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/* Copyright 2017 The TensorFlow Authors. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
==============================================================================*/
#include "tensorflow/compiler/xla/client/lib/arithmetic.h"
#include <string>
#include "tensorflow/compiler/xla/client/xla_client/xla_builder.h"
#include "tensorflow/compiler/xla/client/xla_client/xla_computation.h"
#include "tensorflow/compiler/xla/shape_util.h"
#include "tensorflow/compiler/xla/status_macros.h"
#include "tensorflow/compiler/xla/types.h"
#include "tensorflow/compiler/xla/xla_data.pb.h"
#include "tensorflow/core/lib/strings/strcat.h"
namespace xla {
namespace {
using XlaOpGenerator = XlaOp (*)(XlaBuilder*, const XlaOp&, const XlaOp&);
XlaComputation CreateScalarComputation(const string& name, PrimitiveType type,
XlaBuilder* builder,
XlaOpGenerator generator) {
std::unique_ptr<XlaBuilder> b;
if (type == PRED) {
b = builder->CreateSubBuilder(name);
} else {
b = builder->CreateSubBuilder(
tensorflow::strings::StrCat(name, "_", PrimitiveType_Name(type)));
}
const Shape scalar = ShapeUtil::MakeShape(type, {});
auto lhs = Parameter(b.get(), 0, scalar, "lhs");
auto rhs = Parameter(b.get(), 1, scalar, "rhs");
generator(b.get(), lhs, rhs);
return b->BuildAndNoteError();
}
} // namespace
XlaComputation CreateScalarAddComputation(PrimitiveType type,
XlaBuilder* builder) {
return CreateScalarComputation(
"add", type, builder,
[](XlaBuilder* b, const XlaOp& lhs, const XlaOp& rhs) {
return Add(lhs, rhs);
});
}
XlaComputation CreateScalarMultiplyComputation(PrimitiveType type,
XlaBuilder* builder) {
return CreateScalarComputation(
"mul", type, builder,
[](XlaBuilder* b, const XlaOp& lhs, const XlaOp& rhs) {
return Mul(lhs, rhs);
});
}
XlaComputation CreateScalarGeComputation(PrimitiveType type,
XlaBuilder* builder) {
return CreateScalarComputation("ge", type, builder,
[](XlaBuilder* b, const XlaOp& lhs,
const XlaOp& rhs) { return Ge(lhs, rhs); });
}
XlaComputation CreateScalarMaxComputation(PrimitiveType type,
XlaBuilder* builder) {
return CreateScalarComputation(
"max", type, builder,
[](XlaBuilder* b, const XlaOp& lhs, const XlaOp& rhs) {
return Max(lhs, rhs);
});
}
XlaComputation CreateScalarMinComputation(PrimitiveType type,
XlaBuilder* builder) {
return CreateScalarComputation(
"min", type, builder,
[](XlaBuilder* b, const XlaOp& lhs, const XlaOp& rhs) {
return Min(lhs, rhs);
});
}
XlaComputation CreateScalarAndComputation(XlaBuilder* builder) {
return CreateScalarComputation(
"and", PRED, builder,
[](XlaBuilder* b, const XlaOp& lhs, const XlaOp& rhs) {
return And(lhs, rhs);
});
}
XlaComputation CreateScalarOrComputation(XlaBuilder* builder) {
return CreateScalarComputation("or", PRED, builder,
[](XlaBuilder* b, const XlaOp& lhs,
const XlaOp& rhs) { return Or(lhs, rhs); });
}
XlaOp Any(XlaOp predicates) {
XlaBuilder* builder = predicates.builder();
return builder->ReportErrorOrReturn([&]() -> StatusOr<XlaOp> {
auto f = ConstantR0<bool>(builder, false);
XlaComputation logical_or = CreateScalarOrComputation(builder);
TF_ASSIGN_OR_RETURN(const Shape& predicates_shape,
builder->GetShape(predicates));
std::vector<int64> all_dimensions(ShapeUtil::Rank(predicates_shape));
std::iota(all_dimensions.begin(), all_dimensions.end(), 0);
return Reduce(predicates, f, logical_or, all_dimensions);
});
}
namespace {
XlaOp FloatLiteral(XlaBuilder* b, PrimitiveType data_type, float value) {
return ConvertElementType(ConstantR0(b, value), data_type);
}
// Polynomials for computing erf/erfc. Originally from cephes.
// Note we use float for compatibility across devices, at the cost of some
// precision for 64 bit computations.
//
// Coefficients are in descending order.
std::array<float, 9> kErfcPCoefficient = {
2.46196981473530512524E-10, 5.64189564831068821977E-1,
7.46321056442269912687E0, 4.86371970985681366614E1,
1.96520832956077098242E2, 5.26445194995477358631E2,
9.34528527171957607540E2, 1.02755188689515710272E3,
5.57535335369399327526E2};
std::array<float, 9> kErfcQCoefficient = {
1.00000000000000000000E0, 1.32281951154744992508E1,
8.67072140885989742329E1, 3.54937778887819891062E2,
9.75708501743205489753E2, 1.82390916687909736289E3,
2.24633760818710981792E3, 1.65666309194161350182E3,
5.57535340817727675546E2};
std::array<float, 6> kErfcRCoefficient = {
5.64189583547755073984E-1, 1.27536670759978104416E0,
5.01905042251180477414E0, 6.16021097993053585195E0,
7.40974269950448939160E0, 2.97886665372100240670E0};
std::array<float, 7> kErfcSCoefficient = {
1.00000000000000000000E0, 2.26052863220117276590E0,
9.39603524938001434673E0, 1.20489539808096656605E1,
1.70814450747565897222E1, 9.60896809063285878198E0,
3.36907645100081516050E0};
std::array<float, 5> kErfTCoefficient = {
9.60497373987051638749E0, 9.00260197203842689217E1,
2.23200534594684319226E3, 7.00332514112805075473E3,
5.55923013010394962768E4};
std::array<float, 6> kErfUCoefficient = {
1.00000000000000000000E0, 3.35617141647503099647E1,
5.21357949780152679795E2, 4.59432382970980127987E3,
2.26290000613890934246E4, 4.92673942608635921086E4};
} // namespace
// Evaluate the polynomial given coefficients and `x`.
// N.B. Coefficients should be supplied in decreasing order.
XlaOp EvaluatePolynomial(XlaOp x,
tensorflow::gtl::ArraySlice<float> coefficients,
PrimitiveType data_type) {
XlaBuilder* b = x.builder();
XlaOp poly = FloatLiteral(b, data_type, 0.0);
for (float c : coefficients) {
poly = Add(Mul(poly, x), FloatLiteral(b, data_type, c));
}
return poly;
}
// Compute an approximation of the error function complement (1 - erf(x)).
XlaOp Erfc(XlaOp x, PrimitiveType data_type) {
XlaBuilder* b = x.builder();
XlaOp zero = FloatLiteral(b, data_type, 0.0);
XlaOp two = FloatLiteral(b, data_type, 2.0);
XlaOp eight = FloatLiteral(b, data_type, 8.0);
XlaOp abs_x = Abs(x);
XlaOp z = Exp(Mul(Neg(x), x));
XlaOp pp = EvaluatePolynomial(abs_x, kErfcPCoefficient, data_type);
XlaOp pq = EvaluatePolynomial(abs_x, kErfcQCoefficient, data_type);
XlaOp pr = EvaluatePolynomial(abs_x, kErfcRCoefficient, data_type);
XlaOp ps = EvaluatePolynomial(abs_x, kErfcSCoefficient, data_type);
XlaOp y = Select(Lt(abs_x, eight), Div(Mul(z, pp), pq), Div(Mul(z, pr), ps));
return Select(Lt(x, zero), Sub(two, y), y);
}
// Compute a polynomial approximation of the error function.
XlaOp Erf(XlaOp x, PrimitiveType data_type) {
XlaOp z = Mul(x, x);
XlaOp pt = EvaluatePolynomial(z, kErfTCoefficient, data_type);
XlaOp pu = EvaluatePolynomial(z, kErfUCoefficient, data_type);
return Div(Mul(x, pt), pu);
}
// Approximation for the inverse error function from
// Giles, M., "Approximating the erfinv function".
// The approximation has the form:
// w = -log((1 - x) * (1 + x))
// if ( w < 5 ) {
// w = w - 2.5
// p = sum_{i=1}^n lq[i]*w^i
// } else {
// w = sqrt(w) - 3
// p = sum_{i=1}^n gq[i]*w^i
// }
// return p*x
XlaOp ErfInv(XlaOp x) {
XlaBuilder* b = x.builder();
return b->ReportErrorOrReturn([&]() -> StatusOr<XlaOp> {
TF_ASSIGN_OR_RETURN(Shape shape, b->GetShape(x));
constexpr int kDegree = 9;
constexpr std::array<float, 9> w_less_than_5_constants = {
2.81022636e-08f, 3.43273939e-07f, -3.5233877e-06f,
-4.39150654e-06f, 0.00021858087f, -0.00125372503f,
-0.00417768164f, 0.246640727f, 1.50140941f};
constexpr std::array<float, 9> w_greater_than_5_constants = {
-0.000200214257f, 0.000100950558f, 0.00134934322f,
-0.00367342844f, 0.00573950773f, -0.0076224613f,
0.00943887047f, 1.00167406f, 2.83297682f};
auto one = ConstantR0<float>(b, 1.0);
auto w = Neg(Log(Mul(Sub(one, x), Add(one, x))));
auto lt = Lt(w, ConstantR0<float>(b, 5.0));
auto coefficient = [&](int i) {
return Select(
lt,
Broadcast(ConstantR0<float>(b, w_less_than_5_constants[i]),
AsInt64Slice(shape.dimensions())),
Broadcast(ConstantR0<float>(b, w_greater_than_5_constants[i]),
AsInt64Slice(shape.dimensions())));
};
w = Select(lt, Sub(w, ConstantR0<float>(b, 2.5f)),
Sub(SqrtF32(w), ConstantR0<float>(b, 3.0f)));
auto p = coefficient(0);
for (int i = 1; i < kDegree; ++i) {
p = Add(coefficient(i), Mul(p, w));
}
return Mul(p, x);
});
}
} // namespace xla
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