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/*
Copyright (c) 2010, Warmux Team
Large parts of the code are from the fixed point library of Markus Trenkwalder
Copyright (c) 2007, Markus Trenkwalder
Portions taken from the Vicent 3D rendering library
Copyright (c) 2004, David Blythe, Hans Martin Will
All rights reserved.
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 library's copyright owner 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 THE COPYRIGHT OWNER OR
CONTRIBUTORS 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 TORT (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 FIXEDP_FUNC_H_INCLUDED
#define FIXEDP_FUNC_H_INCLUDED
#include <math.h>
#ifdef _MSC_VER
# pragma once
# include "stdint_fallback.h"
#else
# include <stdint.h>
#endif
#ifdef _WIN32
# define PRIi64 "I64d"
#endif
#define FIXINT_BITS 64
namespace fp {
#if FIXINT_BITS == 64
typedef int64_t fint_t;
typedef uint64_t fuint_t;
#else
typedef int32_t fint_t;
typedef uint32_t fuint_t;
#endif
// The template argument p in all of the following functions refers to the
// fixed point precision (e.g. p = 8 gives 24.8 fixed point functions).
// Perform a fixed point multiplication without a 64-bit intermediate result.
// This is fast but beware of overflow!
template <int p>
inline fint_t fixmulf(fint_t a, fint_t b)
{
return (a * b) >> p;
}
// Perform a fixed point multiplication using a 64-bit intermediate result to
// prevent overflow problems.
template <int p>
inline fint_t fixmul(fint_t a, fint_t b)
{
return ((a * b) >> p);
}
// Fixed point division
template <int p>
inline int fixdiv(fint_t a, fint_t b)
{
#if 1
return int((a << p) / b);
#else
// The following produces the same results as the above but gcc 4.0.3
// generates fewer instructions (at least on the ARM processor).
union {
fint_t a;
struct {
int32_t l;
int32_t h;
};
} x;
x.l = a << p;
x.h = a >> (sizeof(int32_t) * 8 - p);
return (int32_t)(x.a / b);
#endif
}
namespace detail {
inline uint32_t CountLeadingZeros(uint32_t x)
{
uint32_t exp = 31;
if (x & 0xffff0000) {
exp -= 16;
x >>= 16;
}
if (x & 0xff00) {
exp -= 8;
x >>= 8;
}
if (x & 0xf0) {
exp -= 4;
x >>= 4;
}
if (x & 0xc) {
exp -= 2;
x >>= 2;
}
if (x & 0x2) {
exp -= 1;
}
return exp;
}
}
// q is the precision of the input
// output has 32-q bits of fraction
template <int p>
inline fint_t fixinv(fint_t a)
{
return fixdiv<p>(1 << p, a);
}
/* TODO fast 64 bit version of:
template <int q>
inline int fixinv(int32_t a)
{
int32_t x;
bool sign = false;
if (a < 0) {
sign = true;
a = -a;
}
static const uint16_t rcp_tab[] = {
0x8000, 0x71c7, 0x6666, 0x5d17, 0x5555, 0x4ec4, 0x4924, 0x4444
};
int32_t exp = detail::CountLeadingZeros(a);
x = ((int32_t)rcp_tab[(a>>(28-exp))&0x7]) << 2;
exp -= 16;
if (exp <= 0)
x >>= -exp;
else
x <<= exp;
// two iterations of newton-raphson x = x(2-ax)
x = fixmul<(32-q)>(x,((2<<(32-q)) - fixmul<q>(a,x)));
x = fixmul<(32-q)>(x,((2<<(32-q)) - fixmul<q>(a,x)));
if (sign)fix2float
return -x;
else
return x;
}
*/
// Conversion from and to float
template <int p>
inline float fix2float(fint_t f)
{
static const float inv = 1.0f / (1<<p);
return f * inv;
}
template <int p>
inline fint_t float2fix(float f)
{
return (fint_t)(f * (1 << p));
}
template <int p>
inline fint_t float2fix(double f)
{
return (fint_t)(f * (1 << p));
}
fint_t fixcos16(fint_t a);
fint_t fixsin16(fint_t a);
fint_t fixacos16(fint_t a);
fint_t fixasin16(fint_t a);
fint_t fixatan16(fint_t a);
fint_t fixrsqrt16(fint_t a);
fint_t fixsqrt16(fint_t a);
fint_t fixsqrt16_approx(fint_t a);
} // end namespace fp
#endif
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