560 lines
11 KiB
V
560 lines
11 KiB
V
/*
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atof util
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Copyright (c) 2019 Dario Deledda. All rights reserved.
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Use of this source code is governed by an MIT license
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that can be found in the LICENSE file.
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This file contains utilities for convert a string in a f64 variable
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IEEE 754 standard is used
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Know limitation:
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- limited to 18 significant digits
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The code is inspired by:
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Grzegorz Kraszewski krashan@teleinfo.pb.edu.pl
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URL: http://krashan.ppa.pl/articles/stringtofloat/
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Original license: MIT
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*/
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module strconv
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union Float64u {
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mut:
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f f64
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u u64
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}
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/*
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96 bit operation utilities
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Note: when u128 will be available these function can be refactored
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*/
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// right logical shift 96 bit
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fn lsr96(s2 u32, s1 u32, s0 u32) (u32,u32,u32) {
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mut r0 := u32(0)
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mut r1 := u32(0)
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mut r2 := u32(0)
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r0 = (s0>>1) | ((s1 & u32(1))<<31)
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r1 = (s1>>1) | ((s2 & u32(1))<<31)
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r2 = s2>>1
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return r2,r1,r0
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}
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// left logical shift 96 bit
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fn lsl96(s2 u32, s1 u32, s0 u32) (u32,u32,u32) {
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mut r0 := u32(0)
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mut r1 := u32(0)
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mut r2 := u32(0)
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r2 = (s2<<1) | ((s1 & (u32(1)<<31))>>31)
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r1 = (s1<<1) | ((s0 & (u32(1)<<31))>>31)
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r0 = s0<<1
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return r2,r1,r0
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}
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// sum on 96 bit
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fn add96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32,u32,u32) {
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mut w := u64(0)
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mut r0 := u32(0)
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mut r1 := u32(0)
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mut r2 := u32(0)
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w = u64(s0) + u64(d0)
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r0 = u32(w)
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w >>= 32
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w += u64(s1) + u64(d1)
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r1 = u32(w)
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w >>= 32
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w += u64(s2) + u64(d2)
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r2 = u32(w)
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return r2,r1,r0
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}
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// subtraction on 96 bit
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fn sub96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32,u32,u32) {
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mut w := u64(0)
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mut r0 := u32(0)
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mut r1 := u32(0)
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mut r2 := u32(0)
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w = u64(s0) - u64(d0)
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r0 = u32(w)
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w >>= 32
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w += u64(s1) - u64(d1)
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r1 = u32(w)
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w >>= 32
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w += u64(s2) - u64(d2)
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r2 = u32(w)
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return r2,r1,r0
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}
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/*
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Constants
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*/
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const (
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//
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// f64 constants
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//
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digits = 18
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double_plus_zero = u64(0x0000000000000000)
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double_minus_zero = u64(0x8000000000000000)
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double_plus_infinity = u64(0x7FF0000000000000)
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double_minus_infinity = u64(0xFFF0000000000000)
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//
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// parser state machine states
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//
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fsm_a = 0
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fsm_b = 1
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fsm_c = 2
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fsm_d = 3
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fsm_e = 4
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fsm_f = 5
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fsm_g = 6
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fsm_h = 7
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fsm_i = 8
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fsm_stop = 9
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//
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// Possible parser return values.
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//
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parser_ok = 0 // parser finished OK
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parser_pzero = 1 // no digits or number is smaller than +-2^-1022
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parser_mzero = 2 // number is negative, module smaller
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parser_pinf = 3 // number is higher than +HUGE_VAL
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parser_minf = 4 // number is lower than -HUGE_VAL
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//
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// char constants
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// Note: Modify these if working with non-ASCII encoding
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//
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c_dpoint = `.`
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c_plus = `+`
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c_minus = `-`
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c_zero = `0`
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c_nine = `9`
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c_ten = u32(10)
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)
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/*
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Utility
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*/
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// NOTE: Modify these if working with non-ASCII encoding
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fn is_digit(x byte) bool {
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return (x >= c_zero && x <= c_nine) == true
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}
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fn is_space(x byte) bool {
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return (x == `\t` || x == `\n` || x == `\v` || x == `\f` || x == `\r` || x == ` `)
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}
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fn is_exp(x byte) bool {
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return (x == `E` || x == `e`) == true
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}
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/*
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Support struct
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*/
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// The structure is filled by parser, then given to converter.
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pub struct PrepNumber {
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pub mut:
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negative bool // 0 if positive number, 1 if negative
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exponent int // power of 10 exponent
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mantissa u64 // integer mantissa
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}
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/*
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String parser
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NOTE: #TOFIX need one char after the last char of the number
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*/
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// parser return a support struct with all the parsing information for the converter
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fn parser(s string) (int,PrepNumber) {
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mut state := fsm_a
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mut digx := 0
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mut c := ` ` // initial value for kicking off the state machine
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mut result := parser_ok
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mut expneg := false
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mut expexp := 0
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mut i := 0
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mut pn := PrepNumber{
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}
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for state != fsm_stop {
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match state {
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// skip starting spaces
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fsm_a {
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if is_space(c) == true {
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c = s[i++]
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}
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else {
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state = fsm_b
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}
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}
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// check for the sign or point
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fsm_b {
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state = fsm_c
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if c == c_plus {
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c = s[i++]
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//i++
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}
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else if c == c_minus {
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pn.negative = true
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c = s[i++]
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}
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else if is_digit(c) {
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}
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else if c == c_dpoint {
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}
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else {
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state = fsm_stop
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}
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}
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// skip the inital zeros
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fsm_c {
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if c == c_zero {
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c = s[i++]
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}
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else if c == c_dpoint {
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c = s[i++]
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state = fsm_d
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}
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else {
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state = fsm_e
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}
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}
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// reading leading zeros in the fractional part of mantissa
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fsm_d {
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if c == c_zero {
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c = s[i++]
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if pn.exponent > -2147483647 {
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pn.exponent--
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}
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}
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else {
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state = fsm_f
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}
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}
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// reading integer part of mantissa
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fsm_e {
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if is_digit(c) {
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if digx < digits {
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pn.mantissa *= 10
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pn.mantissa += u64(c - c_zero)
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digx++
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}
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else if pn.exponent < 2147483647 {
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pn.exponent++
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}
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c = s[i++]
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}
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else if c == c_dpoint {
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c = s[i++]
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state = fsm_f
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}
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else {
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state = fsm_f
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}
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}
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// reading fractional part of mantissa
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fsm_f {
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if is_digit(c) {
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if digx < digits {
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pn.mantissa *= 10
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pn.mantissa += u64(c - c_zero)
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pn.exponent--
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digx++
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}
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c = s[i++]
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}
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else if is_exp(c) {
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c = s[i++]
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state = fsm_g
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}
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else {
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state = fsm_g
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}
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}
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// reading sign of exponent
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fsm_g {
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if c == c_plus {
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c = s[i++]
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}
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else if c == c_minus {
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expneg = true
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c = s[i++]
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}
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state = fsm_h
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}
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// skipping leading zeros of exponent
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fsm_h {
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if c == c_zero {
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c = s[i++]
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}
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else {
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state = fsm_i
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}
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}
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// reading exponent digits
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fsm_i {
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if is_digit(c) {
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if expexp < 214748364 {
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expexp *= 10
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expexp += int(c - c_zero)
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}
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c = s[i++]
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}
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else {
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state = fsm_stop
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}
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}
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else {
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}}
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// C.printf("len: %d i: %d str: %s \n",s.len,i,s[..i])
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if i >= s.len {
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state = fsm_stop
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}
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}
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if expneg {
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expexp = -expexp
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}
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pn.exponent += expexp
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if pn.mantissa == 0 {
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if pn.negative {
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result = parser_mzero
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}
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else {
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result = parser_pzero
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}
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}
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else if pn.exponent > 309 {
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if pn.negative {
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result = parser_minf
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}
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else {
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result = parser_pinf
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}
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}
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else if pn.exponent < -328 {
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if pn.negative {
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result = parser_mzero
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}
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else {
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result = parser_pzero
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}
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}
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return result,pn
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}
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/*
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Converter to the bit form of the f64 number
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*/
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// converter return a u64 with the bit image of the f64 number
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fn converter(mut pn PrepNumber) u64 {
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mut binexp := 92
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mut s2 := u32(0) // 96-bit precision integer
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mut s1 := u32(0)
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mut s0 := u32(0)
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mut q2 := u32(0) // 96-bit precision integer
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mut q1 := u32(0)
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mut q0 := u32(0)
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mut r2 := u32(0) // 96-bit precision integer
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mut r1 := u32(0)
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mut r0 := u32(0)
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mask28 := u32(0xF<<28)
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mut result := u64(0)
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// working on 3 u32 to have 96 bit precision
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s0 = u32(pn.mantissa & u64(0x00000000FFFFFFFF))
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s1 = u32(pn.mantissa>>32)
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s2 = u32(0)
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// so we take the decimal exponent off
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for pn.exponent > 0 {
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q2,q1,q0 = lsl96(s2, s1, s0) // q = s * 2
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r2,r1,r0 = lsl96(q2, q1, q0) // r = s * 4 <=> q * 2
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s2,s1,s0 = lsl96(r2, r1, r0) // s = s * 8 <=> r * 2
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s2,s1,s0 = add96(s2, s1, s0, q2, q1, q0) // s = (s * 8) + (s * 2) <=> s*10
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pn.exponent--
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for (s2 & mask28) != 0 {
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q2,q1,q0 = lsr96(s2, s1, s0)
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binexp++
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s2 = q2
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s1 = q1
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s0 = q0
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}
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}
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for pn.exponent < 0 {
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for !((s2 & (u32(1)<<31)) != 0) {
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q2,q1,q0 = lsl96(s2, s1, s0)
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binexp--
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s2 = q2
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s1 = q1
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s0 = q0
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}
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q2 = s2 / c_ten
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r1 = s2 % c_ten
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r2 = (s1>>8) | (r1<<24)
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q1 = r2 / c_ten
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r1 = r2 % c_ten
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r2 = ((s1 & u32(0xFF))<<16) | (s0>>16) | (r1<<24)
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r0 = r2 / c_ten
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r1 = r2 % c_ten
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q1 = (q1<<8) | ((r0 & u32(0x00FF0000))>>16)
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q0 = r0<<16
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r2 = (s0 & u32(0xFFFF)) | (r1<<16)
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q0 |= r2 / c_ten
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s2 = q2
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s1 = q1
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s0 = q0
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pn.exponent++
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}
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// C.printf("mantissa before normalization: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
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// normalization, the 28 bit in s2 must the leftest one in the variable
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if s2 != 0 || s1 != 0 || s0 != 0 {
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for (s2 & mask28) == 0 {
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q2,q1,q0 = lsl96(s2, s1, s0)
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binexp--
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s2 = q2
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s1 = q1
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s0 = q0
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}
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}
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// rounding if needed
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/*
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* "round half to even" algorithm
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* Example for f32, just a reminder
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*
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* If bit 54 is 0, round down
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* If bit 54 is 1
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* If any bit beyond bit 54 is 1, round up
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* If all bits beyond bit 54 are 0 (meaning the number is halfway between two floating-point numbers)
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* If bit 53 is 0, round down
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* If bit 53 is 1, round up
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*/
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/* test case 1 complete
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s2=0x1FFFFFFF
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s1=0xFFFFFF80
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s0=0x0
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*/
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/* test case 1 check_round_bit
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s2=0x18888888
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s1=0x88888880
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s0=0x0
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*/
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/* test case check_round_bit + normalization
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s2=0x18888888
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s1=0x88888F80
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s0=0x0
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*/
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// C.printf("mantissa before rounding: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
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// s1 => 0xFFFFFFxx only F are rapresented
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nbit := 7
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check_round_bit := u32(1)<<u32(nbit)
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check_round_mask := u32(0xFFFFFFFF)<<u32(nbit)
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if (s1 & check_round_bit) != 0 {
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// C.printf("need round!! cehck mask: %08x\n", s1 & ~check_round_mask )
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if (s1 & ~check_round_mask) != 0 {
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// C.printf("Add 1!\n")
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s2,s1,s0 = add96(s2, s1, s0, 0, check_round_bit, 0)
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}
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else {
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// C.printf("All 0!\n")
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if (s1 & (check_round_bit<<u32(1))) != 0 {
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// C.printf("Add 1 form -1 bit control!\n")
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s2,s1,s0 = add96(s2, s1, s0, 0, check_round_bit, 0)
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}
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}
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s1 = s1 & check_round_mask
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s0 = u32(0)
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// recheck normalization
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if s2 & (mask28<<u32(1)) != 0 {
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// C.printf("Renormalize!!")
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q2,q1,q0 = lsr96(s2, s1, s0)
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binexp--
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s2 = q2
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s1 = q1
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s0 = q0
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}
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}
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// tmp := ( u64(s2 & ~mask28) << 24) | ((u64(s1) + u64(128)) >> 8)
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// C.printf("mantissa after rounding : %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
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// C.printf("Tmp result: %016x\n",tmp)
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// end rounding
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// offset the binary exponent IEEE 754
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binexp += 1023
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if binexp > 2046 {
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if pn.negative {
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result = double_minus_infinity
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}
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else {
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result = double_plus_infinity
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}
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}
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else if binexp < 1 {
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if pn.negative {
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result = double_minus_zero
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}
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else {
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result = double_plus_zero
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}
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}
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else if s2 != 0 {
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mut q := u64(0)
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binexs2 := u64(binexp)<<52
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q = (u64(s2 & ~mask28)<<24) | ((u64(s1) + u64(128))>>8) | binexs2
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if pn.negative {
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q |= (u64(1)<<63)
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}
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result = q
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}
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return result
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}
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/*
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Public functions
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*/
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// atof64 return a f64 from a string doing a parsing operation
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pub fn atof64(s string) f64 {
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mut pn := PrepNumber{
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}
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mut res_parsing := 0
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mut res := Float64u{}
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res_parsing,pn = parser(s + ' ') // TODO: need an extra char for now
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// println(pn)
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match res_parsing {
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parser_ok {
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res.u = converter(mut pn)
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}
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parser_pzero {
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res.u = double_plus_zero
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}
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parser_mzero {
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res.u = double_minus_zero
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|
}
|
|
parser_pinf {
|
|
res.u = double_plus_infinity
|
|
}
|
|
parser_minf {
|
|
res.u = double_minus_infinity
|
|
}
|
|
else {
|
|
}}
|
|
return res.f
|
|
}
|