masahi commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375470574
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File path: topi/include/topi/elemwise.h
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@@ -360,5 +359,66 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+/*
+ * \brief Fast exponential function implementation
+ * log2(e^x) = x * log2(e) * log2(2) =>
+ * log2(e^x) = log2(2^(x*log2(e))) =>
+ * e^x = 2^(x*log2(e))
+ * Splitting power x*log2(e) into integer and fractional parts:
+ * e^(n+f) = e^n * e^f
+ * n = floor(x*log2(e) + 1/2)
+ * f = x - n * ln(2)
+ * exp(x) = 2^n * exp(y)
+ * Approximation for fractional part:
+ * y = exp(f) = 1 + 2 * P(x**2)/(Q(x**2) - P(x**2))
+ */
+inline Tensor fast_exp(const Tensor& _x,
+ std::string name,
+ std::string tag) {
+ auto x_hi = make_const(DataType::Float(32), 88.3762626647950f);
+ auto x_lo = make_const(DataType::Float(32), -88.3762626647949f);
+ auto log2e = make_const(DataType::Float(32), 1.44269504088896341f);
+ auto ln2 = make_const(DataType::Float(32), 0.6931471805599453f);
+ PrimExpr p[6] = {make_const(DataType::Float(32), 1.9875691500E-4f),
+ make_const(DataType::Float(32), 1.3981999507E-3f),
+ make_const(DataType::Float(32), 8.3334519073E-3f),
+ make_const(DataType::Float(32), 4.1665795894E-2f),
+ make_const(DataType::Float(32), 1.6666665459E-1f),
+ make_const(DataType::Float(32), 5.0000001201E-1f)};
+ auto one = make_const(DataType::Float(32), 1.0f);
+ auto one_half = make_const(DataType::Float(32), 0.5f);
+ auto b = make_const(DataType::Float(32), 127.0f);
+
+ return compute(_x->shape,
+ [&](const Array<Var>& i) {
+ // clamp x
+ auto x = ::tvm::max(::tvm::min(_x(i), x_hi), x_lo);
+ // integer part
+ auto n = ::tvm::floor(x * log2e + one_half);
+ // fractional part
+ auto f = x - n * ln2;
+ auto y = (((((p[0] * f + p[1]) * f + p[2]) * f + p[3])* f+
p[4]) * f
+ + p[5]) * f* f + f + one;
+ // Return 2^m * exp(r).
+ auto ef = tvm::reinterpret(DataType::Float(32),
+ ::tvm::cast(DataType::Int(32), n
+ b) << 23);
+ return ::tvm::max(ef * y, _x(i)); // NOLINT(*)
+ },
+ name, tag);
+}
+
+
+inline Tensor exp(const Tensor& x,
+ std::string name = "T_exp",
+ std::string tag = kElementWise) {
+ if (x->dtype == DataType::Float(32)) {
+ return fast_exp(x, name, tag);
Review comment:
I know what I am talking about here because I also did fast_exp for my
internal work in the past. Accurate exp is very slow and the high accuracy is
not required for inference. The biggest benefit is it enables vectorization if
it is written in topi (in my case it was HalideIR). Vectorizing exp was the
main reason to introduce op fusion improvement in
https://github.com/apache/incubator-tvm/pull/1548
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