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-/***************************************************************************/
-/* */
-/* 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_TRIG_SCALE >> 16; /* constant */
- k2 = 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 += 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 = 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 */
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