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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4; fill-column: 100 -*- */
/*
* libfixmath is Copyright (c) 2011-2021 Flatmush <Flatmush@gmail.com>,
* Petteri Aimonen <Petteri.Aimonen@gmail.com>, & libfixmath AUTHORS
*
* 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.
*/
#include <tools/fix16.hxx>
const fix16_t fix16_minimum = 0x80000000; /*!< the minimum value of fix16_t */
const fix16_t fix16_overflow = 0x80000000; /*!< the value used to indicate overflows */
static inline uint32_t fix_abs(fix16_t in)
{
if (in == fix16_minimum)
{
// minimum negative number has same representation as
// its absolute value in unsigned
return 0x80000000;
}
else
{
return (in >= 0) ? in : -in;
}
}
/* 64-bit implementation for fix16_mul. Fastest version for e.g. ARM Cortex M3.
* Performs a 32*32 -> 64bit multiplication. The middle 32 bits are the result,
* bottom 16 bits are used for rounding, and upper 16 bits are used for overflow
* detection.
*/
fix16_t fix16_mul(fix16_t inArg0, fix16_t inArg1)
{
int64_t product = static_cast<int64_t>(inArg0) * inArg1;
// The upper 17 bits should all be the same (the sign).
uint32_t upper = (product >> 47);
if (product < 0)
{
if (~upper)
return fix16_overflow;
// This adjustment is required in order to round -1/2 correctly
product--;
}
else
{
if (upper)
return fix16_overflow;
}
fix16_t result = product >> 16;
result += (product & 0x8000) >> 15;
return result;
}
/* 32-bit implementation of fix16_div. Fastest version for e.g. ARM Cortex M3.
* Performs 32-bit divisions repeatedly to reduce the remainder. For this to
* be efficient, the processor has to have 32-bit hardware division.
*/
#ifdef __GNUC__
// Count leading zeros, using processor-specific instruction if available.
#define clz(x) (__builtin_clzl(x) - (8 * sizeof(long) - 32))
#else
static uint8_t clz(uint32_t x)
{
uint8_t result = 0;
if (x == 0)
return 32;
while (!(x & 0xF0000000))
{
result += 4;
x <<= 4;
}
while (!(x & 0x80000000))
{
result += 1;
x <<= 1;
}
return result;
}
#endif
fix16_t fix16_div(fix16_t a, fix16_t b)
{
// This uses a hardware 32/32 bit division multiple times, until we have
// computed all the bits in (a<<17)/b. Usually this takes 1-3 iterations.
if (b == 0)
return fix16_minimum;
uint32_t remainder = fix_abs(a);
uint32_t divider = fix_abs(b);
uint64_t quotient = 0;
int bit_pos = 17;
// Kick-start the division a bit.
// This improves speed in the worst-case scenarios where N and D are large
// It gets a lower estimate for the result by N/(D >> 17 + 1).
if (divider & 0xFFF00000)
{
uint32_t shifted_div = (divider >> 17) + 1;
quotient = remainder / shifted_div;
uint64_t tmp = (quotient * static_cast<uint64_t>(divider)) >> 17;
remainder -= static_cast<uint32_t>(tmp);
}
// If the divider is divisible by 2^n, take advantage of it.
while (!(divider & 0xF) && bit_pos >= 4)
{
divider >>= 4;
bit_pos -= 4;
}
while (remainder && bit_pos >= 0)
{
// Shift remainder as much as we can without overflowing
int shift = clz(remainder);
if (shift > bit_pos)
shift = bit_pos;
remainder <<= shift;
bit_pos -= shift;
uint32_t div = remainder / divider;
remainder = remainder % divider;
quotient += static_cast<uint64_t>(div) << bit_pos;
if (div & ~(0xFFFFFFFF >> bit_pos))
return fix16_overflow;
remainder <<= 1;
bit_pos--;
}
// Quotient is always positive so rounding is easy
quotient++;
fix16_t result = quotient >> 1;
// Figure out the sign of the result
if ((a ^ b) & 0x80000000)
{
if (result == fix16_minimum)
return fix16_overflow;
result = -result;
}
return result;
}
/* vim:set shiftwidth=4 softtabstop=4 expandtab cinoptions=b1,g0,N-s cinkeys+=0=break: */
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