}
// Maximum shift that we can do in one pass without overflow.
-// Signed int has 31 bits, and we have to be able to accommodate 9<<k.
-const maxShift = 27
+// A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k.
+const uintSize = 32 << (^uint(0) >> 63)
+const maxShift = uintSize - 4
// Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow.
func rightShift(a *decimal, k uint) {
w := 0 // write pointer
// Pick up enough leading digits to cover first shift.
- n := 0
+ var n uint
for ; n>>k == 0; r++ {
if r >= a.nd {
if n == 0 {
}
break
}
- c := int(a.d[r])
+ c := uint(a.d[r])
n = n*10 + c - '0'
}
a.dp -= r - 1
// Pick up a digit, put down a digit.
for ; r < a.nd; r++ {
- c := int(a.d[r])
+ c := uint(a.d[r])
dig := n >> k
n -= dig << k
a.d[w] = byte(dig + '0')
type leftCheat struct {
delta int // number of new digits
- cutoff string // minus one digit if original < a.
+ cutoff string // minus one digit if original < a.
}
var leftcheats = []leftCheat{
// Leading digits of 1/2^i = 5^i.
// 5^23 is not an exact 64-bit floating point number,
// so have to use bc for the math.
+ // Go up to 60 to be large enough for 32bit and 64bit platforms.
/*
- seq 27 | sed 's/^/5^/' | bc |
- awk 'BEGIN{ print "\tleftCheat{ 0, \"\" }," }
+ seq 60 | sed 's/^/5^/' | bc |
+ awk 'BEGIN{ print "\t{ 0, \"\" }," }
{
log2 = log(2)/log(10)
- printf("\tleftCheat{ %d, \"%s\" },\t// * %d\n",
+ printf("\t{ %d, \"%s\" },\t// * %d\n",
int(log2*NR+1), $0, 2**NR)
}'
*/
{0, ""},
- {1, "5"}, // * 2
- {1, "25"}, // * 4
- {1, "125"}, // * 8
- {2, "625"}, // * 16
- {2, "3125"}, // * 32
- {2, "15625"}, // * 64
- {3, "78125"}, // * 128
- {3, "390625"}, // * 256
- {3, "1953125"}, // * 512
- {4, "9765625"}, // * 1024
- {4, "48828125"}, // * 2048
- {4, "244140625"}, // * 4096
- {4, "1220703125"}, // * 8192
- {5, "6103515625"}, // * 16384
- {5, "30517578125"}, // * 32768
- {5, "152587890625"}, // * 65536
- {6, "762939453125"}, // * 131072
- {6, "3814697265625"}, // * 262144
- {6, "19073486328125"}, // * 524288
- {7, "95367431640625"}, // * 1048576
- {7, "476837158203125"}, // * 2097152
- {7, "2384185791015625"}, // * 4194304
- {7, "11920928955078125"}, // * 8388608
- {8, "59604644775390625"}, // * 16777216
- {8, "298023223876953125"}, // * 33554432
- {8, "1490116119384765625"}, // * 67108864
- {9, "7450580596923828125"}, // * 134217728
+ {1, "5"}, // * 2
+ {1, "25"}, // * 4
+ {1, "125"}, // * 8
+ {2, "625"}, // * 16
+ {2, "3125"}, // * 32
+ {2, "15625"}, // * 64
+ {3, "78125"}, // * 128
+ {3, "390625"}, // * 256
+ {3, "1953125"}, // * 512
+ {4, "9765625"}, // * 1024
+ {4, "48828125"}, // * 2048
+ {4, "244140625"}, // * 4096
+ {4, "1220703125"}, // * 8192
+ {5, "6103515625"}, // * 16384
+ {5, "30517578125"}, // * 32768
+ {5, "152587890625"}, // * 65536
+ {6, "762939453125"}, // * 131072
+ {6, "3814697265625"}, // * 262144
+ {6, "19073486328125"}, // * 524288
+ {7, "95367431640625"}, // * 1048576
+ {7, "476837158203125"}, // * 2097152
+ {7, "2384185791015625"}, // * 4194304
+ {7, "11920928955078125"}, // * 8388608
+ {8, "59604644775390625"}, // * 16777216
+ {8, "298023223876953125"}, // * 33554432
+ {8, "1490116119384765625"}, // * 67108864
+ {9, "7450580596923828125"}, // * 134217728
+ {9, "37252902984619140625"}, // * 268435456
+ {9, "186264514923095703125"}, // * 536870912
+ {10, "931322574615478515625"}, // * 1073741824
+ {10, "4656612873077392578125"}, // * 2147483648
+ {10, "23283064365386962890625"}, // * 4294967296
+ {10, "116415321826934814453125"}, // * 8589934592
+ {11, "582076609134674072265625"}, // * 17179869184
+ {11, "2910383045673370361328125"}, // * 34359738368
+ {11, "14551915228366851806640625"}, // * 68719476736
+ {12, "72759576141834259033203125"}, // * 137438953472
+ {12, "363797880709171295166015625"}, // * 274877906944
+ {12, "1818989403545856475830078125"}, // * 549755813888
+ {13, "9094947017729282379150390625"}, // * 1099511627776
+ {13, "45474735088646411895751953125"}, // * 2199023255552
+ {13, "227373675443232059478759765625"}, // * 4398046511104
+ {13, "1136868377216160297393798828125"}, // * 8796093022208
+ {14, "5684341886080801486968994140625"}, // * 17592186044416
+ {14, "28421709430404007434844970703125"}, // * 35184372088832
+ {14, "142108547152020037174224853515625"}, // * 70368744177664
+ {15, "710542735760100185871124267578125"}, // * 140737488355328
+ {15, "3552713678800500929355621337890625"}, // * 281474976710656
+ {15, "17763568394002504646778106689453125"}, // * 562949953421312
+ {16, "88817841970012523233890533447265625"}, // * 1125899906842624
+ {16, "444089209850062616169452667236328125"}, // * 2251799813685248
+ {16, "2220446049250313080847263336181640625"}, // * 4503599627370496
+ {16, "11102230246251565404236316680908203125"}, // * 9007199254740992
+ {17, "55511151231257827021181583404541015625"}, // * 18014398509481984
+ {17, "277555756156289135105907917022705078125"}, // * 36028797018963968
+ {17, "1387778780781445675529539585113525390625"}, // * 72057594037927936
+ {18, "6938893903907228377647697925567626953125"}, // * 144115188075855872
+ {18, "34694469519536141888238489627838134765625"}, // * 288230376151711744
+ {18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
+ {19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
}
// Is the leading prefix of b lexicographically less than s?
r := a.nd // read index
w := a.nd + delta // write index
- n := 0
// Pick up a digit, put down a digit.
+ var n uint
for r--; r >= 0; r-- {
- n += (int(a.d[r]) - '0') << k
+ n += (uint(a.d[r]) - '0') << k
quo := n / 10
rem := n - 10*quo
w--