xref: /plan9/sys/src/cmd/gs/src/gxfrac.h (revision 593dc095aefb2a85c828727bbfa9da139a49bdf4)
1 /* Copyright (C) 1992, 1993, 2000 Aladdin Enterprises.  All rights reserved.
2 
3   This software is provided AS-IS with no warranty, either express or
4   implied.
5 
6   This software is distributed under license and may not be copied,
7   modified or distributed except as expressly authorized under the terms
8   of the license contained in the file LICENSE in this distribution.
9 
10   For more information about licensing, please refer to
11   http://www.ghostscript.com/licensing/. For information on
12   commercial licensing, go to http://www.artifex.com/licensing/ or
13   contact Artifex Software, Inc., 101 Lucas Valley Road #110,
14   San Rafael, CA  94903, U.S.A., +1(415)492-9861.
15 */
16 
17 /* $Id: gxfrac.h,v 1.5 2002/02/21 22:24:53 giles Exp $ */
18 /* Fraction representation for Ghostscript */
19 
20 #ifndef gxfrac_INCLUDED
21 #  define gxfrac_INCLUDED
22 
23 /*
24  * Represent a fraction in [0.0..1.0].  Note that the 1.0 endpoint is
25  * included.  Since undercolor removal requires a signed frac, we limit
26  * fracs to 15 bits rather than 16.
27  */
28 typedef short frac;
29 typedef short signed_frac;
30 
31 #define arch_log2_sizeof_frac arch_log2_sizeof_short
32 #define arch_sizeof_frac arch_sizeof_short
33 #define frac_bits 15
34 #define frac_0 ((frac)0)
35 
36 /*
37  * Normally one would represent a fractional value of this kind as a short
38  * integer, in [-32767..32767].  Unfortunately, this approach cannot
39  * represent any of the common values like 1/2, 1/3, or 1/5 exactly, causing
40  * rounding errors.  Instead, we opt for using the range [-32760..32760],
41  * which allows exact representation of almost all commonly used fractions
42  * (e.g., N/360 for 0<=N<=360).
43  */
44 #define frac_1_0bits 3
45 #define frac_1 ((frac)0x7ff8)
46 #define frac_1_long ((long)frac_1)
47 #define frac_1_float ((float)frac_1)
48 /* Conversion between fracs and floats. */
49 #define frac2float(fr) ((fr) / frac_1_float)
50 #define float2frac(fl) ((frac)(((fl) + 0.5 / frac_1_float) * frac_1_float))
51 
52 /*
53  * Conversion between unsigned fracs and bytes (or, in general,
54  * shorter integers) representing fractions. This is highly dependent
55  * on the definition of frac_1 above.
56  */
57 #define _frac2s(fr)\
58   (((fr) >> (frac_bits - frac_1_0bits)) + (fr))
59 #define frac2bits(fr, nb)\
60   ((uint)(_frac2s(fr) >> (frac_bits - (nb))))
61 #define frac2byte(fr) ((byte)frac2bits(fr, 8))
62 /* bits2frac requires frac_bits / 2 <= nb <= frac_bits. */
63 #define bits2frac(v, nb) ((frac)(\
64   ((frac)(v) << (frac_bits - (nb))) +\
65    ((v) >> ((nb) * 2 - frac_bits)) -\
66    ((v) >> ((nb) - frac_1_0bits)) ))
67 #define byte2frac(b) bits2frac(b, 8)
68 /* Produce a result that is guaranteed to convert back to a frac */
69 /* not exceeding the original value fr. */
70 #define frac2bits_floor(fr, nb)\
71   ((uint)((_frac2s(fr) - (_frac2s(fr) >> (nb))) >> (frac_bits - (nb))))
72 /*
73  * Conversion between fracs and unsigned shorts.
74  */
75 #define ushort_bits (arch_sizeof_short * 8)
76 #define frac2ushort(fr) ((ushort)(\
77   ((fr) << (ushort_bits - frac_bits)) +\
78   ((fr) >> (frac_bits * 2 - ushort_bits - frac_1_0bits)) ))
79 #define ushort2frac(us) ((frac)(\
80   ((us) >> (ushort_bits - frac_bits)) -\
81   ((us) >> (ushort_bits - frac_1_0bits)) ))
82 /*
83  * Compute the quotient Q = floor(P / frac_1),
84  * where P is the (ulong) product of a uint or ushort V and a frac F.
85  * See gxarith.h for the underlying algorithm.
86  */
87 #define frac_1_quo(p)\
88   ( (((p) >> frac_1_0bits) + ((p) >> frac_bits) + 1) >> (frac_bits - frac_1_0bits) )
89 /*
90  * Compute the remainder similarly, having already computed the quotient.
91  * This is, of course, P - Q * frac_1.
92  */
93 #define frac_1_rem(p, q)\
94   ((frac)( (uint)(p) - ((q) << frac_bits) + ((q) << frac_1_0bits) ))
95 
96 #endif /* gxfrac_INCLUDED */
97