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1 #include <math.h> | 1 #include <math.h> |
2 #include <stdint.h> | 2 #include <stdint.h> |
3 | 3 |
4 double remquo(double x, double y, int *quo) | 4 double remquo(double x, double y, int* quo) { |
5 { | 5 union { |
6 » union {double f; uint64_t i;} ux = {x}, uy = {y}; | 6 double f; |
7 » int ex = ux.i>>52 & 0x7ff; | 7 uint64_t i; |
8 » int ey = uy.i>>52 & 0x7ff; | 8 } ux = {x}, uy = {y}; |
9 » int sx = ux.i>>63; | 9 int ex = ux.i >> 52 & 0x7ff; |
10 » int sy = uy.i>>63; | 10 int ey = uy.i >> 52 & 0x7ff; |
11 » uint32_t q; | 11 int sx = ux.i >> 63; |
12 » uint64_t i; | 12 int sy = uy.i >> 63; |
13 » uint64_t uxi = ux.i; | 13 uint32_t q; |
| 14 uint64_t i; |
| 15 uint64_t uxi = ux.i; |
14 | 16 |
15 » *quo = 0; | 17 *quo = 0; |
16 » if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff) | 18 if (uy.i << 1 == 0 || isnan(y) || ex == 0x7ff) |
17 » » return (x*y)/(x*y); | 19 return (x * y) / (x * y); |
18 » if (ux.i<<1 == 0) | 20 if (ux.i << 1 == 0) |
19 » » return x; | 21 return x; |
20 | 22 |
21 » /* normalize x and y */ | 23 /* normalize x and y */ |
22 » if (!ex) { | 24 if (!ex) { |
23 » » for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1); | 25 for (i = uxi << 12; i >> 63 == 0; ex--, i <<= 1) |
24 » » uxi <<= -ex + 1; | 26 ; |
25 » } else { | 27 uxi <<= -ex + 1; |
26 » » uxi &= -1ULL >> 12; | 28 } else { |
27 » » uxi |= 1ULL << 52; | 29 uxi &= -1ULL >> 12; |
28 » } | 30 uxi |= 1ULL << 52; |
29 » if (!ey) { | 31 } |
30 » » for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1); | 32 if (!ey) { |
31 » » uy.i <<= -ey + 1; | 33 for (i = uy.i << 12; i >> 63 == 0; ey--, i <<= 1) |
32 » } else { | 34 ; |
33 » » uy.i &= -1ULL >> 12; | 35 uy.i <<= -ey + 1; |
34 » » uy.i |= 1ULL << 52; | 36 } else { |
35 » } | 37 uy.i &= -1ULL >> 12; |
| 38 uy.i |= 1ULL << 52; |
| 39 } |
36 | 40 |
37 » q = 0; | 41 q = 0; |
38 » if (ex < ey) { | 42 if (ex < ey) { |
39 » » if (ex+1 == ey) | 43 if (ex + 1 == ey) |
40 » » » goto end; | 44 goto end; |
41 » » return x; | 45 return x; |
42 » } | 46 } |
43 | 47 |
44 » /* x mod y */ | 48 /* x mod y */ |
45 » for (; ex > ey; ex--) { | 49 for (; ex > ey; ex--) { |
46 » » i = uxi - uy.i; | 50 i = uxi - uy.i; |
47 » » if (i >> 63 == 0) { | 51 if (i >> 63 == 0) { |
48 » » » uxi = i; | 52 uxi = i; |
49 » » » q++; | 53 q++; |
50 » » } | 54 } |
51 » » uxi <<= 1; | 55 uxi <<= 1; |
52 » » q <<= 1; | 56 q <<= 1; |
53 » } | 57 } |
54 » i = uxi - uy.i; | 58 i = uxi - uy.i; |
55 » if (i >> 63 == 0) { | 59 if (i >> 63 == 0) { |
56 » » uxi = i; | 60 uxi = i; |
57 » » q++; | 61 q++; |
58 » } | 62 } |
59 » if (uxi == 0) | 63 if (uxi == 0) |
60 » » ex = -60; | 64 ex = -60; |
61 » else | 65 else |
62 » » for (; uxi>>52 == 0; uxi <<= 1, ex--); | 66 for (; uxi >> 52 == 0; uxi <<= 1, ex--) |
| 67 ; |
63 end: | 68 end: |
64 » /* scale result and decide between |x| and |x|-|y| */ | 69 /* scale result and decide between |x| and |x|-|y| */ |
65 » if (ex > 0) { | 70 if (ex > 0) { |
66 » » uxi -= 1ULL << 52; | 71 uxi -= 1ULL << 52; |
67 » » uxi |= (uint64_t)ex << 52; | 72 uxi |= (uint64_t)ex << 52; |
68 » } else { | 73 } else { |
69 » » uxi >>= -ex + 1; | 74 uxi >>= -ex + 1; |
70 » } | 75 } |
71 » ux.i = uxi; | 76 ux.i = uxi; |
72 » x = ux.f; | 77 x = ux.f; |
73 » if (sy) | 78 if (sy) |
74 » » y = -y; | 79 y = -y; |
75 » if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) { | 80 if (ex == ey || (ex + 1 == ey && (2 * x > y || (2 * x == y && q % 2)))) { |
76 » » x -= y; | 81 x -= y; |
77 » » q++; | 82 q++; |
78 » } | 83 } |
79 » q &= 0x7fffffff; | 84 q &= 0x7fffffff; |
80 » *quo = sx^sy ? -(int)q : (int)q; | 85 *quo = sx ^ sy ? -(int)q : (int)q; |
81 » return sx ? -x : x; | 86 return sx ? -x : x; |
82 } | 87 } |
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