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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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