937 lines
20 KiB
Go
937 lines
20 KiB
Go
/**
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* Copyright 2014 Paul Querna
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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*/
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/* Portions of this file are on Go stdlib's strconv/atof.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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package internal
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// decimal to binary floating point conversion.
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// Algorithm:
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// 1) Store input in multiprecision decimal.
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// 2) Multiply/divide decimal by powers of two until in range [0.5, 1)
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// 3) Multiply by 2^precision and round to get mantissa.
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import "math"
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var optimize = true // can change for testing
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func equalIgnoreCase(s1 []byte, s2 []byte) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i := 0; i < len(s1); i++ {
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c1 := s1[i]
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if 'A' <= c1 && c1 <= 'Z' {
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c1 += 'a' - 'A'
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}
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c2 := s2[i]
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if 'A' <= c2 && c2 <= 'Z' {
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c2 += 'a' - 'A'
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}
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if c1 != c2 {
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return false
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}
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}
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return true
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}
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func special(s []byte) (f float64, ok bool) {
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if len(s) == 0 {
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return
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}
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switch s[0] {
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default:
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return
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case '+':
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if equalIgnoreCase(s, []byte("+inf")) || equalIgnoreCase(s, []byte("+infinity")) {
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return math.Inf(1), true
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}
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case '-':
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if equalIgnoreCase(s, []byte("-inf")) || equalIgnoreCase(s, []byte("-infinity")) {
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return math.Inf(-1), true
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}
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case 'n', 'N':
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if equalIgnoreCase(s, []byte("nan")) {
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return math.NaN(), true
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}
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case 'i', 'I':
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if equalIgnoreCase(s, []byte("inf")) || equalIgnoreCase(s, []byte("infinity")) {
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return math.Inf(1), true
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}
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}
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return
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}
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func (b *decimal) set(s []byte) (ok bool) {
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i := 0
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b.neg = false
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b.trunc = false
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// optional sign
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if i >= len(s) {
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return
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}
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switch {
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case s[i] == '+':
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i++
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case s[i] == '-':
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b.neg = true
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i++
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}
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// digits
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sawdot := false
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sawdigits := false
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for ; i < len(s); i++ {
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switch {
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case s[i] == '.':
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if sawdot {
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return
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}
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sawdot = true
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b.dp = b.nd
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continue
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case '0' <= s[i] && s[i] <= '9':
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sawdigits = true
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if s[i] == '0' && b.nd == 0 { // ignore leading zeros
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b.dp--
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continue
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}
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if b.nd < len(b.d) {
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b.d[b.nd] = s[i]
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b.nd++
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} else if s[i] != '0' {
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b.trunc = true
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}
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continue
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}
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break
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}
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if !sawdigits {
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return
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}
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if !sawdot {
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b.dp = b.nd
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}
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// optional exponent moves decimal point.
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// if we read a very large, very long number,
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// just be sure to move the decimal point by
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// a lot (say, 100000). it doesn't matter if it's
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// not the exact number.
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if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
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i++
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if i >= len(s) {
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return
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}
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esign := 1
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if s[i] == '+' {
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i++
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} else if s[i] == '-' {
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i++
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esign = -1
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}
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if i >= len(s) || s[i] < '0' || s[i] > '9' {
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return
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}
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e := 0
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for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
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if e < 10000 {
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e = e*10 + int(s[i]) - '0'
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}
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}
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b.dp += e * esign
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}
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if i != len(s) {
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return
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}
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ok = true
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return
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}
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// readFloat reads a decimal mantissa and exponent from a float
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// string representation. It sets ok to false if the number could
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// not fit return types or is invalid.
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func readFloat(s []byte) (mantissa uint64, exp int, neg, trunc, ok bool) {
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const uint64digits = 19
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i := 0
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// optional sign
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if i >= len(s) {
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return
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}
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switch {
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case s[i] == '+':
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i++
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case s[i] == '-':
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neg = true
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i++
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}
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// digits
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sawdot := false
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sawdigits := false
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nd := 0
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ndMant := 0
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dp := 0
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for ; i < len(s); i++ {
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switch c := s[i]; true {
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case c == '.':
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if sawdot {
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return
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}
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sawdot = true
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dp = nd
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continue
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case '0' <= c && c <= '9':
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sawdigits = true
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if c == '0' && nd == 0 { // ignore leading zeros
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dp--
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continue
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}
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nd++
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if ndMant < uint64digits {
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mantissa *= 10
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mantissa += uint64(c - '0')
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ndMant++
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} else if s[i] != '0' {
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trunc = true
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}
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continue
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}
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break
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}
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if !sawdigits {
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return
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}
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if !sawdot {
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dp = nd
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}
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// optional exponent moves decimal point.
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// if we read a very large, very long number,
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// just be sure to move the decimal point by
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// a lot (say, 100000). it doesn't matter if it's
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// not the exact number.
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if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
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i++
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if i >= len(s) {
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return
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}
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esign := 1
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if s[i] == '+' {
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i++
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} else if s[i] == '-' {
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i++
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esign = -1
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}
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if i >= len(s) || s[i] < '0' || s[i] > '9' {
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return
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}
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e := 0
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for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
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if e < 10000 {
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e = e*10 + int(s[i]) - '0'
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}
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}
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dp += e * esign
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}
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if i != len(s) {
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return
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}
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exp = dp - ndMant
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ok = true
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return
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}
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// decimal power of ten to binary power of two.
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var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
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func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
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var exp int
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var mant uint64
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// Zero is always a special case.
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if d.nd == 0 {
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mant = 0
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exp = flt.bias
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goto out
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}
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// Obvious overflow/underflow.
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// These bounds are for 64-bit floats.
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// Will have to change if we want to support 80-bit floats in the future.
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if d.dp > 310 {
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goto overflow
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}
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if d.dp < -330 {
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// zero
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mant = 0
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exp = flt.bias
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goto out
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}
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// Scale by powers of two until in range [0.5, 1.0)
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exp = 0
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for d.dp > 0 {
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var n int
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if d.dp >= len(powtab) {
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n = 27
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} else {
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n = powtab[d.dp]
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}
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d.Shift(-n)
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exp += n
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}
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for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
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var n int
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if -d.dp >= len(powtab) {
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n = 27
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} else {
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n = powtab[-d.dp]
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}
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d.Shift(n)
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exp -= n
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}
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// Our range is [0.5,1) but floating point range is [1,2).
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exp--
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// Minimum representable exponent is flt.bias+1.
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// If the exponent is smaller, move it up and
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// adjust d accordingly.
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if exp < flt.bias+1 {
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n := flt.bias + 1 - exp
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d.Shift(-n)
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exp += n
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}
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if exp-flt.bias >= 1<<flt.expbits-1 {
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goto overflow
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}
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// Extract 1+flt.mantbits bits.
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d.Shift(int(1 + flt.mantbits))
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mant = d.RoundedInteger()
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// Rounding might have added a bit; shift down.
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if mant == 2<<flt.mantbits {
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mant >>= 1
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exp++
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if exp-flt.bias >= 1<<flt.expbits-1 {
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goto overflow
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}
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}
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// Denormalized?
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if mant&(1<<flt.mantbits) == 0 {
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exp = flt.bias
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}
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goto out
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overflow:
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// ±Inf
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mant = 0
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exp = 1<<flt.expbits - 1 + flt.bias
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overflow = true
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out:
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// Assemble bits.
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bits := mant & (uint64(1)<<flt.mantbits - 1)
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bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
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if d.neg {
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bits |= 1 << flt.mantbits << flt.expbits
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}
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return bits, overflow
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}
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// Exact powers of 10.
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var float64pow10 = []float64{
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1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
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1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
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1e20, 1e21, 1e22,
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}
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var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
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// If possible to convert decimal representation to 64-bit float f exactly,
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// entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
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// Three common cases:
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// value is exact integer
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// value is exact integer * exact power of ten
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// value is exact integer / exact power of ten
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// These all produce potentially inexact but correctly rounded answers.
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func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
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if mantissa>>float64info.mantbits != 0 {
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return
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}
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f = float64(mantissa)
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if neg {
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f = -f
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}
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switch {
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case exp == 0:
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// an integer.
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return f, true
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// Exact integers are <= 10^15.
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// Exact powers of ten are <= 10^22.
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case exp > 0 && exp <= 15+22: // int * 10^k
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// If exponent is big but number of digits is not,
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// can move a few zeros into the integer part.
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if exp > 22 {
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f *= float64pow10[exp-22]
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exp = 22
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}
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if f > 1e15 || f < -1e15 {
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// the exponent was really too large.
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return
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}
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return f * float64pow10[exp], true
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case exp < 0 && exp >= -22: // int / 10^k
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return f / float64pow10[-exp], true
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}
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return
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}
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// If possible to compute mantissa*10^exp to 32-bit float f exactly,
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// entirely in floating-point math, do so, avoiding the machinery above.
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func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
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if mantissa>>float32info.mantbits != 0 {
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return
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}
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f = float32(mantissa)
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if neg {
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f = -f
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}
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switch {
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case exp == 0:
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return f, true
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// Exact integers are <= 10^7.
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// Exact powers of ten are <= 10^10.
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case exp > 0 && exp <= 7+10: // int * 10^k
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// If exponent is big but number of digits is not,
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// can move a few zeros into the integer part.
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if exp > 10 {
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f *= float32pow10[exp-10]
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exp = 10
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}
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if f > 1e7 || f < -1e7 {
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// the exponent was really too large.
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return
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}
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return f * float32pow10[exp], true
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case exp < 0 && exp >= -10: // int / 10^k
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return f / float32pow10[-exp], true
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}
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return
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}
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const fnParseFloat = "ParseFloat"
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func atof32(s []byte) (f float32, err error) {
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if val, ok := special(s); ok {
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return float32(val), nil
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}
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if optimize {
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// Parse mantissa and exponent.
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mantissa, exp, neg, trunc, ok := readFloat(s)
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if ok {
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// Try pure floating-point arithmetic conversion.
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if !trunc {
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if f, ok := atof32exact(mantissa, exp, neg); ok {
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return f, nil
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}
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}
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// Try another fast path.
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ext := new(extFloat)
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if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
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b, ovf := ext.floatBits(&float32info)
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f = math.Float32frombits(uint32(b))
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if ovf {
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err = rangeError(fnParseFloat, string(s))
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}
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return f, err
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}
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}
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}
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var d decimal
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if !d.set(s) {
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return 0, syntaxError(fnParseFloat, string(s))
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}
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b, ovf := d.floatBits(&float32info)
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f = math.Float32frombits(uint32(b))
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if ovf {
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err = rangeError(fnParseFloat, string(s))
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}
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return f, err
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}
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func atof64(s []byte) (f float64, err error) {
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if val, ok := special(s); ok {
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return val, nil
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}
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if optimize {
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// Parse mantissa and exponent.
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mantissa, exp, neg, trunc, ok := readFloat(s)
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if ok {
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// Try pure floating-point arithmetic conversion.
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if !trunc {
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if f, ok := atof64exact(mantissa, exp, neg); ok {
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return f, nil
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}
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}
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// Try another fast path.
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ext := new(extFloat)
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if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
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b, ovf := ext.floatBits(&float64info)
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f = math.Float64frombits(b)
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if ovf {
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err = rangeError(fnParseFloat, string(s))
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}
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return f, err
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}
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}
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}
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var d decimal
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if !d.set(s) {
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return 0, syntaxError(fnParseFloat, string(s))
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}
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b, ovf := d.floatBits(&float64info)
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f = math.Float64frombits(b)
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if ovf {
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err = rangeError(fnParseFloat, string(s))
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}
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return f, err
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}
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|
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// ParseFloat converts the string s to a floating-point number
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// with the precision specified by bitSize: 32 for float32, or 64 for float64.
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// When bitSize=32, the result still has type float64, but it will be
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// convertible to float32 without changing its value.
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//
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// If s is well-formed and near a valid floating point number,
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// ParseFloat returns the nearest floating point number rounded
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// using IEEE754 unbiased rounding.
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//
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// The errors that ParseFloat returns have concrete type *NumError
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// and include err.Num = s.
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//
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// If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
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//
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// If s is syntactically well-formed but is more than 1/2 ULP
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// away from the largest floating point number of the given size,
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// ParseFloat returns f = ±Inf, err.Err = ErrRange.
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|
func ParseFloat(s []byte, bitSize int) (f float64, err error) {
|
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if bitSize == 32 {
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f1, err1 := atof32(s)
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return float64(f1), err1
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}
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f1, err1 := atof64(s)
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return f1, err1
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}
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|
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// oroginal: strconv/decimal.go, but not exported, and needed for PareFloat.
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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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type decimal struct {
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d [800]byte // digits
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nd int // number of digits used
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dp int // decimal point
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neg bool
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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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// Signed int has 31 bits, and we have to be able to accommodate 9<<k.
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const maxShift = 27
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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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n := 0
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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 := int(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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// Pick up a digit, put down a digit.
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for ; r < a.nd; r++ {
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c := int(a.d[r])
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dig := n >> k
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n -= dig << k
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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 -= dig << k
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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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/*
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seq 27 | sed 's/^/5^/' | bc |
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awk 'BEGIN{ print "\tleftCheat{ 0, \"\" }," }
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{
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log2 = log(2)/log(10)
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printf("\tleftCheat{ %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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}
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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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n := 0
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// Pick up a digit, put down a digit.
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for r--; r >= 0; r-- {
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n += (int(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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