godot/thirdparty/freetype/src/base/fttrigon.c

/****************************************************************************
 *
 * 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 <freetype/internal/ftobjs.h>
#include <freetype/internal/ftcalc.h>
#include <freetype/fttrigon.h>


  /* the Cordic shrink factor 0.858785336480436 * 2^32 */
#define FT_TRIG_SCALE …

  /* the highest bit in overflow-safe vector components, */
  /* MSB of 0.858785336480436 * sqrt(0.5) * 2^30         */
#define FT_TRIG_SAFE_MSB …

  /* this table was generated for FT_PI = 180L << 16, i.e. degrees */
#define FT_TRIG_MAX_ITERS …

  static const FT_Angle
  ft_trig_arctan_table[] = …;


#ifdef FT_INT64

  /* multiply a given value by the CORDIC shrink factor */
  static FT_Fixed
  ft_trig_downscale( FT_Fixed  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 )
  { … }


  static void
  ft_trig_pseudo_rotate( FT_Vector*  vec,
                         FT_Angle    theta )
  { … }


  static void
  ft_trig_pseudo_polarize( FT_Vector*  vec )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Cos( FT_Angle  angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Sin( FT_Angle  angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Tan( FT_Angle  angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Angle )
  FT_Atan2( FT_Fixed  dx,
            FT_Fixed  dy )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Unit( FT_Vector*  vec,
                  FT_Angle    angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Rotate( FT_Vector*  vec,
                    FT_Angle    angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Fixed )
  FT_Vector_Length( FT_Vector*  vec )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_Polarize( FT_Vector*  vec,
                      FT_Fixed   *length,
                      FT_Angle   *angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( void )
  FT_Vector_From_Polar( FT_Vector*  vec,
                        FT_Fixed    length,
                        FT_Angle    angle )
  { … }


  /* documentation is in fttrigon.h */

  FT_EXPORT_DEF( FT_Angle )
  FT_Angle_Diff( FT_Angle  angle1,
                 FT_Angle  angle2 )
  { … }


/* END */