#define HALF_MAX_HALF __float2half(65504.0f/2) // Use neg. of this instead of -INFINITY to initialize KQ max vals to avoid NaN upon subtraction.
#define SOFTMAX_FTZ_THRESHOLD -20.0f // Softmax exp. of values smaller than this are flushed to zero to avoid NaNs.
+// log(2) = 0.6931, by adding this to the KQ maximum used for the softmax the numerical range representable
+// by the VKQ accumulators is effectively being shifted up by a factor of 8.
+// This reduces issues with numerical overflow but also causes larger values to be flushed to zero.
+// However, as the output from FlashAttention will usually be used as an input for a matrix multiplication this should be negligible.
+#define FATTN_KQ_MAX_OFFSET 0.6931f
+
typedef void (* fattn_kernel_t)(
const char * __restrict__ Q,
const char * __restrict__ K,
#pragma unroll
for (int l = 0; l < T_C_KQ::ne; ++l) {
if (!oob_check || k0 + T_C_KQ::get_i(l) < k_VKQ_sup) {
- KQ_max_new[l % 2] = fmaxf(KQ_max_new[l % 2], KQ_C[k0/(np*T_C_KQ::I)].x[l]);
+ KQ_max_new[l % 2] = fmaxf(KQ_max_new[l % 2], KQ_C[k0/(np*T_C_KQ::I)].x[l] + FATTN_KQ_MAX_OFFSET);
}
}
}
for (int l = 0; l < T_C_KQ::ne; ++l) {
if (!oob_check || k0 + T_C_KQ::get_j(l) < k_VKQ_sup) {
// Turing + Volta:
- KQ_max_new[(l/2) % 2] = fmaxf(KQ_max_new[(l/2) % 2], KQ_C[(k0/(np*T_C_KQ::J))].x[l]);
+ KQ_max_new[(l/2) % 2] = fmaxf(KQ_max_new[(l/2) % 2], KQ_C[(k0/(np*T_C_KQ::J))].x[l] + FATTN_KQ_MAX_OFFSET);
}
}
}
KQ_acc[(i_KQ_0/(np*warp_size))*cpw + jc0] += (ncols2 > 1 || mask) ?
slope*__half2float(mask[j*stride_mask + k_VKQ_0 + i_KQ]) : 0.0f;
- KQ_max_new[jc0] = fmaxf(KQ_max_new[jc0], KQ_acc[(i_KQ_0/(np*warp_size))*cpw + jc0]);
+ KQ_max_new[jc0] = fmaxf(KQ_max_new[jc0], KQ_acc[(i_KQ_0/(np*warp_size))*cpw + jc0] + FATTN_KQ_MAX_OFFSET);
}
}
sum += slope*__half2float(maskh[j*ne11 + i_KQ]);
}
- KQ_max_new[j] = fmaxf(KQ_max_new[j], sum);
+ KQ_max_new[j] = fmaxf(KQ_max_new[j], sum + FATTN_KQ_MAX_OFFSET);
if ((nthreads_KQ == WARP_SIZE ? threadIdx.x : threadIdx.x % nthreads_KQ) == uint32_t(i_KQ_0)) {
KQ_reg[j] = sum;
KQ_f_tmp[k0/warp_size] += mask && ic0 + j < int(ne01.z) ?
__half2float(slopeh*maskh[j*(nb31/sizeof(half)) + k_VKQ_0 + k]) : 0.0f;
- KQ_max_new = max(KQ_max_new, KQ_f_tmp[k0/warp_size]);
+ KQ_max_new = max(KQ_max_new, KQ_f_tmp[k0/warp_size] + FATTN_KQ_MAX_OFFSET);
}
KQ_max_new = warp_reduce_max<warp_size>(KQ_max_new);