initial commit

1 files changed, 277 insertions, 0 deletions

diff --git a/src/freetype/fttrigon.c b/src/freetype/fttrigon.c
new file mode 100644
index 0000000..aeb4034
--- /dev/null
+++ b/src/freetype/fttrigon.c
@@ -0,0 +1,277 @@
+/***************************************************************************/
+/*                                                                         */
+/*  fttrigon.c                                                             */
+/*                                                                         */
+/*    FreeType trigonometric functions (body).                             */
+/*                                                                         */
+/*  Copyright 2001-2018 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 "ft2build.h"
+#include FT_INTERNAL_OBJECTS_H
+#include FT_INTERNAL_CALC_H
+#include FT_TRIGONOMETRY_H
+
+
+  /* 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_LONG64
+
+  /* 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_LONG64 */
+
+  /* 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_LONG64 */
+
+
+  /* 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_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_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 );
+  }
+
+
+/* END */