500 lines
11 KiB
Go
500 lines
11 KiB
Go
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// Copyright (c) 2012-2020 Ugorji Nwoke. All rights reserved.
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// Use of this source code is governed by a MIT license found in the LICENSE file.
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package codec
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import (
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"math"
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"strconv"
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)
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// Per go spec, floats are represented in memory as
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// IEEE single or double precision floating point values.
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//
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// We also looked at the source for stdlib math/modf.go,
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// reviewed https://github.com/chewxy/math32
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// and read wikipedia documents describing the formats.
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//
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// It became clear that we could easily look at the bits to determine
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// whether any fraction exists.
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func parseFloat32(b []byte) (f float32, err error) {
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return parseFloat32_custom(b)
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}
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func parseFloat64(b []byte) (f float64, err error) {
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return parseFloat64_custom(b)
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}
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func parseFloat32_strconv(b []byte) (f float32, err error) {
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f64, err := strconv.ParseFloat(stringView(b), 32)
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f = float32(f64)
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return
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}
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func parseFloat64_strconv(b []byte) (f float64, err error) {
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return strconv.ParseFloat(stringView(b), 64)
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}
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// ------ parseFloat custom below --------
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// JSON really supports decimal numbers in base 10 notation, with exponent support.
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//
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// We assume the following:
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// - a lot of floating point numbers in json files will have defined precision
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// (in terms of number of digits after decimal point), etc.
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// - these (referenced above) can be written in exact format.
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//
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// strconv.ParseFloat has some unnecessary overhead which we can do without
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// for the common case:
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//
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// - expensive char-by-char check to see if underscores are in right place
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// - testing for and skipping underscores
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// - check if the string matches ignorecase +/- inf, +/- infinity, nan
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// - support for base 16 (0xFFFF...)
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//
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// The functions below will try a fast-path for floats which can be decoded
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// without any loss of precision, meaning they:
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//
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// - fits within the significand bits of the 32-bits or 64-bits
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// - exponent fits within the exponent value
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// - there is no truncation (any extra numbers are all trailing zeros)
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//
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// To figure out what the values are for maxMantDigits, use this idea below:
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//
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// 2^23 = 838 8608 (between 10^ 6 and 10^ 7) (significand bits of uint32)
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// 2^32 = 42 9496 7296 (between 10^ 9 and 10^10) (full uint32)
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// 2^52 = 4503 5996 2737 0496 (between 10^15 and 10^16) (significand bits of uint64)
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// 2^64 = 1844 6744 0737 0955 1616 (between 10^19 and 10^20) (full uint64)
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//
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// Note: we only allow for up to what can comfortably fit into the significand
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// ignoring the exponent, and we only try to parse iff significand fits.
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const (
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fMaxMultiplierForExactPow10_64 = 1e15
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fMaxMultiplierForExactPow10_32 = 1e7
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fUint64Cutoff = (1<<64-1)/10 + 1
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// fUint32Cutoff = (1<<32-1)/10 + 1
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fBase = 10
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)
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const (
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thousand = 1000
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million = thousand * thousand
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billion = thousand * million
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trillion = thousand * billion
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quadrillion = thousand * trillion
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quintillion = thousand * quadrillion
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)
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// Exact powers of 10.
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var uint64pow10 = [...]uint64{
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1, 10, 100,
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1 * thousand, 10 * thousand, 100 * thousand,
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1 * million, 10 * million, 100 * million,
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1 * billion, 10 * billion, 100 * billion,
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1 * trillion, 10 * trillion, 100 * trillion,
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1 * quadrillion, 10 * quadrillion, 100 * quadrillion,
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1 * quintillion, 10 * quintillion,
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}
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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{
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1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10,
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}
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type floatinfo struct {
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mantbits uint8
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// expbits uint8 // (unused)
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// bias int16 // (unused)
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// is32bit bool // (unused)
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exactPow10 int8 // Exact powers of ten are <= 10^N (32: 10, 64: 22)
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exactInts int8 // Exact integers are <= 10^N (for non-float, set to 0)
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// maxMantDigits int8 // 10^19 fits in uint64, while 10^9 fits in uint32
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mantCutoffIsUint64Cutoff bool
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mantCutoff uint64
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}
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var fi32 = floatinfo{23, 10, 7, false, 1<<23 - 1}
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var fi64 = floatinfo{52, 22, 15, false, 1<<52 - 1}
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var fi64u = floatinfo{0, 19, 0, true, fUint64Cutoff}
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func noFrac64(fbits uint64) bool {
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if fbits == 0 {
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return true
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}
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exp := uint64(fbits>>52)&0x7FF - 1023 // uint(x>>shift)&mask - bias
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// clear top 12+e bits, the integer part; if the rest is 0, then no fraction.
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return exp < 52 && fbits<<(12+exp) == 0 // means there's no fractional part
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}
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func noFrac32(fbits uint32) bool {
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if fbits == 0 {
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return true
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}
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exp := uint32(fbits>>23)&0xFF - 127 // uint(x>>shift)&mask - bias
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// clear top 9+e bits, the integer part; if the rest is 0, then no fraction.
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return exp < 23 && fbits<<(9+exp) == 0 // means there's no fractional part
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}
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func strconvParseErr(b []byte, fn string) error {
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return &strconv.NumError{
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Func: fn,
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Err: strconv.ErrSyntax,
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Num: string(b),
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}
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}
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func parseFloat32_reader(r readFloatResult) (f float32, fail bool) {
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f = float32(r.mantissa)
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if r.exp == 0 {
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} else if r.exp < 0 { // int / 10^k
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f /= float32pow10[uint8(-r.exp)]
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} else { // exp > 0
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if r.exp > fi32.exactPow10 {
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f *= float32pow10[r.exp-fi32.exactPow10]
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if f > fMaxMultiplierForExactPow10_32 { // exponent too large - outside range
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fail = true
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return // ok = false
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}
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f *= float32pow10[fi32.exactPow10]
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} else {
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f *= float32pow10[uint8(r.exp)]
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}
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}
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if r.neg {
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f = -f
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}
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return
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}
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func parseFloat32_custom(b []byte) (f float32, err error) {
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r := readFloat(b, fi32)
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if r.bad {
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return 0, strconvParseErr(b, "ParseFloat")
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}
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if r.ok {
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f, r.bad = parseFloat32_reader(r)
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if !r.bad {
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return
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}
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}
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return parseFloat32_strconv(b)
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}
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func parseFloat64_reader(r readFloatResult) (f float64, fail bool) {
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f = float64(r.mantissa)
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if r.exp == 0 {
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} else if r.exp < 0 { // int / 10^k
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f /= float64pow10[-uint8(r.exp)]
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} else { // exp > 0
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if r.exp > fi64.exactPow10 {
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f *= float64pow10[r.exp-fi64.exactPow10]
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if f > fMaxMultiplierForExactPow10_64 { // exponent too large - outside range
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fail = true
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return
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}
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f *= float64pow10[fi64.exactPow10]
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} else {
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f *= float64pow10[uint8(r.exp)]
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}
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}
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if r.neg {
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f = -f
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}
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return
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}
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func parseFloat64_custom(b []byte) (f float64, err error) {
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r := readFloat(b, fi64)
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if r.bad {
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return 0, strconvParseErr(b, "ParseFloat")
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}
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if r.ok {
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f, r.bad = parseFloat64_reader(r)
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if !r.bad {
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return
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}
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}
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return parseFloat64_strconv(b)
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}
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func parseUint64_simple(b []byte) (n uint64, ok bool) {
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var i int
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var n1 uint64
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var c uint8
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LOOP:
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if i < len(b) {
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c = b[i]
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// unsigned integers don't overflow well on multiplication, so check cutoff here
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// e.g. (maxUint64-5)*10 doesn't overflow well ...
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// if n >= fUint64Cutoff || !isDigitChar(b[i]) { // if c < '0' || c > '9' {
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if n >= fUint64Cutoff || c < '0' || c > '9' {
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return
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} else if c == '0' {
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n *= fBase
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} else {
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n1 = n
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n = n*fBase + uint64(c-'0')
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if n < n1 {
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return
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}
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}
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i++
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goto LOOP
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}
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ok = true
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return
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}
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func parseUint64_reader(r readFloatResult) (f uint64, fail bool) {
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f = r.mantissa
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if r.exp == 0 {
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} else if r.exp < 0 { // int / 10^k
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if f%uint64pow10[uint8(-r.exp)] != 0 {
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fail = true
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} else {
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f /= uint64pow10[uint8(-r.exp)]
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}
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} else { // exp > 0
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f *= uint64pow10[uint8(r.exp)]
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}
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return
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}
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func parseInteger_bytes(b []byte) (u uint64, neg, ok bool) {
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if len(b) == 0 {
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ok = true
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return
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}
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if b[0] == '-' {
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if len(b) == 1 {
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return
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}
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neg = true
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b = b[1:]
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}
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u, ok = parseUint64_simple(b)
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if ok {
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return
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}
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r := readFloat(b, fi64u)
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if r.ok {
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var fail bool
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u, fail = parseUint64_reader(r)
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if fail {
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f, err := parseFloat64(b)
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if err != nil {
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return
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}
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if !noFrac64(math.Float64bits(f)) {
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return
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}
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u = uint64(f)
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}
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ok = true
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return
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}
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return
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}
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// parseNumber will return an integer if only composed of [-]?[0-9]+
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// Else it will return a float.
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func parseNumber(b []byte, z *fauxUnion, preferSignedInt bool) (err error) {
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var ok, neg bool
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var f uint64
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if len(b) == 0 {
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return
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}
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if b[0] == '-' {
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neg = true
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f, ok = parseUint64_simple(b[1:])
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} else {
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f, ok = parseUint64_simple(b)
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}
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if ok {
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if neg {
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z.v = valueTypeInt
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if chkOvf.Uint2Int(f, neg) {
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return strconvParseErr(b, "ParseInt")
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}
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z.i = -int64(f)
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} else if preferSignedInt {
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z.v = valueTypeInt
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if chkOvf.Uint2Int(f, neg) {
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return strconvParseErr(b, "ParseInt")
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}
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z.i = int64(f)
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} else {
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z.v = valueTypeUint
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z.u = f
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}
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return
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}
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z.v = valueTypeFloat
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z.f, err = parseFloat64_custom(b)
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return
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}
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type readFloatResult struct {
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mantissa uint64
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exp int8
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neg bool
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trunc bool
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bad bool // bad decimal string
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hardexp bool // exponent is hard to handle (> 2 digits, etc)
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ok bool
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// sawdot bool
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// sawexp bool
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//_ [2]bool // padding
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}
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func readFloat(s []byte, y floatinfo) (r readFloatResult) {
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var i uint // uint, so that we eliminate bounds checking
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var slen = uint(len(s))
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if slen == 0 {
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// read an empty string as the zero value
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// r.bad = true
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r.ok = true
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return
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}
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if s[0] == '-' {
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r.neg = true
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i++
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}
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||
|
|
// we considered punting early if string has length > maxMantDigits, but this doesn't account
|
||
|
|
// for trailing 0's e.g. 700000000000000000000 can be encoded exactly as it is 7e20
|
||
|
|
|
||
|
|
var nd, ndMant, dp int8
|
||
|
|
var sawdot, sawexp bool
|
||
|
|
var xu uint64
|
||
|
|
|
||
|
|
LOOP:
|
||
|
|
for ; i < slen; i++ {
|
||
|
|
switch s[i] {
|
||
|
|
case '.':
|
||
|
|
if sawdot {
|
||
|
|
r.bad = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
sawdot = true
|
||
|
|
dp = nd
|
||
|
|
case 'e', 'E':
|
||
|
|
sawexp = true
|
||
|
|
break LOOP
|
||
|
|
case '0':
|
||
|
|
if nd == 0 {
|
||
|
|
dp--
|
||
|
|
continue LOOP
|
||
|
|
}
|
||
|
|
nd++
|
||
|
|
if r.mantissa < y.mantCutoff {
|
||
|
|
r.mantissa *= fBase
|
||
|
|
ndMant++
|
||
|
|
}
|
||
|
|
case '1', '2', '3', '4', '5', '6', '7', '8', '9':
|
||
|
|
nd++
|
||
|
|
if y.mantCutoffIsUint64Cutoff && r.mantissa < fUint64Cutoff {
|
||
|
|
r.mantissa *= fBase
|
||
|
|
xu = r.mantissa + uint64(s[i]-'0')
|
||
|
|
if xu < r.mantissa {
|
||
|
|
r.trunc = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
r.mantissa = xu
|
||
|
|
} else if r.mantissa < y.mantCutoff {
|
||
|
|
// mantissa = (mantissa << 1) + (mantissa << 3) + uint64(c-'0')
|
||
|
|
r.mantissa = r.mantissa*fBase + uint64(s[i]-'0')
|
||
|
|
} else {
|
||
|
|
r.trunc = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
ndMant++
|
||
|
|
default:
|
||
|
|
r.bad = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if !sawdot {
|
||
|
|
dp = nd
|
||
|
|
}
|
||
|
|
|
||
|
|
if sawexp {
|
||
|
|
i++
|
||
|
|
if i < slen {
|
||
|
|
var eneg bool
|
||
|
|
if s[i] == '+' {
|
||
|
|
i++
|
||
|
|
} else if s[i] == '-' {
|
||
|
|
i++
|
||
|
|
eneg = true
|
||
|
|
}
|
||
|
|
if i < slen {
|
||
|
|
// for exact match, exponent is 1 or 2 digits (float64: -22 to 37, float32: -1 to 17).
|
||
|
|
// exit quick if exponent is more than 2 digits.
|
||
|
|
if i+2 < slen {
|
||
|
|
r.hardexp = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
var e int8
|
||
|
|
if s[i] < '0' || s[i] > '9' { // !isDigitChar(s[i]) { //
|
||
|
|
r.bad = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
e = int8(s[i] - '0')
|
||
|
|
i++
|
||
|
|
if i < slen {
|
||
|
|
if s[i] < '0' || s[i] > '9' { // !isDigitChar(s[i]) { //
|
||
|
|
r.bad = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
e = e*fBase + int8(s[i]-'0') // (e << 1) + (e << 3) + int8(s[i]-'0')
|
||
|
|
i++
|
||
|
|
}
|
||
|
|
if eneg {
|
||
|
|
dp -= e
|
||
|
|
} else {
|
||
|
|
dp += e
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if r.mantissa != 0 {
|
||
|
|
r.exp = dp - ndMant
|
||
|
|
// do not set ok=true for cases we cannot handle
|
||
|
|
if r.exp < -y.exactPow10 ||
|
||
|
|
r.exp > y.exactInts+y.exactPow10 ||
|
||
|
|
(y.mantbits != 0 && r.mantissa>>y.mantbits != 0) {
|
||
|
|
r.hardexp = true
|
||
|
|
return
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
r.ok = true
|
||
|
|
return
|
||
|
|
}
|