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```/***************************************************************************/
/*                                                                         */
/*  fttrigon.c                                                             */
/*                                                                         */
/*    FreeType trigonometric functions (body).                             */
/*                                                                         */
/*  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      */
/*  this file you indicate that you have read the license and              */
/*  understand and accept it fully.                                        */
/*                                                                         */
/***************************************************************************/

#include <ft2build.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 & 0xFFFF;

k1 = FT_TRIG_SCALE >> 16;       /* constant */
k2 = FT_TRIG_SCALE & 0xFFFF;    /* 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 += 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 ( 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;
}
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 = ( theta + 16 ) & -32;
else
theta = - (( -theta + 16 ) & -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;
}

/* 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 )
{
vec->x = v.x >> shift;
vec->y = 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 > FT_ANGLE_PI )
delta -= FT_ANGLE_2PI;

return delta;
}

/* END */
```