546 lines
11 KiB
Go
546 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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package strconv
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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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import "runtime"
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var optimize = true // can change for testing
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func equalIgnoreCase(s1, s2 string) 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 string) (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, "+inf") || equalIgnoreCase(s, "+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, "-inf") || equalIgnoreCase(s, "-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, "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, "inf") || equalIgnoreCase(s, "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 string) (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 string) (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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if mantissa != 0 {
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exp = dp - ndMant
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}
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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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// gccgo gets this wrong on 32-bit i386 when not using -msse.
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// See TestRoundTrip in atof_test.go for a test case.
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if runtime.GOARCH == "386" {
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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 string) (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, 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, 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, s)
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}
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return f, err
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}
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func atof64(s string) (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, 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, 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, s)
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}
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return f, err
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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 string, bitSize int) (float64, error) {
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if bitSize == 32 {
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f, err := atof32(s)
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return float64(f), err
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}
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return atof64(s)
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}
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