, [base + mtr * BM, cb + (ct0 + ctr) * BN], o_smem)
for i in gl.static_range(NBUF):
mbarrier.invalidate(c_bars.index(i))
mbarrier.invalidate(mma_bar)
tma.store_wait(pendings=0)
@triton.jit
def _trail_wn(H, A, T, Wo, k, kb, N, sb, si, sj, sttb, stti, swob, swoi, swoj,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, KB: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
pn = tl.program_id(1)
Hb = H + pb * sb
Ab = A + pb * sb
ti = tl.arange(0, KB)
cols = (k + kb) + pn * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < N
Tt = tl.load(T + pb * sttb + ti[:, None] * stti + ti[None, :])
W = tl.zeros([KB, BLOCK_N], tl.float32)
ntk = (N - k + BLOCK_M - 1) // BLOCK_M
for i in range(ntk):
rows = k + i * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
C = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj, mask=rm[:, None] & cm[None, :], other=0.0)
W += tl.dot(tl.trans(V), C, input_precision=PREC)
W2 = tl.dot(tl.trans(Tt), W, input_precision=PREC)
tl.store(Wo + pb * swob + cols[:, None] * swoi + ti[None, :] * swoj, -tl.trans(W2), mask=cm[:, None])
@triton.jit
def _extract_v(H, Vpan, Vlo, k, kb, N, sb, si, sj, svb, svi, svj,
BLOCK_M: tl.constexpr, KB: tl.constexpr, WLO: tl.constexpr):
pb = tl.program_id(0)
rb = tl.program_id(1)
ti = tl.arange(0, KB)
rows = k + rb * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(H + pb * sb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
Vh16 = V.to(tl.float16)
tl.store(Vpan + pb * svb + rows[:, None] * svi + ti[None, :] * svj, Vh16, mask=rm[:, None])
if WLO:
Vl16 = (V - Vh16.to(tl.float32)).to(tl.float16)
tl.store(Vlo + pb * svb + rows[:, None] * svi + ti[None, :] * svj, Vl16, mask=rm[:, None])
@triton.jit
def _apply_top(H, Vpan, Wog, k, kb, N, sb, si, sj, svb, svi, svj, swgb, swgi, swgj,
BLOCK_N: tl.constexpr, KB: tl.constexpr):
pb = tl.program_id(0)
pn = tl.program_id(1)
ti = tl.arange(0, KB)
rows = k + ti
cols = (k + kb) + pn * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < N
Vt = tl.load(Vpan + pb * svb + rows[:, None] * svi + ti[None, :] * svj)
Wg = tl.load(Wog + pb * swgb + cols[None, :] * swgi + ti[:, None] * swgj,
mask=cm[None, :], other=0.0)
C = tl.load(H + pb * sb + rows[:, None] * si + cols[None, :] * sj,
mask=cm[None, :], other=0.0)
Cn = C + tl.dot(Vt, Wg, out_dtype=tl.float32)
tl.store(H + pb * sb + rows[:, None] * si + cols[None, :] * sj, Cn, mask=cm[None, :])
_PREC = "tf32x3"
_NB = 32
_CTOL = 1e-4
_DTOL = 1e-4
_C2TOL = 1e-3
_TBM = 128
@triton.heuristics({"NT_ROW": lambda a: (a["n"] + a["BLOCK_M"] - 1) // a["BLOCK_M"],
"NT_COL": lambda a: (a["n"] + a["BLOCK_N"] - 1) // a["BLOCK_N"]})
@triton.jit
def _maskk(A, OK, n, nf, sb, si, sj, ZTOL, NNZTOL, COLTOL,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr,
NT_ROW: tl.constexpr, NT_COL: tl.constexpr):
pb = tl.program_id(0)
Ab = A + pb * sb
sumsq = tl.zeros([1], tl.float32)
rowsq = tl.zeros([1], tl.float32)
nnz = tl.zeros([1], tl.float32)
for it in tl.static_range(NT_ROW):
rows = it * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < n
rsum = tl.zeros([BLOCK_M], tl.float32)
for ct in tl.static_range(NT_COL):
cols = ct * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < n
x = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj,
mask=rm[:, None] & cm[None, :], other=0.0)
sumsq += tl.sum(x * x)
rsum += tl.sum(x, axis=1)
nnz += tl.sum(tl.where(tl.abs(x) > ZTOL, 1.0, 0.0))
rowsq += tl.sum(rsum * rsum)
collin = tl.sum(rowsq) / (nf * tl.sum(sumsq) + 1e-30)
nnzf = tl.sum(nnz) / (nf * nf)
ok = (nnzf >= NNZTOL) & (collin <= COLTOL)
tl.store(OK + pb, tl.where(ok, 1.0, 0.0))
@triton.jit
def _panel(H, TAU, T, k, kb, N, need_t,
sb, si, sj, stb, sttb, stti,
BLOCK_M: tl.constexpr, KB: tl.constexpr, PREC: tl.constexpr):
pid = tl.program_id(0)
Hb = H + pid * sb
lc = tl.arange(0, KB)
for j in range(kb):
c = k + j
alpha = tl.load(Hb + c * si + c * sj)
ss = tl.zeros([1], tl.float32)
nt = (N - c + BLOCK_M - 1) // BLOCK_M
for i in range(nt):
rows = c + i * BLOCK_M + tl.arange(0, BLOCK_M)
m = rows < N
x = tl.load(Hb + rows * si + c * sj, mask=m, other=0.0)
ss += tl.sum(x * x, axis=0)
xnorm = tl.sqrt(ss)
sgn = tl.where(alpha >= 0.0, 1.0, -1.0)
beta = -sgn * xnorm
isz = xnorm == 0.0
betas = tl.where(isz, alpha, beta)
inv = tl.where(isz, 0.0, 1.0 / (alpha - beta))
tauj = tl.where(isz, 0.0, (beta - alpha) / tl.where(isz, 1.0, beta))
tauj = tl.sum(tauj, axis=0)
inv = tl.sum(inv, axis=0)
betas = tl.sum(betas, axis=0)
tl.store(TAU + pid * stb + c, tauj)
for i in range(nt):
rows = c + i * BLOCK_M + tl.arange(0, BLOCK_M)
m = rows < N
x = tl.load(Hb + rows * si + c * sj, mask=m, other=0.0)
v = x * inv
v = tl.where(rows == c, betas, v)
tl.store(Hb + rows * si + c * sj, v, mask=m)
tl.debug_barrier()
W = tl.zeros([KB], tl.float32)
for i in range(nt):
rows = c + i * BLOCK_M + tl.arange(0, BLOCK_M)
m = rows < N
vc = tl.load(Hb + rows * si + c * sj, mask=m, other=0.0)
v = tl.where(rows == c, 1.0, vc)
v = tl.where(m, v, 0.0)
P = tl.load(Hb + rows[:, None] * si + (k + lc)[None, :] * sj, mask=m[:, None], other=0.0)
W += tl.sum(v[:, None] * P, axis=0)
for i in range(nt):
rows = c + i * BLOCK_M + tl.arange(0, BLOCK_M)
m = rows < N
vc = tl.load(Hb + rows * si + c * sj, mask=m, other=0.0)
v = tl.where(rows == c, 1.0, vc)
v = tl.where(m, v, 0.0)
P = tl.load(Hb + rows[:, None] * si + (k + lc)[None, :] * sj, mask=m[:, None], other=0.0)
upd = P - tauj * v[:, None] * W[None, :]
cmask = (lc[None, :] > j) & (lc[None, :] < kb) & m[:, None]
tl.store(Hb + rows[:, None] * si + (k + lc)[None, :] * sj, upd, mask=cmask)
tl.debug_barrier()
if need_t > 0:
G = tl.zeros([KB, KB], tl.float32)
ntk = (N - k + BLOCK_M - 1) // BLOCK_M
for i in range(ntk):
rows = k + i * BLOCK_M + tl.arange(0, BLOCK_M)
m = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + lc)[None, :] * sj, mask=m[:, None], other=0.0)
V = tl.where(lc[None, :] >= kb, 0.0,
tl.where(rr[:, None] == lc[None, :], 1.0,
tl.where(rr[:, None] < lc[None, :], 0.0, Vr)))
V = tl.where(m[:, None], V, 0.0)
G += tl.dot(tl.trans(V), V, input_precision=PREC)
taus = tl.load(TAU + pid * stb + k + lc, mask=lc < kb, other=0.0)
Tt = tl.zeros([KB, KB], tl.float32)
for i in range(kb):
gcol = tl.sum(tl.where(lc[None, :] == i, G, 0.0), axis=1)
z = tl.where(lc < i, gcol, 0.0)
Tz = tl.sum(Tt * z[None, :], axis=1)
tval = tl.sum(tl.where(lc == i, taus, 0.0), axis=0)
newcol = tl.where(lc == i, tval, tl.where(lc < i, -tval * Tz, 0.0))
Tt = tl.where(lc[None, :] == i, newcol[:, None], Tt)
tl.store(T + pid * sttb + lc[:, None] * stti + lc[None, :], Tt)
@triton.jit
def _hqr(A, rowmask, ROWS: tl.constexpr, NB: tl.constexpr):
rrow = tl.arange(0, ROWS)
nbr = tl.arange(0, NB)
cc = nbr[None, :]
rr = rrow[:, None]
tauv = tl.zeros([NB], tl.float32)
Acur = A
for j in range(NB):
colj = tl.sum(tl.where(cc == j, Acur, 0.0), axis=1)
x = tl.where(rrow >= j, colj, 0.0)
x = tl.where(rowmask, x, 0.0)
alpha = tl.sum(tl.where(rrow == j, colj, 0.0), axis=0)
ss = tl.sum(x * x, axis=0)
xnorm = tl.sqrt(ss)
sgn = tl.where(alpha >= 0.0, 1.0, -1.0)
beta = -sgn * xnorm
isz = xnorm == 0.0
betas = tl.where(isz, alpha, beta)
inv = tl.where(isz, 0.0, 1.0 / (alpha - beta))
tauj = tl.where(isz, 0.0, (beta - alpha) / tl.where(isz, 1.0, beta))
vr = tl.where(rrow == j, 1.0, tl.where(rrow > j, colj * inv, 0.0))
vr = tl.where(rowmask, vr, 0.0)
w = tl.sum(vr[:, None] * Acur, axis=0)
upd = Acur - tauj * vr[:, None] * w[None, :]
Acur = tl.where((cc > j) & (rr >= j), upd, Acur)
vbelow = tl.where(rrow > j, colj * inv, 0.0)
Acur = tl.where((cc == j) & (rr > j), vbelow[:, None], Acur)
Acur = tl.where((cc == j) & (rr == j), betas, Acur)
tauv = tl.where(nbr == j, tauj, tauv)
Q = tl.where(rr == cc, 1.0, 0.0)
for jj in range(NB):
j = NB - 1 - jj
vcol = tl.sum(tl.where(cc == j, Acur, 0.0), axis=1)
vr = tl.where(rrow == j, 1.0, tl.where(rrow > j, vcol, 0.0))
vr = tl.where(rowmask, vr, 0.0)
tauj = tl.sum(tl.where(nbr == j, tauv, 0.0), axis=0)
w = tl.sum(vr[:, None] * Q, axis=0)
Q = Q - tauj * vr[:, None] * w[None, :]
Q = tl.where(rowmask[:, None], Q, 0.0)
return Q, Acur, tauv
@triton.jit
def _trinv_up(U, NB: tl.constexpr):
r = tl.arange(0, NB)
rr = r[:, None]
X = tl.zeros([NB, NB], tl.float32)
for ii in range(NB):
i = NB - 1 - ii
Urowi = tl.sum(tl.where(rr == i, U, 0.0), axis=0)
Uii = tl.sum(tl.where(r == i, Urowi, 0.0), axis=0)
coef = Urowi * tl.where(r > i, 1.0, 0.0)
acc = tl.sum(coef[:, None] * X, axis=0)
ei = tl.where(r == i, 1.0, 0.0)
Xi = (ei - acc) / Uii
X = tl.where(rr == i, Xi[None, :], X)
return X
@triton.jit
def _lu(M, NB: tl.constexpr):
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
A = M
L = tl.where(rr == cc, 1.0, 0.0)
for j in range(NB):
Arowj = tl.sum(tl.where(rr == j, A, 0.0), axis=0)
piv = tl.sum(tl.where(r == j, Arowj, 0.0), axis=0)
safe = tl.abs(piv) < 1e-20
pivs = tl.where(safe, 1.0, piv)
Acolj = tl.sum(tl.where(cc == j, A, 0.0), axis=1)
fac = tl.where(r > j, Acolj / pivs, 0.0)
fac = tl.where(safe, 0.0, fac)
L = tl.where((cc == j) & (rr > j), fac[:, None], L)
A = A - fac[:, None] * Arowj[None, :]
U = tl.where(rr <= cc, A, 0.0)
return L, U
@triton.jit
def _lu_wmat(M, B, sbpre, NB: tl.constexpr, DTOL: tl.constexpr):
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
A = M
L = tl.where(rr == cc, 1.0, 0.0)
W = tl.zeros([NB, NB], tl.float32)
ud = tl.zeros([NB], tl.float32)
for j in range(NB):
Arowj = tl.sum(tl.where(rr == j, A, 0.0), axis=0)
piv = tl.sum(tl.where(r == j, Arowj, 0.0), axis=0)
ud = tl.where(r == j, piv, ud)
safe = tl.abs(piv) < 1e-20
pivs = tl.where(safe, 1.0, piv)
Acolj = tl.sum(tl.where(cc == j, A, 0.0), axis=1)
fac = tl.where(r > j, Acolj / pivs, 0.0)
fac = tl.where(safe, 0.0, fac)
L = tl.where((cc == j) & (rr > j), fac[:, None], L)
A = A - fac[:, None] * Arowj[None, :]
spj = tl.sum(tl.where(r == j, sbpre, 0.0), axis=0)
degj = (spj > 0.5) | (tl.abs(piv) < DTOL)
ujj = tl.where(degj, 1.0, piv)
ustrict = tl.where(r < j, Acolj, 0.0)
wsum = tl.sum(W * ustrict[None, :], axis=1)
Bcolj = tl.sum(tl.where(cc == j, B, 0.0), axis=1)
wcolj = (Bcolj - wsum) / ujj
W = tl.where(cc == j, wcolj[:, None], W)
return L, W, ud
@triton.jit
def _buildT(G, tau, NB: tl.constexpr):
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
T = tl.zeros([NB, NB], tl.float32)
for j in range(NB):
tauj = tl.sum(tl.where(r == j, tau, 0.0), axis=0)
gcol = tl.sum(tl.where(cc == j, G, 0.0), axis=1)
z = tl.where(r < j, gcol, 0.0)
Tz = tl.sum(T * z[None, :], axis=1)
newcol = tl.where(r == j, tauj, tl.where(r < j, -tauj * Tz, 0.0))
T = tl.where(cc == j, newcol[:, None], T)
return T
@triton.jit
def _tsqr_k1(H, Qw, Rw, k, N, sb, si, sj, sqb, sqr, sqi, sqj, srb, srr, sri, srj,
BLOCK_M: tl.constexpr, NB: tl.constexpr):
pb = tl.program_id(0)
rb = tl.program_id(1)
Hb = H + pb * sb
nbr = tl.arange(0, NB)
rrow = tl.arange(0, BLOCK_M)
rows = k + rb * BLOCK_M + rrow
rm = rows < N
A = tl.load(Hb + rows[:, None] * si + (k + nbr)[None, :] * sj, mask=rm[:, None], other=0.0)
Q, Acur, _ = _hqr(A, rm, BLOCK_M, NB)
rr = rrow[:, None]
cc = nbr[None, :]
Rval = tl.where(rr <= cc, Acur, 0.0)
tl.store(Qw + pb * sqb + rb * sqr + rrow[:, None] * sqi + nbr[None, :] * sqj, Q, mask=rm[:, None])
tl.store(Rw + pb * srb + rb * srr + rrow[:, None] * sri + nbr[None, :] * srj, Rval,
mask=(rrow < NB)[:, None])
@triton.jit
def _tsqr_k2(H, Qw, Rw, QRw, Uw, Sw, Tb, TAU, k, num_rb, N,
sb, si, sj, sqb, sqr, sqi, sqj, srb, srr, sri, srj,
sQRb, sQRi, sQRj, sub, sui, suj, ssb, sttb, stti, stb,
NB: tl.constexpr, SROWS: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
Hb = H + pb * sb
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
eye = tl.where(rr == cc, 1.0, 0.0)
srow = tl.arange(0, SROWS)
blkidx = srow // NB
inblk = srow % NB
smask = srow < num_rb * NB
Rstack = tl.load(Rw + pb * srb + blkidx[:, None] * srr + inblk[:, None] * sri + r[None, :] * srj,
mask=smask[:, None], other=0.0)
Q_R, Rfa, _ = _hqr(Rstack, smask, SROWS, NB)
tl.store(QRw + pb * sQRb + srow[:, None] * sQRi + r[None, :] * sQRj, Q_R, mask=smask[:, None])
sel = tl.where(srow[None, :] == r[:, None], 1.0, 0.0)
Q_R_0 = tl.dot(sel, Q_R, input_precision=PREC)
Rfin = tl.dot(sel, Rfa, input_precision=PREC)
R_final = tl.where(rr <= cc, Rfin, 0.0)
rdiag = tl.sum(tl.where(rr == cc, R_final, 0.0), axis=1)
s = tl.where(rdiag >= 0.0, 1.0, -1.0)
Q0top = tl.load(Qw + pb * sqb + r[:, None] * sqi + r[None, :] * sqj)
Qtop = tl.dot(Q0top, Q_R_0, input_precision=PREC) * s[None, :]
M = eye - Qtop
L, U = _lu(M, NB)
ud = tl.sum(tl.where(rr == cc, U, 0.0), axis=1)
tiny = tl.abs(ud) < 1e-12
Usafe = tl.where((rr == cc) & tiny[None, :], 1.0, U)
Uinv = _trinv_up(Usafe, NB)
QbTQb = eye - tl.dot(tl.trans(Qtop), Qtop, input_precision=PREC)
GVV = tl.dot(tl.trans(L), L, input_precision=PREC) + \
tl.dot(tl.dot(tl.trans(Uinv), QbTQb, input_precision=PREC), Uinv, input_precision=PREC)
gd = tl.sum(tl.where(rr == cc, GVV, 0.0), axis=1)
tau = tl.where(tiny, 0.0, 2.0 / gd)
T = _buildT(GVV, tau, NB)
Rp = s[:, None] * R_final
diagblk = tl.where(rr <= cc, Rp, L)
tl.store(Hb + (k + rr) * si + (k + cc) * sj, diagblk)
tl.store(Uw + pb * sub + rr * sui + cc * suj, Uinv)
tl.store(Sw + pb * ssb + r, s)
tl.store(Tb + pb * sttb + rr * stti + cc, T)
tl.store(TAU + pb * stb + k + r, tau)
@triton.jit
def _tsqr_k3(H, Qw, QRw, Uw, Sw, k, N, sb, si, sj, sqb, sqr, sqi, sqj,
sQRb, sQRi, sQRj, sub, sui, suj, ssb,
BLOCK_M: tl.constexpr, NB: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
rb = tl.program_id(1)
Hb = H + pb * sb
nbr = tl.arange(0, NB)
rrow = tl.arange(0, BLOCK_M)
rows = k + rb * BLOCK_M + rrow
rm = rows < N
Qi = tl.load(Qw + pb * sqb + rb * sqr + rrow[:, None] * sqi + nbr[None, :] * sqj,
mask=rm[:, None], other=0.0)
QRi = tl.load(QRw + pb * sQRb + (rb * NB + nbr)[:, None] * sQRi + nbr[None, :] * sQRj)
Uinv = tl.load(Uw + pb * sub + nbr[:, None] * sui + nbr[None, :] * suj)
s = tl.load(Sw + pb * ssb + nbr)
Qg = tl.dot(Qi, QRi, input_precision=PREC)
Qpg = Qg * s[None, :]
Vi = -tl.dot(Qpg, Uinv, input_precision=PREC)
if rb == 0:
wmask = rm & (rrow >= NB)
else:
wmask = rm
tl.store(Hb + rows[:, None] * si + (k + nbr)[None, :] * sj, Vi, mask=wmask[:, None])
@triton.jit
def _trail(H, A, T, k, kb, N, sb, si, sj, sttb, stti,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, KB: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
pn = tl.program_id(1)
Hb = H + pb * sb
Ab = A + pb * sb
ti = tl.arange(0, KB)
cols = (k + kb) + pn * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < N
Tt = tl.load(T + pb * sttb + ti[:, None] * stti + ti[None, :])
W = tl.zeros([KB, BLOCK_N], tl.float32)
ntk = (N - k + BLOCK_M - 1) // BLOCK_M
for i in range(ntk):
rows = k + i * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
C = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj, mask=rm[:, None] & cm[None, :], other=0.0)
W += tl.dot(tl.trans(V), C, input_precision=PREC)
W2 = tl.dot(tl.trans(Tt), W, input_precision=PREC)
for i in range(ntk):
rows = k + i * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
C = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj, mask=rm[:, None] & cm[None, :], other=0.0)
Cn = C - tl.dot(V, W2, input_precision=PREC)
tl.store(Hb + rows[:, None] * si + cols[None, :] * sj, Cn, mask=rm[:, None] & cm[None, :])
@triton.jit
def _trail_w(H, A, T, Wo, k, kb, N, sb, si, sj, sttb, stti, swob, swoi, swoj,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, KB: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
pn = tl.program_id(1)
Hb = H + pb * sb
Ab = A + pb * sb
ti = tl.arange(0, KB)
cols = (k + kb) + pn * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < N
Tt = tl.load(T + pb * sttb + ti[:, None] * stti + ti[None, :])
W = tl.zeros([KB, BLOCK_N], tl.float32)
ntk = (N - k + BLOCK_M - 1) // BLOCK_M
for i in range(ntk):
rows = k + i * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
C = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj, mask=rm[:, None] & cm[None, :], other=0.0)
W += tl.dot(tl.trans(V), C, input_precision=PREC)
W2 = tl.dot(tl.trans(Tt), W, input_precision=PREC)
tl.store(Wo + pb * swob + ti[:, None] * swoi + cols[None, :] * swoj, W2, mask=cm[None, :])
@triton.jit
def _trail_c(H, A, Wo, k, kb, N, sb, si, sj, swob, swoi, swoj,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, KB: tl.constexpr, PREC: tl.constexpr):
pb = tl.program_id(0)
pn = tl.program_id(1)
pm = tl.program_id(2)
Hb = H + pb * sb
Ab = A + pb * sb
ti = tl.arange(0, KB)
cols = (k + kb) + pn * BLOCK_N + tl.arange(0, BLOCK_N)
cm = cols < N
rows = k + pm * BLOCK_M + tl.arange(0, BLOCK_M)
rm = rows < N
rr = rows - k
Vr = tl.load(Hb + rows[:, None] * si + (k + ti)[None, :] * sj, mask=rm[:, None], other=0.0)
V = tl.where(ti[None, :] >= kb, 0.0,
tl.where(rr[:, None] == ti[None, :], 1.0,
tl.where(rr[:, None] < ti[None, :], 0.0, Vr)))
V = tl.where(rm[:, None], V, 0.0)
W2 = tl.load(Wo + pb * swob + ti[:, None] * swoi + cols[None, :] * swoj, mask=cm[None, :], other=0.0)
C = tl.load(Ab + rows[:, None] * si + cols[None, :] * sj, mask=rm[:, None] & cm[None, :], other=0.0)
Cn = C - tl.dot(V, W2, input_precision=PREC)
tl.store(Hb + rows[:, None] * si + cols[None, :] * sj, Cn, mask=rm[:, None] & cm[None, :])
@triton.heuristics({"EVEN_M": lambda a: (a["N"] - a["k"]) % a["BLOCK_M"] == 0})
@triton.jit
def _cqr_g1(H, Gp, k, N, sb, si, sj, sgb, sgr, sgi, sgj,
BLOCK_M: tl.constexpr, NB: tl.constexpr, PREC: tl.constexpr, EVEN_M: tl.constexpr):
pb = tl.program_id(0)
rb = tl.program_id(1)
Hb = H + pb * sb
r = tl.arange(0, NB)
rows = k + rb * BLOCK_M + tl.arange(0, BLOCK_M)
if EVEN_M:
blk = tl.load(Hb + rows[:, None] * si + (k + r)[None, :] * sj)
else:
rm = rows < N
blk = tl.load(Hb + rows[:, None] * si + (k + r)[None, :] * sj, mask=rm[:, None], other=0.0)
G = tl.dot(tl.trans(blk), blk, input_precision=PREC)
tl.store(Gp + pb * sgb + rb * sgr + r[:, None] * sgi + r[None, :] * sgj, G)
@triton.jit
def _chol_inv(G, NB: tl.constexpr, CTOL: tl.constexpr):
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
diagG = tl.sum(tl.where(rr == cc, G, 0.0), axis=1)
maxdiag = tl.maximum(tl.max(diagG), 1e-20)
floor = CTOL * maxdiag
L = tl.zeros([NB, NB], tl.float32)
X = tl.zeros([NB, NB], tl.float32)
degen = tl.zeros([NB], tl.float32)
for j in range(NB):
Lrowj = tl.sum(tl.where(rr == j, L, 0.0), axis=0)
sj = tl.sum(tl.where(r < j, Lrowj * Lrowj, 0.0), axis=0)
Gjj = tl.sum(tl.where(r == j, diagG, 0.0), axis=0)
d = Gjj - sj
deg = d < floor
d = tl.where(deg, floor, d)
degen = tl.where(r == j, tl.where(deg, 1.0, 0.0), degen)
Ljj = tl.sqrt(d)
Gcolj = tl.sum(tl.where(cc == j, G, 0.0), axis=1)
coef = Lrowj * tl.where(r < j, 1.0, 0.0)
dotv = tl.sum(L * coef[None, :], axis=1)
below = (Gcolj - dotv) / Ljj
newcol = tl.where(r == j, Ljj, tl.where(r > j, below, 0.0))
L = tl.where(cc == j, newcol[:, None], L)
accx = tl.sum(coef[:, None] * X, axis=0)
ej = tl.where(r == j, 1.0, 0.0)
Xrowj = (ej - accx) / Ljj
X = tl.where(rr == j, Xrowj[None, :], X)
return L, X, degen
@triton.jit
def _cqr_tiny(H, Gp, Tb, Tbh, Tbl, Wb, TAU, k, num_rb, N,
sb, si, sj, sgb, sgr, sgi, sgj, stb, sti, stj, swb, swi, swj, staub,
NB: tl.constexpr, CTOL: tl.constexpr, DTOL: tl.constexpr, PREC: tl.constexpr,
C2TOL: tl.constexpr):
pb = tl.program_id(0)
Hb = H + pb * sb
r = tl.arange(0, NB)
rr = r[:, None]
cc = r[None, :]
eye = tl.where(rr == cc, 1.0, 0.0)
G1 = tl.zeros([NB, NB], tl.float32)
for rb in range(num_rb):
G1 += tl.load(Gp + pb * sgb + rb * sgr + rr * sgi + cc * sgj)
Lc1, Ri1, deg1 = _chol_inv(G1, NB, CTOL)
G2 = tl.dot(tl.dot(Ri1, G1, input_precision=PREC), tl.trans(Ri1), input_precision=PREC)
offmax = tl.max(tl.abs(G2 - eye))
deg1any = tl.max(deg1)
if (offmax < C2TOL) | (deg1any > 0.5):
deg2 = tl.zeros([NB], tl.float32)
Rc = tl.trans(Lc1)
Rcinv = tl.trans(Ri1)
else:
Lc2, Ri2, deg2 = _chol_inv(G2, NB, CTOL)
Rc = tl.dot(tl.trans(Lc2), tl.trans(Lc1), input_precision=PREC)
Rcinv = tl.dot(tl.trans(Ri1), tl.trans(Ri2), input_precision=PREC)
ptop = tl.load(Hb + (k + rr) * si + (k + cc) * sj)
Qtop = tl.dot(ptop, Rcinv, input_precision=PREC)
qd = tl.sum(tl.where(rr == cc, Qtop, 0.0), axis=1)
s = tl.where(qd > 0.0, -1.0, 1.0)
Mtop = eye - Qtop * s[None, :]
rcd = tl.abs(tl.sum(tl.where(rr == cc, Rc, 0.0), axis=1))
rcmax = tl.max(rcd)
small = tl.maximum(deg1, deg2)
small = tl.maximum(small, tl.where(rcd < DTOL * rcmax, 1.0, 0.0))
smallb = small > 0.5
Mtop = tl.where(smallb[None, :], eye, Mtop)
Bmat = -(Rcinv * s[None, :])
L, Wmat, ud = _lu_wmat(Mtop, Bmat, small, NB, DTOL)
small = tl.maximum(small, tl.where(tl.abs(ud) < DTOL, 1.0, 0.0))
smallb = small > 0.5
Wmat = tl.where(smallb[None, :], 0.0, Wmat)
Ltop = tl.where(smallb[None, :], eye, L)
Gbot = G1 - tl.dot(tl.trans(ptop), ptop, input_precision=PREC)
GVV = tl.dot(tl.trans(Ltop), Ltop, input_precision=PREC) + \
tl.dot(tl.dot(tl.trans(Wmat), Gbot, input_precision=PREC), Wmat, input_precision=PREC)
gd = tl.sum(tl.where(rr == cc, GVV, 0.0), axis=1)
tau = tl.where(smallb, 0.0, 2.0 / gd)
T = _buildT(GVV, tau, NB)
R = s[:, None] * Rc
diagblk = tl.where(rr <= cc, R, Ltop)
tl.store(Hb + (k + rr) * si + (k + cc) * sj, diagblk)
tl.store(Wb + pb * swb + rr * swi + cc * swj, Wmat)
tl.store(Tb + pb * stb + rr * sti + cc * stj, T)
Th16 = T.to(tl.float16)
Tl16 = (T - Th16.to(tl.float32)).to(tl.float16)
tl.store(Tbh + pb * stb + rr * sti + cc * stj, Th16)
tl.store(Tbl + pb * stb + rr * sti + cc * stj, Tl16)
tl.store(TAU + pb * staub + k + r, tau)
@triton.heuristics({"EVEN_M": lambda a: (a["N"] - a["k"] - a["NB"]) % a["BLOCK_M"] == 0})
@triton.jit
def _cqr_v2(H, Wb, k, N, sb, si, sj, swb, swi, swj,
BLOCK_M: tl.constexpr, NB: tl.constexpr, PREC: tl.constexpr, EVEN_M: tl.constexpr):
pb = tl.program_id(0)
rb = tl.program_id(1)
Hb = H + pb * sb
r = tl.arange(0, NB)
rows = (k + NB) + rb * BLOCK_M + tl.arange(0, BLOCK_M)
W = tl.load(Wb + pb * swb + r[:, None] * swi + r[None, :] * swj)
if EVEN_M:
blk = tl.load(Hb + rows[:, None] * si + (k + r)[None, :] * sj)
V2 = tl.dot(blk, W, input_precision=PREC)
tl.store(Hb + rows[:, None] * si + (k + r)[None, :] * sj, V2)
else:
rm = rows < N
blk = tl.load(Hb + rows[:, None] * si + (k + r)[None, :] * sj, mask=rm[:, None], other=0.0)
V2 = tl.dot(blk, W, input_precision=PREC)
tl.store(Hb + rows[:, None] * si + (k + r)[None, :] * sj, V2, mask=rm[:, None])
def _cfg(n):
if n <= 64:
return dict(pBM=32, pW=1, tBM=64, tBN=32, tW=2, tS=2)
if n <= 192:
return dict(pBM=128, pW=4, tBM=64, tBN=64, tW=4, tS=2)
if n <= 384:
return dict(pBM=128, pW=4, tBM=128, tBN=64, tW=4, tS=2)
if n <= 640:
return dict(pBM=128, pW=4, tBM=128, tBN=128, tW=4, tS=2)
if n <= 1280:
return dict(pBM=128, pW=8, tBM=128, tBN=128, tW=8, tS=2)
return dict(pBM=128, pW=8, tBM=128, tBN=128, tW=8, tS=2)
def _cqr_cfg(n):
if n <= 384:
return dict(gBM=64, gW=4, vBM=64, vW=4, tW=4, tBM=128, tBN=128, trW=8, trS=2)
if n <= 640:
return dict(gBM=128, gW=4, vBM=128, vW=4, tW=1, tBM=128, tBN=128, trW=8, trS=2)
if n <= 1280:
return dict(gBM=64, gW=4, vBM=64, vW=4, tW=4, tBM=128, tBN=128, trW=8, trS=3)
if n <= 2560:
return dict(gBM=64, gW=4, vBM=64, vW=4, tW=4, tBM=128, tBN=128, trW=8, trS=2,
split=True, cBM=128, cBN=128, cW=4)
return dict(gBM=64, gW=4, vBM=64, vW=4, tW=4, tBM=128, tBN=64, trW=8, trS=3,
split=True, cBM=128, cBN=64, cW=4)
_GCFG = {}
def _gluon_cfg(n):
c = _GCFG.get(n)
if c is None:
if n >= 1024:
c = dict(BM=64, BN=128, FW_W=8, AP_W=4, CS1=2, NBUF_AP=2, NBUF_FW=3)
else:
c = dict(BM=64, BN=128, FW_W=8, AP_W=4, CS1=2, NBUF_AP=3, NBUF_FW=2)
c["LC16"] = gl.NVMMASharedLayout.get_default_for([c["BM"], c["BN"]], gl.float16)
_GCFG[n] = c
return c
_WS = {}
def _ws(B, n, dev):
nb = _NB
maxrb = (n + 63) // 64 + 1
key = (B, maxrb)
e = _WS.get(key)
if e is None or e[0].shape[0] < B:
Gp = torch.empty((B, maxrb, nb, nb), device=dev, dtype=torch.float32)
Tb = torch.empty((B, nb, nb), device=dev, dtype=torch.float32)
Tbh = torch.empty((B, nb, nb), device=dev, dtype=torch.float16)
Tbl = torch.empty((B, nb, nb), device=dev, dtype=torch.float16)
Wb = torch.empty((B, nb, nb), device=dev, dtype=torch.float32)
Wo = torch.empty((B, nb, n), device=dev, dtype=torch.float32) if n > 1280 else None
_WS[key] = (Gp, Tb, Tbh, Tbl, Wb, Wo)
e = _WS[key]
return e
_GBUF = {}
def _gbuf(B, n, dev):
nb = _NB
WN = n + _gluon_cfg(n)["BN"]
key = (B, n)
e = _GBUF.get(key)
if e is None or e[0].shape[0] < B:
Vpan = torch.empty((B, n, nb), device=dev, dtype=torch.float16)
Vlo = torch.empty((B, n, nb), device=dev, dtype=torch.float16)
Wog = torch.empty((B, WN, nb), device=dev, dtype=torch.float16)
_GBUF[key] = (Vpan, Vlo, Wog)
e = _GBUF[key]
return e
def _build_descs(data, H, Vpan, Wog, B, n, nb, WN, BM, BN):
lcd = gl.NVMMASharedLayout.get_default_for([BM, BN], gl.float32)
lvd = gl.NVMMASharedLayout.get_default_for([BM, nb], gl.float16)
lwd = gl.NVMMASharedLayout.get_default_for([BN, nb], gl.float16)
cdesc_H = TensorDescriptor.from_tensor(H.reshape(B * n, n), [BM, BN], lcd)
cdesc_D = TensorDescriptor.from_tensor(data.reshape(B * n, n), [BM, BN], lcd)
vdesc = TensorDescriptor.from_tensor(Vpan.reshape(B * n, nb), [BM, nb], lvd)
wdesc = TensorDescriptor.from_tensor(Wog.reshape(B * WN, nb), [BN, nb], lwd)
return cdesc_H, cdesc_D, vdesc, wdesc
_SER_TB = {}
def _ser_tb(B, dev):
e = _SER_TB.get(B)
if e is None:
e = torch.empty((B, _NB, _NB), device=dev, dtype=torch.float32)
_SER_TB[B] = e
return e
_TSQR_WS = {}
def _tsqr_ws(B, n, dev, nb, BM):
maxrb = (n + BM - 1) // BM
srows = 1
while srows < maxrb * nb:
srows *= 2
key = (maxrb, srows, nb, BM)
e = _TSQR_WS.get(key)
if e is None or e[0].shape[0] < B:
Bc = B if e is None else max(B, e[0].shape[0])
Qw = torch.empty((Bc, maxrb, BM, nb), device=dev, dtype=torch.float32)
Rw = torch.empty((Bc, maxrb, nb, nb), device=dev, dtype=torch.float32)
QRw = torch.empty((Bc, srows, nb), device=dev, dtype=torch.float32)
Uw = torch.empty((Bc, nb, nb), device=dev, dtype=torch.float32)
Sw = torch.empty((Bc, nb), device=dev, dtype=torch.float32)
_TSQR_WS[key] = (Qw, Rw, QRw, Uw, Sw, srows, maxrb)
e = _TSQR_WS[key]
return e
def _serial_qr(H, B, n, dev, nb=32):
tau = torch.zeros((B, n), device=dev, dtype=torch.float32)
Tb = _ser_tb(B, dev)
c = _cfg(n)
sb, si, sj = H.stride()
stb = tau.stride(0)
sttb, stti, _ = Tb.stride()
pBM = c['pBM']
pW = c['pW']
tBM = c['tBM']
tBN = c['tBN']
tW = c['tW']
tS = c['tS']
panel_launch = _panel[(B,)]
use_tsqr = (nb == 16) and (384 <= n <= 1280)
BM = _TBM
if use_tsqr:
Qw, Rw, QRw, Uw, Sw, srows, maxrb = _tsqr_ws(B, n, dev, nb, BM)
sqb, sqr, sqi, sqj = Qw.stride()
srb, srr, sri, srj = Rw.stride()
sQRb, sQRi, sQRj = QRw.stride()
sub, sui, suj = Uw.stride()
ssb = Sw.stride(0)
for k in range(0, n, nb):
kb = min(nb, n - k)
need_t = 1 if (k + kb) < n else 0
m = n - k
if use_tsqr and m > 2 * BM and kb == nb:
num_rb = triton.cdiv(m, BM)
_tsqr_k1[(B, num_rb)](H, Qw, Rw, k, n, sb, si, sj, sqb, sqr, sqi, sqj,
srb, srr, sri, srj, BLOCK_M=BM, NB=nb, num_warps=4)
_tsqr_k2[(B,)](H, Qw, Rw, QRw, Uw, Sw, Tb, tau, k, num_rb, n,
sb, si, sj, sqb, sqr, sqi, sqj, srb, srr, sri, srj,
sQRb, sQRi, sQRj, sub, sui, suj, ssb, sttb, stti, stb,
NB=nb, SROWS=srows, PREC=_PREC, num_warps=2)
_tsqr_k3[(B, num_rb)](H, Qw, QRw, Uw, Sw, k, n, sb, si, sj, sqb, sqr, sqi, sqj,
sQRb, sQRi, sQRj, sub, sui, suj, ssb,
BLOCK_M=BM, NB=nb, PREC=_PREC, num_warps=4)
else:
panel_launch(H, tau, Tb, k, kb, n, need_t, sb, si, sj, stb, sttb, stti,
BLOCK_M=pBM, KB=nb, PREC=_PREC, num_warps=pW)
if need_t:
ncol = n - (k + kb)
grid = (B, triton.cdiv(ncol, tBN))
_trail[grid](H, H, Tb, k, kb, n, sb, si, sj, sttb, stti,
BLOCK_M=tBM, BLOCK_N=tBN, KB=nb, PREC=_PREC,
num_warps=tW, num_stages=tS)
return H, tau
def _cqr_into(data, H, tau, B, n, dev, descs=None, fcol=None):
nb = _NB
if fcol is None:
fcol = n
H[:, :, :nb] = data[:, :, :nb]
tau.zero_()
Gp, Tb, Tbh, Tbl, Wb, Wo = _ws(B, n, dev)
c = _cqr_cfg(n)
sb, si, sj = H.stride()
sgb, sgr, sgi, sgj = Gp.stride()
stb, sti, stj = Tb.stride()
swb, swi, swj = Wb.stride()
staub = tau.stride(0)
gBM = c['gBM']
vBM = c['vBM']
gW = c['gW']
tW = c['tW']
vW = c['vW']
tBM = c['tBM']
tBN = c['tBN']
trW = c['trW']
trS = c['trS']
split = c.get('split', False)
if split:
swob, swoi, swoj = Wo.stride()
cBM = c['cBM']
cBN = c['cBN']
cW = c['cW']
g512 = (n == 512)
g1024 = (n == 1024)
guse = g512 or g1024
if guse:
gcf = _gluon_cfg(n)
GBM = gcf['BM']
GBN = gcf['BN']
FW_W = gcf['FW_W']
AP_W = gcf['AP_W']
CS1 = gcf['CS1']
NBUF_AP = gcf['NBUF_AP']
NBUF_FW = gcf['NBUF_FW']
LC16 = gcf['LC16']
WN = n + GBN
Vpan, Vlo, Wog = _gbuf(B, n, dev)
svpb, svpi, svpj = Vpan.stride()
swgb, swgi, swgj = Wog.stride()
if descs is None:
cdesc_H, cdesc_D, vdesc, wdesc = _build_descs(data, H, Vpan, Wog, B, n, nb, WN, GBM, GBN)
else:
cdesc_H, cdesc_D, vdesc, wdesc = descs
gC_BYTES = GBM * GBN * 4
gV_BYTES = 2 * (GBM * nb * 2)
_lvd = gl.NVMMASharedLayout.get_default_for([GBM, nb], gl.float16)
_ltd = gl.NVMMASharedLayout.get_default_for([nb, nb], gl.float16)
vl_desc = TensorDescriptor.from_tensor(Vlo.reshape(B * n, nb), [GBM, nb], _lvd)
th_desc = TensorDescriptor.from_tensor(Tbh.reshape(B * nb, nb), [nb, nb], _ltd)
tlo_desc = TensorDescriptor.from_tensor(Tbl.reshape(B * nb, nb), [nb, nb], _ltd)
panel_launch = _panel[(B,)]
cqr_tiny_launch = _cqr_tiny[(B,)]
for k in range(0, fcol, nb):
m = n - k
if m == nb:
panel_launch(H, tau, Tb, k, nb, n, 0, sb, si, sj, staub, stb, sti,
BLOCK_M=64, KB=nb, PREC=_PREC, num_warps=2)
continue
num_rb = triton.cdiv(m, gBM)
_cqr_g1[(B, num_rb)](H, Gp, k, n, sb, si, sj, sgb, sgr, sgi, sgj,
BLOCK_M=gBM, NB=nb, PREC=_PREC, num_warps=gW)
cqr_tiny_launch(H, Gp, Tb, Tbh, Tbl, Wb, tau, k, num_rb, n,
sb, si, sj, sgb, sgr, sgi, sgj, stb, sti, stj, swb, swi, swj, staub,
NB=nb, CTOL=_CTOL, DTOL=_DTOL, PREC=_PREC, C2TOL=_C2TOL, num_warps=tW)
nvb = triton.cdiv(m - nb, vBM)
_cqr_v2[(B, nvb)](H, Wb, k, n, sb, si, sj, swb, swi, swj,
BLOCK_M=vBM, NB=nb, PREC=_PREC, num_warps=vW)
A = data if k == 0 else H
ncols = min(m - nb, fcol - k - nb)
if ncols <= 0:
continue
do_gluon = False
use_cs = False
if guse:
NTN = triton.cdiv(ncols, GBN)
rem = m % GBM
kr = k + rem
Mg = m - rem
NTM = Mg // GBM
even = (rem == 0)
NTN_g = NTN if g512 else (((NTN + CS1 - 1) // CS1) * CS1)
if g512:
do_gluon = (NTM >= 1) and (NTM * NTN >= NBUF_AP)
else:
use_cs = True
do_gluon = (NTM >= 1) and (NTM * (NTN_g // CS1) >= NBUF_AP)
if do_gluon:
nvtiles = triton.cdiv(m, GBM)
_extract_v[(B, nvtiles)](H, Vpan, Vlo, k, nb, n, sb, si, sj, svpb, svpi, svpj,
BLOCK_M=GBM, KB=nb, WLO=guse)
if g512:
cfw = cdesc_D if k == 0 else cdesc_H
fw_NTM = triton.cdiv(m, GBM)
fw_valid = m - (fw_NTM - 1) * GBM
fw_vpre = 2 * (fw_NTM * GBM * nb * 2) + 2 * (nb * nb * 2)
_g_formw[(B,)](vdesc, vl_desc, cfw, th_desc, tlo_desc, wdesc, n, WN, k, k,
NTM=fw_NTM, NTN=NTN, BM=GBM, BN=GBN, K=nb, NBUF=NBUF_FW,
VPRE=fw_vpre, C_BYTES=gC_BYTES, LC16=LC16,
PARTIAL=(not even), VALID=fw_valid, num_warps=FW_W)
else:
cfw = cdesc_D if k == 0 else cdesc_H
fw_NTM = triton.cdiv(m, GBM)
fw_valid = m - (fw_NTM - 1) * GBM
fw_vpre = 2 * (nb * nb * 2)
_g_formw_c1[(B, NTN_g)](vdesc, vl_desc, cfw, th_desc, tlo_desc, wdesc, n, WN, k, k,
NTN_TOT=NTN_g, NTM=fw_NTM, BM=GBM, BN=GBN, K=nb, NBUF=NBUF_FW,
VPRE=fw_vpre, C_BYTES=gC_BYTES, V_BYTES=gV_BYTES, LC16=LC16,
PARTIAL=(not even), VALID=fw_valid, num_warps=FW_W)
if not even:
_apply_top[(B, NTN_g)](H, Vpan, Wog, k, nb, n, sb, si, sj,
svpb, svpi, svpj, swgb, swgi, swgj,
BLOCK_N=GBN, KB=nb, num_warps=4)
cdesc = cdesc_D if k == 0 else cdesc_H
if use_cs:
CTPC = NTN_g // CS1
pre_bytes = NTM * GBM * nb * 2 + CTPC * GBN * nb * 2
_g_apply_cs[(B, CS1)](cdesc, vdesc, wdesc, cdesc_H, n, WN, kr, k,
M=Mg, NTM=NTM, CTPC=CTPC, BM=GBM, BN=GBN, K=nb,
NBUF=NBUF_AP, PRE_BYTES=pre_bytes, C_BYTES=gC_BYTES, num_warps=AP_W)
else:
pre_bytes = NTM * GBM * nb * 2 + NTN * GBN * nb * 2
_g_apply[(B,)](cdesc, vdesc, wdesc, cdesc_H, n, WN, kr, k,
M=Mg, NTM=NTM, NTN=NTN, BM=GBM, BN=GBN, K=nb, NBUF=NBUF_AP,
PRE_BYTES=pre_bytes, C_BYTES=gC_BYTES, num_warps=AP_W)
elif split:
gw = (B, triton.cdiv(ncols, tBN))
_trail_w[gw](H, A, Tb, Wo, k, nb, n, sb, si, sj, stb, sti, swob, swoi, swoj,
BLOCK_M=tBM, BLOCK_N=tBN, KB=nb, PREC=_PREC,
num_warps=trW, num_stages=trS)
gc = (B, triton.cdiv(ncols, cBN), triton.cdiv(m, cBM))
_trail_c[gc](H, A, Wo, k, nb, n, sb, si, sj, swob, swoi, swoj,
BLOCK_M=cBM, BLOCK_N=cBN, KB=nb, PREC=_PREC, num_warps=cW)
else:
grid = (B, triton.cdiv(ncols, tBN))
_trail[grid](H, A, Tb, k, nb, n, sb, si, sj, stb, sti,
BLOCK_M=tBM, BLOCK_N=tBN, KB=nb, PREC=_PREC,
num_warps=trW, num_stages=trS)
_OKBUF = {}
def _okbuf(B, dev):
e = _OKBUF.get(B)
if e is None:
e = torch.empty((B,), device=dev, dtype=torch.float32)
_OKBUF[B] = e
return e
def _ok_mask(data, B, n, dev):
if n == 512 or n == 1024:
ok = _okbuf(B, dev)
sb, si, sj = data.stride()
_maskk[(B,)](data, ok, n, float(n), sb, si, sj, 1e-12, 0.5, 0.1,
BLOCK_M=64, BLOCK_N=128, num_warps=4, num_stages=1)
return ok > 0.5
a = data
fro = (a * a).sum(dim=(1, 2))
rs = a.sum(dim=-1)
collin = (rs * rs).sum(dim=-1) / (n * fro + 1e-30)
nnz = (a.abs() > 1e-12).to(torch.float32).mean(dim=(1, 2))
return (nnz >= 0.5) & (collin <= 0.1)
def _route(data, H, tau, B, n, dev, okmask):
finite = torch.isfinite(H).reshape(B, -1).all(dim=1)
ill = ~finite if okmask is None else ((~finite) | (~okmask))
if not bool(ill.any().item()):
return
idx = ill.nonzero(as_tuple=True)[0]
sub = data.index_select(0, idx).contiguous()
Hb, taub = _serial_qr(sub, int(idx.numel()), n, dev, 16)
H.index_copy_(0, idx, Hb)
tau.index_copy_(0, idx, taub)
_GCACHE = {}
def _graphed_cqr(data, B, n, dev, okmask):
key = (B, n)
e = _GCACHE.get(key)
if e is None:
static_in = data.clone()
Hout = torch.empty_like(data)
tauout = torch.empty((B, n), device=dev, dtype=torch.float32)
descs = None
if n == 1024:
gcf = _gluon_cfg(n)
Vpan, Vlo, Wog = _gbuf(B, n, dev)
descs = _build_descs(static_in, Hout, Vpan, Wog, B, n, _NB,
n + gcf["BN"], gcf["BM"], gcf["BN"])
_cqr_into(static_in, Hout, tauout, B, n, dev, descs)
torch.cuda.synchronize()
g = torch.cuda.CUDAGraph()
with torch.cuda.graph(g):
_cqr_into(static_in, Hout, tauout, B, n, dev, descs)
_GCACHE[key] = (g, static_in, Hout, tauout)
e = _GCACHE[key]
g, static_in, Hout, tauout = e
static_in.copy_(data)
g.replay()
_route(data, Hout, tauout, B, n, dev, okmask)
return Hout.clone(), tauout.clone()
_GCACHE_PAD = {}
def _graphed_pad192(data, B, dev):
e = _GCACHE_PAD.get(B)
if e is None:
Apad = torch.zeros((B, 192, 192), device=dev, dtype=torch.float32)
ar = torch.arange(176, 192, device=dev)
Apad[:, ar, ar] = 1.0
Hpad = torch.empty((B, 192, 192), device=dev, dtype=torch.float32)
taupad = torch.empty((B, 192), device=dev, dtype=torch.float32)
_cqr_into(Apad, Hpad, taupad, B, 192, dev)
torch.cuda.synchronize()
g = torch.cuda.CUDAGraph()
with torch.cuda.graph(g):
_cqr_into(Apad, Hpad, taupad, B, 192, dev)
_GCACHE_PAD[B] = (g, Apad, Hpad, taupad)
e = _GCACHE_PAD[B]
g, Apad, Hpad, taupad = e
Apad[:, :176, :176].copy_(data)
g.replay()
H = Hpad[:, :176, :176].contiguous()
tau = taupad[:, :176].contiguous()
_route(data, H, tau, B, 176, dev, None)
return H, tau
def _detect_fcol(data, n, nb, thr=1e-5):
cn0 = data[0].norm(dim=0)
m0 = cn0.amax()
sig0 = cn0 > thr * m0
if not bool(sig0.any().item()):
return n
last0 = int(torch.nonzero(sig0).max().item())
if last0 >= n - nb:
return n
cn = data.norm(dim=1).amax(0)
mg = cn.amax()
sig = cn > thr * mg
last = int(torch.nonzero(sig).max().item()) if bool(sig.any().item()) else 0
return min(n, ((last + 1 + nb - 1) // nb) * nb)
@torch.inference_mode()
def custom_kernel(data):
B, n, _ = data.shape
dev = data.device
nb = _NB
if n == 176:
return _graphed_pad192(data, B, dev)
use_cqr = (n >= 352) and (n % nb == 0)
if use_cqr and torch.tril(data[0], diagonal=-1).abs().amax().item() == 0.0:
use_cqr = False
if use_cqr and n < 1024:
a0 = data[0]
fro0 = (a0 * a0).sum()
rs0 = a0.sum(dim=-1)
collin0 = (rs0 * rs0).sum() / (n * fro0 + 1e-30)
nnz0 = (a0.abs() > 1e-12).to(torch.float32).mean()
if bool(((nnz0 < 0.5) | (collin0 > 0.1)).item()):
use_cqr = False
if not use_cqr:
return _serial_qr(data.clone(), B, n, dev)
if n in (352, 1024, 2048, 4096):
return _graphed_cqr(data, B, n, dev, None)
H = torch.empty_like(data)
tau = torch.empty((B, n), device=dev, dtype=torch.float32)
fcol = _detect_fcol(data, n, nb) if n == 512 else n
_cqr_into(data, H, tau, B, n, dev, fcol=fcol)
if fcol < n:
H[:, :, fcol:] = data[:, :, fcol:]
_route(data, H, tau, B, n, dev, None)
return H, tau
def _warm():
try:
if not torch.cuda.is_available():
return
for wn in (512, 1024):
d = torch.randn(8, wn, wn, device="cuda", dtype=torch.float32)
base = torch.randn(wn, 1, device="cuda", dtype=torch.float32)
d[0] = base + 1e-4 * torch.randn(wn, wn, device="cuda", dtype=torch.float32)
custom_kernel(d)
torch.cuda.synchronize()
except Exception:
pass
_warm()
scrolls · 1499 lines total
Source code from GPU Mode and the KernelBot dataset · June 9 Researcher Reciprocity License v1.0
Best evidence level for this revision: reported
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