// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Multiprecision decimal numbers.
// For floating-point formatting only; not general purpose.
// Only operations are assign and (binary) left/right shift.
// Can do binary floating point in multiprecision decimal precisely
// because 2 divides 10; cannot do decimal floating point
// in multiprecision binary precisely.
package strconv
type decimal struct {
d [800]byte // digits, big-endian representation
nd int // number of digits used
dp int // decimal point
neg bool // negative flag
trunc bool // discarded nonzero digits beyond d[:nd]
}
func (a *decimal) String() string {
n := 10 + a.nd
if a.dp > 0 {
n += a.dp
}
if a.dp < 0 {
n += -a.dp
}
buf := make([]byte, n)
w := 0
switch {
case a.nd == 0:
return "0"
case a.dp <= 0:
// zeros fill space between decimal point and digits
buf[w] = '0'
w++
buf[w] = '.'
w++
w += digitZero(buf[w : w+-a.dp])
w += copy(buf[w:], a.d[0:a.nd])
case a.dp < a.nd:
// decimal point in middle of digits
w += copy(buf[w:], a.d[0:a.dp])
buf[w] = '.'
w++
w += copy(buf[w:], a.d[a.dp:a.nd])
default:
// zeros fill space between digits and decimal point
w += copy(buf[w:], a.d[0:a.nd])
w += digitZero(buf[w : w+a.dp-a.nd])
}
return string(buf[0:w])
}
func digitZero(dst []byte) int {
for i := range dst {
dst[i] = '0'
}
return len(dst)
}
// trim trailing zeros from number.
// (They are meaningless; the decimal point is tracked
// independent of the number of digits.)
func trim(a *decimal) {
for a.nd > 0 && a.d[a.nd-1] == '0' {
a.nd--
}
if a.nd == 0 {
a.dp = 0
}
}
// Assign v to a.
func (a *decimal) Assign(v uint64) {
var buf [24]byte
// Write reversed decimal in buf.
n := 0
for v > 0 {
v1 := v / 10
v -= 10 * v1
buf[n] = byte(v + '0')
n++
v = v1
}
// Reverse again to produce forward decimal in a.d.
a.nd = 0
for n--; n >= 0; n-- {
a.d[a.nd] = buf[n]
a.nd++
}
a.dp = a.nd
trim(a)
}
// Maximum shift that we can do in one pass without overflow.
// 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) {
r := 0 // read pointer
w := 0 // write pointer
// Pick up enough leading digits to cover first shift.
var n uint
for ; n>>k == 0; r++ {
if r >= a.nd {
if n == 0 {
// a == 0; shouldn't get here, but handle anyway.
a.nd = 0
return
}
for n>>k == 0 {
n = n * 10
r++
}
break
}
c := uint(a.d[r])
n = n*10 + c - '0'
}
a.dp -= r - 1
var mask uint = (1 << k) - 1
// Pick up a digit, put down a digit.
for ; r < a.nd; r++ {
c := uint(a.d[r])
dig := n >> k
n &= mask
a.d[w] = byte(dig + '0')
w++
n = n*10 + c - '0'
}
// Put down extra digits.
for n > 0 {
dig := n >> k
n &= mask
if w < len(a.d) {
a.d[w] = byte(dig + '0')
w++
} else if dig > 0 {
a.trunc = true
}
n = n * 10
}
a.nd = w
trim(a)
}
// Cheat sheet for left shift: table indexed by shift count giving
// number of new digits that will be introduced by that shift.
//
// For example, leftcheats[4] = {2, "625"}. That means that
// if we are shifting by 4 (multiplying by 16), it will add 2 digits
// when the string prefix is "625" through "999", and one fewer digit
// if the string prefix is "000" through "624".
//
// Credit for this trick goes to Ken.
type leftCheat struct {
delta int // number of new digits
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 60 | sed 's/^/5^/' | bc |
awk 'BEGIN{ print "\t{ 0, \"\" }," }
{
log2 = log(2)/log(10)
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
{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?
func prefixIsLessThan(b []byte, s string) bool {
for i := 0; i < len(s); i++ {
if i >= len(b) {
return true
}
if b[i] != s[i] {
return b[i] < s[i]
}
}
return false
}
// Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow.
func leftShift(a *decimal, k uint) {
delta := leftcheats[k].delta
if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
delta--
}
r := a.nd // read index
w := a.nd + delta // write index
// Pick up a digit, put down a digit.
var n uint
for r--; r >= 0; r-- {
n += (uint(a.d[r]) - '0') << k
quo := n / 10
rem := n - 10*quo
w--
if w < len(a.d) {
a.d[w] = byte(rem + '0')
} else if rem != 0 {
a.trunc = true
}
n = quo
}
// Put down extra digits.
for n > 0 {
quo := n / 10
rem := n - 10*quo
w--
if w < len(a.d) {
a.d[w] = byte(rem + '0')
} else if rem != 0 {
a.trunc = true
}
n = quo
}
a.nd += delta
if a.nd >= len(a.d) {
a.nd = len(a.d)
}
a.dp += delta
trim(a)
}
// Binary shift left (k > 0) or right (k < 0).
func (a *decimal) Shift(k int) {
switch {
case a.nd == 0:
// nothing to do: a == 0
case k > 0:
for k > maxShift {
leftShift(a, maxShift)
k -= maxShift
}
leftShift(a, uint(k))
case k < 0:
for k < -maxShift {
rightShift(a, maxShift)
k += maxShift
}
rightShift(a, uint(-k))
}
}
// If we chop a at nd digits, should we round up?
func shouldRoundUp(a *decimal, nd int) bool {
if nd < 0 || nd >= a.nd {
return false
}
if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
// if we truncated, a little higher than what's recorded - always round up
if a.trunc {
return true
}
return nd > 0 && (a.d[nd-1]-'0')%2 != 0
}
// not halfway - digit tells all
return a.d[nd] >= '5'
}
// Round a to nd digits (or fewer).
// If nd is zero, it means we're rounding
// just to the left of the digits, as in
// 0.09 -> 0.1.
func (a *decimal) Round(nd int) {
if nd < 0 || nd >= a.nd {
return
}
if shouldRoundUp(a, nd) {
a.RoundUp(nd)
} else {
a.RoundDown(nd)
}
}
// Round a down to nd digits (or fewer).
func (a *decimal) RoundDown(nd int) {
if nd < 0 || nd >= a.nd {
return
}
a.nd = nd
trim(a)
}
// Round a up to nd digits (or fewer).
func (a *decimal) RoundUp(nd int) {
if nd < 0 || nd >= a.nd {
return
}
// round up
for i := nd - 1; i >= 0; i-- {
c := a.d[i]
if c < '9' { // can stop after this digit
a.d[i]++
a.nd = i + 1
return
}
}
// Number is all 9s.
// Change to single 1 with adjusted decimal point.
a.d[0] = '1'
a.nd = 1
a.dp++
}
// Extract integer part, rounded appropriately.
// No guarantees about overflow.
func (a *decimal) RoundedInteger() uint64 {
if a.dp > 20 {
return 0xFFFFFFFFFFFFFFFF
}
var i int
n := uint64(0)
for i = 0; i < a.dp && i < a.nd; i++ {
n = n*10 + uint64(a.d[i]-'0')
}
for ; i < a.dp; i++ {
n *= 10
}
if shouldRoundUp(a, a.dp) {
n++
}
return n
}
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