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Posted to commits@tvm.apache.org by GitBox <gi...@apache.org> on 2020/01/29 16:27:52 UTC
[GitHub] [incubator-tvm] alexgl-github opened a new pull request #4790: Fast
exponent
alexgl-github opened a new pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790
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[GitHub] [incubator-tvm] FrozenGene commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
FrozenGene commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373309999
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
does MPL2 allow somebody modify the code and doesn't open source? This is critical for company using TVM. I worried about it. However, I am not the expert of open source license. Maybe @tqchen could have more authoritative answer about it. My previous meaning is if you understand it and write it by yourself, you could remove this link so that we could avoid license problem.
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[GitHub] [incubator-tvm] masahi commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375466601
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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 like @tqchen's solution. If you use cmake option it is not configurable after libtvm.so is built. It requires more work, but it can be done in later PR. This PR can be merged with topi only change including test cases.
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[GitHub] [incubator-tvm] anijain2305 commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-585489041
Right. I think `fast_exp` fits better with current naming style.
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[GitHub] [incubator-tvm] alexgl-github commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373157363
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
@FrozenGene
Eigen licence is MPL2 https://www.mozilla.org/en-US/MPL/2.0/
I wrote this TVM fastexp implementation using eigen as reference, and understand the code. Eigen github link in the comment is for the original algorithm.
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[GitHub] [incubator-tvm] alexgl-github commented on issue #4790: Fast
exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-584757028
@masahi @anijain2305 @FrozenGene Would you mind reviewing again?
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[GitHub] [incubator-tvm] anijain2305 commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r377957864
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +360,85 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+/*!
+ * \brief Fast exponential function implementation
+ *
+ * \param _x The input tensor
+ * \param name The name of the operation
+ * \param tag The tag to mark the operation
+ *
+ * \return A Tensor whose op member is exponent operation
+ *
+ * Function computes:
Review comment:
Please add \note
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[GitHub] [incubator-tvm] masahi commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-582577053
@alexgl-github tests cases are absolutely required for a new operator like this.
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[GitHub] [incubator-tvm] masahi commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-586136935
@tqchen please give an approval.
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[GitHub] [incubator-tvm] masahi commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r374431619
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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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[GitHub] [incubator-tvm] tqchen commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373702873
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,66 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+/*
+ * \brief Fast exponential function implementation
Review comment:
please add detailed comments about rguments
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[GitHub] [incubator-tvm] alexgl-github commented on issue #4790: Fast
exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-585506768
> Right. I think `fast_exp` fits better with current naming style.
@anijain2305
I've changed fastexp to fast_exp
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[GitHub] [incubator-tvm] anijain2305 commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r377958380
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +360,85 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+/*!
+ * \brief Fast exponential function implementation
+ *
+ * \param _x The input tensor
+ * \param name The name of the operation
+ * \param tag The tag to mark the operation
+ *
+ * \return A Tensor whose op member is exponent operation
+ *
+ * Function computes:
+ * 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_float32(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,
Review comment:
A high-level design question - Can we do this at Relay level? Relay can then fuse things accordingly.
@masahi
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[GitHub] [incubator-tvm] anijain2305 commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r377959246
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +360,85 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+/*!
+ * \brief Fast exponential function implementation
+ *
+ * \param _x The input tensor
+ * \param name The name of the operation
+ * \param tag The tag to mark the operation
+ *
+ * \return A Tensor whose op member is exponent operation
+ *
+ * Function computes:
+ * 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_float32(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,
Review comment:
Somewhat relevant PR was l2_normalize where unfolding at Relay leads to much better performance - https://github.com/apache/incubator-tvm/pull/4795
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[GitHub] [incubator-tvm] anijain2305 commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-586511407
Lets get this in - @tqchen
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[GitHub] [incubator-tvm] tqchen merged pull request #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen merged pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790
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[GitHub] [incubator-tvm] zhiics commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
zhiics commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-584925474
I have some silly questions: when should we switch to the fast_exp since it is in topi? Do we expect users to select it? Does this mean that this op is only available in topi, but not Relay?
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[GitHub] [incubator-tvm] tqchen commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375464140
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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:
Perhaps a better way would be have a separate operator `fast_exp`, then have a pass(fast-math) in relay to rewrite the exp into the fast_exp
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[GitHub] [incubator-tvm] anijain2305 commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-585443948
Can this get in? I will work on Relay changes.
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[GitHub] [incubator-tvm] anijain2305 commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-585485172
@tqchen @FrozenGene Can you please check if the changes you requested are addressed?
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[GitHub] [incubator-tvm] masahi commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-586890882
ping @tqchen
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[GitHub] [incubator-tvm] alexgl-github commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373157363
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
@FrozenGene
Eigen licence is MPL2 https://www.mozilla.org/en-US/MPL/2.0/
I wrote this fastexp implementation and understand the code. Eigen github link in the comment is for algorithm reference.
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[GitHub] [incubator-tvm] masahi commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
masahi commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375470574
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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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[GitHub] [incubator-tvm] alexgl-github commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375425157
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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:
@masahi It's not identical.
Relative fast exp error vs Tensorflow exp is between [-4.52e-06, 4.17e-06]
Relative fast exp error vs Numpy exp is [-3.11e-06, 3.10e-06]
How about using it only if enabled via cmake option?
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[GitHub] [incubator-tvm] anijain2305 commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375563628
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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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[GitHub] [incubator-tvm] tqchen commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-587092625
Thanks @alexgl-github @anijain2305 @masahi @FrozenGene !
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[GitHub] [incubator-tvm] FrozenGene commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
FrozenGene commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r372741774
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
What is the license of libeigen? If you understand and write the code by yourself, could remove it.
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[GitHub] [incubator-tvm] FrozenGene commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
FrozenGene commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r378637381
##########
File path: topi/python/topi/math.py
##########
@@ -449,3 +449,19 @@ def reinterpret(x, dtype):
The result.
"""
return cpp.reinterpret(x, dtype)
+
+
+def fast_exp(x):
+ """Take exponential of input x using fastexp implementation
Review comment:
fastexp -> fast_exp
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[GitHub] [incubator-tvm] anijain2305 commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
anijain2305 commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r375563628
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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.
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[GitHub] [incubator-tvm] tqchen commented on issue #4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-585487279
Overall looks OK, it would be great if we can decide a consistent naming convention. In this case, we can have `fastexp` vs `fast_exp`
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[GitHub] [incubator-tvm] tqchen commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373583565
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
The code in the main repo need to be licensed under ASv2.
If the code comes from a difference license, We will need to put the code in the thirdparty and specify the license clearly. If we reference an existing algorithm and is implemented from scratch. It is better to declare ASv2
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[GitHub] [incubator-tvm] alexgl-github commented on a change in pull request
#4790: Fast exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373624561
##########
File path: topi/include/topi/elemwise.h
##########
@@ -360,5 +359,71 @@ inline Tensor full_like(const Tensor& x,
}, name, tag);
}
+ /*
+ * \brief Fast exponential function implementation from Eigen
+ * https://github.com/eigenteam/eigen-git-mirror/blob/master/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h#L183
Review comment:
Please see updated fast_exp implementation.
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[GitHub] [incubator-tvm] alexgl-github commented on issue #4790: Fast
exponent
Posted by GitBox <gi...@apache.org>.
alexgl-github commented on issue #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#issuecomment-584949689
> I have some silly questions: when should we switch to the fast_exp since it is in topi? Do we expect users to select it? Does this mean that this op is only available in topi, but not Relay?
@zhiics In a separate PR we'll introduce relay optimization pass that should select fast_exp if opt_level=4
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[GitHub] [incubator-tvm] tqchen commented on a change in pull request #4790:
Fast exponent
Posted by GitBox <gi...@apache.org>.
tqchen commented on a change in pull request #4790: Fast exponent
URL: https://github.com/apache/incubator-tvm/pull/4790#discussion_r373702986
##########
File path: topi/include/topi/elemwise.h
##########
@@ -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,
Review comment:
please add doxygen comments for the function
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