| import triton |
| import triton.language as tl |
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| inv_ln2 = 1.44269504 |
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| @triton.jit |
| def fwd_decay_cumsum( |
| g, |
| g_o, |
| s_qk_h, |
| s_qk_t, |
| s_qk_d, |
| B, |
| H, |
| T, |
| scale, |
| BT: tl.constexpr, |
| BK: tl.constexpr, |
| DK: tl.constexpr |
| ): |
| i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
| p_g = g + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| p_go = g_o + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| cum_decay = tl.zeros([BK], dtype=tl.float32) |
| mask = (i_k * BK + tl.arange(0, BK)) < DK |
|
|
| for i in range(BT): |
| _g = tl.load(p_g, mask=mask, other=0).to(tl.float32) |
| cum_decay += _g * inv_ln2 |
| tl.store(p_go, cum_decay.to(p_go.dtype.element_ty), mask=mask) |
| p_g += DK |
| p_go += DK |
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|
| @triton.jit |
| def prepare_qg_kg( |
| q, |
| k, |
| g, |
| qg, |
| kg, |
| s_qk_h, |
| s_qk_t, |
| s_qk_d, |
| B, |
| H, |
| T, |
| scale, |
| BT: tl.constexpr, |
| BK: tl.constexpr, |
| DK: tl.constexpr |
| ): |
|
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| i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
| p_q = q + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| p_g = g + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| p_k = k + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| p_qg = qg + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| p_kg = kg + i_bh * s_qk_h + i_c * BT * DK + i_k * BK + tl.arange(0, BK) |
| |
| mask = (i_k * BK + tl.arange(0, BK)) < DK |
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| last_decay = tl.load(g + i_bh * s_qk_h + (i_c * BT + BT - 1) * DK + i_k * BK + tl.arange(0, BK)) |
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| for i in range(BT): |
| _q = tl.load(p_q, mask=mask, other=0) |
| _k = tl.load(p_k, mask=mask, other=0) |
| _g = tl.load(p_g, mask=mask, other=0).to(tl.float32) |
| _q *= tl.math.exp2(_g) * scale |
| _k *= tl.math.exp2(last_decay - _g) |
| tl.store(p_kg, _k.to(p_kg.dtype.element_ty), mask=mask) |
| tl.store(p_qg, _q.to(p_qg.dtype.element_ty), mask=mask) |
| p_q += DK |
| p_g += DK |
| p_k += DK |
| p_kg += DK |
| p_qg += DK |
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| @triton.jit |
| def bwd_decay_global_cumsum( |
| dq_inner, |
| dq_inter, |
| dk_inner, |
| dk_inter, |
| q, k, g, dg, |
| s_qk_h, |
| s_qk_t, |
| s_qk_d, |
| B, |
| H, |
| T, |
| scale, |
| BT: tl.constexpr, |
| BK: tl.constexpr, |
| DK: tl.constexpr |
| ): |
| i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
| p_q = q + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_k = k + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_g = g + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_dg = dg + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_dq_inner = dq_inner + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_dk_inner = dk_inner + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_dq_inter = dq_inter + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| p_dk_inter = dk_inter + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (i_c * BT + BT - 1) * DK |
| cum_grad_dg = tl.zeros([BK], dtype=tl.float32) |
| mask = (i_k * BK + tl.arange(0, BK)) < DK |
| last_g = tl.zeros([BK], dtype=tl.float32) |
| for j in range(BT-1, -1, -1): |
| _g = tl.load(p_g, mask=mask, other=0).to(tl.float32) |
| if j == (BT-1): |
| last_g = _g |
| _dq1 = tl.load(p_dq_inner, mask=mask, other=0) |
| _dq2 = tl.load(p_dq_inter, mask=mask, other=0) |
| _dq2 *= tl.math.exp2(_g) |
| _dq = _dq1 + _dq2 |
| tl.store(p_dq_inter, _dq, mask=mask) |
| _dk1 = tl.load(p_dk_inner, mask=mask, other=0) |
| _dk2 = tl.load(p_dk_inter, mask=mask, other=0) |
| _dk2 *= tl.math.exp2(last_g - _g) |
| _dk = _dk1 + _dk2 |
| tl.store(p_dk_inter, _dk, mask=mask) |
| _q = tl.load(p_q, mask=mask, other=0) |
| _k = tl.load(p_k, mask=mask, other=0) |
| _dg = _dq * _q - _dk * _k |
| cum_grad_dg += _dg |
| tl.store(p_dg, cum_grad_dg.to(p_dg.dtype.element_ty), mask=mask) |
| p_g -= DK |
| p_k -= DK |
| p_q -= DK |
| p_dq_inner -= DK |
| p_dk_inner -= DK |
| p_dq_inter -= DK |
| p_dk_inter -= DK |
| p_dg -= DK |
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