masahi commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r374431619
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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:
unless this `fast_exp` is guaranteed to give a bit identical output as libc
exp, I don't think it is a good idea to use this by default. I recommend using
something like env var to enable this.
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