Add build files and meta data files am: 0391e51efc am: 534fd519ca
Change-Id: Icf306ff666f160b01192523fe4a4e7ce44f6e558
diff --git a/Android.bp b/Android.bp
new file mode 100644
index 0000000..e58f54f
--- /dev/null
+++ b/Android.bp
@@ -0,0 +1,113 @@
+// Copyright (C) 2020 The Android Open Source Project
+//
+// 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.
+
+cc_library_headers {
+ name: "fp16_headers",
+ export_include_dirs: ["include"],
+ vendor_available: true,
+ sdk_version: "current",
+}
+
+cc_defaults {
+ name: "fp16_tests_default",
+ sdk_version: "current",
+ srcs: [
+ "test/tables.cc",
+ ],
+ header_libs: [
+ "fp16_headers",
+ ],
+ stl: "libc++_static",
+ static_libs: [
+ "libgmock_ndk",
+ ]
+}
+
+cc_test {
+ name: "Fp16AltFromFp32ValueTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/alt-from-fp32-value.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16AltToFp32BitsTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/alt-to-fp32-bits.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16AltToFp32ValueTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/alt-to-fp32-value.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16BitcastsTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/bitcasts.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16IEEEFromFp32ValueTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/ieee-from-fp32-value.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16IEEEToFp32BitsTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/ieee-to-fp32-bits.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
+cc_test {
+ name: "Fp16IEEEToFp32ValueTests",
+ defaults: ["fp16_tests_default"],
+ srcs: [
+ "test/ieee-to-fp32-value.cc",
+ ],
+ test_suites: [
+ "general-tests",
+ ],
+}
+
diff --git a/METADATA b/METADATA
new file mode 100644
index 0000000..dd36746
--- /dev/null
+++ b/METADATA
@@ -0,0 +1,18 @@
+name: "FP16"
+description:
+ "Header-only library for conversion to/from half-precision floating point "
+ "formats"
+
+third_party {
+ url {
+ type: HOMEPAGE
+ value: "https://github.com/Maratyszcza/FP16"
+ }
+ url {
+ type: GIT
+ value: "https://github.com/Maratyszcza/FP16"
+ }
+ version: "ba1d31f5eed2eb4a69e4dea3870a68c7c95f998f"
+ last_upgrade_date { year: 2020 month: 2 day: 3 }
+ license_type: NOTICE
+}
diff --git a/MODULE_LICENSE_MIT b/MODULE_LICENSE_MIT
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/MODULE_LICENSE_MIT
diff --git a/NOTICE b/NOTICE
new file mode 120000
index 0000000..7a694c9
--- /dev/null
+++ b/NOTICE
@@ -0,0 +1 @@
+LICENSE
\ No newline at end of file
diff --git a/TEST_MAPPING b/TEST_MAPPING
new file mode 100644
index 0000000..b03f7be
--- /dev/null
+++ b/TEST_MAPPING
@@ -0,0 +1,25 @@
+{
+ "presubmit": [
+ {
+ "name": "Fp16AltFromFp32ValueTests"
+ },
+ {
+ "name": "Fp16AltToFp32BitsTests"
+ },
+ {
+ "name": "Fp16AltToFp32ValueTests"
+ },
+ {
+ "name": "Fp16BitcastsTests"
+ },
+ {
+ "name": "Fp16IEEEFromFp32ValueTests"
+ },
+ {
+ "name": "Fp16IEEEToFp32BitsTests"
+ },
+ {
+ "name": "Fp16IEEEToFp32ValueTests"
+ }
+ ]
+}
diff --git a/jni/Android.mk b/jni/Android.mk
deleted file mode 100644
index 9e58bd8..0000000
--- a/jni/Android.mk
+++ /dev/null
@@ -1,6 +0,0 @@
-LOCAL_PATH := $(call my-dir)/..
-
-include $(CLEAR_VARS)
-LOCAL_MODULE := FP16
-LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/include
-include $(BUILD_STATIC_LIBRARY)
diff --git a/jni/Application.mk b/jni/Application.mk
deleted file mode 100644
index 0f660e3..0000000
--- a/jni/Application.mk
+++ /dev/null
@@ -1,4 +0,0 @@
-APP_PLATFORM := android-15
-APP_PIE := true
-APP_STL := c++_static
-APP_ABI := all
diff --git a/test/alt-from-fp32-value.cc b/test/alt-from-fp32-value.cc
index 61fd35e..b8272f6 100644
--- a/test/alt-from-fp32-value.cc
+++ b/test/alt-from-fp32-value.cc
@@ -3,7 +3,7 @@
#include <cstdint>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
#if (defined(__i386__) || defined(__x86_64__)) && defined(__F16C__)
#include <x86intrin.h>
diff --git a/test/alt-to-fp32-bits.cc b/test/alt-to-fp32-bits.cc
index f5b61a5..09bdd95 100644
--- a/test/alt-to-fp32-bits.cc
+++ b/test/alt-to-fp32-bits.cc
@@ -3,7 +3,7 @@
#include <cstdint>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
TEST(FP16_ALT_TO_FP32_BITS, normalized_powers_of_2) {
diff --git a/test/alt-to-fp32-value.cc b/test/alt-to-fp32-value.cc
index b9d880e..6277576 100644
--- a/test/alt-to-fp32-value.cc
+++ b/test/alt-to-fp32-value.cc
@@ -4,7 +4,7 @@
#include <cmath>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
TEST(FP16_ALT_TO_FP32_VALUE, normalized_powers_of_2) {
diff --git a/test/ieee-from-fp32-value.cc b/test/ieee-from-fp32-value.cc
index 8e074bc..24e3e7e 100644
--- a/test/ieee-from-fp32-value.cc
+++ b/test/ieee-from-fp32-value.cc
@@ -3,7 +3,7 @@
#include <cstdint>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
#if (defined(__i386__) || defined(__x86_64__)) && defined(__F16C__)
#include <x86intrin.h>
diff --git a/test/ieee-to-fp32-bits.cc b/test/ieee-to-fp32-bits.cc
index 284e1b1..807ef4a 100644
--- a/test/ieee-to-fp32-bits.cc
+++ b/test/ieee-to-fp32-bits.cc
@@ -3,7 +3,7 @@
#include <cstdint>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
TEST(FP16_IEEE_TO_FP32_BITS, normalized_powers_of_2) {
diff --git a/test/ieee-to-fp32-value.cc b/test/ieee-to-fp32-value.cc
index 5258e92..d69faae 100644
--- a/test/ieee-to-fp32-value.cc
+++ b/test/ieee-to-fp32-value.cc
@@ -4,7 +4,7 @@
#include <cmath>
#include <fp16.h>
-#include <tables.h>
+#include "tables.h"
TEST(FP16_IEEE_TO_FP32_VALUE, normalized_powers_of_2) {
diff --git a/test/tables.cc b/test/tables.cc
index 82d6ef5..5f4e877 100644
--- a/test/tables.cc
+++ b/test/tables.cc
@@ -1,6 +1,6 @@
#include <cstdint>
-#include <tables.h>
+#include "tables.h"
namespace fp16 {
diff --git a/third-party/THHalf.h b/third-party/THHalf.h
deleted file mode 100644
index 8bf6450..0000000
--- a/third-party/THHalf.h
+++ /dev/null
@@ -1,92 +0,0 @@
-/*
- * This implementation is extracted from PyTorch:
- * Repo: github.com/pytorch/pytorch
- * File: torch/lib/TH/THHalf.c
- * Commit ID: 92481b59d31199df57420d4b14912348cc780d1d
- * Functions are made "static inline" for performance
- */
-
-/* Copyright 1993-2014 NVIDIA Corporation. All rights reserved. */
-
-// Host functions for converting between FP32 and FP16 formats
-
-static inline void TH_halfbits2float(unsigned short* src, float* res)
-{
- unsigned h = *src;
- unsigned sign = ((h >> 15) & 1);
- unsigned exponent = ((h >> 10) & 0x1f);
- unsigned mantissa = ((h & 0x3ff) << 13);
-
- if (exponent == 0x1f) { /* NaN or Inf */
- mantissa = (mantissa ? (sign = 0, 0x7fffff) : 0);
- exponent = 0xff;
- } else if (!exponent) { /* Denorm or Zero */
- if (mantissa) {
- unsigned int msb;
- exponent = 0x71;
- do {
- msb = (mantissa & 0x400000);
- mantissa <<= 1; /* normalize */
- --exponent;
- } while (!msb);
- mantissa &= 0x7fffff; /* 1.mantissa is implicit */
- }
- } else {
- exponent += 0x70;
- }
-
- *(unsigned*)res = ((sign << 31) | (exponent << 23) | mantissa);
-}
-
-static inline void TH_float2halfbits(float* src, unsigned short* dest)
-{
- unsigned x = *(unsigned*)src;
- unsigned u = (x & 0x7fffffff), remainder, shift, lsb, lsb_s1, lsb_m1;
- unsigned sign, exponent, mantissa;
-
- // Get rid of +NaN/-NaN case first.
- if (u > 0x7f800000) {
- *dest = 0x7fffU;
- return ;
- }
-
- sign = ((x >> 16) & 0x8000);
-
- // Get rid of +Inf/-Inf, +0/-0.
- if (u > 0x477fefff) {
- *dest = sign | 0x7c00U;
- return;
- }
- if (u < 0x33000001) {
- *dest = (sign | 0x0000);
- return;
- }
-
- exponent = ((u >> 23) & 0xff);
- mantissa = (u & 0x7fffff);
-
- if (exponent > 0x70) {
- shift = 13;
- exponent -= 0x70;
- } else {
- shift = 0x7e - exponent;
- exponent = 0;
- mantissa |= 0x800000;
- }
- lsb = (1 << shift);
- lsb_s1 = (lsb >> 1);
- lsb_m1 = (lsb - 1);
-
- // Round to nearest even.
- remainder = (mantissa & lsb_m1);
- mantissa >>= shift;
- if (remainder > lsb_s1 || (remainder == lsb_s1 && (mantissa & 0x1))) {
- ++mantissa;
- if (!(mantissa & 0x3ff)) {
- ++exponent;
- mantissa = 0;
- }
- }
-
- *dest = (sign | (exponent << 10) | mantissa);
-}
diff --git a/third-party/eigen-half.h b/third-party/eigen-half.h
deleted file mode 100644
index f7181cd..0000000
--- a/third-party/eigen-half.h
+++ /dev/null
@@ -1,170 +0,0 @@
-/*
- * This implementation is extracted from Eigen:
- * Repo: bitbucket.org/eigen/eigen
- * File: Eigen/src/Core/arch/CUDA/Half.h
- * Commit ID: 96e0f73a35de54f675d825bef5339b2f08e77eb4
- *
- * Removed a lot of redundant and cuda-specific code.
- */
-
-#define EIGEN_STRONG_INLINE static inline
-#define EIGEN_DEVICE_FUNC
-
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-//
-// The conversion routines are Copyright (c) Fabian Giesen, 2016.
-// The original license follows:
-//
-// Copyright (c) Fabian Giesen, 2016
-// All rights reserved.
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted.
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-
-// Standard 16-bit float type, mostly useful for GPUs. Defines a new
-// type Eigen::half (inheriting from CUDA's __half struct) with
-// operator overloads such that it behaves basically as an arithmetic
-// type. It will be quite slow on CPUs (so it is recommended to stay
-// in fp32 for CPUs, except for simple parameter conversions, I/O
-// to disk and the likes), but fast on GPUs.
-
-
-#ifndef EIGEN_HALF_CUDA_H
-#define EIGEN_HALF_CUDA_H
-
-namespace Eigen {
-
-namespace half_impl {
-
-// Make our own __half definition that is similar to CUDA's.
-struct __half {
- EIGEN_DEVICE_FUNC __half() : x(0) {}
- explicit EIGEN_DEVICE_FUNC __half(unsigned short raw) : x(raw) {}
- unsigned short x;
-};
-
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x);
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff);
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h);
-
-// Conversion routines, including fallbacks for the host or older CUDA.
-// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of
-// these in hardware. If we need more performance on older/other CPUs, they are
-// also possible to vectorize directly.
-
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x) {
- __half h;
- h.x = x;
- return h;
-}
-
-union FP32 {
- unsigned int u;
- float f;
-};
-
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff) {
-#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
- return __float2half(ff);
-
-#elif defined(EIGEN_HAS_FP16_C)
- __half h;
- h.x = _cvtss_sh(ff, 0);
- return h;
-
-#else
- FP32 f; f.f = ff;
-
- const FP32 f32infty = { 255 << 23 };
- const FP32 f16max = { (127 + 16) << 23 };
- const FP32 denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
- unsigned int sign_mask = 0x80000000u;
- __half o;
- o.x = static_cast<unsigned short>(0x0u);
-
- unsigned int sign = f.u & sign_mask;
- f.u ^= sign;
-
- // NOTE all the integer compares in this function can be safely
- // compiled into signed compares since all operands are below
- // 0x80000000. Important if you want fast straight SSE2 code
- // (since there's no unsigned PCMPGTD).
-
- if (f.u >= f16max.u) { // result is Inf or NaN (all exponent bits set)
- o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
- } else { // (De)normalized number or zero
- if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero
- // use a magic value to align our 10 mantissa bits at the bottom of
- // the float. as long as FP addition is round-to-nearest-even this
- // just works.
- f.f += denorm_magic.f;
-
- // and one integer subtract of the bias later, we have our final float!
- o.x = static_cast<unsigned short>(f.u - denorm_magic.u);
- } else {
- unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
-
- // update exponent, rounding bias part 1
- f.u += ((unsigned int)(15 - 127) << 23) + 0xfff;
- // rounding bias part 2
- f.u += mant_odd;
- // take the bits!
- o.x = static_cast<unsigned short>(f.u >> 13);
- }
- }
-
- o.x |= static_cast<unsigned short>(sign >> 16);
- return o;
-#endif
-}
-
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h) {
-#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
- return __half2float(h);
-
-#elif defined(EIGEN_HAS_FP16_C)
- return _cvtsh_ss(h.x);
-
-#else
- const FP32 magic = { 113 << 23 };
- const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
- FP32 o;
-
- o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits
- unsigned int exp = shifted_exp & o.u; // just the exponent
- o.u += (127 - 15) << 23; // exponent adjust
-
- // handle exponent special cases
- if (exp == shifted_exp) { // Inf/NaN?
- o.u += (128 - 16) << 23; // extra exp adjust
- } else if (exp == 0) { // Zero/Denormal?
- o.u += 1 << 23; // extra exp adjust
- o.f -= magic.f; // renormalize
- }
-
- o.u |= (h.x & 0x8000) << 16; // sign bit
- return o.f;
-#endif
-}
-
-} // end namespace half_impl
-
-} // end namespace Eigen
-
-#endif // EIGEN_HALF_CUDA_H
diff --git a/third-party/float16-compressor.h b/third-party/float16-compressor.h
deleted file mode 100644
index 8cd33ed..0000000
--- a/third-party/float16-compressor.h
+++ /dev/null
@@ -1,80 +0,0 @@
-#pragma once
-
-/*
- * This code snippet posted by user Phernost on
- * https://stackoverflow.com/questions/1659440/32-bit-to-16-bit-floating-point-conversion
- *
- * compress and decompress methods are made "inline" for performance
- */
-
-class Float16Compressor
-{
- union Bits
- {
- float f;
- int32_t si;
- uint32_t ui;
- };
-
- static int const shift = 13;
- static int const shiftSign = 16;
-
- static int32_t const infN = 0x7F800000; // flt32 infinity
- static int32_t const maxN = 0x477FE000; // max flt16 normal as a flt32
- static int32_t const minN = 0x38800000; // min flt16 normal as a flt32
- static int32_t const signN = 0x80000000; // flt32 sign bit
-
- static int32_t const infC = infN >> shift;
- static int32_t const nanN = (infC + 1) << shift; // minimum flt16 nan as a flt32
- static int32_t const maxC = maxN >> shift;
- static int32_t const minC = minN >> shift;
- static int32_t const signC = signN >> shiftSign; // flt16 sign bit
-
- static int32_t const mulN = 0x52000000; // (1 << 23) / minN
- static int32_t const mulC = 0x33800000; // minN / (1 << (23 - shift))
-
- static int32_t const subC = 0x003FF; // max flt32 subnormal down shifted
- static int32_t const norC = 0x00400; // min flt32 normal down shifted
-
- static int32_t const maxD = infC - maxC - 1;
- static int32_t const minD = minC - subC - 1;
-
-public:
-
- inline static uint16_t compress(float value)
- {
- Bits v, s;
- v.f = value;
- uint32_t sign = v.si & signN;
- v.si ^= sign;
- sign >>= shiftSign; // logical shift
- s.si = mulN;
- s.si = s.f * v.f; // correct subnormals
- v.si ^= (s.si ^ v.si) & -(minN > v.si);
- v.si ^= (infN ^ v.si) & -((infN > v.si) & (v.si > maxN));
- v.si ^= (nanN ^ v.si) & -((nanN > v.si) & (v.si > infN));
- v.ui >>= shift; // logical shift
- v.si ^= ((v.si - maxD) ^ v.si) & -(v.si > maxC);
- v.si ^= ((v.si - minD) ^ v.si) & -(v.si > subC);
- return v.ui | sign;
- }
-
- inline static float decompress(uint16_t value)
- {
- Bits v;
- v.ui = value;
- int32_t sign = v.si & signC;
- v.si ^= sign;
- sign <<= shiftSign;
- v.si ^= ((v.si + minD) ^ v.si) & -(v.si > subC);
- v.si ^= ((v.si + maxD) ^ v.si) & -(v.si > maxC);
- Bits s;
- s.si = mulC;
- s.f *= v.si;
- int32_t mask = -(norC > v.si);
- v.si <<= shift;
- v.si ^= (s.si ^ v.si) & mask;
- v.si |= sign;
- return v.f;
- }
-};
\ No newline at end of file
diff --git a/third-party/half.hpp b/third-party/half.hpp
deleted file mode 100644
index 767c4b6..0000000
--- a/third-party/half.hpp
+++ /dev/null
@@ -1,2916 +0,0 @@
-/*
- * This implementation is provided by half library:
- * Website: http://half.sourceforge.net/
- * Release: 1.11.0 (November 16, 2013)
- */
-
-
-// half - IEEE 754-based half-precision floating point library.
-//
-// Copyright (c) 2012-2013 Christian Rau <[email protected]>
-//
-// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation
-// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy,
-// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the
-// Software is furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
-// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
-// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
-// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
-
-// Version 1.11.0
-
-/// \file
-/// Main header file for half precision functionality.
-
-#ifndef HALF_HALF_HPP
-#define HALF_HALF_HPP
-
-/// Combined gcc version number.
-#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__)
-
-//check C++11 language features
-#if defined(__clang__) //clang
- #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
- #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
- #endif
- #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
- #define HALF_ENABLE_CPP11_CONSTEXPR 1
- #endif
- #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
- #define HALF_ENABLE_CPP11_NOEXCEPT 1
- #endif
- #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
- #define HALF_ENABLE_CPP11_USER_LITERALS 1
- #endif
- #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
- #define HALF_ENABLE_CPP11_LONG_LONG 1
- #endif
-/*#elif defined(__INTEL_COMPILER) //Intel C++
- #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ????????
- #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
- #endif
- #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) ????????
- #define HALF_ENABLE_CPP11_CONSTEXPR 1
- #endif
- #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) ????????
- #define HALF_ENABLE_CPP11_NOEXCEPT 1
- #endif
- #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG) ????????
- #define HALF_ENABLE_CPP11_LONG_LONG 1
- #endif*/
-#elif defined(__GNUC__) //gcc
- #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
- #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
- #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
- #endif
- #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
- #define HALF_ENABLE_CPP11_CONSTEXPR 1
- #endif
- #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
- #define HALF_ENABLE_CPP11_NOEXCEPT 1
- #endif
- #if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
- #define HALF_ENABLE_CPP11_USER_LITERALS 1
- #endif
- #if !defined(HALF_ENABLE_CPP11_LONG_LONG)
- #define HALF_ENABLE_CPP11_LONG_LONG 1
- #endif
- #endif
-#elif defined(_MSC_VER) //Visual C++
- #if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
- #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
- #endif
- #if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
- #define HALF_ENABLE_CPP11_LONG_LONG 1
- #endif
- #define HALF_POP_WARNINGS 1
- #pragma warning(push)
- #pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned
-#endif
-
-//check C++11 library features
-#include <utility>
-#if defined(_LIBCPP_VERSION) //libc++
- #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
- #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
- #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
- #endif
- #ifndef HALF_ENABLE_CPP11_CSTDINT
- #define HALF_ENABLE_CPP11_CSTDINT 1
- #endif
- #ifndef HALF_ENABLE_CPP11_CMATH
- #define HALF_ENABLE_CPP11_CMATH 1
- #endif
- #ifndef HALF_ENABLE_CPP11_HASH
- #define HALF_ENABLE_CPP11_HASH 1
- #endif
- #endif
-#elif defined(__GLIBCXX__) //libstdc++
- #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
- #ifdef __clang__
- #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
- #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
- #endif
- #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
- #define HALF_ENABLE_CPP11_CSTDINT 1
- #endif
- #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
- #define HALF_ENABLE_CPP11_CMATH 1
- #endif
- #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
- #define HALF_ENABLE_CPP11_HASH 1
- #endif
- #else
- #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
- #define HALF_ENABLE_CPP11_CSTDINT 1
- #endif
- #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
- #define HALF_ENABLE_CPP11_CMATH 1
- #endif
- #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
- #define HALF_ENABLE_CPP11_HASH 1
- #endif
- #endif
- #endif
-#elif defined(_CPPLIB_VER) //Dinkumware/Visual C++
- #if _CPPLIB_VER >= 520
- #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
- #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
- #endif
- #ifndef HALF_ENABLE_CPP11_CSTDINT
- #define HALF_ENABLE_CPP11_CSTDINT 1
- #endif
- #ifndef HALF_ENABLE_CPP11_HASH
- #define HALF_ENABLE_CPP11_HASH 1
- #endif
- #endif
- #if _CPPLIB_VER >= 610
- #ifndef HALF_ENABLE_CPP11_CMATH
- #define HALF_ENABLE_CPP11_CMATH 1
- #endif
- #endif
-#endif
-#undef HALF_GNUC_VERSION
-
-//support constexpr
-#if HALF_ENABLE_CPP11_CONSTEXPR
- #define HALF_CONSTEXPR constexpr
- #define HALF_CONSTEXPR_CONST constexpr
-#else
- #define HALF_CONSTEXPR
- #define HALF_CONSTEXPR_CONST const
-#endif
-
-//support noexcept
-#if HALF_ENABLE_CPP11_NOEXCEPT
- #define HALF_NOEXCEPT noexcept
- #define HALF_NOTHROW noexcept
-#else
- #define HALF_NOEXCEPT
- #define HALF_NOTHROW throw()
-#endif
-
-#include <algorithm>
-#include <iostream>
-#include <limits>
-#include <climits>
-#include <cmath>
-#include <cstring>
-#if HALF_ENABLE_CPP11_TYPE_TRAITS
- #include <type_traits>
-#endif
-#if HALF_ENABLE_CPP11_CSTDINT
- #include <cstdint>
-#endif
-#if HALF_ENABLE_CPP11_HASH
- #include <functional>
-#endif
-
-
-/// Default rounding mode.
-/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and `float`s as well as
-/// for the half_cast() if not specifying a rounding mode explicitly. It can be redefined (before including half.hpp) to one
-/// of the standard rounding modes using their respective constants or the equivalent values of `std::float_round_style`:
-///
-/// `std::float_round_style` | value | rounding
-/// ---------------------------------|-------|-------------------------
-/// `std::round_indeterminate` | -1 | fastest (default)
-/// `std::round_toward_zero` | 0 | toward zero
-/// `std::round_to_nearest` | 1 | to nearest
-/// `std::round_toward_infinity` | 2 | toward positive infinity
-/// `std::round_toward_neg_infinity` | 3 | toward negative infinity
-///
-/// By default this is set to `-1` (`std::round_indeterminate`), which uses truncation (round toward zero, but with overflows
-/// set to infinity) and is the fastest rounding mode possible. It can even be set to `std::numeric_limits<float>::round_style`
-/// to synchronize the rounding mode with that of the underlying single-precision implementation.
-#ifndef HALF_ROUND_STYLE
- #define HALF_ROUND_STYLE -1 // = std::round_indeterminate
-#endif
-
-/// Tie-breaking behaviour for round to nearest.
-/// This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is
-/// defined to `0` resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and
-/// thus equal to the round() function), but can be redefined to `1` (before including half.hpp) if more IEEE-conformant
-/// behaviour is needed.
-#ifndef HALF_ROUND_TIES_TO_EVEN
- #define HALF_ROUND_TIES_TO_EVEN 0 // ties away from zero
-#endif
-
-/// Value signaling overflow.
-/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to a positive value signaling the overflow of an
-/// operation, in particular it just evaluates to positive infinity.
-#define HUGE_VALH std::numeric_limits<half_float::half>::infinity()
-
-/// Fast half-precision fma function.
-/// This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate
-/// half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all
-/// arithmetic operations, this is in fact always the case.
-#define FP_FAST_FMAH 1
-
-#ifndef FP_ILOGB0
- #define FP_ILOGB0 INT_MIN
-#endif
-#ifndef FP_ILOGBNAN
- #define FP_ILOGBNAN INT_MAX
-#endif
-#ifndef FP_SUBNORMAL
- #define FP_SUBNORMAL 0
-#endif
-#ifndef FP_ZERO
- #define FP_ZERO 1
-#endif
-#ifndef FP_NAN
- #define FP_NAN 2
-#endif
-#ifndef FP_INFINITE
- #define FP_INFINITE 3
-#endif
-#ifndef FP_NORMAL
- #define FP_NORMAL 4
-#endif
-
-
-/// Main namespace for half precision functionality.
-/// This namespace contains all the functionality provided by the library.
-namespace half_float
-{
- class half;
-
- /// \internal
- /// \brief Implementation details.
- namespace detail
- {
- #if HALF_ENABLE_CPP11_TYPE_TRAITS
- /// Conditional type.
- template<bool B,typename T,typename F> struct conditional : std::conditional<B,T,F> {};
-
- /// Helper for tag dispatching.
- template<bool B> struct bool_type : std::integral_constant<bool,B> {};
- using std::true_type;
- using std::false_type;
-
- /// Type traits for floating point types.
- template<typename T> struct is_float : std::is_floating_point<T> {};
- #else
- /// Conditional type.
- template<bool,typename T,typename> struct conditional { typedef T type; };
- template<typename T,typename F> struct conditional<false,T,F> { typedef F type; };
-
- /// Helper for tag dispatching.
- template<bool> struct bool_type {};
- typedef bool_type<true> true_type;
- typedef bool_type<false> false_type;
-
- /// Type traits for floating point types.
- template<typename> struct is_float : false_type {};
- template<typename T> struct is_float<const T> : is_float<T> {};
- template<typename T> struct is_float<volatile T> : is_float<T> {};
- template<typename T> struct is_float<const volatile T> : is_float<T> {};
- template<> struct is_float<float> : true_type {};
- template<> struct is_float<double> : true_type {};
- template<> struct is_float<long double> : true_type {};
- #endif
-
- #if HALF_ENABLE_CPP11_CSTDINT
- /// Unsigned integer of (at least) 16 bits width.
- typedef std::uint_least16_t uint16;
-
- /// Unsigned integer of (at least) 32 bits width.
- typedef std::uint_least32_t uint32;
-
- /// Fastest signed integer capable of holding all values of type uint16.
- typedef std::int_fast32_t int17;
- #else
- /// Unsigned integer of (at least) 16 bits width.
- typedef unsigned short uint16;
-
- /// Unsigned integer of (at least) 32 bits width.
- typedef conditional<std::numeric_limits<unsigned int>::digits>=32,unsigned int,unsigned long>::type uint32;
-
- /// Fastest signed integer capable of holding all values of type uint16.
- typedef conditional<std::numeric_limits<int>::digits>=16,int,long>::type int17;
- #endif
-
- /// Tag type for binary construction.
- struct binary_t {};
-
- /// Tag for binary construction.
- HALF_CONSTEXPR_CONST binary_t binary = binary_t();
-
- /// Temporary half-precision expression.
- /// This class represents a half-precision expression which just stores a single-precision value internally.
- struct expr
- {
- /// Conversion constructor.
- /// \param f single-precision value to convert
- explicit HALF_CONSTEXPR expr(float f) : value_(f) {}
-
- /// Conversion to single-precision.
- /// \return single precision value representing expression value
- HALF_CONSTEXPR operator float() const { return value_; }
-
- private:
- /// Internal expression value stored in single-precision.
- float value_;
- };
-
- /// SFINAE helper for generic half-precision functions.
- /// This class template has to be specialized for each valid combination of argument types to provide a corresponding
- /// `type` member equivalent to \a T.
- /// \tparam T type to return
- template<typename T,typename,typename=void,typename=void> struct enable {};
- template<typename T> struct enable<T,half,void,void> { typedef T type; };
- template<typename T> struct enable<T,expr,void,void> { typedef T type; };
- template<typename T> struct enable<T,half,half,void> { typedef T type; };
- template<typename T> struct enable<T,half,expr,void> { typedef T type; };
- template<typename T> struct enable<T,expr,half,void> { typedef T type; };
- template<typename T> struct enable<T,expr,expr,void> { typedef T type; };
- template<typename T> struct enable<T,half,half,half> { typedef T type; };
- template<typename T> struct enable<T,half,half,expr> { typedef T type; };
- template<typename T> struct enable<T,half,expr,half> { typedef T type; };
- template<typename T> struct enable<T,half,expr,expr> { typedef T type; };
- template<typename T> struct enable<T,expr,half,half> { typedef T type; };
- template<typename T> struct enable<T,expr,half,expr> { typedef T type; };
- template<typename T> struct enable<T,expr,expr,half> { typedef T type; };
- template<typename T> struct enable<T,expr,expr,expr> { typedef T type; };
-
- /// Return type for specialized generic 2-argument half-precision functions.
- /// This class template has to be specialized for each valid combination of argument types to provide a corresponding
- /// `type` member denoting the appropriate return type.
- /// \tparam T first argument type
- /// \tparam U first argument type
- template<typename T,typename U> struct result : enable<expr,T,U> {};
- template<> struct result<half,half> { typedef half type; };
-
- /// \name Classification helpers
- /// \{
-
- /// Check for infinity.
- /// \tparam T argument type (builtin floating point type)
- /// \param arg value to query
- /// \retval true if infinity
- /// \retval false else
- template<typename T> bool builtin_isinf(T arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return std::isinf(arg);
- #elif defined(_MSC_VER)
- return !_finite(static_cast<double>(arg)) && !_isnan(static_cast<double>(arg));
- #else
- return arg == std::numeric_limits<T>::infinity() || arg == -std::numeric_limits<T>::infinity();
- #endif
- }
-
- /// Check for NaN.
- /// \tparam T argument type (builtin floating point type)
- /// \param arg value to query
- /// \retval true if not a number
- /// \retval false else
- template<typename T> bool builtin_isnan(T arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return std::isnan(arg);
- #elif defined(_MSC_VER)
- return _isnan(static_cast<double>(arg)) != 0;
- #else
- return arg != arg;
- #endif
- }
-
- /// Check sign.
- /// \tparam T argument type (builtin floating point type)
- /// \param arg value to query
- /// \retval true if signbit set
- /// \retval false else
- template<typename T> bool builtin_signbit(T arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return std::signbit(arg);
- #else
- return arg < T() || (arg == T() && T(1)/arg < T());
- #endif
- }
-
- /// \}
- /// \name Conversion
- /// \{
-
- /// Convert IEEE single-precision to half-precision.
- /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \param value single-precision value
- /// \return binary representation of half-precision value
- template<std::float_round_style R> uint16 float2half_impl(float value, true_type)
- {
- #if HALF_ENABLE_CPP11_STATIC_ASSERT
- static_assert(std::numeric_limits<float>::is_iec559, "float to half conversion needs IEEE 754 conformant 'float' type");
- static_assert(sizeof(uint32)==sizeof(float), "float to half conversion needs unsigned integer type of exactly the size of a 'float'");
- #endif
- static const uint16 base_table[512] = {
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100,
- 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00,
- 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
- 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100,
- 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00,
- 0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
- 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 };
- static const unsigned char shift_table[512] = {
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
- 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
- 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
- 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
- uint32 bits;// = *reinterpret_cast<uint32*>(&value); //violating strict aliasing!
- std::memcpy(&bits, &value, sizeof(float));
- uint16 hbits = base_table[bits>>23] + static_cast<uint16>((bits&0x7FFFFF)>>shift_table[bits>>23]);
- if(R == std::round_to_nearest)
- hbits += (((bits&0x7FFFFF)>>(shift_table[bits>>23]-1))|(((bits>>23)&0xFF)==102)) & ((hbits&0x7C00)!=0x7C00)
- #if HALF_ROUND_TIES_TO_EVEN
- & (((((static_cast<uint32>(1)<<(shift_table[bits>>23]-1))-1)&bits)!=0)|hbits)
- #endif
- ;
- else if(R == std::round_toward_zero)
- hbits -= ((hbits&0x7FFF)==0x7C00) & ~shift_table[bits>>23];
- else if(R == std::round_toward_infinity)
- hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=102)&
- ((bits>>23)!=0)))&(hbits<0x7C00)) - ((hbits==0xFC00)&((bits>>23)!=511));
- else if(R == std::round_toward_neg_infinity)
- hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=358)&
- ((bits>>23)!=256)))&(hbits<0xFC00)&(hbits>>15)) - ((hbits==0x7C00)&((bits>>23)!=255));
- return hbits;
- }
-
- /// Convert non-IEEE single-precision to half-precision.
- /// \param value single-precision value
- /// \return binary representation of half-precision value
- template<std::float_round_style R> uint16 float2half_impl(float value, false_type)
- {
- uint16 hbits = builtin_signbit(value) << 15;
- if(value == 0.0f)
- return hbits;
- if(builtin_isnan(value))
- return hbits | 0x7FFF;
- if(builtin_isinf(value))
- return hbits | 0x7C00;
- int exp;
- std::frexp(value, &exp);
- if(exp > 16)
- {
- if(R == std::round_toward_zero)
- return hbits | 0x7BFF;
- else if(R == std::round_toward_infinity)
- return hbits | 0x7C00 - (hbits>>15);
- else if(R == std::round_toward_neg_infinity)
- return hbits | 0x7BFF + (hbits>>15);
- return hbits | 0x7C00;
- }
- if(exp < -13)
- value = std::ldexp(value, 24);
- else
- {
- value = std::ldexp(value, 11-exp);
- hbits |= ((exp+14)<<10);
- }
- int ival = static_cast<int>(value);
- hbits |= static_cast<uint16>(std::abs(ival)&0x3FF);
- if(R == std::round_to_nearest)
- {
- float diff = std::abs(value-static_cast<float>(ival));
- #if HALF_ROUND_TIES_TO_EVEN
- hbits += (diff>0.5f) | ((diff==0.5f)&hbits);
- #else
- hbits += diff >= 0.5f;
- #endif
- }
- else if(R == std::round_toward_infinity)
- hbits += value > static_cast<float>(ival);
- else if(R == std::round_toward_neg_infinity)
- hbits += value < static_cast<float>(ival);
- return hbits;
- }
-
- /// Convert single-precision to half-precision.
- /// \param value single-precision value
- /// \return binary representation of half-precision value
- template<std::float_round_style R> uint16 float2half(float value)
- {
- return float2half_impl<R>(value, bool_type<std::numeric_limits<float>::is_iec559&&sizeof(uint32)==sizeof(float)>());
- }
-
- /// Convert integer to half-precision floating point.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \tparam S `true` if value negative, `false` else
- /// \tparam T type to convert (builtin integer type)
- /// \param value non-negative integral value
- /// \return binary representation of half-precision value
- template<std::float_round_style R,bool S,typename T> uint16 int2half_impl(T value)
- {
- if(S)
- value = -value;
- uint16 bits = S << 15;
- if(value > 65504)
- {
- if(R == std::round_toward_infinity)
- bits |= 0x7C00 - S;
- else if(R == std::round_toward_neg_infinity)
- bits |= 0x7BFF + S;
- else
- bits |= 0x7BFF + (R!=std::round_toward_zero);
- }
- else if(value)
- {
- unsigned int m = value, exp = 25;
- for(; m<0x400; m<<=1,--exp) ;
- for(; m>0x7FF; m>>=1,++exp) ;
- bits |= (exp<<10) | (m&0x3FF);
- if(exp > 25)
- {
- if(R == std::round_to_nearest)
- bits += (value>>(exp-26)) & 1
- #if HALF_ROUND_TIES_TO_EVEN
- & (((((1<<(exp-26))-1)&value)!=0)|bits)
- #endif
- ;
- else if(R == std::round_toward_infinity)
- bits += ((value&((1<<(exp-25))-1))!=0) & !S;
- else if(R == std::round_toward_neg_infinity)
- bits += ((value&((1<<(exp-25))-1))!=0) & S;
- }
- }
- return bits;
- }
-
- /// Convert integer to half-precision floating point.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \tparam T type to convert (builtin integer type)
- /// \param value integral value
- /// \return binary representation of half-precision value
- template<std::float_round_style R,typename T> uint16 int2half(T value)
- {
- return (value<0) ? int2half_impl<R,true>(value) : int2half_impl<R,false>(value);
- }
-
- /// Convert half-precision to IEEE single-precision.
- /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
- /// \param value binary representation of half-precision value
- /// \return single-precision value
- inline float half2float_impl(uint16 value, true_type)
- {
- #if HALF_ENABLE_CPP11_STATIC_ASSERT
- static_assert(std::numeric_limits<float>::is_iec559, "half to float conversion needs IEEE 754 conformant 'float' type");
- static_assert(sizeof(uint32)==sizeof(float), "half to float conversion needs unsigned integer type of exactly the size of a 'float'");
- #endif
- static const uint32 mantissa_table[2048] = {
- 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000,
- 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000,
- 0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
- 0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000,
- 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000,
- 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
- 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
- 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000,
- 0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
- 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000,
- 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000,
- 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
- 0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000,
- 0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000,
- 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
- 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
- 0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000,
- 0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
- 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000,
- 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000,
- 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
- 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000,
- 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000,
- 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
- 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
- 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000,
- 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
- 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000,
- 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000,
- 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
- 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000,
- 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000,
- 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
- 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
- 0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000,
- 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
- 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000,
- 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000,
- 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
- 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000,
- 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000,
- 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
- 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
- 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000,
- 0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
- 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000,
- 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000,
- 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
- 0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000,
- 0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000,
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- 0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
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- 0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000,
- 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000,
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- 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000,
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- 0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000,
- 0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000,
- 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
- 0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000,
- 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000,
- 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000,
- 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
- static const uint32 exponent_table[64] = {
- 0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000,
- 0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000,
- 0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000,
- 0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
- static const unsigned short offset_table[64] = {
- 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
- 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
- uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
-// uint32 bits = mantissa_table[(((value&0x7C00)!=0)<<10)+(value&0x3FF)] + exponent_table[value>>10];
-// return *reinterpret_cast<float*>(&bits); //violating strict aliasing!
- float out;
- std::memcpy(&out, &bits, sizeof(float));
- return out;
- }
-
- /// Convert half-precision to non-IEEE single-precision.
- /// \param value binary representation of half-precision value
- /// \return single-precision value
- inline float half2float_impl(uint16 value, false_type)
- {
- float out;
- int abs = value & 0x7FFF;
- if(abs > 0x7C00)
- out = std::numeric_limits<float>::has_quiet_NaN ? std::numeric_limits<float>::quiet_NaN() : 0.0f;
- else if(abs == 0x7C00)
- out = std::numeric_limits<float>::has_infinity ? std::numeric_limits<float>::infinity() : std::numeric_limits<float>::max();
- else if(abs > 0x3FF)
- out = std::ldexp(static_cast<float>((value&0x3FF)|0x400), (abs>>10)-25);
- else
- out = std::ldexp(static_cast<float>(abs), -24);
- return (value&0x8000) ? -out : out;
- }
-
- /// Convert half-precision to single-precision.
- /// \param value binary representation of half-precision value
- /// \return single-precision value
- inline float half2float(uint16 value)
- {
- return half2float_impl(value, bool_type<std::numeric_limits<float>::is_iec559&&sizeof(uint32)==sizeof(float)>());
- }
-
- /// Convert half-precision floating point to integer.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \tparam E `true` for round to even, `false` for round away from zero
- /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
- /// \param value binary representation of half-precision value
- /// \return integral value
- template<std::float_round_style R,bool E,typename T> T half2int_impl(uint16 value)
- {
- unsigned int e = value & 0x7FFF;
- if(e >= 0x7C00)
- return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
- if(e < 0x3800)
- {
- if(R == std::round_toward_infinity)
- return T(~(value>>15)&(e!=0));
- else if(R == std::round_toward_neg_infinity)
- return -T(value>0x8000);
- return T();
- }
- int17 m = (value&0x3FF) | 0x400;
- e >>= 10;
- if(e < 25)
- {
- if(R == std::round_indeterminate || R == std::round_toward_zero)
- m >>= 25 - e;
- else
- {
- if(R == std::round_to_nearest)
- m += (1<<(24-e)) - (~(m>>(25-e))&E);
- else if(R == std::round_toward_infinity)
- m += ((value>>15)-1) & ((1<<(25-e))-1U);
- else if(R == std::round_toward_neg_infinity)
- m += -(value>>15) & ((1<<(25-e))-1U);
- m >>= 25 - e;
- }
- }
- else
- m <<= e - 25;
-// if(std::numeric_limits<T>::digits < 16)
-// return std::min(std::max(m, static_cast<int17>(std::numeric_limits<T>::min())), static_cast<int17>(std::numeric_limits<T>::max()));
- return static_cast<T>((value&0x8000) ? -m : m);
- }
-
- /// Convert half-precision floating point to integer.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
- /// \param value binary representation of half-precision value
- /// \return integral value
- template<std::float_round_style R,typename T> T half2int(uint16 value) { return half2int_impl<R,HALF_ROUND_TIES_TO_EVEN,T>(value); }
-
- /// Convert half-precision floating point to integer using round-to-nearest-away-from-zero.
- /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
- /// \param value binary representation of half-precision value
- /// \return integral value
- template<typename T> T half2int_up(uint16 value) { return half2int_impl<std::round_to_nearest,0,T>(value); }
-
- /// Round half-precision number to nearest integer value.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \tparam E `true` for round to even, `false` for round away from zero
- /// \param value binary representation of half-precision value
- /// \return half-precision bits for nearest integral value
- template<std::float_round_style R,bool E> uint16 round_half_impl(uint16 value)
- {
- unsigned int e = value & 0x7FFF;
- uint16 result = value;
- if(e < 0x3C00)
- {
- result &= 0x8000;
- if(R == std::round_to_nearest)
- result |= 0x3C00U & -(e>=(0x3800+E));
- else if(R == std::round_toward_infinity)
- result |= 0x3C00U & -(~(value>>15)&(e!=0));
- else if(R == std::round_toward_neg_infinity)
- result |= 0x3C00U & -(value>0x8000);
- }
- else if(e < 0x6400)
- {
- e = 25 - (e>>10);
- unsigned int mask = (1<<e) - 1;
- if(R == std::round_to_nearest)
- result += (1<<(e-1)) - (~(result>>e)&E);
- else if(R == std::round_toward_infinity)
- result += mask & ((value>>15)-1);
- else if(R == std::round_toward_neg_infinity)
- result += mask & -(value>>15);
- result &= ~mask;
- }
- return result;
- }
-
- /// Round half-precision number to nearest integer value.
- /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
- /// \param value binary representation of half-precision value
- /// \return half-precision bits for nearest integral value
- template<std::float_round_style R> uint16 round_half(uint16 value) { return round_half_impl<R,HALF_ROUND_TIES_TO_EVEN>(value); }
-
- /// Round half-precision number to nearest integer value using round-to-nearest-away-from-zero.
- /// \param value binary representation of half-precision value
- /// \return half-precision bits for nearest integral value
- inline uint16 round_half_up(uint16 value) { return round_half_impl<std::round_to_nearest,0>(value); }
- /// \}
-
- struct functions;
- template<typename> struct unary_specialized;
- template<typename,typename> struct binary_specialized;
- template<typename,typename,std::float_round_style> struct half_caster;
- }
-
- /// Half-precision floating point type.
- /// This class implements an IEEE-conformant half-precision floating point type with the usual arithmetic operators and
- /// conversions. It is implicitly convertible to single-precision floating point, which makes artihmetic expressions and
- /// functions with mixed-type operands to be of the most precise operand type. Additionally all arithmetic operations
- /// (and many mathematical functions) are carried out in single-precision internally. All conversions from single- to
- /// half-precision are done using truncation (round towards zero), but temporary results inside chained arithmetic
- /// expressions are kept in single-precision as long as possible (while of course still maintaining a strong half-precision type).
- ///
- /// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and
- /// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which
- /// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the
- /// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of
- /// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most
- /// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit
- /// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if
- /// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on
- /// nearly any reasonable platform.
- ///
- /// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable
- /// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.
- class half
- {
- friend struct detail::functions;
- friend struct detail::unary_specialized<half>;
- friend struct detail::binary_specialized<half,half>;
- template<typename,typename,std::float_round_style> friend struct detail::half_caster;
- friend class std::numeric_limits<half>;
- #if HALF_ENABLE_CPP11_HASH
- friend struct std::hash<half>;
- #endif
-
- public:
- /// Default constructor.
- /// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics
- /// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.
- HALF_CONSTEXPR half() : data_() {}
-
- /// Copy constructor.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to copy from
- half(detail::expr rhs) : data_(detail::float2half<round_style>(rhs)) {}
-
- /// Conversion constructor.
- /// \param rhs float to convert
- explicit half(float rhs) : data_(detail::float2half<round_style>(rhs)) {}
-
- /// Conversion to single-precision.
- /// \return single precision value representing expression value
- operator float() const { return detail::half2float(data_); }
-
- /// Assignment operator.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to copy from
- /// \return reference to this half
- half& operator=(detail::expr rhs) { return *this = static_cast<float>(rhs); }
-
- /// Arithmetic assignment.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to add
- /// \return reference to this half
- template<typename T> typename detail::enable<half&,T>::type operator+=(T rhs) { return *this += static_cast<float>(rhs); }
-
- /// Arithmetic assignment.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to subtract
- /// \return reference to this half
- template<typename T> typename detail::enable<half&,T>::type operator-=(T rhs) { return *this -= static_cast<float>(rhs); }
-
- /// Arithmetic assignment.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to multiply with
- /// \return reference to this half
- template<typename T> typename detail::enable<half&,T>::type operator*=(T rhs) { return *this *= static_cast<float>(rhs); }
-
- /// Arithmetic assignment.
- /// \tparam T type of concrete half expression
- /// \param rhs half expression to divide by
- /// \return reference to this half
- template<typename T> typename detail::enable<half&,T>::type operator/=(T rhs) { return *this /= static_cast<float>(rhs); }
-
- /// Assignment operator.
- /// \param rhs single-precision value to copy from
- /// \return reference to this half
- half& operator=(float rhs) { data_ = detail::float2half<round_style>(rhs); return *this; }
-
- /// Arithmetic assignment.
- /// \param rhs single-precision value to add
- /// \return reference to this half
- half& operator+=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float(data_)+rhs); return *this; }
-
- /// Arithmetic assignment.
- /// \param rhs single-precision value to subtract
- /// \return reference to this half
- half& operator-=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float(data_)-rhs); return *this; }
-
- /// Arithmetic assignment.
- /// \param rhs single-precision value to multiply with
- /// \return reference to this half
- half& operator*=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float(data_)*rhs); return *this; }
-
- /// Arithmetic assignment.
- /// \param rhs single-precision value to divide by
- /// \return reference to this half
- half& operator/=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float(data_)/rhs); return *this; }
-
- /// Prefix increment.
- /// \return incremented half value
- half& operator++() { return *this += 1.0f; }
-
- /// Prefix decrement.
- /// \return decremented half value
- half& operator--() { return *this -= 1.0f; }
-
- /// Postfix increment.
- /// \return non-incremented half value
- half operator++(int) { half out(*this); ++*this; return out; }
-
- /// Postfix decrement.
- /// \return non-decremented half value
- half operator--(int) { half out(*this); --*this; return out; }
-
- private:
- /// Rounding mode to use (always `std::round_indeterminate`)
- static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
-
- /// Constructor.
- /// \param bits binary representation to set half to
- HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) : data_(bits) {}
-
- /// Internal binary representation
- detail::uint16 data_;
- };
-
-#if HALF_ENABLE_CPP11_USER_LITERALS
- /// Library-defined half-precision literals.
- /// Import this namespace to enable half-precision floating point literals:
- /// ~~~~{.cpp}
- /// using namespace half_float::literal;
- /// half_float::half = 4.2_h;
- /// ~~~~
- namespace literal
- {
- /// Half literal.
- /// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due
- /// to rather involved single-to-half conversion.
- /// \param value literal value
- /// \return half with given value (if representable)
- inline half operator "" _h(long double value) { return half(static_cast<float>(value)); }
- }
-#endif
-
- namespace detail
- {
- /// Wrapper implementing unspecialized half-precision functions.
- struct functions
- {
- /// Addition implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision sum stored in single-precision
- static expr plus(float x, float y) { return expr(x+y); }
-
- /// Subtraction implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision difference stored in single-precision
- static expr minus(float x, float y) { return expr(x-y); }
-
- /// Multiplication implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision product stored in single-precision
- static expr multiplies(float x, float y) { return expr(x*y); }
-
- /// Division implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision quotient stored in single-precision
- static expr divides(float x, float y) { return expr(x/y); }
-
- /// Output implementation.
- /// \param out stream to write to
- /// \param arg value to write
- /// \return reference to stream
- template<typename charT,typename traits> static std::basic_ostream<charT,traits>& write(std::basic_ostream<charT,traits> &out, float arg) { return out << arg; }
-
- /// Input implementation.
- /// \param in stream to read from
- /// \param arg half to read into
- /// \return reference to stream
- template<typename charT,typename traits> static std::basic_istream<charT,traits>& read(std::basic_istream<charT,traits> &in, half &arg)
- {
- float f;
- if(in >> f)
- arg = f;
- return in;
- }
-
- /// Modulo implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision division remainder stored in single-precision
- static expr fmod(float x, float y) { return expr(std::fmod(x, y)); }
-
- /// Remainder implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Half-precision division remainder stored in single-precision
- static expr remainder(float x, float y)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::remainder(x, y));
- #else
- if(builtin_isnan(x) || builtin_isnan(y))
- return expr(std::numeric_limits<float>::quiet_NaN());
- float ax = std::fabs(x), ay = std::fabs(y);
- if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
- return expr(std::numeric_limits<float>::quiet_NaN());
- if(ay >= 65536.0f)
- return expr(x);
- if(ax == ay)
- return expr(builtin_signbit(x) ? -0.0f : 0.0f);
- ax = std::fmod(ax, ay+ay);
- float y2 = 0.5f * ay;
- if(ax > y2)
- {
- ax -= ay;
- if(ax >= y2)
- ax -= ay;
- }
- return expr(builtin_signbit(x) ? -ax : ax);
- #endif
- }
-
- /// Remainder implementation.
- /// \param x first operand
- /// \param y second operand
- /// \param quo address to store quotient bits at
- /// \return Half-precision division remainder stored in single-precision
- static expr remquo(float x, float y, int *quo)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::remquo(x, y, quo));
- #else
- if(builtin_isnan(x) || builtin_isnan(y))
- return expr(std::numeric_limits<float>::quiet_NaN());
- bool sign = builtin_signbit(x), qsign = static_cast<bool>(sign^builtin_signbit(y));
- float ax = std::fabs(x), ay = std::fabs(y);
- if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
- return expr(std::numeric_limits<float>::quiet_NaN());
- if(ay >= 65536.0f)
- return expr(x);
- if(ax == ay)
- return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f);
- ax = std::fmod(ax, 8.0f*ay);
- int cquo = 0;
- if(ax >= 4.0f * ay)
- {
- ax -= 4.0f * ay;
- cquo += 4;
- }
- if(ax >= 2.0f * ay)
- {
- ax -= 2.0f * ay;
- cquo += 2;
- }
- float y2 = 0.5f * ay;
- if(ax > y2)
- {
- ax -= ay;
- ++cquo;
- if(ax >= y2)
- {
- ax -= ay;
- ++cquo;
- }
- }
- return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax);
- #endif
- }
-
- /// Positive difference implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return Positive difference stored in single-precision
- static expr fdim(float x, float y)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::fdim(x, y));
- #else
- return expr((x<=y) ? 0.0f : (x-y));
- #endif
- }
-
- /// Fused multiply-add implementation.
- /// \param x first operand
- /// \param y second operand
- /// \param z third operand
- /// \return \a x * \a y + \a z stored in single-precision
- static expr fma(float x, float y, float z)
- {
- #if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF)
- return expr(std::fma(x, y, z));
- #else
- return expr(x*y+z);
- #endif
- }
-
- /// Get NaN.
- /// \return Half-precision quiet NaN
- static half nanh(const char*) { return half(binary, 0x7FFF); }
-
- /// Exponential implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr exp(float arg) { return expr(std::exp(arg)); }
-
- /// Exponential implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr expm1(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::expm1(arg));
- #else
- return expr(static_cast<float>(std::exp(static_cast<double>(arg))-1.0));
- #endif
- }
-
- /// Binary exponential implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr exp2(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::exp2(arg));
- #else
- return expr(static_cast<float>(std::exp(arg*0.69314718055994530941723212145818)));
- #endif
- }
-
- /// Logarithm implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr log(float arg) { return expr(std::log(arg)); }
-
- /// Common logarithm implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr log10(float arg) { return expr(std::log10(arg)); }
-
- /// Logarithm implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr log1p(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::log1p(arg));
- #else
- return expr(static_cast<float>(std::log(1.0+arg)));
- #endif
- }
-
- /// Binary logarithm implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr log2(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::log2(arg));
- #else
- return expr(static_cast<float>(std::log(static_cast<double>(arg))*1.4426950408889634073599246810019));
- #endif
- }
-
- /// Square root implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr sqrt(float arg) { return expr(std::sqrt(arg)); }
-
- /// Cubic root implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr cbrt(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::cbrt(arg));
- #else
- if(builtin_isnan(arg) || builtin_isinf(arg))
- return expr(arg);
- return expr(builtin_signbit(arg) ? -static_cast<float>(std::pow(std::fabs(static_cast<double>(arg)), 1.0/3.0)) :
- static_cast<float>(std::pow(static_cast<double>(arg), 1.0/3.0)));
- #endif
- }
-
- /// Hypotenuse implementation.
- /// \param x first argument
- /// \param y second argument
- /// \return function value stored in single-preicision
- static expr hypot(float x, float y)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::hypot(x, y));
- #else
- return expr((builtin_isinf(x) || builtin_isinf(y)) ? std::numeric_limits<float>::infinity() :
- static_cast<float>(std::sqrt(static_cast<double>(x)*x+static_cast<double>(y)*y)));
- #endif
- }
-
- /// Power implementation.
- /// \param base value to exponentiate
- /// \param exp power to expontiate to
- /// \return function value stored in single-preicision
- static expr pow(float base, float exp) { return expr(std::pow(base, exp)); }
-
- /// Sine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr sin(float arg) { return expr(std::sin(arg)); }
-
- /// Cosine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr cos(float arg) { return expr(std::cos(arg)); }
-
- /// Tan implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr tan(float arg) { return expr(std::tan(arg)); }
-
- /// Arc sine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr asin(float arg) { return expr(std::asin(arg)); }
-
- /// Arc cosine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr acos(float arg) { return expr(std::acos(arg)); }
-
- /// Arc tangent implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr atan(float arg) { return expr(std::atan(arg)); }
-
- /// Arc tangent implementation.
- /// \param x first argument
- /// \param y second argument
- /// \return function value stored in single-preicision
- static expr atan2(float x, float y) { return expr(std::atan2(x, y)); }
-
- /// Hyperbolic sine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr sinh(float arg) { return expr(std::sinh(arg)); }
-
- /// Hyperbolic cosine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr cosh(float arg) { return expr(std::cosh(arg)); }
-
- /// Hyperbolic tangent implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr tanh(float arg) { return expr(std::tanh(arg)); }
-
- /// Hyperbolic area sine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr asinh(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::asinh(arg));
- #else
- return expr((arg==-std::numeric_limits<float>::infinity()) ? arg : static_cast<float>(std::log(arg+std::sqrt(arg*arg+1.0))));
- #endif
- }
-
- /// Hyperbolic area cosine implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr acosh(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::acosh(arg));
- #else
- return expr((arg<-1.0f) ? std::numeric_limits<float>::quiet_NaN() : static_cast<float>(std::log(arg+std::sqrt(arg*arg-1.0))));
- #endif
- }
-
- /// Hyperbolic area tangent implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr atanh(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::atanh(arg));
- #else
- return expr(static_cast<float>(0.5*std::log((1.0+arg)/(1.0-arg))));
- #endif
- }
-
- /// Error function implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr erf(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::erf(arg));
- #else
- return expr(static_cast<float>(erf(static_cast<double>(arg))));
- #endif
- }
-
- /// Complementary implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr erfc(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::erfc(arg));
- #else
- return expr(static_cast<float>(1.0-erf(static_cast<double>(arg))));
- #endif
- }
-
- /// Gamma logarithm implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr lgamma(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::lgamma(arg));
- #else
- if(builtin_isinf(arg))
- return expr(std::numeric_limits<float>::infinity());
- double z = static_cast<double>(arg);
- if(z < 0)
- {
- double i, f = std::modf(-z, &i);
- if(f == 0.0)
- return expr(std::numeric_limits<float>::infinity());
- return expr(static_cast<float>(1.1447298858494001741434273513531-std::log(std::abs(std::sin(3.1415926535897932384626433832795*f)))-lgamma(1.0-z)));
- }
-// if(z < 8.0)
- return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
- return expr(static_cast<float>(0.5*(1.8378770664093454835606594728112-std::log(z))+z*(std::log(z+1.0/(12.0*z-1.0/(10.0*z)-1.0))-1.0)));
- #endif
- }
-
- /// Gamma implementation.
- /// \param arg function argument
- /// \return function value stored in single-preicision
- static expr tgamma(float arg)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::tgamma(arg));
- #else
- double z = static_cast<double>(arg);
- if(z == 0.0)
- return builtin_signbit(z) ? expr(-std::numeric_limits<float>::infinity()) : expr(std::numeric_limits<float>::infinity());
- if(z < 0.0)
- {
- double i, f = std::modf(-z, &i);
- if(f == 0.0)
- return expr(std::numeric_limits<float>::quiet_NaN());
- double sign = (std::fmod(i, 2.0)==0.0) ? -1.0 : 1.0;
- return expr(static_cast<float>(sign*3.1415926535897932384626433832795/(std::sin(3.1415926535897932384626433832795*f)*std::exp(lgamma(1.0-z)))));
- }
- if(builtin_isinf(arg))
- return expr(arg);
-// if(arg < 8.0f)
- return expr(static_cast<float>(std::exp(lgamma(z))));
- return expr(static_cast<float>(std::sqrt(6.283185307179586476925286766559/z)*std::pow(0.36787944117144232159552377016146*(z+1.0/(12.0*z-1.0/(10.0*z))), z)));
- #endif
- }
-
- /// Floor implementation.
- /// \param arg value to round
- /// \return rounded value
- static half floor(half arg) { return half(binary, round_half<std::round_toward_neg_infinity>(arg.data_)); }
-
- /// Ceiling implementation.
- /// \param arg value to round
- /// \return rounded value
- static half ceil(half arg) { return half(binary, round_half<std::round_toward_infinity>(arg.data_)); }
-
- /// Truncation implementation.
- /// \param arg value to round
- /// \return rounded value
- static half trunc(half arg) { return half(binary, round_half<std::round_toward_zero>(arg.data_)); }
-
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static half round(half arg) { return half(binary, round_half_up(arg.data_)); }
-
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static long lround(half arg) { return detail::half2int_up<long>(arg.data_); }
-
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static half rint(half arg) { return half(binary, round_half<half::round_style>(arg.data_)); }
-
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static long lrint(half arg) { return detail::half2int<half::round_style,long>(arg.data_); }
-
- #if HALF_ENABLE_CPP11_LONG_LONG
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static long long llround(half arg) { return detail::half2int_up<long long>(arg.data_); }
-
- /// Nearest integer implementation.
- /// \param arg value to round
- /// \return rounded value
- static long long llrint(half arg) { return detail::half2int<half::round_style,long long>(arg.data_); }
- #endif
-
- /// Decompression implementation.
- /// \param arg number to decompress
- /// \param exp address to store exponent at
- /// \return normalized significant
- static half frexp(half arg, int *exp)
- {
- unsigned int m = arg.data_ & 0x7FFF;
- if(m >= 0x7C00 || !m)
- return *exp = 0, arg;
- int e = m >> 10;
- if(!e)
- for(m<<=1; m<0x400; m<<=1,--e) ;
- return *exp = e-14, half(binary, static_cast<uint16>((arg.data_&0x8000)|0x3800|(m&0x3FF)));
- }
-
- /// Decompression implementation.
- /// \param arg number to decompress
- /// \param iptr address to store integer part at
- /// \return fractional part
- static half modf(half arg, half *iptr)
- {
- unsigned int e = arg.data_ & 0x7C00;
- if(e > 0x6000)
- return *iptr = arg, (e==0x7C00&&(arg.data_&0x3FF)) ? arg : half(binary, arg.data_&0x8000);
- if(e < 0x3C00)
- return iptr->data_ = arg.data_ & 0x8000, arg;
- e >>= 10;
- unsigned int mask = (1<<(25-e)) - 1, m = arg.data_ & mask;
- iptr->data_ = arg.data_ & ~mask;
- if(!m)
- return half(binary, arg.data_&0x8000);
- for(; m<0x400; m<<=1,--e) ;
- return half(binary, static_cast<uint16>((arg.data_&0x8000)|(e<<10)|(m&0x3FF)));
- }
-
- /// Scaling implementation.
- /// \param arg number to scale
- /// \param exp power of two to scale by
- /// \return scaled number
- static half scalbln(half arg, long exp)
- {
- long e = arg.data_ & 0x7C00;
- if(e == 0x7C00)
- return arg;
- unsigned int m = arg.data_ & 0x3FF;
- if(e >>= 10)
- m |= 0x400;
- else
- {
- if(!m)
- return arg;
- for(m<<=1; m<0x400; m<<=1,--e) ;
- }
- e += exp;
- uint16 value = arg.data_ & 0x8000;
- if(e > 30)
- {
- if(half::round_style == std::round_toward_zero)
- value |= 0x7BFF;
- else if(half::round_style == std::round_toward_infinity)
- value |= 0x7C00 - (value>>15);
- else if(half::round_style == std::round_toward_neg_infinity)
- value |= 0x7BFF + (value>>15);
- else
- value |= 0x7C00;
- }
- else if(e > 0)
- value |= (e<<10) | (m&0x3FF);
- else if(e > -11)
- {
- if(half::round_style == std::round_to_nearest)
- {
- m += 1 << -e;
- #if HALF_ROUND_TIES_TO_EVEN
- m -= (m>>(1-e)) & 1;
- #endif
- }
- else if(half::round_style == std::round_toward_infinity)
- m += ((value>>15)-1) & ((1<<(1-e))-1U);
- else if(half::round_style == std::round_toward_neg_infinity)
- m += -(value>>15) & ((1<<(1-e))-1U);
- value |= m >> (1-e);
- }
- else if(half::round_style == std::round_toward_infinity)
- value |= ((value>>15)-1) & 1;
- else if(half::round_style == std::round_toward_neg_infinity)
- value |= value >> 15;
- return half(binary, value);
- }
-
- /// Exponent implementation.
- /// \param arg number to query
- /// \return floating point exponent
- static int ilogb(half arg)
- {
- int exp = arg.data_ & 0x7FFF;
- if(!exp)
- return FP_ILOGB0;
- if(exp < 0x7C00)
- {
- if(!(exp>>=10))
- for(unsigned int m=(arg.data_&0x3FF); m<0x200; m<<=1,--exp) ;
- return exp - 15;
- }
- if(exp > 0x7C00)
- return FP_ILOGBNAN;
- return INT_MAX;
- }
-
- /// Exponent implementation.
- /// \param arg number to query
- /// \return floating point exponent
- static half logb(half arg)
- {
- int exp = arg.data_ & 0x7FFF;
- if(!exp)
- return half(binary, 0xFC00);
- if(exp < 0x7C00)
- {
- if(!(exp>>=10))
- for(unsigned int m=(arg.data_&0x3FF); m<0x200; m<<=1,--exp) ;
- return half(static_cast<float>(exp-15));
- }
- if(exp > 0x7C00)
- return arg;
- return half(binary, 0x7C00);
- }
-
- /// Enumeration implementation.
- /// \param from number to increase/decrease
- /// \param to direction to enumerate into
- /// \return next representable number
- static half nextafter(half from, half to)
- {
- uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
- if(fabs > 0x7C00)
- return from;
- if(tabs > 0x7C00 || from.data_ == to.data_ || !(fabs|tabs))
- return to;
- if(!fabs)
- return half(binary, (to.data_&0x8000)+1);
- bool lt = (signbit(from) ? (static_cast<int17>(0x8000)-from.data_) : static_cast<int17>(from.data_)) <
- (signbit(to) ? (static_cast<int17>(0x8000)-to.data_) : static_cast<int17>(to.data_));
- return half(binary, from.data_+(((from.data_>>15)^static_cast<uint16>(lt))<<1)-1);
- }
-
- /// Enumeration implementation.
- /// \param from number to increase/decrease
- /// \param to direction to enumerate into
- /// \return next representable number
- static half nexttoward(half from, long double to)
- {
- if(isnan(from))
- return from;
- long double lfrom = static_cast<long double>(from);
- if(builtin_isnan(to) || lfrom == to)
- return half(static_cast<float>(to));
- if(!(from.data_&0x7FFF))
- return half(binary, (static_cast<detail::uint16>(builtin_signbit(to))<<15)+1);
- return half(binary, from.data_+(((from.data_>>15)^static_cast<uint16>(lfrom<to))<<1)-1);
- }
-
- /// Sign implementation
- /// \param x first operand
- /// \param y second operand
- /// \return composed value
- static half copysign(half x, half y) { return half(binary, x.data_^((x.data_^y.data_)&0x8000)); }
-
- /// Classification implementation.
- /// \param arg value to classify
- /// \retval true if infinite number
- /// \retval false else
- static int fpclassify(half arg)
- {
- unsigned int abs = arg.data_ & 0x7FFF;
- if(abs > 0x7C00)
- return FP_NAN;
- if(abs == 0x7C00)
- return FP_INFINITE;
- if(abs > 0x3FF)
- return FP_NORMAL;
- return abs ? FP_SUBNORMAL : FP_ZERO;
- }
-
- /// Classification implementation.
- /// \param arg value to classify
- /// \retval true if finite number
- /// \retval false else
- static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }
-
- /// Classification implementation.
- /// \param arg value to classify
- /// \retval true if infinite number
- /// \retval false else
- static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }
-
- /// Classification implementation.
- /// \param arg value to classify
- /// \retval true if not a number
- /// \retval false else
- static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }
-
- /// Classification implementation.
- /// \param arg value to classify
- /// \retval true if normal number
- /// \retval false else
- static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }
-
- /// Sign bit implementation.
- /// \param arg value to check
- /// \retval true if signed
- /// \retval false if unsigned
- static bool signbit(half arg) { return (arg.data_&0x8000) != 0; }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if operands equal
- /// \retval false else
- static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if operands not equal
- /// \retval false else
- static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x > \a y
- /// \retval false else
- static bool isgreater(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
- static_cast<int17>(x.data_)) > (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x >= \a y
- /// \retval false else
- static bool isgreaterequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
- static_cast<int17>(x.data_)) >= (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x < \a y
- /// \retval false else
- static bool isless(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
- static_cast<int17>(x.data_)) < (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x <= \a y
- /// \retval false else
- static bool islessequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
- static_cast<int17>(x.data_)) <= (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true neither \a x > \a y nor \a x < \a y
- /// \retval false else
- static bool islessgreater(half x, half y)
- {
- if(isnan(x) || isnan(y))
- return false;
- int17 a = signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_);
- int17 b = signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_);
- return a < b || a > b;
- }
-
- /// Comparison implementation.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if operand unordered
- /// \retval false else
- static bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
-
- private:
- static double erf(double arg)
- {
- if(builtin_isinf(arg))
- return (arg<0.0) ? -1.0 : 1.0;
- double x2 = static_cast<double>(arg) * static_cast<double>(arg), ax2 = 0.147 * x2;
- double value = std::sqrt(1.0-std::exp(-x2*(1.2732395447351626861510701069801+ax2)/(1.0+ax2)));
- return builtin_signbit(arg) ? -value : value;
- }
-
- static double lgamma(double arg)
- {
- double v = 1.0;
- for(; arg<8.0; ++arg) v *= arg;
- double w = 1.0 / (arg * arg);
- return (((((((-0.02955065359477124183006535947712*w+0.00641025641025641025641025641026)*w+
- -0.00191752691752691752691752691753)*w+8.4175084175084175084175084175084e-4)*w+
- -5.952380952380952380952380952381e-4)*w+7.9365079365079365079365079365079e-4)*w+
- -0.00277777777777777777777777777778)*w+0.08333333333333333333333333333333)/arg +
- 0.91893853320467274178032973640562 - std::log(v) - arg + (arg-0.5) * std::log(arg);
- }
- };
-
- /// Wrapper for unary half-precision functions needing specialization for individual argument types.
- /// \tparam T argument type
- template<typename T> struct unary_specialized
- {
- /// Negation implementation.
- /// \param arg value to negate
- /// \return negated value
- static HALF_CONSTEXPR half negate(half arg) { return half(binary, arg.data_^0x8000); }
-
- /// Absolute value implementation.
- /// \param arg function argument
- /// \return absolute value
- static half fabs(half arg) { return half(binary, arg.data_&0x7FFF); }
- };
- template<> struct unary_specialized<expr>
- {
- static HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); }
- static expr fabs(float arg) { return expr(std::fabs(arg)); }
- };
-
- /// Wrapper for binary half-precision functions needing specialization for individual argument types.
- /// \tparam T first argument type
- /// \tparam U first argument type
- template<typename T,typename U> struct binary_specialized
- {
- /// Minimum implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return minimum value
- static expr fmin(float x, float y)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::fmin(x, y));
- #else
- if(builtin_isnan(x))
- return expr(y);
- if(builtin_isnan(y))
- return expr(x);
- return expr(std::min(x, y));
- #endif
- }
-
- /// Maximum implementation.
- /// \param x first operand
- /// \param y second operand
- /// \return maximum value
- static expr fmax(float x, float y)
- {
- #if HALF_ENABLE_CPP11_CMATH
- return expr(std::fmax(x, y));
- #else
- if(builtin_isnan(x))
- return expr(y);
- if(builtin_isnan(y))
- return expr(x);
- return expr(std::max(x, y));
- #endif
- }
- };
- template<> struct binary_specialized<half,half>
- {
- static half fmin(half x, half y)
- {
- if(functions::isnan(x))
- return y;
- if(functions::isnan(y))
- return x;
- return ((functions::signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_)) >
- (functions::signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))) ? y : x;
- }
- static half fmax(half x, half y)
- {
- if(functions::isnan(x))
- return y;
- if(functions::isnan(y))
- return x;
- return ((functions::signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_)) <
- (functions::signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))) ? y : x;
- }
- };
-
- /// Helper class for half casts.
- /// This class template has to be specialized for all valid cast argument to define an appropriate static `cast` member
- /// function and a corresponding `type` member denoting its return type.
- /// \tparam T destination type
- /// \tparam U source type
- /// \tparam R rounding mode to use
- template<typename T,typename U,std::float_round_style R=(std::float_round_style)(HALF_ROUND_STYLE)> struct half_caster {};
- template<typename U,std::float_round_style R> struct half_caster<half,U,R>
- {
- #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
- static_assert(std::is_arithmetic<U>::value, "half_cast from non-arithmetic type unsupported");
- #endif
-
- typedef half type;
- static half cast(U arg) { return cast_impl(arg, is_float<U>()); };
-
- private:
- static half cast_impl(U arg, true_type) { return half(binary, float2half<R>(static_cast<float>(arg))); }
- static half cast_impl(U arg, false_type) { return half(binary, int2half<R>(arg)); }
- };
- template<typename T,std::float_round_style R> struct half_caster<T,half,R>
- {
- #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
- static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");
- #endif
-
- typedef T type;
- template<typename U> static T cast(U arg) { return cast_impl(arg, is_float<T>()); }
-
- private:
- static T cast_impl(float arg, true_type) { return static_cast<T>(arg); }
- static T cast_impl(half arg, false_type) { return half2int<R,T>(arg.data_); }
- };
- template<typename T,std::float_round_style R> struct half_caster<T,expr,R> : public half_caster<T,half,R> {};
- template<std::float_round_style R> struct half_caster<half,half,R>
- {
- typedef half type;
- static half cast(half arg) { return arg; }
- };
- template<std::float_round_style R> struct half_caster<half,expr,R> : public half_caster<half,half,R> {};
-
- /// \name Comparison operators
- /// \{
-
- /// Comparison for equality.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if operands equal
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator==(T x, U y) { return functions::isequal(x, y); }
-
- /// Comparison for inequality.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if operands not equal
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator!=(T x, U y) { return functions::isnotequal(x, y); }
-
- /// Comparison for less than.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x less than \a y
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator<(T x, U y) { return functions::isless(x, y); }
-
- /// Comparison for greater than.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x greater than \a y
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator>(T x, U y) { return functions::isgreater(x, y); }
-
- /// Comparison for less equal.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x less equal \a y
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator<=(T x, U y) { return functions::islessequal(x, y); }
-
- /// Comparison for greater equal.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x greater equal \a y
- /// \retval false else
- template<typename T,typename U> typename enable<bool,T,U>::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); }
-
- /// \}
- /// \name Arithmetic operators
- /// \{
-
- /// Add halfs.
- /// \param x left operand
- /// \param y right operand
- /// \return sum of half expressions
- template<typename T,typename U> typename enable<expr,T,U>::type operator+(T x, U y) { return functions::plus(x, y); }
-
- /// Subtract halfs.
- /// \param x left operand
- /// \param y right operand
- /// \return difference of half expressions
- template<typename T,typename U> typename enable<expr,T,U>::type operator-(T x, U y) { return functions::minus(x, y); }
-
- /// Multiply halfs.
- /// \param x left operand
- /// \param y right operand
- /// \return product of half expressions
- template<typename T,typename U> typename enable<expr,T,U>::type operator*(T x, U y) { return functions::multiplies(x, y); }
-
- /// Divide halfs.
- /// \param x left operand
- /// \param y right operand
- /// \return quotient of half expressions
- template<typename T,typename U> typename enable<expr,T,U>::type operator/(T x, U y) { return functions::divides(x, y); }
-
- /// Identity.
- /// \param arg operand
- /// \return uncahnged operand
- template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator+(T arg) { return arg; }
-
- /// Negation.
- /// \param arg operand
- /// \return negated operand
- template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator-(T arg) { return unary_specialized<T>::negate(arg); }
-
- /// \}
- /// \name Input and output
- /// \{
-
- /// Output operator.
- /// \param out output stream to write into
- /// \param arg half expression to write
- /// \return reference to output stream
- template<typename T,typename charT,typename traits> typename enable<std::basic_ostream<charT,traits>&,T>::type
- operator<<(std::basic_ostream<charT,traits> &out, T arg) { return functions::write(out, arg); }
-
- /// Input operator.
- /// \param in input stream to read from
- /// \param arg half to read into
- /// \return reference to input stream
- template<typename charT,typename traits> std::basic_istream<charT,traits>&
- operator>>(std::basic_istream<charT,traits> &in, half &arg) { return functions::read(in, arg); }
-
- /// \}
- /// \name Basic mathematical operations
- /// \{
-
- /// Absolute value.
- /// \param arg operand
- /// \return absolute value of \a arg
-// template<typename T> typename enable<T,T>::type abs(T arg) { return unary_specialized<T>::fabs(arg); }
- inline half abs(half arg) { return unary_specialized<half>::fabs(arg); }
- inline expr abs(expr arg) { return unary_specialized<expr>::fabs(arg); }
-
- /// Absolute value.
- /// \param arg operand
- /// \return absolute value of \a arg
-// template<typename T> typename enable<T,T>::type fabs(T arg) { return unary_specialized<T>::fabs(arg); }
- inline half fabs(half arg) { return unary_specialized<half>::fabs(arg); }
- inline expr fabs(expr arg) { return unary_specialized<expr>::fabs(arg); }
-
- /// Remainder of division.
- /// \param x first operand
- /// \param y second operand
- /// \return remainder of floating point division.
-// template<typename T,typename U> typename enable<expr,T,U>::type fmod(T x, U y) { return functions::fmod(x, y); }
- inline expr fmod(half x, half y) { return functions::fmod(x, y); }
- inline expr fmod(half x, expr y) { return functions::fmod(x, y); }
- inline expr fmod(expr x, half y) { return functions::fmod(x, y); }
- inline expr fmod(expr x, expr y) { return functions::fmod(x, y); }
-
- /// Remainder of division.
- /// \param x first operand
- /// \param y second operand
- /// \return remainder of floating point division.
-// template<typename T,typename U> typename enable<expr,T,U>::type remainder(T x, U y) { return functions::remainder(x, y); }
- inline expr remainder(half x, half y) { return functions::remainder(x, y); }
- inline expr remainder(half x, expr y) { return functions::remainder(x, y); }
- inline expr remainder(expr x, half y) { return functions::remainder(x, y); }
- inline expr remainder(expr x, expr y) { return functions::remainder(x, y); }
-
- /// Remainder of division.
- /// \param x first operand
- /// \param y second operand
- /// \param quo address to store some bits of quotient at
- /// \return remainder of floating point division.
-// template<typename T,typename U> typename enable<expr,T,U>::type remquo(T x, U y, int *quo) { return functions::remquo(x, y, quo); }
- inline expr remquo(half x, half y, int *quo) { return functions::remquo(x, y, quo); }
- inline expr remquo(half x, expr y, int *quo) { return functions::remquo(x, y, quo); }
- inline expr remquo(expr x, half y, int *quo) { return functions::remquo(x, y, quo); }
- inline expr remquo(expr x, expr y, int *quo) { return functions::remquo(x, y, quo); }
-
- /// Fused multiply add.
- /// \param x first operand
- /// \param y second operand
- /// \param z third operand
- /// \return ( \a x * \a y ) + \a z rounded as one operation.
-// template<typename T,typename U,typename V> typename enable<expr,T,U,V>::type fma(T x, U y, V z) { return functions::fma(x, y, z); }
- inline expr fma(half x, half y, half z) { return functions::fma(x, y, z); }
- inline expr fma(half x, half y, expr z) { return functions::fma(x, y, z); }
- inline expr fma(half x, expr y, half z) { return functions::fma(x, y, z); }
- inline expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); }
- inline expr fma(expr x, half y, half z) { return functions::fma(x, y, z); }
- inline expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); }
- inline expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); }
- inline expr fma(expr x, expr y, expr z) { return functions::fma(x, y, z); }
-
- /// Maximum of half expressions.
- /// \param x first operand
- /// \param y second operand
- /// \return maximum of operands
-// template<typename T,typename U> typename result<T,U>::type fmax(T x, U y) { return binary_specialized<T,U>::fmax(x, y); }
- inline half fmax(half x, half y) { return binary_specialized<half,half>::fmax(x, y); }
- inline expr fmax(half x, expr y) { return binary_specialized<half,expr>::fmax(x, y); }
- inline expr fmax(expr x, half y) { return binary_specialized<expr,half>::fmax(x, y); }
- inline expr fmax(expr x, expr y) { return binary_specialized<expr,expr>::fmax(x, y); }
-
- /// Minimum of half expressions.
- /// \param x first operand
- /// \param y second operand
- /// \return minimum of operands
-// template<typename T,typename U> typename result<T,U>::type fmin(T x, U y) { return binary_specialized<T,U>::fmin(x, y); }
- inline half fmin(half x, half y) { return binary_specialized<half,half>::fmin(x, y); }
- inline expr fmin(half x, expr y) { return binary_specialized<half,expr>::fmin(x, y); }
- inline expr fmin(expr x, half y) { return binary_specialized<expr,half>::fmin(x, y); }
- inline expr fmin(expr x, expr y) { return binary_specialized<expr,expr>::fmin(x, y); }
-
- /// Positive difference.
- /// \param x first operand
- /// \param y second operand
- /// \return \a x - \a y or 0 if difference negative
-// template<typename T,typename U> typename enable<expr,T,U>::type fdim(T x, U y) { return functions::fdim(x, y); }
- inline expr fdim(half x, half y) { return functions::fdim(x, y); }
- inline expr fdim(half x, expr y) { return functions::fdim(x, y); }
- inline expr fdim(expr x, half y) { return functions::fdim(x, y); }
- inline expr fdim(expr x, expr y) { return functions::fdim(x, y); }
-
- /// Get NaN value.
- /// \param arg descriptive string (ignored)
- /// \return quiet NaN
- inline half nanh(const char *arg) { return functions::nanh(arg); }
-
- /// \}
- /// \name Exponential functions
- /// \{
-
- /// Exponential function.
- /// \param arg function argument
- /// \return e raised to \a arg
-// template<typename T> typename enable<expr,T>::type exp(T arg) { return functions::exp(arg); }
- inline expr exp(half arg) { return functions::exp(arg); }
- inline expr exp(expr arg) { return functions::exp(arg); }
-
- /// Exponential minus one.
- /// \param arg function argument
- /// \return e raised to \a arg subtracted by 1
-// template<typename T> typename enable<expr,T>::type expm1(T arg) { return functions::expm1(arg); }
- inline expr expm1(half arg) { return functions::expm1(arg); }
- inline expr expm1(expr arg) { return functions::expm1(arg); }
-
- /// Binary exponential.
- /// \param arg function argument
- /// \return 2 raised to \a arg
-// template<typename T> typename enable<expr,T>::type exp2(T arg) { return functions::exp2(arg); }
- inline expr exp2(half arg) { return functions::exp2(arg); }
- inline expr exp2(expr arg) { return functions::exp2(arg); }
-
- /// Natural logorithm.
- /// \param arg function argument
- /// \return logarithm of \a arg to base e
-// template<typename T> typename enable<expr,T>::type log(T arg) { return functions::log(arg); }
- inline expr log(half arg) { return functions::log(arg); }
- inline expr log(expr arg) { return functions::log(arg); }
-
- /// Common logorithm.
- /// \param arg function argument
- /// \return logarithm of \a arg to base 10
-// template<typename T> typename enable<expr,T>::type log10(T arg) { return functions::log10(arg); }
- inline expr log10(half arg) { return functions::log10(arg); }
- inline expr log10(expr arg) { return functions::log10(arg); }
-
- /// Natural logorithm.
- /// \param arg function argument
- /// \return logarithm of \a arg plus 1 to base e
-// template<typename T> typename enable<expr,T>::type log1p(T arg) { return functions::log1p(arg); }
- inline expr log1p(half arg) { return functions::log1p(arg); }
- inline expr log1p(expr arg) { return functions::log1p(arg); }
-
- /// Binary logorithm.
- /// \param arg function argument
- /// \return logarithm of \a arg to base 2
-// template<typename T> typename enable<expr,T>::type log2(T arg) { return functions::log2(arg); }
- inline expr log2(half arg) { return functions::log2(arg); }
- inline expr log2(expr arg) { return functions::log2(arg); }
-
- /// \}
- /// \name Power functions
- /// \{
-
- /// Square root.
- /// \param arg function argument
- /// \return square root of \a arg
-// template<typename T> typename enable<expr,T>::type sqrt(T arg) { return functions::sqrt(arg); }
- inline expr sqrt(half arg) { return functions::sqrt(arg); }
- inline expr sqrt(expr arg) { return functions::sqrt(arg); }
-
- /// Cubic root.
- /// \param arg function argument
- /// \return cubic root of \a arg
-// template<typename T> typename enable<expr,T>::type cbrt(T arg) { return functions::cbrt(arg); }
- inline expr cbrt(half arg) { return functions::cbrt(arg); }
- inline expr cbrt(expr arg) { return functions::cbrt(arg); }
-
- /// Hypotenuse function.
- /// \param x first argument
- /// \param y second argument
- /// \return square root of sum of squares without internal over- or underflows
-// template<typename T,typename U> typename enable<expr,T,U>::type hypot(T x, U y) { return functions::hypot(x, y); }
- inline expr hypot(half x, half y) { return functions::hypot(x, y); }
- inline expr hypot(half x, expr y) { return functions::hypot(x, y); }
- inline expr hypot(expr x, half y) { return functions::hypot(x, y); }
- inline expr hypot(expr x, expr y) { return functions::hypot(x, y); }
-
- /// Power function.
- /// \param base first argument
- /// \param exp second argument
- /// \return \a base raised to \a exp
-// template<typename T,typename U> typename enable<expr,T,U>::type pow(T base, U exp) { return functions::pow(base, exp); }
- inline expr pow(half base, half exp) { return functions::pow(base, exp); }
- inline expr pow(half base, expr exp) { return functions::pow(base, exp); }
- inline expr pow(expr base, half exp) { return functions::pow(base, exp); }
- inline expr pow(expr base, expr exp) { return functions::pow(base, exp); }
-
- /// \}
- /// \name Trigonometric functions
- /// \{
-
- /// Sine function.
- /// \param arg function argument
- /// \return sine value of \a arg
-// template<typename T> typename enable<expr,T>::type sin(T arg) { return functions::sin(arg); }
- inline expr sin(half arg) { return functions::sin(arg); }
- inline expr sin(expr arg) { return functions::sin(arg); }
-
- /// Cosine function.
- /// \param arg function argument
- /// \return cosine value of \a arg
-// template<typename T> typename enable<expr,T>::type cos(T arg) { return functions::cos(arg); }
- inline expr cos(half arg) { return functions::cos(arg); }
- inline expr cos(expr arg) { return functions::cos(arg); }
-
- /// Tangent function.
- /// \param arg function argument
- /// \return tangent value of \a arg
-// template<typename T> typename enable<expr,T>::type tan(T arg) { return functions::tan(arg); }
- inline expr tan(half arg) { return functions::tan(arg); }
- inline expr tan(expr arg) { return functions::tan(arg); }
-
- /// Arc sine.
- /// \param arg function argument
- /// \return arc sine value of \a arg
-// template<typename T> typename enable<expr,T>::type asin(T arg) { return functions::asin(arg); }
- inline expr asin(half arg) { return functions::asin(arg); }
- inline expr asin(expr arg) { return functions::asin(arg); }
-
- /// Arc cosine function.
- /// \param arg function argument
- /// \return arc cosine value of \a arg
-// template<typename T> typename enable<expr,T>::type acos(T arg) { return functions::acos(arg); }
- inline expr acos(half arg) { return functions::acos(arg); }
- inline expr acos(expr arg) { return functions::acos(arg); }
-
- /// Arc tangent function.
- /// \param arg function argument
- /// \return arc tangent value of \a arg
-// template<typename T> typename enable<expr,T>::type atan(T arg) { return functions::atan(arg); }
- inline expr atan(half arg) { return functions::atan(arg); }
- inline expr atan(expr arg) { return functions::atan(arg); }
-
- /// Arc tangent function.
- /// \param x first argument
- /// \param y second argument
- /// \return arc tangent value
-// template<typename T,typename U> typename enable<expr,T,U>::type atan2(T x, U y) { return functions::atan2(x, y); }
- inline expr atan2(half x, half y) { return functions::atan2(x, y); }
- inline expr atan2(half x, expr y) { return functions::atan2(x, y); }
- inline expr atan2(expr x, half y) { return functions::atan2(x, y); }
- inline expr atan2(expr x, expr y) { return functions::atan2(x, y); }
-
- /// \}
- /// \name Hyperbolic functions
- /// \{
-
- /// Hyperbolic sine.
- /// \param arg function argument
- /// \return hyperbolic sine value of \a arg
-// template<typename T> typename enable<expr,T>::type sinh(T arg) { return functions::sinh(arg); }
- inline expr sinh(half arg) { return functions::sinh(arg); }
- inline expr sinh(expr arg) { return functions::sinh(arg); }
-
- /// Hyperbolic cosine.
- /// \param arg function argument
- /// \return hyperbolic cosine value of \a arg
-// template<typename T> typename enable<expr,T>::type cosh(T arg) { return functions::cosh(arg); }
- inline expr cosh(half arg) { return functions::cosh(arg); }
- inline expr cosh(expr arg) { return functions::cosh(arg); }
-
- /// Hyperbolic tangent.
- /// \param arg function argument
- /// \return hyperbolic tangent value of \a arg
-// template<typename T> typename enable<expr,T>::type tanh(T arg) { return functions::tanh(arg); }
- inline expr tanh(half arg) { return functions::tanh(arg); }
- inline expr tanh(expr arg) { return functions::tanh(arg); }
-
- /// Hyperbolic area sine.
- /// \param arg function argument
- /// \return area sine value of \a arg
-// template<typename T> typename enable<expr,T>::type asinh(T arg) { return functions::asinh(arg); }
- inline expr asinh(half arg) { return functions::asinh(arg); }
- inline expr asinh(expr arg) { return functions::asinh(arg); }
-
- /// Hyperbolic area cosine.
- /// \param arg function argument
- /// \return area cosine value of \a arg
-// template<typename T> typename enable<expr,T>::type acosh(T arg) { return functions::acosh(arg); }
- inline expr acosh(half arg) { return functions::acosh(arg); }
- inline expr acosh(expr arg) { return functions::acosh(arg); }
-
- /// Hyperbolic area tangent.
- /// \param arg function argument
- /// \return area tangent value of \a arg
-// template<typename T> typename enable<expr,T>::type atanh(T arg) { return functions::atanh(arg); }
- inline expr atanh(half arg) { return functions::atanh(arg); }
- inline expr atanh(expr arg) { return functions::atanh(arg); }
-
- /// \}
- /// \name Error and gamma functions
- /// \{
-
- /// Error function.
- /// \param arg function argument
- /// \return error function value of \a arg
-// template<typename T> typename enable<expr,T>::type erf(T arg) { return functions::erf(arg); }
- inline expr erf(half arg) { return functions::erf(arg); }
- inline expr erf(expr arg) { return functions::erf(arg); }
-
- /// Complementary error function.
- /// \param arg function argument
- /// \return 1 minus error function value of \a arg
-// template<typename T> typename enable<expr,T>::type erfc(T arg) { return functions::erfc(arg); }
- inline expr erfc(half arg) { return functions::erfc(arg); }
- inline expr erfc(expr arg) { return functions::erfc(arg); }
-
- /// Natural logarithm of gamma function.
- /// \param arg function argument
- /// \return natural logarith of gamma function for \a arg
-// template<typename T> typename enable<expr,T>::type lgamma(T arg) { return functions::lgamma(arg); }
- inline expr lgamma(half arg) { return functions::lgamma(arg); }
- inline expr lgamma(expr arg) { return functions::lgamma(arg); }
-
- /// Gamma function.
- /// \param arg function argument
- /// \return gamma function value of \a arg
-// template<typename T> typename enable<expr,T>::type tgamma(T arg) { return functions::tgamma(arg); }
- inline expr tgamma(half arg) { return functions::tgamma(arg); }
- inline expr tgamma(expr arg) { return functions::tgamma(arg); }
-
- /// \}
- /// \name Rounding
- /// \{
-
- /// Nearest integer not less than half value.
- /// \param arg half to round
- /// \return nearest integer not less than \a arg
-// template<typename T> typename enable<half,T>::type ceil(T arg) { return functions::ceil(arg); }
- inline half ceil(half arg) { return functions::ceil(arg); }
- inline half ceil(expr arg) { return functions::ceil(arg); }
-
- /// Nearest integer not greater than half value.
- /// \param arg half to round
- /// \return nearest integer not greater than \a arg
-// template<typename T> typename enable<half,T>::type floor(T arg) { return functions::floor(arg); }
- inline half floor(half arg) { return functions::floor(arg); }
- inline half floor(expr arg) { return functions::floor(arg); }
-
- /// Nearest integer not greater in magnitude than half value.
- /// \param arg half to round
- /// \return nearest integer not greater in magnitude than \a arg
-// template<typename T> typename enable<half,T>::type trunc(T arg) { return functions::trunc(arg); }
- inline half trunc(half arg) { return functions::trunc(arg); }
- inline half trunc(expr arg) { return functions::trunc(arg); }
-
- /// Nearest integer.
- /// \param arg half to round
- /// \return nearest integer, rounded away from zero in half-way cases
-// template<typename T> typename enable<half,T>::type round(T arg) { return functions::round(arg); }
- inline half round(half arg) { return functions::round(arg); }
- inline half round(expr arg) { return functions::round(arg); }
-
- /// Nearest integer.
- /// \param arg half to round
- /// \return nearest integer, rounded away from zero in half-way cases
-// template<typename T> typename enable<long,T>::type lround(T arg) { return functions::lround(arg); }
- inline long lround(half arg) { return functions::lround(arg); }
- inline long lround(expr arg) { return functions::lround(arg); }
-
- /// Nearest integer using half's internal rounding mode.
- /// \param arg half expression to round
- /// \return nearest integer using default rounding mode
-// template<typename T> typename enable<half,T>::type nearbyint(T arg) { return functions::nearbyint(arg); }
- inline half nearbyint(half arg) { return functions::rint(arg); }
- inline half nearbyint(expr arg) { return functions::rint(arg); }
-
- /// Nearest integer using half's internal rounding mode.
- /// \param arg half expression to round
- /// \return nearest integer using default rounding mode
-// template<typename T> typename enable<half,T>::type rint(T arg) { return functions::rint(arg); }
- inline half rint(half arg) { return functions::rint(arg); }
- inline half rint(expr arg) { return functions::rint(arg); }
-
- /// Nearest integer using half's internal rounding mode.
- /// \param arg half expression to round
- /// \return nearest integer using default rounding mode
-// template<typename T> typename enable<long,T>::type lrint(T arg) { return functions::lrint(arg); }
- inline long lrint(half arg) { return functions::lrint(arg); }
- inline long lrint(expr arg) { return functions::lrint(arg); }
- #if HALF_ENABLE_CPP11_LONG_LONG
- /// Nearest integer.
- /// \param arg half to round
- /// \return nearest integer, rounded away from zero in half-way cases
-// template<typename T> typename enable<long long,T>::type llround(T arg) { return functions::llround(arg); }
- inline long long llround(half arg) { return functions::llround(arg); }
- inline long long llround(expr arg) { return functions::llround(arg); }
-
- /// Nearest integer using half's internal rounding mode.
- /// \param arg half expression to round
- /// \return nearest integer using default rounding mode
-// template<typename T> typename enable<long long,T>::type llrint(T arg) { return functions::llrint(arg); }
- inline long long llrint(half arg) { return functions::llrint(arg); }
- inline long long llrint(expr arg) { return functions::llrint(arg); }
- #endif
-
- /// \}
- /// \name Floating point manipulation
- /// \{
-
- /// Decompress floating point number.
- /// \param arg number to decompress
- /// \param exp address to store exponent at
- /// \return significant in range [0.5, 1)
-// template<typename T> typename enable<half,T>::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); }
- inline half frexp(half arg, int *exp) { return functions::frexp(arg, exp); }
- inline half frexp(expr arg, int *exp) { return functions::frexp(arg, exp); }
-
- /// Multiply by power of two.
- /// \param arg number to modify
- /// \param exp power of two to multiply with
- /// \return \a arg multplied by 2 raised to \a exp
-// template<typename T> typename enable<half,T>::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp); }
- inline half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); }
- inline half ldexp(expr arg, int exp) { return functions::scalbln(arg, exp); }
-
- /// Extract integer and fractional parts.
- /// \param arg number to decompress
- /// \param iptr address to store integer part at
- /// \return fractional part
-// template<typename T> typename enable<half,T>::type modf(T arg, half *iptr) { return functions::modf(arg, iptr); }
- inline half modf(half arg, half *iptr) { return functions::modf(arg, iptr); }
- inline half modf(expr arg, half *iptr) { return functions::modf(arg, iptr); }
-
- /// Multiply by power of two.
- /// \param arg number to modify
- /// \param exp power of two to multiply with
- /// \return \a arg multplied by 2 raised to \a exp
-// template<typename T> typename enable<half,T>::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp); }
- inline half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); }
- inline half scalbn(expr arg, int exp) { return functions::scalbln(arg, exp); }
-
- /// Multiply by power of two.
- /// \param arg number to modify
- /// \param exp power of two to multiply with
- /// \return \a arg multplied by 2 raised to \a exp
-// template<typename T> typename enable<half,T>::type scalbln(T arg, long exp) { return functions::scalbln(arg, exp); }
- inline half scalbln(half arg, long exp) { return functions::scalbln(arg, exp); }
- inline half scalbln(expr arg, long exp) { return functions::scalbln(arg, exp); }
-
- /// Extract exponent.
- /// \param arg number to query
- /// \return floating point exponent
- /// \retval FP_ILOGB0 for zero
- /// \retval FP_ILOGBNAN for NaN
- /// \retval MAX_INT for infinity
-// template<typename T> typename enable<int,T>::type ilogb(T arg) { return functions::ilogb(arg); }
- inline int ilogb(half arg) { return functions::ilogb(arg); }
- inline int ilogb(expr arg) { return functions::ilogb(arg); }
-
- /// Extract exponent.
- /// \param arg number to query
- /// \return floating point exponent
-// template<typename T> typename enable<half,T>::type logb(T arg) { return functions::logb(arg); }
- inline half logb(half arg) { return functions::logb(arg); }
- inline half logb(expr arg) { return functions::logb(arg); }
-
- /// Next representable value.
- /// \param from value to compute next representable value for
- /// \param to direction towards which to compute next value
- /// \return next representable value after \a from in direction towards \a to
-// template<typename T,typename U> typename enable<half,T,U>::type nextafter(T from, U to) { return functions::nextafter(from, to); }
- inline half nextafter(half from, half to) { return functions::nextafter(from, to); }
- inline half nextafter(half from, expr to) { return functions::nextafter(from, to); }
- inline half nextafter(expr from, half to) { return functions::nextafter(from, to); }
- inline half nextafter(expr from, expr to) { return functions::nextafter(from, to); }
-
- /// Next representable value.
- /// \param from value to compute next representable value for
- /// \param to direction towards which to compute next value
- /// \return next representable value after \a from in direction towards \a to
-// template<typename T> typename enable<half,T>::type nexttoward(T from, long double to) { return functions::nexttoward(from, to); }
- inline half nexttoward(half from, long double to) { return functions::nexttoward(from, to); }
- inline half nexttoward(expr from, long double to) { return functions::nexttoward(from, to); }
-
- /// Take sign.
- /// \param x value to change sign for
- /// \param y value to take sign from
- /// \return value equal to \a x in magnitude and to \a y in sign
-// template<typename T,typename U> typename enable<half,T,U>::type copysign(T x, U y) { return functions::copysign(x, y); }
- inline half copysign(half x, half y) { return functions::copysign(x, y); }
- inline half copysign(half x, expr y) { return functions::copysign(x, y); }
- inline half copysign(expr x, half y) { return functions::copysign(x, y); }
- inline half copysign(expr x, expr y) { return functions::copysign(x, y); }
-
- /// \}
- /// \name Floating point classification
- /// \{
-
-
- /// Classify floating point value.
- /// \param arg number to classify
- /// \retval FP_ZERO for positive and negative zero
- /// \retval FP_SUBNORMAL for subnormal numbers
- /// \retval FP_INFINITY for positive and negative infinity
- /// \retval FP_NAN for NaNs
- /// \retval FP_NORMAL for all other (normal) values
-// template<typename T> typename enable<int,T>::type fpclassify(T arg) { return functions::fpclassify(arg); }
- inline int fpclassify(half arg) { return functions::fpclassify(arg); }
- inline int fpclassify(expr arg) { return functions::fpclassify(arg); }
-
- /// Check if finite number.
- /// \param arg number to check
- /// \retval true if neither infinity nor NaN
- /// \retval false else
-// template<typename T> typename enable<bool,T>::type isfinite(T arg) { return functions::isfinite(arg); }
- inline bool isfinite(half arg) { return functions::isfinite(arg); }
- inline bool isfinite(expr arg) { return functions::isfinite(arg); }
-
- /// Check for infinity.
- /// \param arg number to check
- /// \retval true for positive or negative infinity
- /// \retval false else
-// template<typename T> typename enable<bool,T>::type isinf(T arg) { return functions::isinf(arg); }
- inline bool isinf(half arg) { return functions::isinf(arg); }
- inline bool isinf(expr arg) { return functions::isinf(arg); }
-
- /// Check for NaN.
- /// \param arg number to check
- /// \retval true for NaNs
- /// \retval false else
-// template<typename T> typename enable<bool,T>::type isnan(T arg) { return functions::isnan(arg); }
- inline bool isnan(half arg) { return functions::isnan(arg); }
- inline bool isnan(expr arg) { return functions::isnan(arg); }
-
- /// Check if normal number.
- /// \param arg number to check
- /// \retval true if normal number
- /// \retval false if either subnormal, zero, infinity or NaN
-// template<typename T> typename enable<bool,T>::type isnormal(T arg) { return functions::isnormal(arg); }
- inline bool isnormal(half arg) { return functions::isnormal(arg); }
- inline bool isnormal(expr arg) { return functions::isnormal(arg); }
-
- /// Check sign.
- /// \param arg number to check
- /// \retval true for negative number
- /// \retval false for positive number
-// template<typename T> typename enable<bool,T>::type signbit(T arg) { return functions::signbit(arg); }
- inline bool signbit(half arg) { return functions::signbit(arg); }
- inline bool signbit(expr arg) { return functions::signbit(arg); }
-
- /// \}
- /// \name Comparison
- /// \{
-
- /// Comparison for greater than.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x greater than \a y
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type isgreater(T x, U y) { return functions::isgreater(x, y); }
- inline bool isgreater(half x, half y) { return functions::isgreater(x, y); }
- inline bool isgreater(half x, expr y) { return functions::isgreater(x, y); }
- inline bool isgreater(expr x, half y) { return functions::isgreater(x, y); }
- inline bool isgreater(expr x, expr y) { return functions::isgreater(x, y); }
-
- /// Comparison for greater equal.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x greater equal \a y
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type isgreaterequal(T x, U y) { return functions::isgreaterequal(x, y); }
- inline bool isgreaterequal(half x, half y) { return functions::isgreaterequal(x, y); }
- inline bool isgreaterequal(half x, expr y) { return functions::isgreaterequal(x, y); }
- inline bool isgreaterequal(expr x, half y) { return functions::isgreaterequal(x, y); }
- inline bool isgreaterequal(expr x, expr y) { return functions::isgreaterequal(x, y); }
-
- /// Comparison for less than.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x less than \a y
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type isless(T x, U y) { return functions::isless(x, y); }
- inline bool isless(half x, half y) { return functions::isless(x, y); }
- inline bool isless(half x, expr y) { return functions::isless(x, y); }
- inline bool isless(expr x, half y) { return functions::isless(x, y); }
- inline bool isless(expr x, expr y) { return functions::isless(x, y); }
-
- /// Comparison for less equal.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if \a x less equal \a y
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type islessequal(T x, U y) { return functions::islessequal(x, y); }
- inline bool islessequal(half x, half y) { return functions::islessequal(x, y); }
- inline bool islessequal(half x, expr y) { return functions::islessequal(x, y); }
- inline bool islessequal(expr x, half y) { return functions::islessequal(x, y); }
- inline bool islessequal(expr x, expr y) { return functions::islessequal(x, y); }
-
- /// Comarison for less or greater.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if either less or greater
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type islessgreater(T x, U y) { return functions::islessgreater(x, y); }
- inline bool islessgreater(half x, half y) { return functions::islessgreater(x, y); }
- inline bool islessgreater(half x, expr y) { return functions::islessgreater(x, y); }
- inline bool islessgreater(expr x, half y) { return functions::islessgreater(x, y); }
- inline bool islessgreater(expr x, expr y) { return functions::islessgreater(x, y); }
-
- /// Check if unordered.
- /// \param x first operand
- /// \param y second operand
- /// \retval true if unordered (one or two NaN operands)
- /// \retval false else
-// template<typename T,typename U> typename enable<bool,T,U>::type isunordered(T x, U y) { return functions::isunordered(x, y); }
- inline bool isunordered(half x, half y) { return functions::isunordered(x, y); }
- inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); }
- inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); }
- inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); }
-
- /// \name Casting
- /// \{
-
- /// Cast to or from half-precision floating point number.
- /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. Floating point types are
- /// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
- /// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
- /// suppressed. Integer types are converted directly using the given rounding mode, without any roundtrip over `float`
- /// that a `static_cast` would otherwise do. It uses the default rounding mode.
- ///
- /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
- /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
- /// error and casting between [half](\ref half_float::half)s is just a no-op.
- /// \tparam T destination type (half or built-in arithmetic type)
- /// \tparam U source type (half or built-in arithmetic type)
- /// \param arg value to cast
- /// \return \a arg converted to destination type
- template<typename T,typename U> typename half_caster<T,U>::type half_cast(U arg) { return half_caster<T,U>::cast(arg); }
-
- /// Cast to or from half-precision floating point number.
- /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. Floating point types are
- /// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
- /// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
- /// suppressed. Integer types are converted directly using the given rounding mode, without any roundtrip over `float`
- /// that a `static_cast` would otherwise do.
- ///
- /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
- /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
- /// error and casting between [half](\ref half_float::half)s is just a no-op.
- /// \tparam T destination type (half or built-in arithmetic type)
- /// \tparam R rounding mode to use.
- /// \tparam U source type (half or built-in arithmetic type)
- /// \param arg value to cast
- /// \return \a arg converted to destination type
- template<typename T,std::float_round_style R,typename U> typename half_caster<T,U,R>::type half_cast(U arg)
- { return half_caster<T,U,R>::cast(arg); }
- /// \}
- }
-
- using detail::operator==;
- using detail::operator!=;
- using detail::operator<;
- using detail::operator>;
- using detail::operator<=;
- using detail::operator>=;
- using detail::operator+;
- using detail::operator-;
- using detail::operator*;
- using detail::operator/;
- using detail::operator<<;
- using detail::operator>>;
-
- using detail::abs;
- using detail::fabs;
- using detail::fmod;
- using detail::remainder;
- using detail::remquo;
- using detail::fma;
- using detail::fmax;
- using detail::fmin;
- using detail::fdim;
- using detail::nanh;
- using detail::exp;
- using detail::expm1;
- using detail::exp2;
- using detail::log;
- using detail::log10;
- using detail::log1p;
- using detail::log2;
- using detail::sqrt;
- using detail::cbrt;
- using detail::hypot;
- using detail::pow;
- using detail::sin;
- using detail::cos;
- using detail::tan;
- using detail::asin;
- using detail::acos;
- using detail::atan;
- using detail::atan2;
- using detail::sinh;
- using detail::cosh;
- using detail::tanh;
- using detail::asinh;
- using detail::acosh;
- using detail::atanh;
- using detail::erf;
- using detail::erfc;
- using detail::lgamma;
- using detail::tgamma;
- using detail::ceil;
- using detail::floor;
- using detail::trunc;
- using detail::round;
- using detail::lround;
- using detail::nearbyint;
- using detail::rint;
- using detail::lrint;
-#if HALF_ENABLE_CPP11_LONG_LONG
- using detail::llround;
- using detail::llrint;
-#endif
- using detail::frexp;
- using detail::ldexp;
- using detail::modf;
- using detail::scalbn;
- using detail::scalbln;
- using detail::ilogb;
- using detail::logb;
- using detail::nextafter;
- using detail::nexttoward;
- using detail::copysign;
- using detail::fpclassify;
- using detail::isfinite;
- using detail::isinf;
- using detail::isnan;
- using detail::isnormal;
- using detail::signbit;
- using detail::isgreater;
- using detail::isgreaterequal;
- using detail::isless;
- using detail::islessequal;
- using detail::islessgreater;
- using detail::isunordered;
-
- using detail::half_cast;
-}
-
-
-/// Extensions to the C++ standard library.
-namespace std
-{
- /// Numeric limits for half-precision floats.
- /// Because of the underlying single-precision implementation of many operations, it inherits some properties from
- /// `std::numeric_limits<float>`.
- template<> class numeric_limits<half_float::half> : public numeric_limits<float>
- {
- public:
- /// Supports signed values.
- static HALF_CONSTEXPR_CONST bool is_signed = true;
-
- /// Is not exact.
- static HALF_CONSTEXPR_CONST bool is_exact = false;
-
- /// Doesn't provide modulo arithmetic.
- static HALF_CONSTEXPR_CONST bool is_modulo = false;
-
- /// IEEE conformant.
- static HALF_CONSTEXPR_CONST bool is_iec559 = true;
-
- /// Supports infinity.
- static HALF_CONSTEXPR_CONST bool has_infinity = true;
-
- /// Supports quiet NaNs.
- static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;
-
- /// Supports subnormal values.
- static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
-
- /// Rounding mode.
- /// Due to the mix of internal single-precision computations (using the rounding mode of the underlying
- /// single-precision implementation) with explicit truncation of the single-to-half conversions, the actual rounding
- /// mode is indeterminate.
- static HALF_CONSTEXPR_CONST float_round_style round_style = (std::numeric_limits<float>::round_style==
- half_float::half::round_style) ? half_float::half::round_style : round_indeterminate;
-
- /// Significant digits.
- static HALF_CONSTEXPR_CONST int digits = 11;
-
- /// Significant decimal digits.
- static HALF_CONSTEXPR_CONST int digits10 = 3;
-
- /// Required decimal digits to represent all possible values.
- static HALF_CONSTEXPR_CONST int max_digits10 = 5;
-
- /// Number base.
- static HALF_CONSTEXPR_CONST int radix = 2;
-
- /// One more than smallest exponent.
- static HALF_CONSTEXPR_CONST int min_exponent = -13;
-
- /// Smallest normalized representable power of 10.
- static HALF_CONSTEXPR_CONST int min_exponent10 = -4;
-
- /// One more than largest exponent
- static HALF_CONSTEXPR_CONST int max_exponent = 16;
-
- /// Largest finitely representable power of 10.
- static HALF_CONSTEXPR_CONST int max_exponent10 = 4;
-
- /// Smallest positive normal value.
- static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); }
-
- /// Smallest finite value.
- static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); }
-
- /// Largest finite value.
- static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); }
-
- /// Difference between one and next representable value.
- static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); }
-
- /// Maximum rounding error.
- static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW
- { return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); }
-
- /// Positive infinity.
- static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); }
-
- /// Quiet NaN.
- static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); }
-
- /// Signalling NaN.
- static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); }
-
- /// Smallest positive subnormal value.
- static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); }
- };
-
-#if HALF_ENABLE_CPP11_HASH
- /// Hash function for half-precision floats.
- /// This is only defined if C++11 `std::hash` is supported and enabled.
- template<> struct hash<half_float::half> //: unary_function<half_float::half,size_t>
- {
- /// Type of function argument.
- typedef half_float::half argument_type;
-
- /// Function return type.
- typedef size_t result_type;
-
- /// Compute hash function.
- /// \param arg half to hash
- /// \return hash value
- result_type operator()(argument_type arg) const
- { return hash<half_float::detail::uint16>()(static_cast<unsigned int>(arg.data_)&-(arg.data_!=0x8000)); }
- };
-#endif
-}
-
-
-#undef HALF_CONSTEXPR
-#undef HALF_CONSTEXPR_CONST
-#undef HALF_NOEXCEPT
-#undef HALF_NOTHROW
-#ifdef HALF_POP_WARNINGS
- #pragma warning(pop)
- #undef HALF_POP_WARNINGS
-#endif
-
-#endif
diff --git a/third-party/npy-halffloat.h b/third-party/npy-halffloat.h
deleted file mode 100644
index ae29b22..0000000
--- a/third-party/npy-halffloat.h
+++ /dev/null
@@ -1,328 +0,0 @@
-/*
- * This implementation is extracted from numpy:
- * Repo: github.com/numpy/numpy
- * File: numpy/core/src/npymath/halffloat.c
- * Commit ID: 25c23f1d956104a072a95355ffaa7a38b53710b7
- * Functions are made "static inline" for performance, and
- * non-conversion functions are removed, and generation of
- * exceptions is disabled.
- */
-
-#include <cstdint>
-typedef uint16_t npy_uint16;
-typedef uint32_t npy_uint32;
-typedef uint64_t npy_uint64;
-
-/*
- * This chooses between 'ties to even' and 'ties away from zero'.
- */
-#define NPY_HALF_ROUND_TIES_TO_EVEN 1
-/*
- * If these are 1, the conversions try to trigger underflow,
- * overflow, and invalid exceptions in the FP system when needed.
- */
-#define NPY_HALF_GENERATE_OVERFLOW 0
-#define NPY_HALF_GENERATE_UNDERFLOW 0
-#define NPY_HALF_GENERATE_INVALID 0
-
-/*
- ********************************************************************
- * BIT-LEVEL CONVERSIONS *
- ********************************************************************
- */
-
-static inline npy_uint16 npy_floatbits_to_halfbits(npy_uint32 f)
-{
- npy_uint32 f_exp, f_sig;
- npy_uint16 h_sgn, h_exp, h_sig;
-
- h_sgn = (npy_uint16) ((f&0x80000000u) >> 16);
- f_exp = (f&0x7f800000u);
-
- /* Exponent overflow/NaN converts to signed inf/NaN */
- if (f_exp >= 0x47800000u) {
- if (f_exp == 0x7f800000u) {
- /* Inf or NaN */
- f_sig = (f&0x007fffffu);
- if (f_sig != 0) {
- /* NaN - propagate the flag in the significand... */
- npy_uint16 ret = (npy_uint16) (0x7c00u + (f_sig >> 13));
- /* ...but make sure it stays a NaN */
- if (ret == 0x7c00u) {
- ret++;
- }
- return h_sgn + ret;
- } else {
- /* signed inf */
- return (npy_uint16) (h_sgn + 0x7c00u);
- }
- } else {
- /* overflow to signed inf */
-#if NPY_HALF_GENERATE_OVERFLOW
- npy_set_floatstatus_overflow();
-#endif
- return (npy_uint16) (h_sgn + 0x7c00u);
- }
- }
-
- /* Exponent underflow converts to a subnormal half or signed zero */
- if (f_exp <= 0x38000000u) {
- /*
- * Signed zeros, subnormal floats, and floats with small
- * exponents all convert to signed zero halfs.
- */
- if (f_exp < 0x33000000u) {
-#if NPY_HALF_GENERATE_UNDERFLOW
- /* If f != 0, it underflowed to 0 */
- if ((f&0x7fffffff) != 0) {
- npy_set_floatstatus_underflow();
- }
-#endif
- return h_sgn;
- }
- /* Make the subnormal significand */
- f_exp >>= 23;
- f_sig = (0x00800000u + (f&0x007fffffu));
-#if NPY_HALF_GENERATE_UNDERFLOW
- /* If it's not exactly represented, it underflowed */
- if ((f_sig&(((npy_uint32)1 << (126 - f_exp)) - 1)) != 0) {
- npy_set_floatstatus_underflow();
- }
-#endif
- f_sig >>= (113 - f_exp);
- /* Handle rounding by adding 1 to the bit beyond half precision */
-#if NPY_HALF_ROUND_TIES_TO_EVEN
- /*
- * If the last bit in the half significand is 0 (already even), and
- * the remaining bit pattern is 1000...0, then we do not add one
- * to the bit after the half significand. In all other cases, we do.
- */
- if ((f_sig&0x00003fffu) != 0x00001000u) {
- f_sig += 0x00001000u;
- }
-#else
- f_sig += 0x00001000u;
-#endif
- h_sig = (npy_uint16) (f_sig >> 13);
- /*
- * If the rounding causes a bit to spill into h_exp, it will
- * increment h_exp from zero to one and h_sig will be zero.
- * This is the correct result.
- */
- return (npy_uint16) (h_sgn + h_sig);
- }
-
- /* Regular case with no overflow or underflow */
- h_exp = (npy_uint16) ((f_exp - 0x38000000u) >> 13);
- /* Handle rounding by adding 1 to the bit beyond half precision */
- f_sig = (f&0x007fffffu);
-#if NPY_HALF_ROUND_TIES_TO_EVEN
- /*
- * If the last bit in the half significand is 0 (already even), and
- * the remaining bit pattern is 1000...0, then we do not add one
- * to the bit after the half significand. In all other cases, we do.
- */
- if ((f_sig&0x00003fffu) != 0x00001000u) {
- f_sig += 0x00001000u;
- }
-#else
- f_sig += 0x00001000u;
-#endif
- h_sig = (npy_uint16) (f_sig >> 13);
- /*
- * If the rounding causes a bit to spill into h_exp, it will
- * increment h_exp by one and h_sig will be zero. This is the
- * correct result. h_exp may increment to 15, at greatest, in
- * which case the result overflows to a signed inf.
- */
-#if NPY_HALF_GENERATE_OVERFLOW
- h_sig += h_exp;
- if (h_sig == 0x7c00u) {
- npy_set_floatstatus_overflow();
- }
- return h_sgn + h_sig;
-#else
- return h_sgn + h_exp + h_sig;
-#endif
-}
-
-static inline npy_uint16 npy_doublebits_to_halfbits(npy_uint64 d)
-{
- npy_uint64 d_exp, d_sig;
- npy_uint16 h_sgn, h_exp, h_sig;
-
- h_sgn = (d&0x8000000000000000ULL) >> 48;
- d_exp = (d&0x7ff0000000000000ULL);
-
- /* Exponent overflow/NaN converts to signed inf/NaN */
- if (d_exp >= 0x40f0000000000000ULL) {
- if (d_exp == 0x7ff0000000000000ULL) {
- /* Inf or NaN */
- d_sig = (d&0x000fffffffffffffULL);
- if (d_sig != 0) {
- /* NaN - propagate the flag in the significand... */
- npy_uint16 ret = (npy_uint16) (0x7c00u + (d_sig >> 42));
- /* ...but make sure it stays a NaN */
- if (ret == 0x7c00u) {
- ret++;
- }
- return h_sgn + ret;
- } else {
- /* signed inf */
- return h_sgn + 0x7c00u;
- }
- } else {
- /* overflow to signed inf */
-#if NPY_HALF_GENERATE_OVERFLOW
- npy_set_floatstatus_overflow();
-#endif
- return h_sgn + 0x7c00u;
- }
- }
-
- /* Exponent underflow converts to subnormal half or signed zero */
- if (d_exp <= 0x3f00000000000000ULL) {
- /*
- * Signed zeros, subnormal floats, and floats with small
- * exponents all convert to signed zero halfs.
- */
- if (d_exp < 0x3e60000000000000ULL) {
-#if NPY_HALF_GENERATE_UNDERFLOW
- /* If d != 0, it underflowed to 0 */
- if ((d&0x7fffffffffffffffULL) != 0) {
- npy_set_floatstatus_underflow();
- }
-#endif
- return h_sgn;
- }
- /* Make the subnormal significand */
- d_exp >>= 52;
- d_sig = (0x0010000000000000ULL + (d&0x000fffffffffffffULL));
-#if NPY_HALF_GENERATE_UNDERFLOW
- /* If it's not exactly represented, it underflowed */
- if ((d_sig&(((npy_uint64)1 << (1051 - d_exp)) - 1)) != 0) {
- npy_set_floatstatus_underflow();
- }
-#endif
- d_sig >>= (1009 - d_exp);
- /* Handle rounding by adding 1 to the bit beyond half precision */
-#if NPY_HALF_ROUND_TIES_TO_EVEN
- /*
- * If the last bit in the half significand is 0 (already even), and
- * the remaining bit pattern is 1000...0, then we do not add one
- * to the bit after the half significand. In all other cases, we do.
- */
- if ((d_sig&0x000007ffffffffffULL) != 0x0000020000000000ULL) {
- d_sig += 0x0000020000000000ULL;
- }
-#else
- d_sig += 0x0000020000000000ULL;
-#endif
- h_sig = (npy_uint16) (d_sig >> 42);
- /*
- * If the rounding causes a bit to spill into h_exp, it will
- * increment h_exp from zero to one and h_sig will be zero.
- * This is the correct result.
- */
- return h_sgn + h_sig;
- }
-
- /* Regular case with no overflow or underflow */
- h_exp = (npy_uint16) ((d_exp - 0x3f00000000000000ULL) >> 42);
- /* Handle rounding by adding 1 to the bit beyond half precision */
- d_sig = (d&0x000fffffffffffffULL);
-#if NPY_HALF_ROUND_TIES_TO_EVEN
- /*
- * If the last bit in the half significand is 0 (already even), and
- * the remaining bit pattern is 1000...0, then we do not add one
- * to the bit after the half significand. In all other cases, we do.
- */
- if ((d_sig&0x000007ffffffffffULL) != 0x0000020000000000ULL) {
- d_sig += 0x0000020000000000ULL;
- }
-#else
- d_sig += 0x0000020000000000ULL;
-#endif
- h_sig = (npy_uint16) (d_sig >> 42);
-
- /*
- * If the rounding causes a bit to spill into h_exp, it will
- * increment h_exp by one and h_sig will be zero. This is the
- * correct result. h_exp may increment to 15, at greatest, in
- * which case the result overflows to a signed inf.
- */
-#if NPY_HALF_GENERATE_OVERFLOW
- h_sig += h_exp;
- if (h_sig == 0x7c00u) {
- npy_set_floatstatus_overflow();
- }
- return h_sgn + h_sig;
-#else
- return h_sgn + h_exp + h_sig;
-#endif
-}
-
-static inline npy_uint32 npy_halfbits_to_floatbits(npy_uint16 h)
-{
- npy_uint16 h_exp, h_sig;
- npy_uint32 f_sgn, f_exp, f_sig;
-
- h_exp = (h&0x7c00u);
- f_sgn = ((npy_uint32)h&0x8000u) << 16;
- switch (h_exp) {
- case 0x0000u: /* 0 or subnormal */
- h_sig = (h&0x03ffu);
- /* Signed zero */
- if (h_sig == 0) {
- return f_sgn;
- }
- /* Subnormal */
- h_sig <<= 1;
- while ((h_sig&0x0400u) == 0) {
- h_sig <<= 1;
- h_exp++;
- }
- f_exp = ((npy_uint32)(127 - 15 - h_exp)) << 23;
- f_sig = ((npy_uint32)(h_sig&0x03ffu)) << 13;
- return f_sgn + f_exp + f_sig;
- case 0x7c00u: /* inf or NaN */
- /* All-ones exponent and a copy of the significand */
- return f_sgn + 0x7f800000u + (((npy_uint32)(h&0x03ffu)) << 13);
- default: /* normalized */
- /* Just need to adjust the exponent and shift */
- return f_sgn + (((npy_uint32)(h&0x7fffu) + 0x1c000u) << 13);
- }
-}
-
-static inline npy_uint64 npy_halfbits_to_doublebits(npy_uint16 h)
-{
- npy_uint16 h_exp, h_sig;
- npy_uint64 d_sgn, d_exp, d_sig;
-
- h_exp = (h&0x7c00u);
- d_sgn = ((npy_uint64)h&0x8000u) << 48;
- switch (h_exp) {
- case 0x0000u: /* 0 or subnormal */
- h_sig = (h&0x03ffu);
- /* Signed zero */
- if (h_sig == 0) {
- return d_sgn;
- }
- /* Subnormal */
- h_sig <<= 1;
- while ((h_sig&0x0400u) == 0) {
- h_sig <<= 1;
- h_exp++;
- }
- d_exp = ((npy_uint64)(1023 - 15 - h_exp)) << 52;
- d_sig = ((npy_uint64)(h_sig&0x03ffu)) << 42;
- return d_sgn + d_exp + d_sig;
- case 0x7c00u: /* inf or NaN */
- /* All-ones exponent and a copy of the significand */
- return d_sgn + 0x7ff0000000000000ULL +
- (((npy_uint64)(h&0x03ffu)) << 42);
- default: /* normalized */
- /* Just need to adjust the exponent and shift */
- return d_sgn + (((npy_uint64)(h&0x7fffu) + 0xfc000u) << 42);
- }
-}
