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/* Copyright (C) 1992, 1993, 2000 Aladdin Enterprises. All rights reserved.
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This software is provided AS-IS with no warranty, either express or
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implied.
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This software is distributed under license and may not be copied,
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modified or distributed except as expressly authorized under the terms
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of the license contained in the file LICENSE in this distribution.
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For more information about licensing, please refer to
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http://www.ghostscript.com/licensing/. For information on
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commercial licensing, go to http://www.artifex.com/licensing/ or
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contact Artifex Software, Inc., 101 Lucas Valley Road #110,
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San Rafael, CA 94903, U.S.A., +1(415)492-9861.
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*/
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/* $Id: gxfrac.h,v 1.5 2002/02/21 22:24:53 giles Exp $ */
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/* Fraction representation for Ghostscript */
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#ifndef gxfrac_INCLUDED
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# define gxfrac_INCLUDED
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/*
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* Represent a fraction in [0.0..1.0]. Note that the 1.0 endpoint is
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* included. Since undercolor removal requires a signed frac, we limit
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* fracs to 15 bits rather than 16.
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*/
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typedef short frac;
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typedef short signed_frac;
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#define arch_log2_sizeof_frac arch_log2_sizeof_short
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#define arch_sizeof_frac arch_sizeof_short
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#define frac_bits 15
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#define frac_0 ((frac)0)
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/*
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* Normally one would represent a fractional value of this kind as a short
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* integer, in [-32767..32767]. Unfortunately, this approach cannot
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* represent any of the common values like 1/2, 1/3, or 1/5 exactly, causing
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* rounding errors. Instead, we opt for using the range [-32760..32760],
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* which allows exact representation of almost all commonly used fractions
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* (e.g., N/360 for 0<=N<=360).
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*/
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#define frac_1_0bits 3
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#define frac_1 ((frac)0x7ff8)
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#define frac_1_long ((long)frac_1)
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#define frac_1_float ((float)frac_1)
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/* Conversion between fracs and floats. */
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#define frac2float(fr) ((fr) / frac_1_float)
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#define float2frac(fl) ((frac)(((fl) + 0.5 / frac_1_float) * frac_1_float))
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/*
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* Conversion between unsigned fracs and bytes (or, in general,
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* shorter integers) representing fractions. This is highly dependent
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* on the definition of frac_1 above.
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*/
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#define _frac2s(fr)\
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(((fr) >> (frac_bits - frac_1_0bits)) + (fr))
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#define frac2bits(fr, nb)\
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((uint)(_frac2s(fr) >> (frac_bits - (nb))))
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#define frac2byte(fr) ((byte)frac2bits(fr, 8))
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/* bits2frac requires frac_bits / 2 <= nb <= frac_bits. */
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#define bits2frac(v, nb) ((frac)(\
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((frac)(v) << (frac_bits - (nb))) +\
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((v) >> ((nb) * 2 - frac_bits)) -\
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((v) >> ((nb) - frac_1_0bits)) ))
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#define byte2frac(b) bits2frac(b, 8)
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/* Produce a result that is guaranteed to convert back to a frac */
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/* not exceeding the original value fr. */
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#define frac2bits_floor(fr, nb)\
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((uint)((_frac2s(fr) - (_frac2s(fr) >> (nb))) >> (frac_bits - (nb))))
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/*
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* Conversion between fracs and unsigned shorts.
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*/
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#define ushort_bits (arch_sizeof_short * 8)
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#define frac2ushort(fr) ((ushort)(\
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((fr) << (ushort_bits - frac_bits)) +\
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((fr) >> (frac_bits * 2 - ushort_bits - frac_1_0bits)) ))
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#define ushort2frac(us) ((frac)(\
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((us) >> (ushort_bits - frac_bits)) -\
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((us) >> (ushort_bits - frac_1_0bits)) ))
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/*
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* Compute the quotient Q = floor(P / frac_1),
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* where P is the (ulong) product of a uint or ushort V and a frac F.
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* See gxarith.h for the underlying algorithm.
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*/
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#define frac_1_quo(p)\
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( (((p) >> frac_1_0bits) + ((p) >> frac_bits) + 1) >> (frac_bits - frac_1_0bits) )
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/*
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* Compute the remainder similarly, having already computed the quotient.
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* This is, of course, P - Q * frac_1.
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*/
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#define frac_1_rem(p, q)\
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((frac)( (uint)(p) - ((q) << frac_bits) + ((q) << frac_1_0bits) ))
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#endif /* gxfrac_INCLUDED */
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