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| /*************************************************************************************************** | ||
| * Copyright (c) 2017-2018, NVIDIA CORPORATION. All rights reserved. | ||
| * Modifications copyright (C) 2018 Uber Technologies, Inc. | ||
| * | ||
| * Redistribution and use in source and binary forms, with or without modification, are permitted | ||
| * provided that the following conditions are met: | ||
| * * Redistributions of source code must retain the above copyright notice, this list of | ||
| * conditions and the following disclaimer. | ||
| * * Redistributions in binary form must reproduce the above copyright notice, this list of | ||
| * conditions and the following disclaimer in the documentation and/or other materials | ||
| * provided with the distribution. | ||
| * * Neither the name of the NVIDIA CORPORATION nor the names of its contributors may be used | ||
| * to endorse or promote products derived from this software without specific prior written | ||
| * permission. | ||
| * | ||
| * 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 NVIDIA CORPORATION 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 TOR (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
| * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
| * | ||
| **************************************************************************************************/ | ||
| #ifndef HOROVOD_HALF_H | ||
| #define HOROVOD_HALF_H | ||
|
|
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| namespace horovod { | ||
| namespace common { | ||
|
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| inline void HalfBits2Float(unsigned short* src, float* res) { | ||
| unsigned h = *src; | ||
| int sign = ((h >> 15) & 1); | ||
| int exp = ((h >> 10) & 0x1f); | ||
| int mantissa = (h & 0x3ff); | ||
| unsigned f = 0; | ||
|
|
||
| if (exp > 0 && exp < 31) { | ||
| // normal | ||
| exp += 112; | ||
| f = (sign << 31) | (exp << 23) | (mantissa << 13); | ||
| } else if (exp == 0) { | ||
| if (mantissa) { | ||
| // subnormal | ||
| exp += 113; | ||
| while ((mantissa & (1 << 10)) == 0) { | ||
| mantissa <<= 1; | ||
| exp--; | ||
| } | ||
| mantissa &= 0x3ff; | ||
| f = (sign << 31) | (exp << 23) | (mantissa << 13); | ||
| } else { | ||
| // sign-preserving zero | ||
| f = (sign << 31); | ||
| } | ||
| } else if (exp == 31) { | ||
| if (mantissa) { | ||
| f = 0x7fffffff; // not a number | ||
| } else { | ||
| f = (0xff << 23) | (sign << 31); // inf | ||
| } | ||
| } | ||
|
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| *res = *reinterpret_cast<float const*>(&f); | ||
| } | ||
|
|
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| inline void Float2HalfBits(float* src, unsigned short* dest) { | ||
| // software implementation rounds toward nearest even | ||
| unsigned const& s = *reinterpret_cast<unsigned const*>(src); | ||
| uint16_t sign = uint16_t((s >> 16) & 0x8000); | ||
| int16_t exp = uint16_t(((s >> 23) & 0xff) - 127); | ||
| int mantissa = s & 0x7fffff; | ||
| uint16_t u = 0; | ||
|
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| if ((s & 0x7fffffff) == 0) { | ||
| // sign-preserving zero | ||
| *dest = sign; | ||
| return; | ||
| } | ||
|
|
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| if (exp > 15) { | ||
| if (exp == 128 && mantissa) { | ||
| // not a number | ||
| u = 0x7fff; | ||
| } else { | ||
| // overflow to infinity | ||
| u = sign | 0x7c00; | ||
| } | ||
| *dest = u; | ||
| return; | ||
| } | ||
|
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| int sticky_bit = 0; | ||
|
|
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| if (exp >= -14) { | ||
| // normal fp32 to normal fp16 | ||
| exp = uint16_t(exp + uint16_t(15)); | ||
| u = uint16_t(((exp & 0x1f) << 10)); | ||
| u = uint16_t(u | (mantissa >> 13)); | ||
| } else { | ||
| // normal single-precision to subnormal half_t-precision representation | ||
| int rshift = (-14 - exp); | ||
| if (rshift < 32) { | ||
| mantissa |= (1 << 23); | ||
|
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| sticky_bit = ((mantissa & ((1 << rshift) - 1)) != 0); | ||
|
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| mantissa = (mantissa >> rshift); | ||
| u = (uint16_t(mantissa >> 13) & 0x3ff); | ||
| } else { | ||
| mantissa = 0; | ||
| u = 0; | ||
| } | ||
| } | ||
|
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| // round to nearest even | ||
| int round_bit = ((mantissa >> 12) & 1); | ||
| sticky_bit |= ((mantissa & ((1 << 12) - 1)) != 0); | ||
|
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| if ((round_bit && sticky_bit) || (round_bit && (u & 1))) { | ||
| u = uint16_t(u + 1); | ||
| } | ||
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| u |= sign; | ||
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| *dest = u; | ||
| } | ||
|
|
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| } // namespace common | ||
| } // namespace horovod | ||
|
|
||
| #endif // HOROVOD_HALF_H |
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