/**********************************************************************
*
* atof util
*
* Copyright (c) 2019 Dario Deledda. All rights reserved.
* Use of this source code is governed by an MIT license
* that can be found in the LICENSE file.
*
* This file contains utilities for convert a string in a f64 variable
* IEEE 754 standard is used
*
* Know limitation:
* - limited to 18 significant digits
*
* The code is inspired by:
* Grzegorz Kraszewski krashan@teleinfo.pb.edu.pl
* URL: http://krashan.ppa.pl/articles/stringtofloat/
* Original license: MIT
*
**********************************************************************/
module strconv
union Float64u {
mut:
f f64
u u64
}
/**********************************************************************
*
* 96 bit operation utilities
* Note: when u128 will be available these function can be refactored
*
**********************************************************************/
// right logical shift 96 bit
fn lsr96(s2 u32, s1 u32, s0 u32) (u32,u32,u32) {
mut r0 := u32(0)
mut r1 := u32(0)
mut r2 := u32(0)
r0 = (s0>>1) | ((s1 & u32(1))<<31)
r1 = (s1>>1) | ((s2 & u32(1))<<31)
r2 = s2>>1
return r2,r1,r0
}
// left logical shift 96 bit
fn lsl96(s2 u32, s1 u32, s0 u32) (u32,u32,u32) {
mut r0 := u32(0)
mut r1 := u32(0)
mut r2 := u32(0)
r2 = (s2<<1) | ((s1 & (u32(1)<<31))>>31)
r1 = (s1<<1) | ((s0 & (u32(1)<<31))>>31)
r0 = s0<<1
return r2,r1,r0
}
// sum on 96 bit
fn add96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32,u32,u32) {
mut w := u64(0)
mut r0 := u32(0)
mut r1 := u32(0)
mut r2 := u32(0)
w = u64(s0) + u64(d0)
r0 = u32(w)
w >>= 32
w += u64(s1) + u64(d1)
r1 = u32(w)
w >>= 32
w += u64(s2) + u64(d2)
r2 = u32(w)
return r2,r1,r0
}
// subtraction on 96 bit
fn sub96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32,u32,u32) {
mut w := u64(0)
mut r0 := u32(0)
mut r1 := u32(0)
mut r2 := u32(0)
w = u64(s0) - u64(d0)
r0 = u32(w)
w >>= 32
w += u64(s1) - u64(d1)
r1 = u32(w)
w >>= 32
w += u64(s2) - u64(d2)
r2 = u32(w)
return r2,r1,r0
}
/**********************************************************************
*
* Constants
*
**********************************************************************/
const (
//
// f64 constants
//
DIGITS = 18
DOUBLE_PLUS_ZERO = u64(0x0000000000000000)
DOUBLE_MINUS_ZERO = u64(0x8000000000000000)
DOUBLE_PLUS_INFINITY = u64(0x7FF0000000000000)
DOUBLE_MINUS_INFINITY = u64(0xFFF0000000000000)
//
// parser state machine states
//
fsm_a = 0
fsm_b = 1
fsm_c = 2
fsm_d = 3
fsm_e = 4
fsm_f = 5
fsm_g = 6
fsm_h = 7
fsm_i = 8
FSM_STOP = 9
//
// Possible parser return values.
//
parser_ok = 0 // parser finished OK
parser_pzero = 1 // no digits or number is smaller than +-2^-1022
parser_mzero = 2 // number is negative, module smaller
parser_pinf = 3 // number is higher than +HUGE_VAL
parser_minf = 4 // number is lower than -HUGE_VAL
//
// char constants
// Note: Modify these if working with non-ASCII encoding
//
DPOINT = `.`
PLUS = `+`
MINUS = `-`
ZERO = `0`
NINE = `9`
TEN = u32(10)
)
/**********************************************************************
*
* Utility
*
**********************************************************************/
// NOTE: Modify these if working with non-ASCII encoding
fn is_digit(x byte) bool {
return (x >= ZERO && x <= NINE) == true
}
fn is_space(x byte) bool {
return ((x >= 0x89 && x <= 0x13) || x == 0x20) == true
}
fn is_exp(x byte) bool {
return (x == `E` || x == `e`) == true
}
/**********************************************************************
*
* Support struct
*
**********************************************************************/
// The structure is filled by parser, then given to converter.
pub struct PrepNumber {
pub mut:
negative bool // 0 if positive number, 1 if negative
exponent int // power of 10 exponent
mantissa u64 // integer mantissa
}
/**********************************************************************
*
* String parser
* NOTE: #TOFIX need one char after the last char of the number
*
**********************************************************************/
// parser return a support struct with all the parsing information for the converter
fn parser(s string) (int,PrepNumber) {
mut state := fsm_a
mut digx := 0
mut c := ` ` // initial value for kicking off the state machine
mut result := parser_ok
mut expneg := false
mut expexp := 0
mut i := 0
mut pn := PrepNumber{
}
for state != FSM_STOP {
match state {
// skip starting spaces
fsm_a {
if is_space(c) == true {
c = s[i++]
}
else {
state = fsm_b
}
}
// check for the sign or point
fsm_b {
state = fsm_c
if c == PLUS {
c = s[i++]
//i++
}
else if c == MINUS {
pn.negative = true
c = s[i++]
}
else if is_digit(c) {
}
else if c == DPOINT {
}
else {
state = FSM_STOP
}
}
// skip the inital zeros
fsm_c {
if c == ZERO {
c = s[i++]
}
else if c == DPOINT {
c = s[i++]
state = fsm_d
}
else {
state = fsm_e
}
}
// reading leading zeros in the fractional part of mantissa
fsm_d {
if c == ZERO {
c = s[i++]
if pn.exponent > -2147483647 {
pn.exponent--
}
}
else {
state = fsm_f
}
}
// reading integer part of mantissa
fsm_e {
if is_digit(c) {
if digx < DIGITS {
pn.mantissa *= 10
pn.mantissa += u64(c - ZERO)
digx++
}
else if pn.exponent < 2147483647 {
pn.exponent++
}
c = s[i++]
}
else if c == DPOINT {
c = s[i++]
state = fsm_f
}
else {
state = fsm_f
}
}
// reading fractional part of mantissa
fsm_f {
if is_digit(c) {
if digx < DIGITS {
pn.mantissa *= 10
pn.mantissa += u64(c - ZERO)
pn.exponent--
digx++
}
c = s[i++]
}
else if is_exp(c) {
c = s[i++]
state = fsm_g
}
else {
state = fsm_g
}
}
// reading sign of exponent
fsm_g {
if c == PLUS {
c = s[i++]
}
else if c == MINUS {
expneg = true
c = s[i++]
}
state = fsm_h
}
// skipping leading zeros of exponent
fsm_h {
if c == ZERO {
c = s[i++]
}
else {
state = fsm_i
}
}
// reading exponent digits
fsm_i {
if is_digit(c) {
if expexp < 214748364 {
expexp *= 10
expexp += int(c - ZERO)
}
c = s[i++]
}
else {
state = FSM_STOP
}
}
else {
}}
// C.printf("len: %d i: %d str: %s \n",s.len,i,s[..i])
if i >= s.len {
state = FSM_STOP
}
}
if expneg {
expexp = -expexp
}
pn.exponent += expexp
if pn.mantissa == 0 {
if pn.negative {
result = parser_mzero
}
else {
result = parser_pzero
}
}
else if pn.exponent > 309 {
if pn.negative {
result = parser_minf
}
else {
result = parser_pinf
}
}
else if pn.exponent < -328 {
if pn.negative {
result = parser_mzero
}
else {
result = parser_pzero
}
}
return result,pn
}
/**********************************************************************
*
* Converter to the bit form of the f64 number
*
**********************************************************************/
// converter return a u64 with the bit image of the f64 number
fn converter(pn mut PrepNumber) u64 {
mut binexp := 92
mut s2 := u32(0) // 96-bit precision integer
mut s1 := u32(0)
mut s0 := u32(0)
mut q2 := u32(0) // 96-bit precision integer
mut q1 := u32(0)
mut q0 := u32(0)
mut r2 := u32(0) // 96-bit precision integer
mut r1 := u32(0)
mut r0 := u32(0)
mask28 := u32(0xF<<28)
mut result := u64(0)
// working on 3 u32 to have 96 bit precision
s0 = u32(pn.mantissa & u64(0x00000000FFFFFFFF))
s1 = u32(pn.mantissa>>32)
s2 = u32(0)
// so we take the decimal exponent off
for pn.exponent > 0 {
q2,q1,q0 = lsl96(s2, s1, s0) // q = s * 2
r2,r1,r0 = lsl96(q2, q1, q0) // r = s * 4 <=> q * 2
s2,s1,s0 = lsl96(r2, r1, r0) // s = s * 8 <=> r * 2
s2,s1,s0 = add96(s2, s1, s0, q2, q1, q0) // s = (s * 8) + (s * 2) <=> s*10
pn.exponent--
for (s2 & mask28) != 0 {
q2,q1,q0 = lsr96(s2, s1, s0)
binexp++
s2 = q2
s1 = q1
s0 = q0
}
}
for pn.exponent < 0 {
for !((s2 & (u32(1)<<31)) != 0) {
q2,q1,q0 = lsl96(s2, s1, s0)
binexp--
s2 = q2
s1 = q1
s0 = q0
}
q2 = s2 / TEN
r1 = s2 % TEN
r2 = (s1>>8) | (r1<<24)
q1 = r2 / TEN
r1 = r2 % TEN
r2 = ((s1 & u32(0xFF))<<16) | (s0>>16) | (r1<<24)
r0 = r2 / TEN
r1 = r2 % TEN
q1 = (q1<<8) | ((r0 & u32(0x00FF0000))>>16)
q0 = r0<<16
r2 = (s0 & u32(0xFFFF)) | (r1<<16)
q0 |= r2 / TEN
s2 = q2
s1 = q1
s0 = q0
pn.exponent++
}
// C.printf("mantissa before normalization: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
// normalization, the 28 bit in s2 must the leftest one in the variable
if s2 != 0 || s1 != 0 || s0 != 0 {
for (s2 & mask28) == 0 {
q2,q1,q0 = lsl96(s2, s1, s0)
binexp--
s2 = q2
s1 = q1
s0 = q0
}
}
// rounding if needed
/*
* "round half to even" algorithm
* Example for f32, just a reminder
*
* If bit 54 is 0, round down
* If bit 54 is 1
* If any bit beyond bit 54 is 1, round up
* If all bits beyond bit 54 are 0 (meaning the number is halfway between two floating-point numbers)
* If bit 53 is 0, round down
* If bit 53 is 1, round up
*/
/* test case 1 complete
s2=0x1FFFFFFF
s1=0xFFFFFF80
s0=0x0
*/
/* test case 1 check_round_bit
s2=0x18888888
s1=0x88888880
s0=0x0
*/
/* test case check_round_bit + normalization
s2=0x18888888
s1=0x88888F80
s0=0x0
*/
// C.printf("mantissa before rounding: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
// s1 => 0xFFFFFFxx only F are rapresented
nbit := 7
check_round_bit := u32(1)<<u32(nbit)
check_round_mask := u32(0xFFFFFFFF)<<u32(nbit)
if (s1 & check_round_bit) != 0 {
// C.printf("need round!! cehck mask: %08x\n", s1 & ~check_round_mask )
if (s1 & ~check_round_mask) != 0 {
// C.printf("Add 1!\n")
s2,s1,s0 = add96(s2, s1, s0, 0, check_round_bit, 0)
}
else {
// C.printf("All 0!\n")
if (s1 & (check_round_bit<<u32(1))) != 0 {
// C.printf("Add 1 form -1 bit control!\n")
s2,s1,s0 = add96(s2, s1, s0, 0, check_round_bit, 0)
}
}
s1 = s1 & check_round_mask
s0 = u32(0)
// recheck normalization
if s2 & (mask28<<u32(1)) != 0 {
// C.printf("Renormalize!!")
q2,q1,q0 = lsr96(s2, s1, s0)
binexp--
s2 = q2
s1 = q1
s0 = q0
}
}
// tmp := ( u64(s2 & ~mask28) << 24) | ((u64(s1) + u64(128)) >> 8)
// C.printf("mantissa after rounding : %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp)
// C.printf("Tmp result: %016x\n",tmp)
// end rounding
// offset the binary exponent IEEE 754
binexp += 1023
if binexp > 2046 {
if pn.negative {
result = DOUBLE_MINUS_INFINITY
}
else {
result = DOUBLE_PLUS_INFINITY
}
}
else if binexp < 1 {
if pn.negative {
result = DOUBLE_MINUS_ZERO
}
else {
result = DOUBLE_PLUS_ZERO
}
}
else if s2 != 0 {
mut q := u64(0)
binexs2 := u64(binexp)<<52
q = (u64(s2 & ~mask28)<<24) | ((u64(s1) + u64(128))>>8) | binexs2
if pn.negative {
q |= (u64(1)<<63)
}
result = q
}
return result
}
/**********************************************************************
*
* Public functions
*
**********************************************************************/
// atof64 return a f64 from a string doing a parsing operation
pub fn atof64(s string) f64 {
mut pn := PrepNumber{
}
mut res_parsing := 0
mut res := Float64u{}
res_parsing,pn = parser(s + ' ') // TODO: need an extra char for now
// println(pn)
match res_parsing {
parser_ok {
res.u = converter(mut pn)
}
parser_pzero {
res.u = DOUBLE_PLUS_ZERO
}
parser_mzero {
res.u = DOUBLE_MINUS_ZERO
}
parser_pinf {
res.u = DOUBLE_PLUS_INFINITY
}
parser_minf {
res.u = DOUBLE_MINUS_INFINITY
}
else {
}}
return res.f
}