mirror of
https://github.com/shopspring/decimal.git
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cd690d0c9e
* Make NewFromFloat respect the precision of the input Restores the previous behaviour where input converted from float is truncated at the precision of the float. The precision is depending on the actual value. Simply making it 15 digits would make it faster, but would in some cases lose some precision. So the code from the stdlib that does this calculation (very well) has been included. Lots of good articles here: https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ Performance is around the same as the previous string roundtrip since it basically does the same, but allocations are a bit less. `BenchmarkNewFromStringFloat` is the old method, `BenchmarkNewFromFloat` is the new. ``` BenchmarkNewFromFloatWithExponent-8 10000000 260 ns/op 174 B/op 4 allocs/op BenchmarkNewFromFloat-8 2000000 744 ns/op 90 B/op 2 allocs/op BenchmarkNewFromStringFloat-8 2000000 822 ns/op 258 B/op 6 allocs/op ``` * Update Sin/Tan/Cos tests.
414 lines
11 KiB
Go
414 lines
11 KiB
Go
// 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)
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} else {
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a.RoundDown(nd)
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}
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}
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// Round a down to nd digits (or fewer).
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func (a *decimal) RoundDown(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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a.nd = nd
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trim(a)
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}
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// Round a up to nd digits (or fewer).
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func (a *decimal) RoundUp(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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// round up
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for i := nd - 1; i >= 0; i-- {
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c := a.d[i]
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if c < '9' { // can stop after this digit
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a.d[i]++
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a.nd = i + 1
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return
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}
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}
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// Number is all 9s.
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// Change to single 1 with adjusted decimal point.
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a.d[0] = '1'
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a.nd = 1
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a.dp++
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}
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// Extract integer part, rounded appropriately.
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// No guarantees about overflow.
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func (a *decimal) RoundedInteger() uint64 {
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if a.dp > 20 {
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return 0xFFFFFFFFFFFFFFFF
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}
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var i int
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n := uint64(0)
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for i = 0; i < a.dp && i < a.nd; i++ {
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n = n*10 + uint64(a.d[i]-'0')
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}
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for ; i < a.dp; i++ {
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n *= 10
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}
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if shouldRoundUp(a, a.dp) {
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n++
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}
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return n
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}
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