forked from KolibriOS/kolibrios
853 lines
19 KiB
C
853 lines
19 KiB
C
/* cairo - a vector graphics library with display and print output
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*
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* Copyright © 2004 Keith Packard
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*
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* This library is free software; you can redistribute it and/or
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* modify it either under the terms of the GNU Lesser General Public
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* License version 2.1 as published by the Free Software Foundation
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* (the "LGPL") or, at your option, under the terms of the Mozilla
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* Public License Version 1.1 (the "MPL"). If you do not alter this
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* notice, a recipient may use your version of this file under either
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* the MPL or the LGPL.
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*
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* You should have received a copy of the LGPL along with this library
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* in the file COPYING-LGPL-2.1; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
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* You should have received a copy of the MPL along with this library
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* in the file COPYING-MPL-1.1
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*
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* The contents of this file are subject to the Mozilla Public License
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* Version 1.1 (the "License"); you may not use this file except in
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* compliance with the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
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* OF ANY KIND, either express or implied. See the LGPL or the MPL for
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* the specific language governing rights and limitations.
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*
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* The Original Code is the cairo graphics library.
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*
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* The Initial Developer of the Original Code is Keith Packard
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*
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* Contributor(s):
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* Keith R. Packard <keithp@keithp.com>
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*/
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#include "cairoint.h"
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#if HAVE_UINT64_T
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#define uint64_lo32(i) ((i) & 0xffffffff)
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#define uint64_hi32(i) ((i) >> 32)
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#define uint64_lo(i) ((i) & 0xffffffff)
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#define uint64_hi(i) ((i) >> 32)
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#define uint64_shift32(i) ((i) << 32)
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#define uint64_carry32 (((uint64_t) 1) << 32)
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#define _cairo_uint32s_to_uint64(h,l) ((uint64_t) (h) << 32 | (l))
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#else
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#define uint64_lo32(i) ((i).lo)
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#define uint64_hi32(i) ((i).hi)
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static cairo_uint64_t
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uint64_lo (cairo_uint64_t i)
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{
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cairo_uint64_t s;
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s.lo = i.lo;
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s.hi = 0;
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return s;
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}
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static cairo_uint64_t
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uint64_hi (cairo_uint64_t i)
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{
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cairo_uint64_t s;
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s.lo = i.hi;
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s.hi = 0;
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return s;
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}
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static cairo_uint64_t
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uint64_shift32 (cairo_uint64_t i)
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{
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cairo_uint64_t s;
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s.lo = 0;
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s.hi = i.lo;
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return s;
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}
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static const cairo_uint64_t uint64_carry32 = { 0, 1 };
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cairo_uint64_t
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_cairo_double_to_uint64 (double i)
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{
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cairo_uint64_t q;
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q.hi = i * (1. / 4294967296.);
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q.lo = i - q.hi * 4294967296.;
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return q;
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}
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double
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_cairo_uint64_to_double (cairo_uint64_t i)
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{
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return i.hi * 4294967296. + i.lo;
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}
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cairo_int64_t
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_cairo_double_to_int64 (double i)
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{
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cairo_uint64_t q;
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q.hi = i * (1. / INT32_MAX);
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q.lo = i - q.hi * (double)INT32_MAX;
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return q;
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}
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double
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_cairo_int64_to_double (cairo_int64_t i)
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{
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return i.hi * INT32_MAX + i.lo;
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}
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cairo_uint64_t
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_cairo_uint32_to_uint64 (uint32_t i)
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{
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cairo_uint64_t q;
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q.lo = i;
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q.hi = 0;
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return q;
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}
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cairo_int64_t
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_cairo_int32_to_int64 (int32_t i)
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{
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cairo_uint64_t q;
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q.lo = i;
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q.hi = i < 0 ? -1 : 0;
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return q;
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}
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static cairo_uint64_t
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_cairo_uint32s_to_uint64 (uint32_t h, uint32_t l)
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{
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cairo_uint64_t q;
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q.lo = l;
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q.hi = h;
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return q;
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}
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cairo_uint64_t
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_cairo_uint64_add (cairo_uint64_t a, cairo_uint64_t b)
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{
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cairo_uint64_t s;
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s.hi = a.hi + b.hi;
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s.lo = a.lo + b.lo;
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if (s.lo < a.lo)
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s.hi++;
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return s;
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}
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cairo_uint64_t
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_cairo_uint64_sub (cairo_uint64_t a, cairo_uint64_t b)
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{
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cairo_uint64_t s;
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s.hi = a.hi - b.hi;
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s.lo = a.lo - b.lo;
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if (s.lo > a.lo)
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s.hi--;
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return s;
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}
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#define uint32_lo(i) ((i) & 0xffff)
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#define uint32_hi(i) ((i) >> 16)
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#define uint32_carry16 ((1) << 16)
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cairo_uint64_t
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_cairo_uint32x32_64_mul (uint32_t a, uint32_t b)
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{
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cairo_uint64_t s;
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uint16_t ah, al, bh, bl;
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uint32_t r0, r1, r2, r3;
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al = uint32_lo (a);
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ah = uint32_hi (a);
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bl = uint32_lo (b);
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bh = uint32_hi (b);
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r0 = (uint32_t) al * bl;
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r1 = (uint32_t) al * bh;
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r2 = (uint32_t) ah * bl;
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r3 = (uint32_t) ah * bh;
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r1 += uint32_hi(r0); /* no carry possible */
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r1 += r2; /* but this can carry */
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if (r1 < r2) /* check */
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r3 += uint32_carry16;
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s.hi = r3 + uint32_hi(r1);
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s.lo = (uint32_lo (r1) << 16) + uint32_lo (r0);
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return s;
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}
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cairo_int64_t
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_cairo_int32x32_64_mul (int32_t a, int32_t b)
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{
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cairo_int64_t s;
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s = _cairo_uint32x32_64_mul ((uint32_t) a, (uint32_t) b);
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if (a < 0)
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s.hi -= b;
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if (b < 0)
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s.hi -= a;
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return s;
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}
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cairo_uint64_t
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_cairo_uint64_mul (cairo_uint64_t a, cairo_uint64_t b)
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{
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cairo_uint64_t s;
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s = _cairo_uint32x32_64_mul (a.lo, b.lo);
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s.hi += a.lo * b.hi + a.hi * b.lo;
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return s;
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}
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cairo_uint64_t
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_cairo_uint64_lsl (cairo_uint64_t a, int shift)
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{
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if (shift >= 32)
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{
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a.hi = a.lo;
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a.lo = 0;
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shift -= 32;
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}
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if (shift)
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{
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a.hi = a.hi << shift | a.lo >> (32 - shift);
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a.lo = a.lo << shift;
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}
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return a;
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}
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cairo_uint64_t
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_cairo_uint64_rsl (cairo_uint64_t a, int shift)
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{
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if (shift >= 32)
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{
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a.lo = a.hi;
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a.hi = 0;
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shift -= 32;
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}
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if (shift)
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{
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a.lo = a.lo >> shift | a.hi << (32 - shift);
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a.hi = a.hi >> shift;
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}
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return a;
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}
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#define _cairo_uint32_rsa(a,n) ((uint32_t) (((int32_t) (a)) >> (n)))
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cairo_int64_t
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_cairo_uint64_rsa (cairo_int64_t a, int shift)
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{
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if (shift >= 32)
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{
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a.lo = a.hi;
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a.hi = _cairo_uint32_rsa (a.hi, 31);
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shift -= 32;
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}
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if (shift)
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{
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a.lo = a.lo >> shift | a.hi << (32 - shift);
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a.hi = _cairo_uint32_rsa (a.hi, shift);
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}
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return a;
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}
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int
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_cairo_uint64_lt (cairo_uint64_t a, cairo_uint64_t b)
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{
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return (a.hi < b.hi ||
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(a.hi == b.hi && a.lo < b.lo));
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}
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int
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_cairo_uint64_eq (cairo_uint64_t a, cairo_uint64_t b)
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{
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return a.hi == b.hi && a.lo == b.lo;
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}
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int
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_cairo_int64_lt (cairo_int64_t a, cairo_int64_t b)
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{
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if (_cairo_int64_negative (a) && !_cairo_int64_negative (b))
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return 1;
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if (!_cairo_int64_negative (a) && _cairo_int64_negative (b))
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return 0;
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return _cairo_uint64_lt (a, b);
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}
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int
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_cairo_uint64_cmp (cairo_uint64_t a, cairo_uint64_t b)
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{
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if (a.hi < b.hi)
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return -1;
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else if (a.hi > b.hi)
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return 1;
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else if (a.lo < b.lo)
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return -1;
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else if (a.lo > b.lo)
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return 1;
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else
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return 0;
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}
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int
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_cairo_int64_cmp (cairo_int64_t a, cairo_int64_t b)
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{
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if (_cairo_int64_negative (a) && !_cairo_int64_negative (b))
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return -1;
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if (!_cairo_int64_negative (a) && _cairo_int64_negative (b))
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return 1;
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return _cairo_uint64_cmp (a, b);
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}
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cairo_uint64_t
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_cairo_uint64_not (cairo_uint64_t a)
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{
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a.lo = ~a.lo;
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a.hi = ~a.hi;
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return a;
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}
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cairo_uint64_t
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_cairo_uint64_negate (cairo_uint64_t a)
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{
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a.lo = ~a.lo;
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a.hi = ~a.hi;
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if (++a.lo == 0)
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++a.hi;
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return a;
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}
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/*
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* Simple bit-at-a-time divide.
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*/
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cairo_uquorem64_t
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_cairo_uint64_divrem (cairo_uint64_t num, cairo_uint64_t den)
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{
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cairo_uquorem64_t qr;
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cairo_uint64_t bit;
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cairo_uint64_t quo;
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bit = _cairo_uint32_to_uint64 (1);
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/* normalize to make den >= num, but not overflow */
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while (_cairo_uint64_lt (den, num) && (den.hi & 0x80000000) == 0)
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{
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bit = _cairo_uint64_lsl (bit, 1);
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den = _cairo_uint64_lsl (den, 1);
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}
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quo = _cairo_uint32_to_uint64 (0);
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/* generate quotient, one bit at a time */
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while (bit.hi | bit.lo)
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{
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if (_cairo_uint64_le (den, num))
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{
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num = _cairo_uint64_sub (num, den);
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quo = _cairo_uint64_add (quo, bit);
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}
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bit = _cairo_uint64_rsl (bit, 1);
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den = _cairo_uint64_rsl (den, 1);
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}
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qr.quo = quo;
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qr.rem = num;
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return qr;
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}
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#endif /* !HAVE_UINT64_T */
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#if HAVE_UINT128_T
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cairo_uquorem128_t
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_cairo_uint128_divrem (cairo_uint128_t num, cairo_uint128_t den)
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{
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cairo_uquorem128_t qr;
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qr.quo = num / den;
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qr.rem = num % den;
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return qr;
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}
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#else
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cairo_uint128_t
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_cairo_uint32_to_uint128 (uint32_t i)
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{
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cairo_uint128_t q;
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q.lo = _cairo_uint32_to_uint64 (i);
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q.hi = _cairo_uint32_to_uint64 (0);
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return q;
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}
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cairo_int128_t
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_cairo_int32_to_int128 (int32_t i)
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{
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cairo_int128_t q;
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q.lo = _cairo_int32_to_int64 (i);
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q.hi = _cairo_int32_to_int64 (i < 0 ? -1 : 0);
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return q;
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}
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cairo_uint128_t
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_cairo_uint64_to_uint128 (cairo_uint64_t i)
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{
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cairo_uint128_t q;
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q.lo = i;
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q.hi = _cairo_uint32_to_uint64 (0);
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return q;
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}
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cairo_int128_t
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_cairo_int64_to_int128 (cairo_int64_t i)
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{
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cairo_int128_t q;
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q.lo = i;
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q.hi = _cairo_int32_to_int64 (_cairo_int64_negative(i) ? -1 : 0);
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return q;
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}
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cairo_uint128_t
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_cairo_uint128_add (cairo_uint128_t a, cairo_uint128_t b)
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{
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cairo_uint128_t s;
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s.hi = _cairo_uint64_add (a.hi, b.hi);
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s.lo = _cairo_uint64_add (a.lo, b.lo);
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if (_cairo_uint64_lt (s.lo, a.lo))
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s.hi = _cairo_uint64_add (s.hi, _cairo_uint32_to_uint64 (1));
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return s;
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}
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cairo_uint128_t
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_cairo_uint128_sub (cairo_uint128_t a, cairo_uint128_t b)
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{
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cairo_uint128_t s;
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s.hi = _cairo_uint64_sub (a.hi, b.hi);
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s.lo = _cairo_uint64_sub (a.lo, b.lo);
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if (_cairo_uint64_gt (s.lo, a.lo))
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s.hi = _cairo_uint64_sub (s.hi, _cairo_uint32_to_uint64(1));
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return s;
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}
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cairo_uint128_t
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_cairo_uint64x64_128_mul (cairo_uint64_t a, cairo_uint64_t b)
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{
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cairo_uint128_t s;
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uint32_t ah, al, bh, bl;
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cairo_uint64_t r0, r1, r2, r3;
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al = uint64_lo32 (a);
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ah = uint64_hi32 (a);
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bl = uint64_lo32 (b);
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bh = uint64_hi32 (b);
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r0 = _cairo_uint32x32_64_mul (al, bl);
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r1 = _cairo_uint32x32_64_mul (al, bh);
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r2 = _cairo_uint32x32_64_mul (ah, bl);
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r3 = _cairo_uint32x32_64_mul (ah, bh);
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r1 = _cairo_uint64_add (r1, uint64_hi (r0)); /* no carry possible */
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r1 = _cairo_uint64_add (r1, r2); /* but this can carry */
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if (_cairo_uint64_lt (r1, r2)) /* check */
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r3 = _cairo_uint64_add (r3, uint64_carry32);
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s.hi = _cairo_uint64_add (r3, uint64_hi(r1));
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s.lo = _cairo_uint64_add (uint64_shift32 (r1),
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uint64_lo (r0));
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return s;
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}
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cairo_int128_t
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_cairo_int64x64_128_mul (cairo_int64_t a, cairo_int64_t b)
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{
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cairo_int128_t s;
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s = _cairo_uint64x64_128_mul (_cairo_int64_to_uint64(a),
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_cairo_int64_to_uint64(b));
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if (_cairo_int64_negative (a))
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s.hi = _cairo_uint64_sub (s.hi,
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_cairo_int64_to_uint64 (b));
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if (_cairo_int64_negative (b))
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s.hi = _cairo_uint64_sub (s.hi,
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_cairo_int64_to_uint64 (a));
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return s;
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}
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cairo_uint128_t
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_cairo_uint128_mul (cairo_uint128_t a, cairo_uint128_t b)
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{
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cairo_uint128_t s;
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s = _cairo_uint64x64_128_mul (a.lo, b.lo);
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s.hi = _cairo_uint64_add (s.hi,
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_cairo_uint64_mul (a.lo, b.hi));
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s.hi = _cairo_uint64_add (s.hi,
|
|
_cairo_uint64_mul (a.hi, b.lo));
|
|
return s;
|
|
}
|
|
|
|
cairo_uint128_t
|
|
_cairo_uint128_lsl (cairo_uint128_t a, int shift)
|
|
{
|
|
if (shift >= 64)
|
|
{
|
|
a.hi = a.lo;
|
|
a.lo = _cairo_uint32_to_uint64 (0);
|
|
shift -= 64;
|
|
}
|
|
if (shift)
|
|
{
|
|
a.hi = _cairo_uint64_add (_cairo_uint64_lsl (a.hi, shift),
|
|
_cairo_uint64_rsl (a.lo, (64 - shift)));
|
|
a.lo = _cairo_uint64_lsl (a.lo, shift);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
cairo_uint128_t
|
|
_cairo_uint128_rsl (cairo_uint128_t a, int shift)
|
|
{
|
|
if (shift >= 64)
|
|
{
|
|
a.lo = a.hi;
|
|
a.hi = _cairo_uint32_to_uint64 (0);
|
|
shift -= 64;
|
|
}
|
|
if (shift)
|
|
{
|
|
a.lo = _cairo_uint64_add (_cairo_uint64_rsl (a.lo, shift),
|
|
_cairo_uint64_lsl (a.hi, (64 - shift)));
|
|
a.hi = _cairo_uint64_rsl (a.hi, shift);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
cairo_uint128_t
|
|
_cairo_uint128_rsa (cairo_int128_t a, int shift)
|
|
{
|
|
if (shift >= 64)
|
|
{
|
|
a.lo = a.hi;
|
|
a.hi = _cairo_uint64_rsa (a.hi, 64-1);
|
|
shift -= 64;
|
|
}
|
|
if (shift)
|
|
{
|
|
a.lo = _cairo_uint64_add (_cairo_uint64_rsl (a.lo, shift),
|
|
_cairo_uint64_lsl (a.hi, (64 - shift)));
|
|
a.hi = _cairo_uint64_rsa (a.hi, shift);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
int
|
|
_cairo_uint128_lt (cairo_uint128_t a, cairo_uint128_t b)
|
|
{
|
|
return (_cairo_uint64_lt (a.hi, b.hi) ||
|
|
(_cairo_uint64_eq (a.hi, b.hi) &&
|
|
_cairo_uint64_lt (a.lo, b.lo)));
|
|
}
|
|
|
|
int
|
|
_cairo_int128_lt (cairo_int128_t a, cairo_int128_t b)
|
|
{
|
|
if (_cairo_int128_negative (a) && !_cairo_int128_negative (b))
|
|
return 1;
|
|
if (!_cairo_int128_negative (a) && _cairo_int128_negative (b))
|
|
return 0;
|
|
return _cairo_uint128_lt (a, b);
|
|
}
|
|
|
|
int
|
|
_cairo_uint128_cmp (cairo_uint128_t a, cairo_uint128_t b)
|
|
{
|
|
int cmp;
|
|
|
|
cmp = _cairo_uint64_cmp (a.hi, b.hi);
|
|
if (cmp)
|
|
return cmp;
|
|
return _cairo_uint64_cmp (a.lo, b.lo);
|
|
}
|
|
|
|
int
|
|
_cairo_int128_cmp (cairo_int128_t a, cairo_int128_t b)
|
|
{
|
|
if (_cairo_int128_negative (a) && !_cairo_int128_negative (b))
|
|
return -1;
|
|
if (!_cairo_int128_negative (a) && _cairo_int128_negative (b))
|
|
return 1;
|
|
|
|
return _cairo_uint128_cmp (a, b);
|
|
}
|
|
|
|
int
|
|
_cairo_uint128_eq (cairo_uint128_t a, cairo_uint128_t b)
|
|
{
|
|
return (_cairo_uint64_eq (a.hi, b.hi) &&
|
|
_cairo_uint64_eq (a.lo, b.lo));
|
|
}
|
|
|
|
#if HAVE_UINT64_T
|
|
#define _cairo_msbset64(q) (q & ((uint64_t) 1 << 63))
|
|
#else
|
|
#define _cairo_msbset64(q) (q.hi & ((uint32_t) 1 << 31))
|
|
#endif
|
|
|
|
cairo_uquorem128_t
|
|
_cairo_uint128_divrem (cairo_uint128_t num, cairo_uint128_t den)
|
|
{
|
|
cairo_uquorem128_t qr;
|
|
cairo_uint128_t bit;
|
|
cairo_uint128_t quo;
|
|
|
|
bit = _cairo_uint32_to_uint128 (1);
|
|
|
|
/* normalize to make den >= num, but not overflow */
|
|
while (_cairo_uint128_lt (den, num) && !_cairo_msbset64(den.hi))
|
|
{
|
|
bit = _cairo_uint128_lsl (bit, 1);
|
|
den = _cairo_uint128_lsl (den, 1);
|
|
}
|
|
quo = _cairo_uint32_to_uint128 (0);
|
|
|
|
/* generate quotient, one bit at a time */
|
|
while (_cairo_uint128_ne (bit, _cairo_uint32_to_uint128(0)))
|
|
{
|
|
if (_cairo_uint128_le (den, num))
|
|
{
|
|
num = _cairo_uint128_sub (num, den);
|
|
quo = _cairo_uint128_add (quo, bit);
|
|
}
|
|
bit = _cairo_uint128_rsl (bit, 1);
|
|
den = _cairo_uint128_rsl (den, 1);
|
|
}
|
|
qr.quo = quo;
|
|
qr.rem = num;
|
|
return qr;
|
|
}
|
|
|
|
cairo_int128_t
|
|
_cairo_int128_negate (cairo_int128_t a)
|
|
{
|
|
a.lo = _cairo_uint64_not (a.lo);
|
|
a.hi = _cairo_uint64_not (a.hi);
|
|
return _cairo_uint128_add (a, _cairo_uint32_to_uint128 (1));
|
|
}
|
|
|
|
cairo_int128_t
|
|
_cairo_int128_not (cairo_int128_t a)
|
|
{
|
|
a.lo = _cairo_uint64_not (a.lo);
|
|
a.hi = _cairo_uint64_not (a.hi);
|
|
return a;
|
|
}
|
|
|
|
#endif /* !HAVE_UINT128_T */
|
|
|
|
cairo_quorem128_t
|
|
_cairo_int128_divrem (cairo_int128_t num, cairo_int128_t den)
|
|
{
|
|
int num_neg = _cairo_int128_negative (num);
|
|
int den_neg = _cairo_int128_negative (den);
|
|
cairo_uquorem128_t uqr;
|
|
cairo_quorem128_t qr;
|
|
|
|
if (num_neg)
|
|
num = _cairo_int128_negate (num);
|
|
if (den_neg)
|
|
den = _cairo_int128_negate (den);
|
|
uqr = _cairo_uint128_divrem (num, den);
|
|
if (num_neg)
|
|
qr.rem = _cairo_int128_negate (uqr.rem);
|
|
else
|
|
qr.rem = uqr.rem;
|
|
if (num_neg != den_neg)
|
|
qr.quo = _cairo_int128_negate (uqr.quo);
|
|
else
|
|
qr.quo = uqr.quo;
|
|
return qr;
|
|
}
|
|
|
|
/**
|
|
* _cairo_uint_96by64_32x64_divrem:
|
|
*
|
|
* Compute a 32 bit quotient and 64 bit remainder of a 96 bit unsigned
|
|
* dividend and 64 bit divisor. If the quotient doesn't fit into 32
|
|
* bits then the returned remainder is equal to the divisor, and the
|
|
* quotient is the largest representable 64 bit integer. It is an
|
|
* error to call this function with the high 32 bits of @num being
|
|
* non-zero.
|
|
**/
|
|
cairo_uquorem64_t
|
|
_cairo_uint_96by64_32x64_divrem (cairo_uint128_t num,
|
|
cairo_uint64_t den)
|
|
{
|
|
cairo_uquorem64_t result;
|
|
cairo_uint64_t B = _cairo_uint32s_to_uint64 (1, 0);
|
|
|
|
/* These are the high 64 bits of the *96* bit numerator. We're
|
|
* going to represent the numerator as xB + y, where x is a 64,
|
|
* and y is a 32 bit number. */
|
|
cairo_uint64_t x = _cairo_uint128_to_uint64 (_cairo_uint128_rsl(num, 32));
|
|
|
|
/* Initialise the result to indicate overflow. */
|
|
result.quo = _cairo_uint32s_to_uint64 (-1U, -1U);
|
|
result.rem = den;
|
|
|
|
/* Don't bother if the quotient is going to overflow. */
|
|
if (_cairo_uint64_ge (x, den)) {
|
|
return /* overflow */ result;
|
|
}
|
|
|
|
if (_cairo_uint64_lt (x, B)) {
|
|
/* When the final quotient is known to fit in 32 bits, then
|
|
* num < 2^64 if and only if den < 2^32. */
|
|
return _cairo_uint64_divrem (_cairo_uint128_to_uint64 (num), den);
|
|
}
|
|
else {
|
|
/* Denominator is >= 2^32. the numerator is >= 2^64, and the
|
|
* division won't overflow: need two divrems. Write the
|
|
* numerator and denominator as
|
|
*
|
|
* num = xB + y x : 64 bits, y : 32 bits
|
|
* den = uB + v u, v : 32 bits
|
|
*/
|
|
uint32_t y = _cairo_uint128_to_uint32 (num);
|
|
uint32_t u = uint64_hi32 (den);
|
|
uint32_t v = _cairo_uint64_to_uint32 (den);
|
|
|
|
/* Compute a lower bound approximate quotient of num/den
|
|
* from x/(u+1). Then we have
|
|
*
|
|
* x = q(u+1) + r ; q : 32 bits, r <= u : 32 bits.
|
|
*
|
|
* xB + y = q(u+1)B + (rB+y)
|
|
* = q(uB + B + v - v) + (rB+y)
|
|
* = q(uB + v) + qB - qv + (rB+y)
|
|
* = q(uB + v) + q(B-v) + (rB+y)
|
|
*
|
|
* The true quotient of num/den then is q plus the
|
|
* contribution of q(B-v) + (rB+y). The main contribution
|
|
* comes from the term q(B-v), with the term (rB+y) only
|
|
* contributing at most one part.
|
|
*
|
|
* The term q(B-v) must fit into 64 bits, since q fits into 32
|
|
* bits on account of being a lower bound to the true
|
|
* quotient, and as B-v <= 2^32, we may safely use a single
|
|
* 64/64 bit division to find its contribution. */
|
|
|
|
cairo_uquorem64_t quorem;
|
|
cairo_uint64_t remainder; /* will contain final remainder */
|
|
uint32_t quotient; /* will contain final quotient. */
|
|
uint32_t q;
|
|
uint32_t r;
|
|
|
|
/* Approximate quotient by dividing the high 64 bits of num by
|
|
* u+1. Watch out for overflow of u+1. */
|
|
if (u+1) {
|
|
quorem = _cairo_uint64_divrem (x, _cairo_uint32_to_uint64 (u+1));
|
|
q = _cairo_uint64_to_uint32 (quorem.quo);
|
|
r = _cairo_uint64_to_uint32 (quorem.rem);
|
|
}
|
|
else {
|
|
q = uint64_hi32 (x);
|
|
r = _cairo_uint64_to_uint32 (x);
|
|
}
|
|
quotient = q;
|
|
|
|
/* Add the main term's contribution to quotient. Note B-v =
|
|
* -v as an uint32 (unless v = 0) */
|
|
if (v)
|
|
quorem = _cairo_uint64_divrem (_cairo_uint32x32_64_mul (q, -v), den);
|
|
else
|
|
quorem = _cairo_uint64_divrem (_cairo_uint32s_to_uint64 (q, 0), den);
|
|
quotient += _cairo_uint64_to_uint32 (quorem.quo);
|
|
|
|
/* Add the contribution of the subterm and start computing the
|
|
* true remainder. */
|
|
remainder = _cairo_uint32s_to_uint64 (r, y);
|
|
if (_cairo_uint64_ge (remainder, den)) {
|
|
remainder = _cairo_uint64_sub (remainder, den);
|
|
quotient++;
|
|
}
|
|
|
|
/* Add the contribution of the main term's remainder. The
|
|
* funky test here checks that remainder + main_rem >= den,
|
|
* taking into account overflow of the addition. */
|
|
remainder = _cairo_uint64_add (remainder, quorem.rem);
|
|
if (_cairo_uint64_ge (remainder, den) ||
|
|
_cairo_uint64_lt (remainder, quorem.rem))
|
|
{
|
|
remainder = _cairo_uint64_sub (remainder, den);
|
|
quotient++;
|
|
}
|
|
|
|
result.quo = _cairo_uint32_to_uint64 (quotient);
|
|
result.rem = remainder;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
cairo_quorem64_t
|
|
_cairo_int_96by64_32x64_divrem (cairo_int128_t num, cairo_int64_t den)
|
|
{
|
|
int num_neg = _cairo_int128_negative (num);
|
|
int den_neg = _cairo_int64_negative (den);
|
|
cairo_uint64_t nonneg_den;
|
|
cairo_uquorem64_t uqr;
|
|
cairo_quorem64_t qr;
|
|
|
|
if (num_neg)
|
|
num = _cairo_int128_negate (num);
|
|
if (den_neg)
|
|
nonneg_den = _cairo_int64_negate (den);
|
|
else
|
|
nonneg_den = den;
|
|
|
|
uqr = _cairo_uint_96by64_32x64_divrem (num, nonneg_den);
|
|
if (_cairo_uint64_eq (uqr.rem, nonneg_den)) {
|
|
/* bail on overflow. */
|
|
qr.quo = _cairo_uint32s_to_uint64 (0x7FFFFFFF, -1U);
|
|
qr.rem = den;
|
|
return qr;
|
|
}
|
|
|
|
if (num_neg)
|
|
qr.rem = _cairo_int64_negate (uqr.rem);
|
|
else
|
|
qr.rem = uqr.rem;
|
|
if (num_neg != den_neg)
|
|
qr.quo = _cairo_int64_negate (uqr.quo);
|
|
else
|
|
qr.quo = uqr.quo;
|
|
return qr;
|
|
}
|