From 6bf0a5cb5034a7e684dcc3500e841785237ce2dd Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Sun, 7 Apr 2024 19:32:43 +0200 Subject: Adding upstream version 1:115.7.0. Signed-off-by: Daniel Baumann --- modules/freetype2/src/base/fttrigon.c | 517 ++++++++++++++++++++++++++++++++++ 1 file changed, 517 insertions(+) create mode 100644 modules/freetype2/src/base/fttrigon.c (limited to 'modules/freetype2/src/base/fttrigon.c') diff --git a/modules/freetype2/src/base/fttrigon.c b/modules/freetype2/src/base/fttrigon.c new file mode 100644 index 0000000000..2dd2c3459e --- /dev/null +++ b/modules/freetype2/src/base/fttrigon.c @@ -0,0 +1,517 @@ +/**************************************************************************** + * + * fttrigon.c + * + * FreeType trigonometric functions (body). + * + * Copyright (C) 2001-2023 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. + * + */ + + /************************************************************************** + * + * This is a fixed-point CORDIC implementation of trigonometric + * functions as well as transformations between Cartesian and polar + * coordinates. The angles are represented as 16.16 fixed-point values + * in degrees, i.e., the angular resolution is 2^-16 degrees. Note that + * only vectors longer than 2^16*180/pi (or at least 22 bits) on a + * discrete Cartesian grid can have the same or better angular + * resolution. Therefore, to maintain this precision, some functions + * require an interim upscaling of the vectors, whereas others operate + * with 24-bit long vectors directly. + * + */ + +#include +#include +#include + + + /* the Cordic shrink factor 0.858785336480436 * 2^32 */ +#define FT_TRIG_SCALE 0xDBD95B16UL + + /* the highest bit in overflow-safe vector components, */ + /* MSB of 0.858785336480436 * sqrt(0.5) * 2^30 */ +#define FT_TRIG_SAFE_MSB 29 + + /* this table was generated for FT_PI = 180L << 16, i.e. degrees */ +#define FT_TRIG_MAX_ITERS 23 + + static const FT_Angle + ft_trig_arctan_table[] = + { + 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, + 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, + 57L, 29L, 14L, 7L, 4L, 2L, 1L + }; + + +#ifdef FT_INT64 + + /* multiply a given value by the CORDIC shrink factor */ + static FT_Fixed + ft_trig_downscale( FT_Fixed val ) + { + FT_Int s = 1; + + + if ( val < 0 ) + { + val = -val; + s = -1; + } + + /* 0x40000000 comes from regression analysis between true */ + /* and CORDIC hypotenuse, so it minimizes the error */ + val = (FT_Fixed)( + ( (FT_UInt64)val * FT_TRIG_SCALE + 0x40000000UL ) >> 32 ); + + return s < 0 ? -val : val; + } + +#else /* !FT_INT64 */ + + /* multiply a given value by the CORDIC shrink factor */ + static FT_Fixed + ft_trig_downscale( FT_Fixed val ) + { + FT_Int s = 1; + FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2; + + + if ( val < 0 ) + { + val = -val; + s = -1; + } + + lo1 = (FT_UInt32)val & 0x0000FFFFU; + hi1 = (FT_UInt32)val >> 16; + lo2 = FT_TRIG_SCALE & 0x0000FFFFU; + hi2 = FT_TRIG_SCALE >> 16; + + lo = lo1 * lo2; + i1 = lo1 * hi2; + i2 = lo2 * hi1; + hi = hi1 * hi2; + + /* Check carry overflow of i1 + i2 */ + i1 += i2; + hi += (FT_UInt32)( i1 < i2 ) << 16; + + hi += i1 >> 16; + i1 = i1 << 16; + + /* Check carry overflow of i1 + lo */ + lo += i1; + hi += ( lo < i1 ); + + /* 0x40000000 comes from regression analysis between true */ + /* and CORDIC hypotenuse, so it minimizes the error */ + + /* Check carry overflow of lo + 0x40000000 */ + lo += 0x40000000UL; + hi += ( lo < 0x40000000UL ); + + val = (FT_Fixed)hi; + + return s < 0 ? -val : val; + } + +#endif /* !FT_INT64 */ + + + /* undefined and never called for zero vector */ + static FT_Int + ft_trig_prenorm( FT_Vector* vec ) + { + FT_Pos x, y; + FT_Int shift; + + + x = vec->x; + y = vec->y; + + shift = FT_MSB( (FT_UInt32)( FT_ABS( x ) | FT_ABS( y ) ) ); + + if ( shift <= FT_TRIG_SAFE_MSB ) + { + shift = FT_TRIG_SAFE_MSB - shift; + vec->x = (FT_Pos)( (FT_ULong)x << shift ); + vec->y = (FT_Pos)( (FT_ULong)y << shift ); + } + else + { + shift -= FT_TRIG_SAFE_MSB; + 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, b; + const FT_Angle *arctanptr; + + + x = vec->x; + y = vec->y; + + /* Rotate inside [-PI/4,PI/4] sector */ + while ( theta < -FT_ANGLE_PI4 ) + { + xtemp = y; + y = -x; + x = xtemp; + theta += FT_ANGLE_PI2; + } + + while ( theta > FT_ANGLE_PI4 ) + { + xtemp = -y; + y = x; + x = xtemp; + theta -= FT_ANGLE_PI2; + } + + arctanptr = ft_trig_arctan_table; + + /* Pseudorotations, with right shifts */ + for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) + { + if ( theta < 0 ) + { + xtemp = x + ( ( y + b ) >> i ); + y = y - ( ( x + b ) >> i ); + x = xtemp; + theta += *arctanptr++; + } + else + { + xtemp = x - ( ( y + b ) >> i ); + y = y + ( ( x + b ) >> i ); + x = xtemp; + theta -= *arctanptr++; + } + } + + vec->x = x; + vec->y = y; + } + + + static void + ft_trig_pseudo_polarize( FT_Vector* vec ) + { + FT_Angle theta; + FT_Int i; + FT_Fixed x, y, xtemp, b; + const FT_Angle *arctanptr; + + + x = vec->x; + y = vec->y; + + /* Get the vector into [-PI/4,PI/4] sector */ + if ( y > x ) + { + if ( y > -x ) + { + theta = FT_ANGLE_PI2; + xtemp = y; + y = -x; + x = xtemp; + } + else + { + theta = y > 0 ? FT_ANGLE_PI : -FT_ANGLE_PI; + x = -x; + y = -y; + } + } + else + { + if ( y < -x ) + { + theta = -FT_ANGLE_PI2; + xtemp = -y; + y = x; + x = xtemp; + } + else + { + theta = 0; + } + } + + arctanptr = ft_trig_arctan_table; + + /* Pseudorotations, with right shifts */ + for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) + { + if ( y > 0 ) + { + xtemp = x + ( ( y + b ) >> i ); + y = y - ( ( x + b ) >> i ); + x = xtemp; + theta += *arctanptr++; + } + else + { + xtemp = x - ( ( y + b ) >> i ); + y = y + ( ( x + b ) >> i ); + x = xtemp; + theta -= *arctanptr++; + } + } + + /* round theta to acknowledge its error that mostly comes */ + /* from accumulated rounding errors in the arctan table */ + if ( theta >= 0 ) + theta = FT_PAD_ROUND( theta, 16 ); + else + theta = -FT_PAD_ROUND( -theta, 16 ); + + vec->x = x; + vec->y = theta; + } + + + /* documentation is in fttrigon.h */ + + FT_EXPORT_DEF( FT_Fixed ) + FT_Cos( FT_Angle angle ) + { + FT_Vector v; + + + FT_Vector_Unit( &v, angle ); + + return v.x; + } + + + /* documentation is in fttrigon.h */ + + FT_EXPORT_DEF( FT_Fixed ) + FT_Sin( FT_Angle angle ) + { + FT_Vector v; + + + FT_Vector_Unit( &v, angle ); + + return v.y; + } + + + /* documentation is in fttrigon.h */ + + FT_EXPORT_DEF( FT_Fixed ) + FT_Tan( FT_Angle angle ) + { + FT_Vector v = { 1 << 24, 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 ) + { + if ( !vec ) + return; + + vec->x = FT_TRIG_SCALE >> 8; + vec->y = 0; + ft_trig_pseudo_rotate( vec, angle ); + vec->x = ( vec->x + 0x80L ) >> 8; + vec->y = ( vec->y + 0x80L ) >> 8; + } + + + /* documentation is in fttrigon.h */ + + FT_EXPORT_DEF( void ) + FT_Vector_Rotate( FT_Vector* vec, + FT_Angle angle ) + { + FT_Int shift; + FT_Vector v; + + + if ( !vec || !angle ) + return; + + v = *vec; + + if ( v.x == 0 && v.y == 0 ) + return; + + 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 - ( v.x < 0 ) ) >> shift; + vec->y = ( v.y + half - ( v.y < 0 ) ) >> shift; + } + else + { + shift = -shift; + vec->x = (FT_Pos)( (FT_ULong)v.x << shift ); + vec->y = (FT_Pos)( (FT_ULong)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; + + + if ( !vec ) + return 0; + + v = *vec; + + /* handle trivial cases */ + if ( v.x == 0 ) + { + return FT_ABS( v.y ); + } + else if ( v.y == 0 ) + { + return FT_ABS( 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 + ( 1L << ( shift - 1 ) ) ) >> shift; + + return (FT_Fixed)( (FT_UInt32)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; + + + if ( !vec || !length || !angle ) + return; + + 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 ) + : (FT_Fixed)( (FT_UInt32)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 ) + { + if ( !vec ) + return; + + 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; + + + while ( delta <= -FT_ANGLE_PI ) + delta += FT_ANGLE_2PI; + + while ( delta > FT_ANGLE_PI ) + delta -= FT_ANGLE_2PI; + + return delta; + } + + +/* END */ -- cgit v1.2.3