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#pragma once
/*
* Copyright (C) 2005-2013 Team XBMC
* http://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, see
* <http://www.gnu.org/licenses/>.
*
*/
#include <stdint.h>
#include <cassert>
#include <climits>
#include <cmath>
#if defined(HAVE_SSE2) && defined(__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(__mips__) || \
defined(__arm__) || \
defined(__s390x__) || \
defined(__aarch64__) || \
defined(__alpha__)
#define DISABLE_MATHUTILS_ASM_ROUND_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) (INT_MIN / 2)) - 1.0);
assert(x < static_cast<double>((int) (INT_MAX / 2)) + 1.0);
#if defined(DISABLE_MATHUTILS_ASM_ROUND_INT)
/* This implementation warrants some further explanation.
*
* First, a couple of notes on rounding:
* 1) C casts from float/double to integer round towards zero.
* 2) Float/double additions are rounded according to the normal rules,
* in other words: on some architectures, it's fixed at compile-time,
* and on others it can be set using fesetround()). The following
* analysis assumes round-to-nearest with ties rounding to even. This
* is a fairly sensible choice, and is the default with ARM VFP.
*
* What this function wants is round-to-nearest with ties rounding to
* +infinity. This isn't an IEEE rounding mode, even if we could guarantee
* that all architectures supported fesetround(), which they don't. Instead,
* this adds an offset of 2147483648.5 (= 0x80000000.8p0), then casts to
* an unsigned int (crucially, all possible inputs are now in a range where
* round to zero acts the same as round to -infinity) and then subtracts
* 0x80000000 in the integer domain. The 0.5 component of the offset
* converts what is effectively a round down into a round to nearest, with
* ties rounding up, as desired.
*
* There is a catch, that because there is a double rounding, there is a
* small region where the input falls just *below* a tie, where the addition
* of the offset causes a round *up* to an exact integer, due to the finite
* level of precision available in floating point. You need to be aware of
* this when calling this function, although at present it is not believed
* that XBMC ever attempts to round numbers in this window.
*
* It is worth proving the size of the affected window. Recall that double
* precision employs a mantissa of 52 bits.
* 1) For all inputs -0.5 <= x <= INT_MAX
* Once the offset is applied, the most significant binary digit in the
* floating-point representation is +2^31.
* At this magnitude, the smallest step representable in double precision
* is 2^31 / 2^52 = 0.000000476837158203125
* So the size of the range which is rounded up due to the addition is
* half the size of this step, or 0.0000002384185791015625
*
* 2) For all inputs INT_MIN/2 < x < -0.5
* Once the offset is applied, the most significant binary digit in the
* floating-point representation is +2^30.
* At this magnitude, the smallest step representable in double precision
* is 2^30 / 2^52 = 0.0000002384185791015625
* So the size of the range which is rounded up due to the addition is
* half the size of this step, or 0.00000011920928955078125
*
* 3) For all inputs INT_MIN <= x <= INT_MIN/2
* The representation once the offset is applied has equal or greater
* precision than the input, so the addition does not cause rounding.
*/
return ((unsigned int) (x + 0x80000000.8p0)) - 0x80000000;
#else
const float round_to_nearest = 0.5f;
int i;
#if defined(HAVE_SSE2) && 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(TARGET_WINDOWS)
__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;
#endif
}
/*! \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);
return static_cast<int>(x);
}
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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