412 lines
15 KiB
C++
412 lines
15 KiB
C++
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// SPDX-License-Identifier: Apache-2.0
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// ----------------------------------------------------------------------------
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// Copyright 2011-2021 Arm Limited
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//
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// Licensed under the Apache License, Version 2.0 (the "License"); you may not
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// use this file except in compliance with the License. You may obtain a copy
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// of the License at:
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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// License for the specific language governing permissions and limitations
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// under the License.
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// ----------------------------------------------------------------------------
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/**
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* @brief Soft-float library for IEEE-754.
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*/
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#if (ASTCENC_F16C == 0) && (ASTCENC_NEON == 0)
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#include "astcenc_mathlib.h"
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/* sized soft-float types. These are mapped to the sized integer
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types of C99, instead of C's floating-point types; this is because
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the library needs to maintain exact, bit-level control on all
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operations on these data types. */
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typedef uint16_t sf16;
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typedef uint32_t sf32;
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/******************************************
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helper functions and their lookup tables
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******************************************/
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/* count leading zeros functions. Only used when the input is nonzero. */
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#if defined(__GNUC__) && (defined(__i386) || defined(__amd64))
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#elif defined(__arm__) && defined(__ARMCC_VERSION)
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#elif defined(__arm__) && defined(__GNUC__)
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#else
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/* table used for the slow default versions. */
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static const uint8_t clz_table[256] =
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{
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8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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};
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#endif
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/*
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32-bit count-leading-zeros function: use the Assembly instruction whenever possible. */
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static uint32_t clz32(uint32_t inp)
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{
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#if defined(__GNUC__) && (defined(__i386) || defined(__amd64))
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uint32_t bsr;
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__asm__("bsrl %1, %0": "=r"(bsr):"r"(inp | 1));
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return 31 - bsr;
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#else
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#if defined(__arm__) && defined(__ARMCC_VERSION)
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return __clz(inp); /* armcc builtin */
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#else
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#if defined(__arm__) && defined(__GNUC__)
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uint32_t lz;
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__asm__("clz %0, %1": "=r"(lz):"r"(inp));
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return lz;
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#else
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/* slow default version */
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uint32_t summa = 24;
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if (inp >= UINT32_C(0x10000))
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{
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inp >>= 16;
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summa -= 16;
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}
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if (inp >= UINT32_C(0x100))
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{
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inp >>= 8;
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summa -= 8;
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}
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return summa + clz_table[inp];
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#endif
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#endif
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#endif
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}
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/* the five rounding modes that IEEE-754r defines */
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typedef enum
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{
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SF_UP = 0, /* round towards positive infinity */
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SF_DOWN = 1, /* round towards negative infinity */
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SF_TOZERO = 2, /* round towards zero */
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SF_NEARESTEVEN = 3, /* round toward nearest value; if mid-between, round to even value */
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SF_NEARESTAWAY = 4 /* round toward nearest value; if mid-between, round away from zero */
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} roundmode;
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static uint32_t rtne_shift32(uint32_t inp, uint32_t shamt)
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{
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uint32_t vl1 = UINT32_C(1) << shamt;
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uint32_t inp2 = inp + (vl1 >> 1); /* added 0.5 ULP */
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uint32_t msk = (inp | UINT32_C(1)) & vl1; /* nonzero if odd. '| 1' forces it to 1 if the shamt is 0. */
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msk--; /* negative if even, nonnegative if odd. */
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inp2 -= (msk >> 31); /* subtract epsilon before shift if even. */
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inp2 >>= shamt;
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return inp2;
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}
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static uint32_t rtna_shift32(uint32_t inp, uint32_t shamt)
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{
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uint32_t vl1 = (UINT32_C(1) << shamt) >> 1;
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inp += vl1;
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inp >>= shamt;
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return inp;
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}
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static uint32_t rtup_shift32(uint32_t inp, uint32_t shamt)
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{
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uint32_t vl1 = UINT32_C(1) << shamt;
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inp += vl1;
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inp--;
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inp >>= shamt;
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return inp;
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}
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/* convert from FP16 to FP32. */
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static sf32 sf16_to_sf32(sf16 inp)
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{
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uint32_t inpx = inp;
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/*
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This table contains, for every FP16 sign/exponent value combination,
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the difference between the input FP16 value and the value obtained
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by shifting the correct FP32 result right by 13 bits.
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This table allows us to handle every case except denormals and NaN
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with just 1 table lookup, 2 shifts and 1 add.
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*/
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#define WITH_MSB(a) (UINT32_C(a) | (1u << 31))
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static const uint32_t tbl[64] =
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{
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WITH_MSB(0x00000), 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000,
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0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000,
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0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000,
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0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, 0x1C000, WITH_MSB(0x38000),
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WITH_MSB(0x38000), 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000,
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0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000,
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0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000,
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0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, 0x54000, WITH_MSB(0x70000)
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};
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uint32_t res = tbl[inpx >> 10];
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res += inpx;
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/* Normal cases: MSB of 'res' not set. */
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if ((res & WITH_MSB(0)) == 0)
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{
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return res << 13;
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}
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/* Infinity and Zero: 10 LSB of 'res' not set. */
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if ((res & 0x3FF) == 0)
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{
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return res << 13;
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}
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/* NaN: the exponent field of 'inp' is non-zero. */
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if ((inpx & 0x7C00) != 0)
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{
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/* All NaNs are quietened. */
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return (res << 13) | 0x400000;
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}
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/* Denormal cases */
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uint32_t sign = (inpx & 0x8000) << 16;
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uint32_t mskval = inpx & 0x7FFF;
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uint32_t leadingzeroes = clz32(mskval);
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mskval <<= leadingzeroes;
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return (mskval >> 8) + ((0x85 - leadingzeroes) << 23) + sign;
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}
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/* Conversion routine that converts from FP32 to FP16. It supports denormals and all rounding modes. If a NaN is given as input, it is quietened. */
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static sf16 sf32_to_sf16(sf32 inp, roundmode rmode)
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{
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/* for each possible sign/exponent combination, store a case index. This gives a 512-byte table */
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static const uint8_t tab[512] {
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0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
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20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
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30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50,
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5, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 15, 15, 15, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
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25, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35,
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35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55,
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};
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/* many of the cases below use a case-dependent magic constant. So we look up a magic constant before actually performing the switch. This table allows us to group cases, thereby minimizing code
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size. */
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static const uint32_t tabx[60] {
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UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0x8000), UINT32_C(0x80000000), UINT32_C(0x8000), UINT32_C(0x8000), UINT32_C(0x8000),
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UINT32_C(1), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0x8000), UINT32_C(0x8001), UINT32_C(0x8000), UINT32_C(0x8000), UINT32_C(0x8000),
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UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0), UINT32_C(0x8000), UINT32_C(0x8000), UINT32_C(0x8000), UINT32_C(0x8000), UINT32_C(0x8000),
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UINT32_C(0xC8001FFF), UINT32_C(0xC8000000), UINT32_C(0xC8000000), UINT32_C(0xC8000FFF), UINT32_C(0xC8001000),
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UINT32_C(0x58000000), UINT32_C(0x38001FFF), UINT32_C(0x58000000), UINT32_C(0x58000FFF), UINT32_C(0x58001000),
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UINT32_C(0x7C00), UINT32_C(0x7BFF), UINT32_C(0x7BFF), UINT32_C(0x7C00), UINT32_C(0x7C00),
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UINT32_C(0xFBFF), UINT32_C(0xFC00), UINT32_C(0xFBFF), UINT32_C(0xFC00), UINT32_C(0xFC00),
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UINT32_C(0x90000000), UINT32_C(0x90000000), UINT32_C(0x90000000), UINT32_C(0x90000000), UINT32_C(0x90000000),
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UINT32_C(0x20000000), UINT32_C(0x20000000), UINT32_C(0x20000000), UINT32_C(0x20000000), UINT32_C(0x20000000)
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};
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uint32_t p;
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uint32_t idx = rmode + tab[inp >> 23];
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uint32_t vlx = tabx[idx];
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switch (idx)
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{
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/*
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Positive number which may be Infinity or NaN.
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We need to check whether it is NaN; if it is, quieten it by setting the top bit of the mantissa.
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(If we don't do this quieting, then a NaN that is distinguished only by having
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its low-order bits set, would be turned into an INF. */
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case 50:
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case 51:
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case 52:
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case 53:
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case 54:
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case 55:
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case 56:
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case 57:
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case 58:
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case 59:
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/*
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the input value is 0x7F800000 or 0xFF800000 if it is INF.
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By subtracting 1, we get 7F7FFFFF or FF7FFFFF, that is, bit 23 becomes zero.
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For NaNs, however, this operation will keep bit 23 with the value 1.
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We can then extract bit 23, and logical-OR bit 9 of the result with this
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bit in order to quieten the NaN (a Quiet NaN is a NaN where the top bit
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of the mantissa is set.)
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*/
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p = (inp - 1) & UINT32_C(0x800000); /* zero if INF, nonzero if NaN. */
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return static_cast<sf16>(((inp + vlx) >> 13) | (p >> 14));
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/*
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positive, exponent = 0, round-mode == UP; need to check whether number actually is 0.
|
||
|
|
If it is, then return 0, else return 1 (the smallest representable nonzero number)
|
||
|
|
*/
|
||
|
|
case 0:
|
||
|
|
/*
|
||
|
|
-inp will set the MSB if the input number is nonzero.
|
||
|
|
Thus (-inp) >> 31 will turn into 0 if the input number is 0 and 1 otherwise.
|
||
|
|
*/
|
||
|
|
return static_cast<sf16>(static_cast<uint32_t>((-static_cast<int32_t>(inp))) >> 31);
|
||
|
|
|
||
|
|
/*
|
||
|
|
negative, exponent = , round-mode == DOWN, need to check whether number is
|
||
|
|
actually 0. If it is, return 0x8000 ( float -0.0 )
|
||
|
|
Else return the smallest negative number ( 0x8001 ) */
|
||
|
|
case 6:
|
||
|
|
/*
|
||
|
|
in this case 'vlx' is 0x80000000. By subtracting the input value from it,
|
||
|
|
we obtain a value that is 0 if the input value is in fact zero and has
|
||
|
|
the MSB set if it isn't. We then right-shift the value by 31 places to
|
||
|
|
get a value that is 0 if the input is -0.0 and 1 otherwise.
|
||
|
|
*/
|
||
|
|
return static_cast<sf16>(((vlx - inp) >> 31) + UINT32_C(0x8000));
|
||
|
|
|
||
|
|
/*
|
||
|
|
for all other cases involving underflow/overflow, we don't need to
|
||
|
|
do actual tests; we just return 'vlx'.
|
||
|
|
*/
|
||
|
|
case 1:
|
||
|
|
case 2:
|
||
|
|
case 3:
|
||
|
|
case 4:
|
||
|
|
case 5:
|
||
|
|
case 7:
|
||
|
|
case 8:
|
||
|
|
case 9:
|
||
|
|
case 10:
|
||
|
|
case 11:
|
||
|
|
case 12:
|
||
|
|
case 13:
|
||
|
|
case 14:
|
||
|
|
case 15:
|
||
|
|
case 16:
|
||
|
|
case 17:
|
||
|
|
case 18:
|
||
|
|
case 19:
|
||
|
|
case 40:
|
||
|
|
case 41:
|
||
|
|
case 42:
|
||
|
|
case 43:
|
||
|
|
case 44:
|
||
|
|
case 45:
|
||
|
|
case 46:
|
||
|
|
case 47:
|
||
|
|
case 48:
|
||
|
|
case 49:
|
||
|
|
return static_cast<sf16>(vlx);
|
||
|
|
|
||
|
|
/*
|
||
|
|
for normal numbers, 'vlx' is the difference between the FP32 value of a number and the
|
||
|
|
FP16 representation of the same number left-shifted by 13 places. In addition, a rounding constant is
|
||
|
|
baked into 'vlx': for rounding-away-from zero, the constant is 2^13 - 1, causing roundoff away
|
||
|
|
from zero. for round-to-nearest away, the constant is 2^12, causing roundoff away from zero.
|
||
|
|
for round-to-nearest-even, the constant is 2^12 - 1. This causes correct round-to-nearest-even
|
||
|
|
except for odd input numbers. For odd input numbers, we need to add 1 to the constant. */
|
||
|
|
|
||
|
|
/* normal number, all rounding modes except round-to-nearest-even: */
|
||
|
|
case 30:
|
||
|
|
case 31:
|
||
|
|
case 32:
|
||
|
|
case 34:
|
||
|
|
case 35:
|
||
|
|
case 36:
|
||
|
|
case 37:
|
||
|
|
case 39:
|
||
|
|
return static_cast<sf16>((inp + vlx) >> 13);
|
||
|
|
|
||
|
|
/* normal number, round-to-nearest-even. */
|
||
|
|
case 33:
|
||
|
|
case 38:
|
||
|
|
p = inp + vlx;
|
||
|
|
p += (inp >> 13) & 1;
|
||
|
|
return static_cast<sf16>(p >> 13);
|
||
|
|
|
||
|
|
/*
|
||
|
|
the various denormal cases. These are not expected to be common, so their performance is a bit
|
||
|
|
less important. For each of these cases, we need to extract an exponent and a mantissa
|
||
|
|
(including the implicit '1'!), and then right-shift the mantissa by a shift-amount that
|
||
|
|
depends on the exponent. The shift must apply the correct rounding mode. 'vlx' is used to supply the
|
||
|
|
sign of the resulting denormal number.
|
||
|
|
*/
|
||
|
|
case 21:
|
||
|
|
case 22:
|
||
|
|
case 25:
|
||
|
|
case 27:
|
||
|
|
/* denormal, round towards zero. */
|
||
|
|
p = 126 - ((inp >> 23) & 0xFF);
|
||
|
|
return static_cast<sf16>((((inp & UINT32_C(0x7FFFFF)) + UINT32_C(0x800000)) >> p) | vlx);
|
||
|
|
case 20:
|
||
|
|
case 26:
|
||
|
|
/* denormal, round away from zero. */
|
||
|
|
p = 126 - ((inp >> 23) & 0xFF);
|
||
|
|
return static_cast<sf16>(rtup_shift32((inp & UINT32_C(0x7FFFFF)) + UINT32_C(0x800000), p) | vlx);
|
||
|
|
case 24:
|
||
|
|
case 29:
|
||
|
|
/* denormal, round to nearest-away */
|
||
|
|
p = 126 - ((inp >> 23) & 0xFF);
|
||
|
|
return static_cast<sf16>(rtna_shift32((inp & UINT32_C(0x7FFFFF)) + UINT32_C(0x800000), p) | vlx);
|
||
|
|
case 23:
|
||
|
|
case 28:
|
||
|
|
/* denormal, round to nearest-even. */
|
||
|
|
p = 126 - ((inp >> 23) & 0xFF);
|
||
|
|
return static_cast<sf16>(rtne_shift32((inp & UINT32_C(0x7FFFFF)) + UINT32_C(0x800000), p) | vlx);
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* convert from soft-float to native-float */
|
||
|
|
float sf16_to_float(uint16_t p)
|
||
|
|
{
|
||
|
|
if32 i;
|
||
|
|
i.u = sf16_to_sf32(p);
|
||
|
|
return i.f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* convert from native-float to soft-float */
|
||
|
|
uint16_t float_to_sf16(float p)
|
||
|
|
{
|
||
|
|
if32 i;
|
||
|
|
i.f = p;
|
||
|
|
return sf32_to_sf16(i.u, SF_NEARESTEVEN);
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|