ref: a64c55b17fa2e61e4ae5f4214e50a652291cd483
dir: /src/base/fttrigon.c/
#include <ft2build.h>
#include FT_TRIGONOMETRY_H
/* the following is 0.2715717684432231 * 2^30 */
#define FT_TRIG_COSCALE 0x11616E8E /* 291597966 = 0.2715717684432241 * 2^30, valid for j>13 */
/* 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 ] =
{
4157273, 2949120, 1740967, 919879, 466945, 234379, 117304, 58666,
29335, 14668, 7334, 3667, 1833, 917, 458, 229, 115, 57, 29, 14, 7,
4, 2, 1
};
/* the Cordic shrink factor, multiplied by 2^32 */
#define FT_TRIG_SCALE 1166391785 /* 0x4585BA38U */
#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) + 0x100000000L;
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 += 0x10000U;
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;
}
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 >> 12;
}
FT_EXPORT_DEF(FT_Fixed)
FT_Sin( FT_Angle angle )
{
return FT_Cos( FT_ANGLE_PI2-angle );
}
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 );
}
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;
}
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;
}
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;
}
}
}
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 );
return ( shift >= 0 ) ? (v.x >> shift) : (v.x << -shift);
}
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;
}