416 lines
11 KiB
Go
416 lines
11 KiB
Go
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// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Multiprecision decimal numbers.
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// For floating-point formatting only; not general purpose.
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// Only operations are assign and (binary) left/right shift.
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// Can do binary floating point in multiprecision decimal precisely
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// because 2 divides 10; cannot do decimal floating point
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// in multiprecision binary precisely.
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package decimal
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type decimal struct {
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d [800]byte // digits, big-endian representation
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nd int // number of digits used
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dp int // decimal point
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neg bool // negative flag
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trunc bool // discarded nonzero digits beyond d[:nd]
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}
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func (a *decimal) String() string {
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n := 10 + a.nd
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if a.dp > 0 {
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n += a.dp
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}
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if a.dp < 0 {
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n += -a.dp
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}
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buf := make([]byte, n)
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w := 0
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switch {
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case a.nd == 0:
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return "0"
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case a.dp <= 0:
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// zeros fill space between decimal point and digits
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buf[w] = '0'
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w++
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buf[w] = '.'
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w++
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w += digitZero(buf[w : w+-a.dp])
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w += copy(buf[w:], a.d[0:a.nd])
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case a.dp < a.nd:
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// decimal point in middle of digits
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w += copy(buf[w:], a.d[0:a.dp])
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buf[w] = '.'
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w++
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w += copy(buf[w:], a.d[a.dp:a.nd])
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default:
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// zeros fill space between digits and decimal point
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w += copy(buf[w:], a.d[0:a.nd])
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w += digitZero(buf[w : w+a.dp-a.nd])
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}
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return string(buf[0:w])
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}
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func digitZero(dst []byte) int {
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for i := range dst {
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dst[i] = '0'
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}
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return len(dst)
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}
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// trim trailing zeros from number.
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// (They are meaningless; the decimal point is tracked
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// independent of the number of digits.)
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func trim(a *decimal) {
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for a.nd > 0 && a.d[a.nd-1] == '0' {
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a.nd--
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}
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if a.nd == 0 {
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a.dp = 0
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}
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}
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// Assign v to a.
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func (a *decimal) Assign(v uint64) {
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var buf [24]byte
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// Write reversed decimal in buf.
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n := 0
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for v > 0 {
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v1 := v / 10
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v -= 10 * v1
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buf[n] = byte(v + '0')
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n++
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v = v1
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}
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// Reverse again to produce forward decimal in a.d.
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a.nd = 0
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for n--; n >= 0; n-- {
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a.d[a.nd] = buf[n]
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a.nd++
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}
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a.dp = a.nd
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trim(a)
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}
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// Maximum shift that we can do in one pass without overflow.
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// A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k.
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const uintSize = 32 << (^uint(0) >> 63)
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const maxShift = uintSize - 4
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// Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow.
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func rightShift(a *decimal, k uint) {
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r := 0 // read pointer
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w := 0 // write pointer
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// Pick up enough leading digits to cover first shift.
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var n uint
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for ; n>>k == 0; r++ {
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if r >= a.nd {
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if n == 0 {
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// a == 0; shouldn't get here, but handle anyway.
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a.nd = 0
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return
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}
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for n>>k == 0 {
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n = n * 10
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r++
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}
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break
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}
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c := uint(a.d[r])
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n = n*10 + c - '0'
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}
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a.dp -= r - 1
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var mask uint = (1 << k) - 1
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// Pick up a digit, put down a digit.
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for ; r < a.nd; r++ {
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c := uint(a.d[r])
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dig := n >> k
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n &= mask
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a.d[w] = byte(dig + '0')
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w++
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n = n*10 + c - '0'
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}
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// Put down extra digits.
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for n > 0 {
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dig := n >> k
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n &= mask
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if w < len(a.d) {
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a.d[w] = byte(dig + '0')
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w++
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} else if dig > 0 {
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a.trunc = true
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}
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n = n * 10
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}
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a.nd = w
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trim(a)
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}
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// Cheat sheet for left shift: table indexed by shift count giving
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// number of new digits that will be introduced by that shift.
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//
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// For example, leftcheats[4] = {2, "625"}. That means that
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// if we are shifting by 4 (multiplying by 16), it will add 2 digits
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// when the string prefix is "625" through "999", and one fewer digit
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// if the string prefix is "000" through "624".
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//
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// Credit for this trick goes to Ken.
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type leftCheat struct {
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delta int // number of new digits
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cutoff string // minus one digit if original < a.
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}
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var leftcheats = []leftCheat{
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// Leading digits of 1/2^i = 5^i.
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// 5^23 is not an exact 64-bit floating point number,
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// so have to use bc for the math.
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// Go up to 60 to be large enough for 32bit and 64bit platforms.
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/*
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seq 60 | sed 's/^/5^/' | bc |
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awk 'BEGIN{ print "\t{ 0, \"\" }," }
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{
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log2 = log(2)/log(10)
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printf("\t{ %d, \"%s\" },\t// * %d\n",
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int(log2*NR+1), $0, 2**NR)
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}'
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*/
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{0, ""},
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{1, "5"}, // * 2
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{1, "25"}, // * 4
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{1, "125"}, // * 8
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{2, "625"}, // * 16
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{2, "3125"}, // * 32
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{2, "15625"}, // * 64
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{3, "78125"}, // * 128
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{3, "390625"}, // * 256
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{3, "1953125"}, // * 512
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{4, "9765625"}, // * 1024
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{4, "48828125"}, // * 2048
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{4, "244140625"}, // * 4096
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{4, "1220703125"}, // * 8192
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{5, "6103515625"}, // * 16384
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{5, "30517578125"}, // * 32768
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{5, "152587890625"}, // * 65536
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{6, "762939453125"}, // * 131072
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{6, "3814697265625"}, // * 262144
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{6, "19073486328125"}, // * 524288
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{7, "95367431640625"}, // * 1048576
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{7, "476837158203125"}, // * 2097152
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{7, "2384185791015625"}, // * 4194304
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{7, "11920928955078125"}, // * 8388608
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{8, "59604644775390625"}, // * 16777216
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{8, "298023223876953125"}, // * 33554432
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{8, "1490116119384765625"}, // * 67108864
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{9, "7450580596923828125"}, // * 134217728
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{9, "37252902984619140625"}, // * 268435456
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{9, "186264514923095703125"}, // * 536870912
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{10, "931322574615478515625"}, // * 1073741824
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{10, "4656612873077392578125"}, // * 2147483648
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{10, "23283064365386962890625"}, // * 4294967296
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{10, "116415321826934814453125"}, // * 8589934592
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{11, "582076609134674072265625"}, // * 17179869184
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{11, "2910383045673370361328125"}, // * 34359738368
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{11, "14551915228366851806640625"}, // * 68719476736
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{12, "72759576141834259033203125"}, // * 137438953472
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{12, "363797880709171295166015625"}, // * 274877906944
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{12, "1818989403545856475830078125"}, // * 549755813888
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{13, "9094947017729282379150390625"}, // * 1099511627776
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{13, "45474735088646411895751953125"}, // * 2199023255552
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{13, "227373675443232059478759765625"}, // * 4398046511104
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{13, "1136868377216160297393798828125"}, // * 8796093022208
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{14, "5684341886080801486968994140625"}, // * 17592186044416
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{14, "28421709430404007434844970703125"}, // * 35184372088832
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{14, "142108547152020037174224853515625"}, // * 70368744177664
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{15, "710542735760100185871124267578125"}, // * 140737488355328
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{15, "3552713678800500929355621337890625"}, // * 281474976710656
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{15, "17763568394002504646778106689453125"}, // * 562949953421312
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{16, "88817841970012523233890533447265625"}, // * 1125899906842624
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{16, "444089209850062616169452667236328125"}, // * 2251799813685248
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{16, "2220446049250313080847263336181640625"}, // * 4503599627370496
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{16, "11102230246251565404236316680908203125"}, // * 9007199254740992
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{17, "55511151231257827021181583404541015625"}, // * 18014398509481984
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{17, "277555756156289135105907917022705078125"}, // * 36028797018963968
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{17, "1387778780781445675529539585113525390625"}, // * 72057594037927936
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{18, "6938893903907228377647697925567626953125"}, // * 144115188075855872
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{18, "34694469519536141888238489627838134765625"}, // * 288230376151711744
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{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
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{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
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}
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// Is the leading prefix of b lexicographically less than s?
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func prefixIsLessThan(b []byte, s string) bool {
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for i := 0; i < len(s); i++ {
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if i >= len(b) {
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return true
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}
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if b[i] != s[i] {
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return b[i] < s[i]
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}
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}
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return false
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}
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// Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow.
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func leftShift(a *decimal, k uint) {
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delta := leftcheats[k].delta
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if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
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delta--
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}
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r := a.nd // read index
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w := a.nd + delta // write index
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// Pick up a digit, put down a digit.
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var n uint
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for r--; r >= 0; r-- {
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n += (uint(a.d[r]) - '0') << k
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quo := n / 10
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rem := n - 10*quo
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w--
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if w < len(a.d) {
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a.d[w] = byte(rem + '0')
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} else if rem != 0 {
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a.trunc = true
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}
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n = quo
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}
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// Put down extra digits.
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for n > 0 {
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quo := n / 10
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rem := n - 10*quo
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w--
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if w < len(a.d) {
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a.d[w] = byte(rem + '0')
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} else if rem != 0 {
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a.trunc = true
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}
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n = quo
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}
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a.nd += delta
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if a.nd >= len(a.d) {
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a.nd = len(a.d)
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}
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a.dp += delta
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trim(a)
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}
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// Binary shift left (k > 0) or right (k < 0).
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func (a *decimal) Shift(k int) {
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switch {
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case a.nd == 0:
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// nothing to do: a == 0
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case k > 0:
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for k > maxShift {
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leftShift(a, maxShift)
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k -= maxShift
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}
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leftShift(a, uint(k))
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case k < 0:
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for k < -maxShift {
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rightShift(a, maxShift)
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k += maxShift
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}
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rightShift(a, uint(-k))
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}
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}
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// If we chop a at nd digits, should we round up?
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func shouldRoundUp(a *decimal, nd int) bool {
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if nd < 0 || nd >= a.nd {
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return false
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}
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if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
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// if we truncated, a little higher than what's recorded - always round up
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if a.trunc {
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return true
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}
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return nd > 0 && (a.d[nd-1]-'0')%2 != 0
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}
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// not halfway - digit tells all
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return a.d[nd] >= '5'
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}
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// Round a to nd digits (or fewer).
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// If nd is zero, it means we're rounding
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// just to the left of the digits, as in
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// 0.09 -> 0.1.
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func (a *decimal) Round(nd int) {
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if nd < 0 || nd >= a.nd {
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return
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}
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if shouldRoundUp(a, nd) {
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|
|
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
|
||
|
|
}
|