path: root/base/gxfixed.h

/* Copyright (C) 2001-2020 Artifex Software, Inc.
   All Rights Reserved.

   This software is provided AS-IS with no warranty, either express or
   implied.

   This software is distributed under license and may not be copied,
   modified or distributed except as expressly authorized under the terms
   of the license contained in the file LICENSE in this distribution.

   Refer to licensing information at http://www.artifex.com or contact
   Artifex Software, Inc.,  1305 Grant Avenue - Suite 200, Novato,
   CA 94945, U.S.A., +1(415)492-9861, for further information.
*/


/* Fixed-point arithmetic for Ghostscript */

#ifndef gxfixed_INCLUDED
#  define gxfixed_INCLUDED

#include "std.h"

/*
 * Coordinates are generally represented internally by fixed-point
 * quantities: integers lose accuracy in crucial places,
 * and floating point arithmetic is slow.
 */
#if ARCH_SIZEOF_INT == 4
typedef int fixed;
typedef uint ufixed;		/* only used in a very few places */
# define ARCH_SIZEOF_FIXED ARCH_SIZEOF_INT
# define max_fixed max_int
# define min_fixed min_int
#else
# if ARCH_SIZEOF_LONG == 4
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
# endif
#endif

#define fixed_0 0L
#define fixed_epsilon 1L
/*
 * 8 bits of fraction provides both the necessary accuracy and
 * a sufficiently large range of coordinates.
 */
#define _fixed_shift 8
#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 fixed2int_pixround_perfect(x) ((x) < 0 && ((x) & (fixed_1 - fixed_epsilon)) == fixed_half \
        ? (int)_fixed_rshift(x) + 1 : fixed2int_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))
#define float2fixed_rounded(f) ((fixed)floor((f)*(float)fixed_scale + 0.5))

/* 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. */
#define max_int_in_fixed fixed2int(max_fixed)
#define min_int_in_fixed fixed2int(min_fixed)

/*
 * 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.
 */

/*
 * Define a function for finding intersection of small bars.
 * Coordinates must be so small that their cubes fit into 60 bits.
 * This function doesn't check intersections at end of bars,
 * so  the caller must care of them on necessity.
 * Returns : *ry is the Y-coordinate of the intersection
 * truncated to 'fixed'; *ey is 1 iff the precise Y coordinate of
 * the intersection is greater than *ry (used by the shading algorithm).
 */
bool
gx_intersect_small_bars(fixed q0x, fixed q0y, fixed q1x, fixed q1y, fixed q2x, fixed q2y,
                        fixed q3x, fixed q3y, fixed *ry, fixed *ey);

/*
 * 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);
 */

#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)

/*
 * 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.
 */

# 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))

/* 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 */