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/* cairo - a vector graphics library with display and print output
*
* Copyright © 2003 University of Southern California
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*
* The Original Code is the cairo graphics library.
*
* The Initial Developer of the Original Code is University of Southern
* California.
*
* Contributor(s):
* Carl D. Worth <cworth@cworth.org>
*/
#include "cairoint.h"
cairo_fixed_t
_cairo_fixed_from_int (int i)
{
return i << 16;
}
/* This is the "magic number" approach to converting a double into fixed
* point as described here:
*
* http://www.stereopsis.com/sree/fpu2006.html (an overview)
* http://www.d6.com/users/checker/pdfs/gdmfp.pdf (in detail)
*
* The basic idea is to add a large enough number to the double that the
* literal floating point is moved up to the extent that it forces the
* double's value to be shifted down to the bottom of the mantissa (to make
* room for the large number being added in). Since the mantissa is, at a
* given moment in time, a fixed point integer itself, one can convert a
* float to various fixed point representations by moving around the point
* of a floating point number through arithmetic operations. This behavior
* is reliable on most modern platforms as it is mandated by the IEEE-754
* standard for floating point arithmetic.
*
* For our purposes, a "magic number" must be carefully selected that is
* both large enough to produce the desired point-shifting effect, and also
* has no lower bits in its representation that would interfere with our
* value at the bottom of the mantissa. The magic number is calculated as
* follows:
*
* (2 ^ (MANTISSA_SIZE - FRACTIONAL_SIZE)) * 1.5
*
* where in our case:
* - MANTISSA_SIZE for 64-bit doubles is 52
* - FRACTIONAL_SIZE for 16.16 fixed point is 16
*
* Although this approach provides a very large speedup of this function
* on a wide-array of systems, it does come with two caveats:
*
* 1) It uses banker's rounding as opposed to arithmetic rounding.
* 2) It doesn't function properly if the FPU is in single-precision
* mode.
*/
#define CAIRO_MAGIC_NUMBER_FIXED_16_16 (103079215104.0)
cairo_fixed_t
_cairo_fixed_from_double (double d)
{
union {
double d;
int32_t i[2];
} u;
u.d = d + CAIRO_MAGIC_NUMBER_FIXED_16_16;
#ifdef FLOAT_WORDS_BIGENDIAN
return u.i[1];
#else
return u.i[0];
#endif
}
cairo_fixed_t
_cairo_fixed_from_26_6 (uint32_t i)
{
return i << 10;
}
double
_cairo_fixed_to_double (cairo_fixed_t f)
{
return ((double) f) / 65536.0;
}
int
_cairo_fixed_is_integer (cairo_fixed_t f)
{
return (f & 0xFFFF) == 0;
}
int
_cairo_fixed_integer_part (cairo_fixed_t f)
{
return f >> 16;
}
int
_cairo_fixed_integer_floor (cairo_fixed_t f)
{
if (f >= 0)
return f >> 16;
else
return -((-f - 1) >> 16) - 1;
}
int
_cairo_fixed_integer_ceil (cairo_fixed_t f)
{
if (f > 0)
return ((f - 1)>>16) + 1;
else
return - (-f >> 16);
}
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