#include "cairoint.h"
#if HAVE_UINT64_T
#define uint64_lo32(i) ((i) & 0xffffffff)
#define uint64_hi32(i) ((i) >> 32)
#define uint64_lo(i) ((i) & 0xffffffff)
#define uint64_hi(i) ((i) >> 32)
#define uint64_shift32(i) ((i) << 32)
#define uint64_carry32 (((uint64_t) 1) << 32)
#define _cairo_uint32s_to_uint64(h,l) ((uint64_t) (h) << 32 | (l))
#else
#define uint64_lo32(i) ((i).lo)
#define uint64_hi32(i) ((i).hi)
static cairo_uint64_t
uint64_lo (cairo_uint64_t i)
{
cairo_uint64_t s;
s.lo = i.lo;
s.hi = 0;
return s;
}
static cairo_uint64_t
uint64_hi (cairo_uint64_t i)
{
cairo_uint64_t s;
s.lo = i.hi;
s.hi = 0;
return s;
}
static cairo_uint64_t
uint64_shift32 (cairo_uint64_t i)
{
cairo_uint64_t s;
s.lo = 0;
s.hi = i.lo;
return s;
}
static const cairo_uint64_t uint64_carry32 = { 0, 1 };
cairo_uint64_t
_cairo_uint32_to_uint64 (uint32_t i)
{
cairo_uint64_t q;
q.lo = i;
q.hi = 0;
return q;
}
cairo_int64_t
_cairo_int32_to_int64 (int32_t i)
{
cairo_uint64_t q;
q.lo = i;
q.hi = i < 0 ? -1 : 0;
return q;
}
static cairo_uint64_t
_cairo_uint32s_to_uint64 (uint32_t h, uint32_t l)
{
cairo_uint64_t q;
q.lo = l;
q.hi = h;
return q;
}
cairo_uint64_t
_cairo_uint64_add (cairo_uint64_t a, cairo_uint64_t b)
{
cairo_uint64_t s;
s.hi = a.hi + b.hi;
s.lo = a.lo + b.lo;
if (s.lo < a.lo)
s.hi++;
return s;
}
cairo_uint64_t
_cairo_uint64_sub (cairo_uint64_t a, cairo_uint64_t b)
{
cairo_uint64_t s;
s.hi = a.hi - b.hi;
s.lo = a.lo - b.lo;
if (s.lo > a.lo)
s.hi--;
return s;
}
#define uint32_lo(i) ((i) & 0xffff)
#define uint32_hi(i) ((i) >> 16)
#define uint32_carry16 ((1) << 16)
cairo_uint64_t
_cairo_uint32x32_64_mul (uint32_t a, uint32_t b)
{
cairo_uint64_t s;
uint16_t ah, al, bh, bl;
uint32_t r0, r1, r2, r3;
al = uint32_lo (a);
ah = uint32_hi (a);
bl = uint32_lo (b);
bh = uint32_hi (b);
r0 = (uint32_t) al * bl;
r1 = (uint32_t) al * bh;
r2 = (uint32_t) ah * bl;
r3 = (uint32_t) ah * bh;
r1 += uint32_hi(r0);
r1 += r2;
if (r1 < r2)
r3 += uint32_carry16;
s.hi = r3 + uint32_hi(r1);
s.lo = (uint32_lo (r1) << 16) + uint32_lo (r0);
return s;
}
cairo_int64_t
_cairo_int32x32_64_mul (int32_t a, int32_t b)
{
cairo_int64_t s;
s = _cairo_uint32x32_64_mul ((uint32_t) a, (uint32_t) b);
if (a < 0)
s.hi -= b;
if (b < 0)
s.hi -= a;
return s;
}
cairo_uint64_t
_cairo_uint64_mul (cairo_uint64_t a, cairo_uint64_t b)
{
cairo_uint64_t s;
s = _cairo_uint32x32_64_mul (a.lo, b.lo);
s.hi += a.lo * b.hi + a.hi * b.lo;
return s;
}
cairo_uint64_t
_cairo_uint64_lsl (cairo_uint64_t a, int shift)
{
if (shift >= 32)
{
a.hi = a.lo;
a.lo = 0;
shift -= 32;
}
if (shift)
{
a.hi = a.hi << shift | a.lo >> (32 - shift);
a.lo = a.lo << shift;
}
return a;
}
cairo_uint64_t
_cairo_uint64_rsl (cairo_uint64_t a, int shift)
{
if (shift >= 32)
{
a.lo = a.hi;
a.hi = 0;
shift -= 32;
}
if (shift)
{
a.lo = a.lo >> shift | a.hi << (32 - shift);
a.hi = a.hi >> shift;
}
return a;
}
#define _cairo_uint32_rsa(a,n) ((uint32_t) (((int32_t) (a)) >> (n)))
cairo_int64_t
_cairo_uint64_rsa (cairo_int64_t a, int shift)
{
if (shift >= 32)
{
a.lo = a.hi;
a.hi = _cairo_uint32_rsa (a.hi, 31);
shift -= 32;
}
if (shift)
{
a.lo = a.lo >> shift | a.hi << (32 - shift);
a.hi = _cairo_uint32_rsa (a.hi, shift);
}
return a;
}
int
_cairo_uint64_lt (cairo_uint64_t a, cairo_uint64_t b)
{
return (a.hi < b.hi ||
(a.hi == b.hi && a.lo < b.lo));
}
int
_cairo_uint64_eq (cairo_uint64_t a, cairo_uint64_t b)
{
return a.hi == b.hi && a.lo == b.lo;
}
int
_cairo_int64_lt (cairo_int64_t a, cairo_int64_t b)
{
if (_cairo_int64_negative (a) && !_cairo_int64_negative (b))
return 1;
if (!_cairo_int64_negative (a) && _cairo_int64_negative (b))
return 0;
return _cairo_uint64_lt (a, b);
}
int
_cairo_uint64_cmp (cairo_uint64_t a, cairo_uint64_t b)
{
if (a.hi < b.hi)
return -1;
else if (a.hi > b.hi)
return 1;
else if (a.lo < b.lo)
return -1;
else if (a.lo > b.lo)
return 1;
else
return 0;
}
int
_cairo_int64_cmp (cairo_int64_t a, cairo_int64_t b)
{
if (_cairo_int64_negative (a) && !_cairo_int64_negative (b))
return -1;
if (!_cairo_int64_negative (a) && _cairo_int64_negative (b))
return 1;
return _cairo_uint64_cmp (a, b);
}
cairo_uint64_t
_cairo_uint64_not (cairo_uint64_t a)
{
a.lo = ~a.lo;
a.hi = ~a.hi;
return a;
}
cairo_uint64_t
_cairo_uint64_negate (cairo_uint64_t a)
{
a.lo = ~a.lo;
a.hi = ~a.hi;
if (++a.lo == 0)
++a.hi;
return a;
}
cairo_uquorem64_t
_cairo_uint64_divrem (cairo_uint64_t num, cairo_uint64_t den)
{
cairo_uquorem64_t qr;
cairo_uint64_t bit;
cairo_uint64_t quo;
bit = _cairo_uint32_to_uint64 (1);
while (_cairo_uint64_lt (den, num) && (den.hi & 0x80000000) == 0)
{
bit = _cairo_uint64_lsl (bit, 1);
den = _cairo_uint64_lsl (den, 1);
}
quo = _cairo_uint32_to_uint64 (0);
while (bit.hi | bit.lo)
{
if (_cairo_uint64_le (den, num))
{
num = _cairo_uint64_sub (num, den);
quo = _cairo_uint64_add (quo, bit);
}
bit = _cairo_uint64_rsl (bit, 1);
den = _cairo_uint64_rsl (den, 1);
}
qr.quo = quo;
qr.rem = num;
return qr;
}
#endif
#if HAVE_UINT128_T
cairo_uquorem128_t
_cairo_uint128_divrem (cairo_uint128_t num, cairo_uint128_t den)
{
cairo_uquorem128_t qr;
qr.quo = num / den;
qr.rem = num % den;
return qr;
}
#else
cairo_uint128_t
_cairo_uint32_to_uint128 (uint32_t i)
{
cairo_uint128_t q;
q.lo = _cairo_uint32_to_uint64 (i);
q.hi = _cairo_uint32_to_uint64 (0);
return q;
}
cairo_int128_t
_cairo_int32_to_int128 (int32_t i)
{
cairo_int128_t q;
q.lo = _cairo_int32_to_int64 (i);
q.hi = _cairo_int32_to_int64 (i < 0 ? -1 : 0);
return q;
}
cairo_uint128_t
_cairo_uint64_to_uint128 (cairo_uint64_t i)
{
cairo_uint128_t q;
q.lo = i;
q.hi = _cairo_uint32_to_uint64 (0);
return q;
}
cairo_int128_t
_cairo_int64_to_int128 (cairo_int64_t i)
{
cairo_int128_t q;
q.lo = i;
q.hi = _cairo_int32_to_int64 (_cairo_int64_negative(i) ? -1 : 0);
return q;
}
cairo_uint128_t
_cairo_uint128_add (cairo_uint128_t a, cairo_uint128_t b)
{
cairo_uint128_t s;
s.hi = _cairo_uint64_add (a.hi, b.hi);
s.lo = _cairo_uint64_add (a.lo, b.lo);
if (_cairo_uint64_lt (s.lo, a.lo))
s.hi = _cairo_uint64_add (s.hi, _cairo_uint32_to_uint64 (1));
return s;
}
cairo_uint128_t
_cairo_uint128_sub (cairo_uint128_t a, cairo_uint128_t b)
{
cairo_uint128_t s;
s.hi = _cairo_uint64_sub (a.hi, b.hi);
s.lo = _cairo_uint64_sub (a.lo, b.lo);
if (_cairo_uint64_gt (s.lo, a.lo))
s.hi = _cairo_uint64_sub (s.hi, _cairo_uint32_to_uint64(1));
return s;
}
cairo_uint128_t
_cairo_uint64x64_128_mul (cairo_uint64_t a, cairo_uint64_t b)
{
cairo_uint128_t s;
uint32_t ah, al, bh, bl;
cairo_uint64_t r0, r1, r2, r3;
al = uint64_lo32 (a);
ah = uint64_hi32 (a);
bl = uint64_lo32 (b);
bh = uint64_hi32 (b);
r0 = _cairo_uint32x32_64_mul (al, bl);
r1 = _cairo_uint32x32_64_mul (al, bh);
r2 = _cairo_uint32x32_64_mul (ah, bl);
r3 = _cairo_uint32x32_64_mul (ah, bh);
r1 = _cairo_uint64_add (r1, uint64_hi (r0));
r1 = _cairo_uint64_add (r1, r2);
if (_cairo_uint64_lt (r1, r2))
r3 = _cairo_uint64_add (r3, uint64_carry32);
s.hi = _cairo_uint64_add (r3, uint64_hi(r1));
s.lo = _cairo_uint64_add (uint64_shift32 (r1),
uint64_lo (r0));
return s;
}
cairo_int128_t
_cairo_int64x64_128_mul (cairo_int64_t a, cairo_int64_t b)
{
cairo_int128_t s;
s = _cairo_uint64x64_128_mul (_cairo_int64_to_uint64(a),
_cairo_int64_to_uint64(b));
if (_cairo_int64_negative (a))
s.hi = _cairo_uint64_sub (s.hi,
_cairo_int64_to_uint64 (b));
if (_cairo_int64_negative (b))
s.hi = _cairo_uint64_sub (s.hi,
_cairo_int64_to_uint64 (a));
return s;
}
cairo_uint128_t
_cairo_uint128_mul (cairo_uint128_t a, cairo_uint128_t b)
{
cairo_uint128_t s;
s = _cairo_uint64x64_128_mul (a.lo, b.lo);
s.hi = _cairo_uint64_add (s.hi,
_cairo_uint64_mul (a.lo, b.hi));
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);
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);
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
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_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);
cairo_uint64_t x = _cairo_uint128_to_uint64 (_cairo_uint128_rsl(num, 32));
result.quo = _cairo_uint32s_to_uint64 (-1U, -1U);
result.rem = den;
if (_cairo_uint64_ge (x, den)) {
return result;
}
if (_cairo_uint64_lt (x, B)) {
return _cairo_uint64_divrem (_cairo_uint128_to_uint64 (num), den);
}
else {
uint32_t y = _cairo_uint128_to_uint32 (num);
uint32_t u = uint64_hi32 (den);
uint32_t v = _cairo_uint64_to_uint32 (den);
cairo_uquorem64_t quorem;
cairo_uint64_t remainder;
uint32_t quotient;
uint32_t q;
uint32_t r;
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;
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);
remainder = _cairo_uint32s_to_uint64 (r, y);
if (_cairo_uint64_ge (remainder, den)) {
remainder = _cairo_uint64_sub (remainder, den);
quotient++;
}
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)) {
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;
}