/***************************************************************************//*                                                                         *//*  fttrigon.c                                                             *//*                                                                         *//*    FreeType trigonometric functions (body).                             *//*                                                                         *//*  Copyright 2001 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_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 & 0xFFFF;     k1 = FT_TRIG_SCALE >> 16;       /* constant */    k2 = FT_TRIG_SCALE & 0xFFFF;    /* 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 ( 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;    }    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 = ( theta + 16 ) & -32;    else      theta = - (( -theta + 16 ) & -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;  }    /* 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 )      {        vec->x = v.x >> shift;        vec->y = 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 > FT_ANGLE_PI )      delta -= FT_ANGLE_2PI;     return delta;  }  /* END */