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#pragma once
/*
* Copyright (C) 2005-2008 Team XBMC
* http://www.xbmc.org
*
* This Program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2, or (at your option)
* any later version.
*
* This Program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with XBMC; see the file COPYING. If not, write to
* the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
* http://www.gnu.org/copyleft/gpl.html
*
*/
#include <stdint.h>
#include <cassert>
#include <climits>
#include <cmath>
#ifdef __SSE2__
#include <emmintrin.h>
#endif
// use real compiler defines in here as we want to
// avoid including system.h or other magic includes.
// use 'gcc -dM -E - < /dev/null' or similar to find them.
#if defined(__ppc__) || \
defined(__powerpc__) || \
(defined(__APPLE__) && defined(__arm__) && defined(__llvm__)) || \
(defined(__ANDROID__) && defined(__arm__)) || \
defined(TARGET_RASPBERRY_PI)
#define DISABLE_MATHUTILS_ASM_ROUND_INT
#endif
#if defined(__ppc__) || \
defined(__powerpc__) || \
(defined(__APPLE__) && defined(__llvm__)) || \
(defined(__ANDROID__) && defined(__arm__)) || \
defined(TARGET_RASPBERRY_PI)
#define DISABLE_MATHUTILS_ASM_TRUNCATE_INT
#endif
/*! \brief Math utility class.
Note that the test() routine should return true for all implementations
See http://ldesoras.free.fr/doc/articles/rounding_en.pdf for an explanation
of the technique used on x86.
*/
namespace MathUtils
{
// GCC does something stupid with optimization on release builds if we try
// to assert in these functions
/*! \brief Round to nearest integer.
This routine does fast rounding to the nearest integer.
In the case (k + 0.5 for any integer k) we round up to k+1, and in all other
instances we should return the nearest integer.
Thus, { -1.5, -0.5, 0.5, 1.5 } is rounded to { -1, 0, 1, 2 }.
It preserves the property that round(k) - round(k-1) = 1 for all doubles k.
Make sure MathUtils::test() returns true for each implementation.
\sa truncate_int, test
*/
inline int round_int(double x)
{
assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
assert(x < static_cast<double>(INT_MAX / 2) + 1.0);
const float round_to_nearest = 0.5f;
int i;
#if defined(DISABLE_MATHUTILS_ASM_ROUND_INT)
i = floor(x + round_to_nearest);
#elif defined(__arm__)
// From 'ARM-v7-M Architecture Reference Manual' page A7-569:
// "The floating-point to integer operation (vcvt) [normally] uses the Round towards Zero rounding mode"
// Because of this...we must use some less-than-straightforward logic to perform this operation without
// changing the rounding mode flags
/* The assembly below implements the following logic:
if (x < 0)
inc = -0.5f
else
inc = 0.5f
int_val = trunc(x+inc);
err = x - int_val;
if (err == 0.5f)
int_val++;
return int_val;
*/
__asm__ __volatile__ (
#if defined(__ARM_PCS_VFP)
"fconstd d1,#%G[rnd_val] \n\t" // Copy round_to_nearest into a working register (d1 = 0.5)
#else
"vmov.F64 d1,%[rnd_val] \n\t"
#endif
"fcmpezd %P[value] \n\t" // Check value against zero (value == 0?)
"fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
"it mi \n\t"
"vnegmi.F64 d1, d1 \n\t" // if N-flag is set, negate round_to_nearest (if (value < 0) d1 = -1 * d1)
"vadd.F64 d1,%P[value],d1 \n\t" // Add round_to_nearest to value, store result in working register (d1 += value)
"vcvt.S32.F64 s3,d1 \n\t" // Truncate(round towards zero) (s3 = (int)d1)
"vmov %[result],s3 \n\t" // Store the integer result in a general-purpose register (result = s3)
"vcvt.F64.S32 d1,s3 \n\t" // Convert back to floating-point (d1 = (double)s3)
"vsub.F64 d1,%P[value],d1 \n\t" // Calculate the error (d1 = value - d1)
#if defined(__ARM_PCS_VFP)
"fconstd d2,#%G[rnd_val] \n\t" // d2 = 0.5;
#else
"vmov.F64 d2,%[rnd_val] \n\t"
#endif
"fcmped d1, d2 \n\t" // (d1 == 0.5?)
"fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
"it eq \n\t"
"addeq %[result],#1 \n\t" // (if (d1 == d2) result++;)
: [result] "=r"(i) // Outputs
: [rnd_val] "Dv" (round_to_nearest), [value] "w"(x) // Inputs
: "d1", "d2", "s3" // Clobbers
);
#elif defined(__SSE2__)
const float round_dn_to_nearest = 0.4999999f;
i = (x > 0) ? _mm_cvttsd_si32(_mm_set_sd(x + round_to_nearest)) : _mm_cvttsd_si32(_mm_set_sd(x - round_dn_to_nearest));
#elif defined(_WIN32)
__asm
{
fld x
fadd st, st (0)
fadd round_to_nearest
fistp i
sar i, 1
}
#else
__asm__ __volatile__ (
"fadd %%st\n\t"
"fadd %%st(1)\n\t"
"fistpl %0\n\t"
"sarl $1, %0\n"
: "=m"(i) : "u"(round_to_nearest), "t"(x) : "st"
);
#endif
return i;
}
/*! \brief Truncate to nearest integer.
This routine does fast truncation to an integer.
It should simply drop the fractional portion of the floating point number.
Make sure MathUtils::test() returns true for each implementation.
\sa round_int, test
*/
inline int truncate_int(double x)
{
assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
assert(x < static_cast<double>(INT_MAX / 2) + 1.0);
int i;
#if defined(DISABLE_MATHUTILS_ASM_TRUNCATE_INT)
return i = (int)x;
#elif defined(__arm__)
__asm__ __volatile__ (
"vcvt.S32.F64 %[result],%P[value] \n\t" // Truncate(round towards zero) and store the result
: [result] "=w"(i) // Outputs
: [value] "w"(x) // Inputs
);
return i;
#elif defined(_WIN32)
const float round_towards_m_i = -0.5f;
__asm
{
fld x
fadd st, st (0)
fabs
fadd round_towards_m_i
fistp i
sar i, 1
}
#else
const float round_towards_m_i = -0.5f;
__asm__ __volatile__ (
"fadd %%st\n\t"
"fabs\n\t"
"fadd %%st(1)\n\t"
"fistpl %0\n\t"
"sarl $1, %0\n"
: "=m"(i) : "u"(round_towards_m_i), "t"(x) : "st"
);
#endif
if (x < 0)
i = -i;
return (i);
}
inline int64_t abs(int64_t a)
{
return (a < 0) ? -a : a;
}
inline unsigned bitcount(unsigned v)
{
unsigned c = 0;
for (c = 0; v; c++)
v &= v - 1; // clear the least significant bit set
return c;
}
inline void hack()
{
// stupid hack to keep compiler from dropping these
// functions as unused
MathUtils::round_int(0.0);
MathUtils::truncate_int(0.0);
MathUtils::abs(0);
}
#if 0
/*! \brief test routine for round_int and truncate_int
Must return true on all platforms.
*/
inline bool test()
{
for (int i = -8; i < 8; ++i)
{
double d = 0.25*i;
int r = (i < 0) ? (i - 1) / 4 : (i + 2) / 4;
int t = i / 4;
if (round_int(d) != r || truncate_int(d) != t)
return false;
}
return true;
}
#endif
} // namespace MathUtils
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