anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375563628
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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:
How about having 3 new relay contrib operators - contrib.fast_exp,
contrib.fast_tanh, contrib.fast_softmax. We can then add a Relay pass with
opt_level 4, that legalizes these functions to their approximate counterparts.
Edit - Sorry should have told why these 3. For softmax, we are essentially
playing with exp op. Softmax takes substantial time in SSD models, where input
shape is very large. For tanh, we already have a fast_tanh that is enabled by
default. We should change that.
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