initial commit for float16

paddle/math/float16.h

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+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. */
+
+#pragma once
+
+#include <cstdint>
+#include <istream>
+#include <ostream>
+
+#include <cuda.h>
+
+#ifdef __arm__
+#define PADDLE_ARM_32
+#endif
+
+#ifdef __aarch64__
+#define PADDLE_ARM_64
+#endif
+
+#if defined(PADDLE_ARM_32) || defined(PADDLE_ARM_64)
+#define PADDLE_ARM
+#endif
+
+#if defined(__ARM_NEON) || defined(__ARM_NEON__)
+#define PADDLE_NEON
+#endif
+
+#if defined(PADDLE_NEON) && defined(PADDLE_ARM_32)
+#define PADDLE_NEON_32
+#endif
+
+#if defined(PADDLE_NEON) && defined(PADDLE_ARM_64)
+#define PADDLE_NEON_64
+#endif
+
+#ifdef __CUDA_ARCH__  // use __CUDACC__ instead
+#define PADDLE_HOSTDEVICE __host__ __device__
+#if CUDA_VERSION >= 7050
+#define PADDLE_CUDA_FP16
+#include <cuda_fp16.h>
+#endif  // CUDA_VERSION >= 7050
+#else
+#define PADDLE_HOSTDEVICE
+#endif  // __CUDA_ARCH__
+
+#if !defined(__ANDROID__) && !defined(__APPLE__) && !defined(PADDLE_ARM)
+#include <immintrin.h>
+#else
+#ifdef __F16C__
+#undef __F16C__
+#endif
+#endif
+
+#define PADDLE_ALIGNED(x) __attribute__((aligned(x)))
+
+// https://github.com/pytorch/pytorch/blob/master/torch/lib/ATen/Half.h
+template <typename To, typename From>
+To convert(From f) {
+  return static_cast<To>(f);
+}
+
+namespace paddle {
+
+class float16;
+
+// convert from float to half precision in round-to-nearest-even mode
+float16 float2half_rn(float f);
+float half2float(float16 h);
+
+class float16 {
+public:
+  uint16_t val_;
+
+  PADDLE_HOSTDEVICE inline explicit float16() : x(0) {}
+
+  PADDLE_HOSTDEVICE inline explicit float16(float val) {
+    float16 res = float2half_rn(val);
+    x = res.x;
+  }
+
+  PADDLE_HOSTDEVICE inline explicit float16(int val) {
+    float16 res = cpu_float2half_rn(static_cast<float>(val));
+    x = res.x;
+  }
+
+  PADDLE_HOSTDEVICE inline explicit float16(double val) {
+    float16 res = cpu_float2half_rn(static_cast<float>(val));
+    x = res.x;
+  }
+
+  // Use PADDLE_ALIGNED(2) to ensure that each float16 will be allocated
+  // and aligned at least on a 2-byte boundary, which leads to efficient
+  // memory access of float16 struct.
+} PADDLE_ALIGNED(2);
+
+namespace fp16_impl {
+
+// Conversion routine adapted from
+// http://stackoverflow.com/questions/1659440/32-bit-to-16-bit-floating-point-conversion
+Union Bits {
+  float f;
+  int32_t si;
+  uint32_t ui;
+};
+
+static const int shift = 13;
+static const int shiftSign = 16;
+
+static const int32_t infN = 0x7F800000;
+static const int32_t maxN = 0x477FE000;  // max flt16 as flt32
+static const int32_t minN = 0x38800000;  // min flt16 normal as flt32
+static const int32_t sigN = 0x80000000;  // sign bit
+
+static constexpr int32_t infC = infN >> shift;
+static constexpr int32_t nanN = (infC + 1)
+                                << shift;  // minimum flt16 nan as float32
+static constexpr int32_t maxC = maxN >> shift;
+static constexpr int32_t minC = minN >> shift;
+static constexpr int32_t sigC = sigN >> shiftSign;
+
+static const int32_t mulN = 0x52000000;  //(1 << 23) / minN
+static const int32_t mulC = 0x33800000;  // minN / (1 << (23 - shift))
+static const int32_t subC = 0x003FF;     // max flt32 subnormal downshifted
+static const int32_t norC = 0x00400;     // min flt32 normal downshifted
+
+static constexpr int32_t maxD = infC - maxC - 1;
+static constexpr int32_t minD = minC - subC - 1;
+
+}  // namespace half_impl
+
+}  // namespace paddle