/***************************************************************************/
/* */
/* fttrigon.c */
/* */
/* FreeType trigonometric functions (body). */
/* */
/* Copyright 2001, 2002, 2003, 2004, 2005 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used, */
/* modified, and distributed under the terms of the FreeType project */
/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
/* this file you indicate that you have read the license and */
/* understand and accept it fully. */
/* */
/***************************************************************************/
#include <ft2build.h>
#include FT_INTERNAL_OBJECTS_H
#include FT_TRIGONOMETRY_H
/* the following is 0.2715717684432231 * 2^30 */
#define FT_TRIG_COSCALE 0x11616E8EUL
/* this table was generated for FT_PI = 180L << 16, i.e. degrees */
#define FT_TRIG_MAX_ITERS 23
static const FT_Fixed
ft_trig_arctan_table[24] =
{
4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
57L, 29L, 14L, 7L, 4L, 2L, 1L
};
/* the Cordic shrink factor, multiplied by 2^32 */
#define FT_TRIG_SCALE 1166391785UL /* 0x4585BA38UL */
#ifdef FT_CONFIG_HAS_INT64
/* multiply a given value by the CORDIC shrink factor */
static FT_Fixed
ft_trig_downscale( FT_Fixed val )
{
FT_Fixed s;
FT_Int64 v;
s = val;
val = ( val >= 0 ) ? val : -val;
v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL;
val = (FT_Fixed)( v >> 32 );
return ( s >= 0 ) ? val : -val;
}
#else /* !FT_CONFIG_HAS_INT64 */
/* multiply a given value by the CORDIC shrink factor */
static FT_Fixed
ft_trig_downscale( FT_Fixed val )
{
FT_Fixed s;
FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3;
s = val;
val = ( val >= 0 ) ? val : -val;
v1 = (FT_UInt32)val >> 16;
v2 = (FT_UInt32)(val & 0xFFFFL);
k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */
k2 = (FT_UInt32)(FT_TRIG_SCALE & 0xFFFFL); /* constant */
hi = k1 * v1;
lo1 = k1 * v2 + k2 * v1; /* can't overflow */
lo2 = ( k2 * v2 ) >> 16;
lo3 = ( lo1 >= lo2 ) ? lo1 : lo2;
lo1 += lo2;
hi += lo1 >> 16;
if ( lo1 < lo3 )
hi += (FT_UInt32)0x10000UL;
val = (FT_Fixed)hi;
return ( s >= 0 ) ? val : -val;
}
#endif /* !FT_CONFIG_HAS_INT64 */
static FT_Int
ft_trig_prenorm( FT_Vector* vec )
{
FT_Fixed x, y, z;
FT_Int shift;
x = vec->x;
y = vec->y;
z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y );
shift = 0;
#if 1
/* determine msb bit index in `shift' */
if ( z >= ( 1L << 16 ) )
{
z >>= 16;
shift += 16;
}
if ( z >= ( 1L << 8 ) )
{
z >>= 8;
shift += 8;
}
if ( z >= ( 1L << 4 ) )
{
z >>= 4;
shift += 4;
}
if ( z >= ( 1L << 2 ) )
{
z >>= 2;
shift += 2;
}
if ( z >= ( 1L << 1 ) )
{
z >>= 1;
shift += 1;
}
if ( shift <= 27 )
{
shift = 27 - shift;
vec->x = x << shift;
vec->y = y << shift;
}
else
{
shift -= 27;
vec->x = x >> shift;
vec->y = y >> shift;
shift = -shift;
}
#else /* 0 */
if ( z < ( 1L << 27 ) )
{
do
{
shift++;
z <<= 1;
} while ( z < ( 1L << 27 ) );
vec->x = x << shift;
vec->y = y << shift;
}
else if ( z > ( 1L << 28 ) )
{
do
{
shift++;
z >>= 1;
} while ( z > ( 1L << 28 ) );
vec->x = x >> shift;
vec->y = y >> shift;
shift = -shift;
}
#endif /* 0 */
return shift;
}
static void
ft_trig_pseudo_rotate( FT_Vector* vec,
FT_Angle theta )
{
FT_Int i;
FT_Fixed x, y, xtemp;
const FT_Fixed *arctanptr;
x = vec->x;
y = vec->y;
/* Get angle between -90 and 90 degrees */
while ( theta <= -FT_ANGLE_PI2 )
{
x = -x;
y = -y;
theta += FT_ANGLE_PI;
}
while ( theta > FT_ANGLE_PI2 )
{
x = -x;
y = -y;
theta -= FT_ANGLE_PI;
}
/* Initial pseudorotation, with left shift */
arctanptr = ft_trig_arctan_table;
if ( theta < 0 )
{
xtemp = x + ( y << 1 );
y = y - ( x << 1 );
x = xtemp;
theta += *arctanptr++;
}
else
{
xtemp = x - ( y << 1 );
y = y + ( x << 1 );
x = xtemp;
theta -= *arctanptr++;
}
/* Subsequent pseudorotations, with right shifts */
i = 0;
do
{
if ( theta < 0 )
{
xtemp = x + ( y >> i );
y = y - ( x >> i );
x = xtemp;
theta += *arctanptr++;
}
else
{
xtemp = x - ( y >> i );
y = y + ( x >> i );
x = xtemp;
theta -= *arctanptr++;
}
} while ( ++i < FT_TRIG_MAX_ITERS );
vec->x = x;
vec->y = y;
}
static void
ft_trig_pseudo_polarize( FT_Vector* vec )
{
FT_Fixed theta;
FT_Fixed yi, i;
FT_Fixed x, y;
const FT_Fixed *arctanptr;
x = vec->x;
y = vec->y;
/* Get the vector into the right half plane */
theta = 0;
if ( x < 0 )
{
x = -x;
y = -y;
theta = 2 * FT_ANGLE_PI2;
}
if ( y > 0 )
theta = - theta;
arctanptr = ft_trig_arctan_table;
if ( y < 0 )
{
/* Rotate positive */
yi = y + ( x << 1 );
x = x - ( y << 1 );
y = yi;
theta -= *arctanptr++; /* Subtract angle */
}
else
{
/* Rotate negative */
yi = y - ( x << 1 );
x = x + ( y << 1 );
y = yi;
theta += *arctanptr++; /* Add angle */
}
i = 0;
do
{
if ( y < 0 )
{
/* Rotate positive */
yi = y + ( x >> i );
x = x - ( y >> i );
y = yi;
theta -= *arctanptr++;
}
else
{
/* Rotate negative */
yi = y - ( x >> i );
x = x + ( y >> i );
y = yi;
theta += *arctanptr++;
}
} while ( ++i < FT_TRIG_MAX_ITERS );
/* round theta */
if ( theta >= 0 )
theta = FT_PAD_ROUND( theta, 32 );
else
theta = -FT_PAD_ROUND( -theta, 32 );
vec->x = x;
vec->y = theta;
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Fixed )
FT_Cos( FT_Angle angle )
{
FT_Vector v;
v.x = FT_TRIG_COSCALE >> 2;
v.y = 0;
ft_trig_pseudo_rotate( &v, angle );
return v.x / ( 1 << 12 );
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Fixed )
FT_Sin( FT_Angle angle )
{
return FT_Cos( FT_ANGLE_PI2 - angle );
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Fixed )
FT_Tan( FT_Angle angle )
{
FT_Vector v;
v.x = FT_TRIG_COSCALE >> 2;
v.y = 0;
ft_trig_pseudo_rotate( &v, angle );
return FT_DivFix( v.y, v.x );
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Angle )
FT_Atan2( FT_Fixed dx,
FT_Fixed dy )
{
FT_Vector v;
if ( dx == 0 && dy == 0 )
return 0;
v.x = dx;
v.y = dy;
ft_trig_prenorm( &v );
ft_trig_pseudo_polarize( &v );
return v.y;
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( void )
FT_Vector_Unit( FT_Vector* vec,
FT_Angle angle )
{
vec->x = FT_TRIG_COSCALE >> 2;
vec->y = 0;
ft_trig_pseudo_rotate( vec, angle );
vec->x >>= 12;
vec->y >>= 12;
}
/* these macros return 0 for positive numbers,
and -1 for negative ones */
#define FT_SIGN_LONG( x ) ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) )
#define FT_SIGN_INT( x ) ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) )
#define FT_SIGN_INT32( x ) ( (x) >> 31 )
#define FT_SIGN_INT16( x ) ( (x) >> 15 )
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( void )
FT_Vector_Rotate( FT_Vector* vec,
FT_Angle angle )
{
FT_Int shift;
FT_Vector v;
v.x = vec->x;
v.y = vec->y;
if ( angle && ( v.x != 0 || v.y != 0 ) )
{
shift = ft_trig_prenorm( &v );
ft_trig_pseudo_rotate( &v, angle );
v.x = ft_trig_downscale( v.x );
v.y = ft_trig_downscale( v.y );
if ( shift > 0 )
{
FT_Int32 half = (FT_Int32)1L << ( shift - 1 );
vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift;
vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift;
}
else
{
shift = -shift;
vec->x = v.x << shift;
vec->y = v.y << shift;
}
}
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Fixed )
FT_Vector_Length( FT_Vector* vec )
{
FT_Int shift;
FT_Vector v;
v = *vec;
/* handle trivial cases */
if ( v.x == 0 )
{
return ( v.y >= 0 ) ? v.y : -v.y;
}
else if ( v.y == 0 )
{
return ( v.x >= 0 ) ? v.x : -v.x;
}
/* general case */
shift = ft_trig_prenorm( &v );
ft_trig_pseudo_polarize( &v );
v.x = ft_trig_downscale( v.x );
if ( shift > 0 )
return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift;
return v.x << -shift;
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( void )
FT_Vector_Polarize( FT_Vector* vec,
FT_Fixed *length,
FT_Angle *angle )
{
FT_Int shift;
FT_Vector v;
v = *vec;
if ( v.x == 0 && v.y == 0 )
return;
shift = ft_trig_prenorm( &v );
ft_trig_pseudo_polarize( &v );
v.x = ft_trig_downscale( v.x );
*length = ( shift >= 0 ) ? ( v.x >> shift ) : ( v.x << -shift );
*angle = v.y;
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( void )
FT_Vector_From_Polar( FT_Vector* vec,
FT_Fixed length,
FT_Angle angle )
{
vec->x = length;
vec->y = 0;
FT_Vector_Rotate( vec, angle );
}
/* documentation is in fttrigon.h */
FT_EXPORT_DEF( FT_Angle )
FT_Angle_Diff( FT_Angle angle1,
FT_Angle angle2 )
{
FT_Angle delta = angle2 - angle1;
delta %= FT_ANGLE_2PI;
if ( delta < 0 )
delta += FT_ANGLE_2PI;
if ( delta > FT_ANGLE_PI )
delta -= FT_ANGLE_2PI;
return delta;
}
/* END */