/* Copyright (C) 1989, 2000 Aladdin Enterprises.  All rights reserved.
  
  This program is free software; you can redistribute it and/or modify it
  under the terms of the GNU General Public License version 2
  as published by the Free Software Foundation.


  This software is provided AS-IS with no warranty, either express or
  implied. That is, this program is distributed in the hope that it will 
  be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  General Public License for more details

  You should have received a copy of the GNU General Public License along
  with this program; if not, write to the Free Software Foundation, Inc.,
  59 Temple Place, Suite 330, Boston, MA, 02111-1307.
  
  For more information about licensing, please refer to
  http://www.ghostscript.com/licensing/. For information on
  commercial licensing, go to http://www.artifex.com/licensing/ or
  contact Artifex Software, Inc., 101 Lucas Valley Road #110,
  San Rafael, CA  94903, U.S.A., +1(415)492-9861.
*/

/* $Id: gxfixed.h,v 1.7 2002/09/04 06:40:50 ray Exp $ */
/* Fixed-point arithmetic for Ghostscript */

#ifndef gxfixed_INCLUDED
#  define gxfixed_INCLUDED

/*
 * Coordinates are generally represented internally by fixed-point
 * quantities: integers lose accuracy in crucial places,
 * and floating point arithmetic is slow.
 */
typedef long fixed;
typedef ulong ufixed;		/* only used in a very few places */
#define ARCH_SIZEOF_FIXED ARCH_SIZEOF_LONG

#define max_fixed max_long
#define min_fixed min_long
#define fixed_0 0L
#define fixed_epsilon 1L
/*
 * 12 bits of fraction provides both the necessary accuracy and
 * a sufficiently large range of coordinates.
 */
#define _fixed_shift 12
#define fixed_fraction_bits _fixed_shift
#define fixed_int_bits (sizeof(fixed) * 8 - _fixed_shift)
#define fixed_scale (1<<_fixed_shift)
#define _fixed_rshift(x) arith_rshift(x,_fixed_shift)
#define _fixed_round_v (fixed_scale>>1)
#define _fixed_fraction_v (fixed_scale-1)
/*
 * We use a center-of-pixel filling rule; Adobe specifies that coordinates
 * designate half-open regions.  Because of this, we need special rounding
 * to go from a coordinate to the pixel it falls in.  We use the term
 * "pixel rounding" for this kind of rounding.
 */
#define _fixed_pixround_v (_fixed_round_v - fixed_epsilon)

/*
 * Most operations can be done directly on fixed-point quantities:
 * addition, subtraction, shifting, multiplication or division by
 * (integer) constants; assignment, assignment with zero;
 * comparison, comparison against zero.
 * Multiplication and division by floats is OK if the result is
 * explicitly cast back to fixed.
 * Conversion to and from int and float types must be done explicitly.
 * Note that if we are casting a fixed to a float in a context where
 * only ratios and not actual values are involved, we don't need to take
 * the scale factor into account: we can simply cast to float directly.
 */
#define int2fixed(i) ((fixed)(i)<<_fixed_shift)
/* Define some useful constants. */
/* Avoid casts, so strict ANSI compilers will accept them in #ifs. */
#define fixed_1 (fixed_epsilon << _fixed_shift)
#define fixed_half (fixed_1 >> 1)
/*
 * On 16-bit systems, we can convert fixed variables to ints more efficiently
 * than general fixed quantities.  For this reason, we define two separate
 * sets of conversion macros.
 */
#define fixed2int(x) ((int)_fixed_rshift(x))
#define fixed2int_rounded(x) ((int)_fixed_rshift((x)+_fixed_round_v))
#define fixed2int_ceiling(x) ((int)_fixed_rshift((x)+_fixed_fraction_v))
#define fixed_pre_pixround(x) ((x)+_fixed_pixround_v)
#define fixed2int_pixround(x) fixed2int(fixed_pre_pixround(x))
#define fixed_is_int(x) !((x)&_fixed_fraction_v)
#if arch_ints_are_short & !arch_is_big_endian
/* Do some of the shifting and extraction ourselves. */
#  define _fixed_hi(x) *((const uint *)&(x)+1)
#  define _fixed_lo(x) *((const uint *)&(x))
#  define fixed2int_var(x)\
	((int)((_fixed_hi(x) << (16-_fixed_shift)) +\
	       (_fixed_lo(x) >> _fixed_shift)))
#  define fixed2int_var_rounded(x)\
	((int)((_fixed_hi(x) << (16-_fixed_shift)) +\
	       (((_fixed_lo(x) >> (_fixed_shift-1))+1)>>1)))
#  define fixed2int_var_ceiling(x)\
	(fixed2int_var(x) -\
	 arith_rshift((int)-(_fixed_lo(x) & _fixed_fraction_v), _fixed_shift))
#else
/* Use reasonable definitions. */
#  define fixed2int_var(x) fixed2int(x)
#  define fixed2int_var_rounded(x) fixed2int_rounded(x)
#  define fixed2int_var_ceiling(x) fixed2int_ceiling(x)
#endif
#define fixed2int_var_pixround(x) fixed2int_pixround(x)
#define fixed2long(x) ((long)_fixed_rshift(x))
#define fixed2long_rounded(x) ((long)_fixed_rshift((x)+_fixed_round_v))
#define fixed2long_ceiling(x) ((long)_fixed_rshift((x)+_fixed_fraction_v))
#define fixed2long_pixround(x) ((long)_fixed_rshift((x)+_fixed_pixround_v))
#define float2fixed(f) ((fixed)((f)*(float)fixed_scale))
/* Note that fixed2float actually produces a double result. */
#define fixed2float(x) ((x)*(1.0/fixed_scale))

/* Rounding and truncation on fixeds */
#define fixed_floor(x) ((x)&(-1L<<_fixed_shift))
#define fixed_rounded(x) (((x)+_fixed_round_v)&(-1L<<_fixed_shift))
#define fixed_ceiling(x) (((x)+_fixed_fraction_v)&(-1L<<_fixed_shift))
#define fixed_pixround(x) (((x)+_fixed_pixround_v)&(-1L<<_fixed_shift))
#define fixed_fraction(x) ((int)(x)&_fixed_fraction_v)
/* I don't see how to do truncation towards 0 so easily.... */
#define fixed_truncated(x) ((x) < 0 ? fixed_ceiling(x) : fixed_floor(x))

/* Define the largest and smallest integer values that fit in a fixed. */
#if arch_sizeof_int == arch_sizeof_long
#  define max_int_in_fixed fixed2int(max_fixed)
#  define min_int_in_fixed fixed2int(min_fixed)
#else
#  define max_int_in_fixed max_int
#  define min_int_in_fixed min_int
#endif

#ifdef USE_FPU
#  define USE_FPU_FIXED (USE_FPU < 0 && arch_floats_are_IEEE && arch_sizeof_long == 4)
#else
#  define USE_FPU_FIXED 0
#endif

/*
 * Define a macro for checking for overflow of the sum of two fixed values
 * and and setting the result to the sum if no overflow.
 * This is a pseudo-function that returns a "limitcheck" if the result
 * will overflow. Set the result to the max/min _fixed value (depending
 * on the sign of the operands (note: overflow can only occur with like
 * signed input values). While the result is only set once, the operand
 * values are used multiply, so pointer modification operand use will
 * result in MANY more increments/decrements of the pointer than desired.
 */
/* usage: (int)code = CHECK_SET_FIXED_SUM(fixed_result, fixed_op1, fixed_op2); */
#define CHECK_SET_FIXED_SUM(r, a, b) \
     ((((a) ^ (b)) >= 0) && ((((a)+(b)) ^ (a)) < 0) ? \
       (((r)=(((a)<0) ? min_fixed : max_fixed)), gs_error_limitcheck) : \
       (((r) = ((a)+(b))), 0))		/* no overflow */
/*
 * Define a procedure for computing a * b / c when b and c are non-negative,
 * b < c, and a * b exceeds (or might exceed) the capacity of a long.
 * Note that this procedure takes the floor, rather than truncating
 * towards zero, if a < 0: this ensures 0 <= R < c, where R is the remainder.
 *
 * It's really annoying that C doesn't provide any way to get at
 * the double-length multiply/divide instructions that almost all hardware
 * provides....
 */
fixed fixed_mult_quo(fixed A, fixed B, fixed C);

/*
 * Transforming coordinates involves multiplying two floats, or a float
 * and a double, and then converting the result to a fixed.  Since this
 * operation is so common, we provide an alternative implementation of it
 * on machines that use IEEE floating point representation but don't have
 * floating point hardware.  The implementation may be in either C or
 * assembler.
 */

/*
 * The macros all use R for the (fixed) result, FB for the second (float)
 * operand, and dtemp for a temporary double variable.  The work is divided
 * between the two macros of each set in order to avoid bogus "possibly
 * uninitialized variable" messages from slow-witted compilers.
 *
 * For the case where the first operand is a float (FA):
 *	code = CHECK_FMUL2FIXED_VARS(R, FA, FB, dtemp);
 *	if (code < 0) ...
 *	FINISH_FMUL2FIXED_VARS(R, dtemp);
 *
 * For the case where the first operand is a double (DA):
 *	code = CHECK_DFMUL2FIXED_VARS(R, DA, FB, dtemp);
 *	if (code < 0) ...;
 *	FINISH_DFMUL2FIXED_VARS(R, dtemp);
 */
#if USE_FPU_FIXED && arch_sizeof_short == 2
#define NEED_SET_FMUL2FIXED
int set_fmul2fixed_(fixed *, long, long);
#define CHECK_FMUL2FIXED_VARS(vr, vfa, vfb, dtemp)\
  set_fmul2fixed_(&vr, *(const long *)&vfa, *(const long *)&vfb)
#define FINISH_FMUL2FIXED_VARS(vr, dtemp)\
  DO_NOTHING
int set_dfmul2fixed_(fixed *, ulong, long, long);
#  if arch_is_big_endian
#  define CHECK_DFMUL2FIXED_VARS(vr, vda, vfb, dtemp)\
     set_dfmul2fixed_(&vr, ((const ulong *)&vda)[1], *(const long *)&vfb, *(const long *)&vda)
#  else
#  define CHECK_DFMUL2FIXED_VARS(vr, vda, vfb, dtemp)\
     set_dfmul2fixed_(&vr, *(const ulong *)&vda, *(const long *)&vfb, ((const long *)&vda)[1])
#  endif
#define FINISH_DFMUL2FIXED_VARS(vr, dtemp)\
  DO_NOTHING

#else /* don't bother */

#undef NEED_SET_FMUL2FIXED
#define CHECK_FMUL2FIXED_VARS(vr, vfa, vfb, dtemp)\
  (dtemp = (vfa) * (vfb),\
   (f_fits_in_bits(dtemp, fixed_int_bits) ? 0 :\
    gs_note_error(gs_error_limitcheck)))
#define FINISH_FMUL2FIXED_VARS(vr, dtemp)\
  vr = float2fixed(dtemp)
#define CHECK_DFMUL2FIXED_VARS(vr, vda, vfb, dtemp)\
  CHECK_FMUL2FIXED_VARS(vr, vda, vfb, dtemp)
#define FINISH_DFMUL2FIXED_VARS(vr, dtemp)\
  FINISH_FMUL2FIXED_VARS(vr, dtemp)

#endif

/*
 * set_float2fixed_vars(R, F) does the equivalent of R = float2fixed(F):
 *      R is a fixed, F is a float or a double.
 * set_fixed2float_var(R, V) does the equivalent of R = fixed2float(V):
 *      R is a float or a double, V is a fixed.
 * set_ldexp_fixed2double(R, V, E) does the equivalent of R=ldexp((double)V,E):
 *      R is a double, V is a fixed, E is an int.
 * R and F must be variables, not expressions; V and E may be expressions.
 */
#if USE_FPU_FIXED
int set_float2fixed_(fixed *, long, int);
int set_double2fixed_(fixed *, ulong, long, int);

# define set_float2fixed_vars(vr,vf)\
    (sizeof(vf) == sizeof(float) ?\
     set_float2fixed_(&vr, *(const long *)&vf, fixed_fraction_bits) :\
     set_double2fixed_(&vr, ((const ulong *)&vf)[arch_is_big_endian],\
		       ((const long *)&vf)[1 - arch_is_big_endian],\
		       fixed_fraction_bits))
long fixed2float_(fixed, int);
void set_fixed2double_(double *, fixed, int);

/*
 * We need the (double *)&vf cast to prevent compile-time error messages,
 * even though the call will only be executed if vf has the correct type.
 */
# define set_fixed2float_var(vf,x)\
    (sizeof(vf) == sizeof(float) ?\
     (*(long *)&vf = fixed2float_(x, fixed_fraction_bits), 0) :\
     (set_fixed2double_((double *)&vf, x, fixed_fraction_bits), 0))
#define set_ldexp_fixed2double(vd, x, exp)\
  set_fixed2double_(&vd, x, -(exp))
#else
# define set_float2fixed_vars(vr,vf)\
    (f_fits_in_bits(vf, fixed_int_bits) ? (vr = float2fixed(vf), 0) :\
     gs_note_error(gs_error_limitcheck))
# define set_fixed2float_var(vf,x)\
    (vf = fixed2float(x), 0)
# define set_ldexp_fixed2double(vd, x, exp)\
    discard(vd = ldexp((double)(x), exp))
#endif

/* A point with fixed coordinates */
typedef struct gs_fixed_point_s {
    fixed x, y;
} gs_fixed_point;

/* A rectangle with fixed coordinates */
typedef struct gs_fixed_rect_s {
    gs_fixed_point p, q;
} gs_fixed_rect;

#endif /* gxfixed_INCLUDED */
