def _apply_ada_max_compute(var, m, v, grad, lr, beta1, beta1_power, beta2,
epsilon):
"""Compute ada_max."""
# cast to float32 for improved accuracy
inp_dtype = var.dtype
if inp_dtype == 'float16':
var = topi.cast(var, 'float32')
m = topi.cast(m, 'float32')
v = topi.cast(v, 'float32')
lr = topi.cast(lr, 'float32')
beta1_power = topi.cast(beta1_power, 'float32')
beta1 = topi.cast(beta1, 'float32')
beta2 = topi.cast(beta2, 'float32')
grad = topi.cast(grad, 'float32')
epsilon = tvm.const(epsilon, 'float32')
# m += (grad - m) * (1 - beta1)
rhs = tvm.compute(beta1.shape,
lambda *i: beta1(*i) * neg_one_const("float32"))
rhs = tvm.compute(rhs.shape, lambda *i: rhs(*i) + one_const("float32"))
lhs = topi.subtract(grad, m)
rhs = tvm.compute(lhs.shape, lambda *i: lhs(*i) * rhs[0])
m = topi.add(m, rhs)
# v = max(beta2*v, abs(grad))
lhs = tvm.compute(v.shape, lambda *i: v(*i) * beta2[0])
rhs = topi.abs(grad)
v = topi.maximum(lhs, rhs)
# var -= lr / (1 - beta1_power) * (m / (v + epsilon))
# lr * m / (1 - beta1_power) * (v + epsilon)
# v + epsilon
rhs = tvm.compute(v.shape, lambda *i: v(*i) + epsilon)
# 1 - beta1_power
lhs = tvm.compute(beta1_power.shape,
lambda *i: beta1_power(*i) * neg_one_const("float32"))
lhs = tvm.compute(lhs.shape, lambda *i: lhs(*i) + one_const("float32"))
# (1 - beta1_power) * (v + epsilon)
rhs = tvm.compute(rhs.shape, lambda *i: rhs(*i) * lhs[0])
# lr * m
lhs = tvm.compute(m.shape, lambda *i: m(*i) * lr[0])
# lr * m / (1 - beta1_power) * (v + epsilon)
rhs = reciprocal(rhs)
rhs = topi.multiply(lhs, rhs)
var = topi.subtract(var, rhs)
if inp_dtype == 'float16':
var = topi.cast(var, inp_dtype)
m = topi.cast(m, inp_dtype)
v = topi.cast(v, inp_dtype)
return var, m, v
def _asin_compute(data_input):
"""Compute asin"""
dtype = data_input.dtype
boundary = tvm.const(BOUNDARY, "float32")
# Change dtype to float32
if dtype == "float16":
data_input = topi.cast(data_input, "float32")
# Sign mask
data_sign = sign(data_input)
# All positive
data1 = topi.multiply(data_input, data_sign)
# x belongs to (0, 2^(-0.5))
choice_1 = topi.minimum(data1, boundary)
choice_1 = topi.subtract(choice_1, boundary)
choice_1_floor = akg.lang.cce.floor(choice_1)
# the dtype of choice_1_floor is int32, need to be cast to fp32.
if utils.product_is_mini():
choice_1_floor = topi.cast(choice_1_floor, "float16")
choice_1_floor = topi.cast(choice_1_floor, "float32")
else:
choice_1_floor = topi.cast(choice_1_floor, "float32")
choice_1 = topi.multiply(choice_1_floor, neg_one_const("float32"))
taylor1 = _taylor_compute(data1)
res_1 = topi.multiply(taylor1, choice_1)
# x belongs to (2^(-0.5), 1)
choice_2 = topi.subtract(one_const("float32"), choice_1)
data2 = topi.subtract(one_const("float32"), topi.multiply(data1, data1))
data2_sqrt = _sqrt(data2)
taylor2 = _taylor_compute(data2_sqrt, data2)
res_2 = topi.multiply(taylor2, neg_one_const("float32"))
res_2 = topi.add(res_2, tvm.const(HALF_PI, "float32"))
res_2 = topi.multiply(res_2, choice_2)
# Restore sign
res_1 = topi.add(res_1, res_2)
res_1 = topi.multiply(res_1, data_sign)
# Restore dtype
if dtype == "float16":
res_1 = topi.cast(res_1, "float16")
return res_1
def _compute_mini(data_input, shape):
"""
Use log and taylor to compute
arctanh has the feature: arctanh(-abs(x)) = -arctanh(abs(x))
"""
data_abs = topi.abs(data_input)
result_ln = _compute_log(data_abs)
result_taylor = _compute_taylor(data_abs)
data_abs = topi.cast(data_abs, "float16")
data_input = topi.cast(data_input, "float16")
result_taylor = topi.cast(result_taylor, "float16")
result_ln = topi.cast(result_ln, "float16")
# when |x| < 0.5 using taylor computing, and when 0.5<|x|<1 using log()
data_res = tvm.compute(shape,
lambda *i : akg.tvm.expr.Select(data_abs(*i) < dc.half_const("float16"),
result_taylor(*i),
result_ln(*i)),
name="le")
# arctanh has the feature: arctanh(-abs(x)) = -arctanh(abs(x))
data_res_neg = topi.multiply(data_res, dc.neg_one_const("float16"))
data_res = tvm.compute(shape,
lambda *i : akg.tvm.expr.Select(data_input(*i) < dc.zero_const("float16"),
data_res_neg(*i),
data_res(*i)),
name="neg")
return data_res
def _newton_iter(data, init_x):
"""Do element-wise Newton compute."""
# Newton begin:x(n+1) = x(n)*(3-a*x(n)^2)/2
init_square = topi.multiply(init_x, init_x)
newton_res = topi.multiply(init_square, data)
newton_res = topi.multiply(newton_res, neg_one_const("float32"))
newton_res = topi.add(newton_res, tvm.const(3, "float32"))
newton_res = topi.multiply(newton_res, init_x)
newton_res = topi.multiply(newton_res, tvm.const(0.5, "float32"))
return newton_res
def _compute_m_t(m, beta, grad):
"""Update m."""
beta_tmp = tvm.compute(m.shape, lambda *indice: m(*indice) * beta[0])
beta_na = tvm.compute(
beta.shape, lambda *indice: beta(*indice) * neg_one_const("float32"))
beta_na = tvm.compute(
beta_na.shape, lambda *indice: beta_na(*indice) + one_const("float32"))
beta_sub_tmp = tvm.compute(grad.shape,
lambda *indice: grad(*indice) * beta_na[0])
m_t = topi.add(beta_tmp, beta_sub_tmp)
return m_t
def _compute_log(data_input, target=utils.CCE):
"""atanh(x) value is 0.5*log((1+x)/(1-x))"""
data_1_sum_x = topi.add(data_input, dc.one_const(data_input.dtype))
data_sub_x = topi.multiply(data_input, dc.neg_one_const(data_input.dtype))
data_1_sub_x = topi.add(data_sub_x, dc.one_const(data_input.dtype))
data_x_mul = data_1_sum_x / data_1_sub_x
data_x_log = log(data_x_mul, target)
data_res = topi.multiply(data_x_log, dc.half_const(data_input.dtype))
return data_res
def _compute_log(data_input):
"""Atanh(x) = 0.5*log((1+x)/(1-x))"""
data_1_sum_x = topi.add(data_input, dc.one_const(data_input.dtype))
data_sub_x = topi.multiply(data_input, dc.neg_one_const(data_input.dtype))
data_1_sub_x = topi.add(data_sub_x, dc.one_const(data_input.dtype))
data_x_mul = data_1_sum_x / data_1_sub_x
data_x_log = log.log(data_x_mul)
data_res = topi.multiply(data_x_log, dc.half_const(data_input.dtype))
return data_res
def _init_atan2_mask(data_y_, data_x_):
"""
Compute mask for atan2.
Args:
data_y (tvm.tensor.Tensor): The y of atan2(y, x).
data_x (tvm.tensor.Tensor): The x of atan2(y, x).
Returns:
mask (tvm.tensor.Tensor): The mask of x's and y's value.
"""
is_cast_for_mini = utils.product_is_mini() and data_y_.dtype == "float32"
# in mini, select only support float16
if is_cast_for_mini:
data_x = topi.cast(data_x_, "float16")
data_y = topi.cast(data_y_, "float16")
else:
data_x = data_x_
data_y = data_y_
dtype_input = data_y.dtype
tensor_one = dc.one_const(dtype_input)
tensor_zero = dc.zero_const(dtype_input)
tensor_neg_one = dc.neg_one_const(dtype_input)
y_ge_zero = tvm.compute(
data_y.shape,
lambda *i: tvm.expr.Select(
data_y(*i) >= tensor_zero, tensor_one, tensor_neg_one),
name="y_ge_zero")
x_lt_zero_y_mask = tvm.compute(
data_y.shape,
lambda *i: tvm.expr.Select(
data_x(*i) < tensor_zero, y_ge_zero(*i), tensor_zero),
name="xlt0_y_mask")
if is_cast_for_mini:
x_lt_zero_y_mask = topi.cast(x_lt_zero_y_mask, "float32")
y_ge_zero = topi.cast(y_ge_zero, "float32")
return (x_lt_zero_y_mask, y_ge_zero)
def erfc(input_x):
r"""
Computes the complementary error of input_x.
.. math::
\operatorname{erfc} (x) = 1 - \operatorname{erf} (x).
Args:
input_x (tvm.tensor.Tensor): Input tensor, only support float16, float32.
Returns:
tvm.tensor.Tensor with the same shape and dtype as input_x.
"""
dtype = input_x.dtype
vc_util.ops_dtype_check(dtype, vc_util.DtypeForDavinci.ALL_FLOAT)
vc_util.check_shape(input_x.shape)
erfc_res = topi.add(dc.one_const(dtype),
topi.multiply(dc.neg_one_const(dtype), erf(input_x)))
return erfc_res
def _erf_compute(input_x):
r"""
Compute erf.
.. math::
\operatorname{erf}(x) = sign(x) \left(
1 - (a_1t+a_2t^2+a_3t^3+a_4t^4+a_5t^5) e^{-x^2} + \epsilon(|x|)
\right), \\
t = \dfrac{1}{1+p|x|} \\
\left|\epsilon(|x|)\right| \le 1.5 \times 10^{-7} \\
where \; p=.3275911 \quad a_1=.254829592 \quad a_2=-.284496736 \\
a_3=1.421413741 \quad a_4=-1.453152027 \quad a_5=1.061405429
Args:
input_x (tvm.tensor.Tensor): Input tensor.
Returns:
tvm.tensor.Tensor as rational approximation.
"""
dtype = input_x.dtype
shape = get_shape(input_x)
cst_one = dc.one_const("float32")
cst_neg_one = dc.neg_one_const("float32")
cst_p = tvm.const(SCALER_P, "float32")
cst_a1 = tvm.const(SCALER_A1, "float32")
cst_a2 = tvm.const(SCALER_A2, "float32")
cst_a3 = tvm.const(SCALER_A3, "float32")
cst_a4 = tvm.const(SCALER_A4, "float32")
cst_a5 = tvm.const(SCALER_A5, "float32")
fp16_max = tvm.const(SCALER_FP16_MAX, "float32")
fp16_min = tvm.const(SCALER_FP16_MIN, "float32")
if dtype == "float16":
input_x = topi.cast(input_x, "float32")
# calculate: sign = floor[(x*fp16max) / (|x*fp16max| + fp16min)]
data_sign_vmuls = topi.multiply(input_x, fp16_max)
data_sign_abs = topi.abs(data_sign_vmuls)
data_adds = topi.add(data_sign_abs, fp16_min)
data_sign_div = div(data_sign_vmuls, data_adds)
data_round = round_value(data_sign_div)
# mini device should cast to fp16 first
if utils.product_is_mini():
data_round = topi.cast(data_round, "float16")
tensor_sign = topi.cast(data_round, "float32")
# t = 1 / (1 + px)
tensor_abs = topi.abs(input_x)
one_plus_px = topi.add(cst_one, topi.multiply(tensor_abs, cst_p))
data_t = div(topi.full(shape, "float32", 1.0), one_plus_px)
# e^{-x^2}
abs_square = topi.multiply(tensor_abs, tensor_abs)
neg_square = topi.multiply(abs_square, cst_neg_one)
exp_neg_square = exp(neg_square)
# a1t + a2t^2 + a3t^3 + a4t^4 + a5t^5 = ((((a5t + a4)t + a3)t + a2)t + a1)t
tmp_a5 = topi.multiply(cst_a5, data_t)
tmp_a5a4 = topi.multiply(topi.add(tmp_a5, cst_a4), data_t)
tmp_a5a4a3 = topi.multiply(topi.add(tmp_a5a4, cst_a3), data_t)
tmp_a5a4a3a2 = topi.multiply(topi.add(tmp_a5a4a3, cst_a2), data_t)
data_muladd = topi.multiply(topi.add(tmp_a5a4a3a2, cst_a1), data_t)
# erf = sign(x) * (1 - data_muladd * e^{-x^2})
erf_res = topi.multiply(
tensor_sign,
topi.add(
cst_one,
topi.multiply(cst_neg_one,
topi.multiply(data_muladd, exp_neg_square))))
if dtype == "float16":
erf_res = topi.cast(erf_res, dtype)
return erf_res
