atof: lots of fixes

* removed sprintf for f64 and f32 use

* removed all pointers from the code, used unions instead

* solved module name problem

* fixed tests on vlib/math

* fix for alpine-linux math test

* small fix on byte allocation for ftoa
pull/3852/head
penguindark 2020-02-26 12:14:06 +01:00 committed by GitHub
parent c4e83faa57
commit 39429f7ac9
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GPG Key ID: 4AEE18F83AFDEB23
9 changed files with 180 additions and 137 deletions

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@ -2,37 +2,64 @@
// Use of this source code is governed by an MIT license
// that can be found in the LICENSE file.
module builtin
import strconv.ftoa
#include <float.h>
// ----- f64 to string functions -----
// str return a f64 as string in scientific notation, auto display digits limit
[inline]
pub fn (d f64) str() string {
buf := malloc(sizeof(double) * 5 + 1) // TODO
C.sprintf(charptr(buf), '%f', d)
return tos(buf, vstrlen(buf))
return ftoa.ftoa_64(d)
}
pub fn (d f32) str() string {
buf := malloc(sizeof(double) * 5 + 1) // TODO
C.sprintf((buf), '%f', d)
return tos(buf, vstrlen(buf))
}
// return a string of the input f64 in scientific notation with digit_num digits displayed
// return a string of the input f64 in scientific notation with digit_num deciamals displayed, max 17 digits
[inline]
pub fn (x f64) strsci(digit_num int) string {
buf := malloc(digit_num * 2 + 2) // TODO
conf_str := '%0.' + digit_num.str() + 'e'
C.sprintf((buf), (conf_str.str), x)
tmpstr := tos(buf, vstrlen(buf))
return tmpstr
mut n_digit := digit_num
if n_digit < 1 {
n_digit = 1
} else if n_digit > 17 {
n_digit = 17
}
return ftoa.f64_to_str(x,n_digit)
}
// return a long string of the input f64, max
// return a decimal notation of the input f64
[inline]
pub fn (x f64) strlong() string {
buf := malloc(18 + 32) // TODO
C.sprintf((buf), '%0.30lf', x)
tmpstr := tos(buf, vstrlen(buf))
return tmpstr
return ftoa.f64_to_str_l(x)
}
// ----- f32 to string functions -----
// str return a f32 as string in scientific notation, auto display digits limit
[inline]
pub fn (d f32) str() string {
return ftoa.ftoa_32(d)
}
// return a string of the input f32 in scientific notation with digit_num deciamals displayed, max 8 digits
[inline]
pub fn (x f32) strsci(digit_num int) string {
mut n_digit := digit_num
if n_digit < 1 {
n_digit = 1
} else if n_digit > 8 {
n_digit = 8
}
return ftoa.f32_to_str(x,n_digit)
}
// return a decimal notation of the input f32
[inline]
pub fn (x f32) strlong() string {
return ftoa.f32_to_str_l(x)
}
// ----- C functions -----
[inline]
fn f32_abs(a f32) f32 {
return if a < 0 { -a } else { a }

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@ -1,6 +1,13 @@
import math
import math.complex as cmplx
fn tst_res(str1 string, str2 string) bool {
if (math.abs(str1.f64() - str2.f64())) < 1e-5 {
return true
}
return false
}
fn test_complex_addition() {
// Test is based on and verified from practice examples of Khan Academy
// https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers
@ -177,14 +184,14 @@ fn test_complex_mod() {
mut c1 := cmplx.complex(5,7)
mut result := c1.mod()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('8.602325')
assert tst_res(result.str(), '8.602325')
c1 = cmplx.complex(-3,4)
result = c1.mod()
assert result == 5
c1 = cmplx.complex(-1,-2)
result = c1.mod()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('2.236068')
assert tst_res(result.str(), '2.236068')
}
fn test_complex_pow() {
@ -269,17 +276,17 @@ fn test_complex_arg() {
mut c2 := cmplx.complex(2.152033,0.950547)
mut result := c1.arg()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('0.950547')
assert tst_res(result.str(), '0.950547')
c1 = cmplx.complex(-3,4)
c2 = cmplx.complex(1.609438,2.214297)
result = c1.arg()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('2.214297')
assert tst_res(result.str(), '2.214297')
c1 = cmplx.complex(-1,-2)
c2 = cmplx.complex(0.804719,-2.034444)
result = c1.arg()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('-2.034444')
assert tst_res(result.str(), '-2.034444')
}
fn test_complex_log() {

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@ -1,5 +1,12 @@
module math
fn tst_res(str1 string, str2 string) bool {
if (math.abs(str1.f64() - str2.f64())) < 1e-5 {
return true
}
return false
}
fn test_gcd() {
assert gcd(6, 9) == 3
assert gcd(6, -9) == 3
@ -39,8 +46,10 @@ fn test_gamma() {
assert gamma(1) == 1
assert gamma(5) == 24
sval := '2.453737'
assert log_gamma(4.5).str() == sval
assert log(gamma(4.5)).str() == sval
assert tst_res(log_gamma(4.5).str(), sval)
assert tst_res(log(gamma(4.5)).str(), sval)
//assert log_gamma(4.5).str() == sval
//assert log(gamma(4.5)).str() == sval
assert abs( log_gamma(4.5) - log(gamma(4.5)) ) < 0.000001
// assert log_gamma(4.5) == log(gamma(4.5)) /* <-- fails on alpine/musl
}

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@ -1,4 +1,5 @@
import math.stats as stats
import math
fn test_freq() {
// Tests were also verified on Wolfram Alpha
@ -11,20 +12,27 @@ fn test_freq() {
assert o == 0
}
fn tst_res(str1 string, str2 string) bool {
if (math.abs(str1.f64() - str2.f64())) < 1e-5 {
return true
}
return false
}
fn test_mean() {
// Tests were also verified on Wolfram Alpha
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('5.762500')
assert tst_res(o.str(), '5.762500')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('17.650000')
assert tst_res(o.str(), '17.650000')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('37.708000')
assert tst_res(o.str(), '37.708000')
}
fn test_geometric_mean() {
@ -32,7 +40,7 @@ fn test_geometric_mean() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.geometric_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('5.159932')
assert tst_res(o.str(),'5.15993')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.geometric_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
@ -40,7 +48,7 @@ fn test_geometric_mean() {
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.geometric_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('25.064496')
assert tst_res(o.str(),'25.064496')
}
fn test_harmonic_mean() {
@ -48,15 +56,15 @@ fn test_harmonic_mean() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.harmonic_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('4.626519')
assert tst_res(o.str(), '4.626519')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.harmonic_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('9.134577')
assert tst_res(o.str(), '9.134577')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.harmonic_mean(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('16.555477')
assert tst_res(o.str(), '16.555477')
}
fn test_median() {
@ -67,15 +75,15 @@ fn test_median() {
mut data := [f64(2.7),f64(4.45),f64(5.9),f64(10.0)]
mut o := stats.median(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('5.175000')
assert tst_res(o.str(), '5.175000')
data = [f64(-3.0),f64(1.89),f64(4.4),f64(67.31)]
o = stats.median(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('3.145000')
assert tst_res(o.str(), '3.145000')
data = [f64(7.88),f64(12.0),f64(54.83),f64(76.122)]
o = stats.median(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('33.415000')
assert tst_res(o.str(), '33.415000')
// Odd
data = [f64(2.7),f64(4.45),f64(5.9),f64(10.0),f64(22)]
@ -108,15 +116,15 @@ fn test_rms() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.rms(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('6.362046')
assert tst_res(o.str(), '6.362046')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.rms(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('33.773393')
assert tst_res(o.str(), '33.773393')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.rms(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('47.452561')
assert tst_res(o.str(), '47.452561')
}
fn test_population_variance() {
@ -124,15 +132,15 @@ fn test_population_variance() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.population_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('7.269219')
assert tst_res(o.str(), '7.269219')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.population_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('829.119550')
assert tst_res(o.str(), '829.119550')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.population_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('829.852282')
assert tst_res(o.str(), '829.852282')
}
fn test_sample_variance() {
@ -140,15 +148,15 @@ fn test_sample_variance() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.sample_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('9.692292')
assert tst_res(o.str(), '9.692292')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.sample_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('1105.492733')
assert tst_res(o.str(), '1105.492733')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.sample_variance(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('1106.469709')
assert tst_res(o.str(), '1106.469709')
}
fn test_population_stddev() {
@ -156,15 +164,15 @@ fn test_population_stddev() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.population_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('2.696149')
assert tst_res(o.str(), '2.696149')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.population_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('28.794436')
assert tst_res(o.str(), '28.794436')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.population_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('28.807157')
assert tst_res(o.str(), '28.807157')
}
fn test_sample_stddev() {
@ -172,15 +180,15 @@ fn test_sample_stddev() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.sample_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('3.113245')
assert tst_res(o.str(), '3.113245')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.sample_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('33.248951')
assert tst_res(o.str(), '33.248951')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.sample_stddev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('33.263639')
assert tst_res(o.str(), '33.263639')
}
fn test_mean_absdev() {
@ -188,15 +196,15 @@ fn test_mean_absdev() {
mut data := [f64(10.0),f64(4.45),f64(5.9),f64(2.7)]
mut o := stats.mean_absdev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('2.187500')
assert tst_res(o.str(), '2.187500')
data = [f64(-3.0),f64(67.31),f64(4.4),f64(1.89)]
o = stats.mean_absdev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('24.830000')
assert tst_res(o.str(), '24.830000')
data = [f64(12.0),f64(7.88),f64(76.122),f64(54.83)]
o = stats.mean_absdev(data)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert o.str().eq('27.768000')
assert tst_res(o.str(), '27.768000')
}
fn test_min() {

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@ -19,6 +19,13 @@
*
**********************************************************************/
module strconv
union Float64u {
mut:
f f64
u u64 = u64(0)
}
/**********************************************************************
*
* 96 bit operation utilities
@ -149,25 +156,6 @@ fn is_exp(x byte) bool {
return (x == `E` || x == `e`) == true
}
/*
// return a string of the input f64 in scientific notation with digit_num digits displayed
pub fn strsci(x f64, digit_num int) string{
buf := malloc(digit_num*2+2)// TODO
conf_str := '%0.'+digit_num.str()+'e'
C.sprintf(charptr(buf), charptr(conf_str.str), x)
tmpstr := tos(buf, vstrlen(buf))
return tmpstr
}
// return a long string of the input f64, max
pub fn strlong(x f64) string {
buf := malloc(18+32)// TODO
C.sprintf(charptr(buf),"%0.30lf",x)
tmpstr := tos(buf, vstrlen(buf))
return tmpstr
}
*/
/**********************************************************************
*
* Support struct
@ -545,29 +533,30 @@ pub fn atof64(s string) f64 {
mut pn := PrepNumber{
}
mut res_parsing := 0
mut result := f64(0)
result = f64(0.0)
mut res_ptr := *u64(&result)
mut res := Float64u{}
res_parsing,pn = parser(s + ' ') // TODO: need an extra char for now
// println(pn)
match res_parsing {
PARSER_OK {
*res_ptr = converter(mut pn)
res.u = converter(mut pn)
}
PARSER_PZERO {
*res_ptr = DOUBLE_PLUS_ZERO
res.u = DOUBLE_PLUS_ZERO
}
PARSER_MZERO {
*res_ptr = DOUBLE_MINUS_ZERO
res.u = DOUBLE_MINUS_ZERO
}
PARSER_PINF {
*res_ptr = DOUBLE_PLUS_INFINITY
res.u = DOUBLE_PLUS_INFINITY
}
PARSER_MINF {
*res_ptr = DOUBLE_MINUS_INFINITY
res.u = DOUBLE_MINUS_INFINITY
}
else {
}}
return result
return res.f
}

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@ -3,7 +3,6 @@
* String to float Test
*
**********************************************************************/
import (
strconv
strconv.atofq
@ -41,15 +40,19 @@ fn test_atof() {
// slow atof
assert strconv.atof64(src_num_str[c]).strlong() == x.strlong()
// quick atof
mut s1 := (atofq.atof_quick(src_num_str[c]).str())
s1 = s1[..src_num_str[c].len]
mut s2 := (x.str())
s2 = s2[..src_num_str[c].len]
assert s1 == s2
delta := s1.f64() - s2.f64()
//println("$s1 $s2 $delta")
assert delta < f64(1e-16)
// test C.atof
assert x.strsci(18) == f64(C.atof(src_num_str[c].str)).strsci(18)
n1 := x.strsci(18)
n2 := f64(C.atof(src_num_str[c].str)).strsci(18)
//println("$n1 $n2")
assert n1 == n2
}
// check conversion case 2 string <==> f64
@ -71,4 +74,5 @@ fn test_atof() {
// DOUBLE_MINUS_ZERO
f1=-0.0
assert *ptr == u64(0x8000000000000000)
//println("DONE!")
}

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@ -18,17 +18,23 @@
module atofq
import strconv
// same used in atof, here only for references
// const(
// DOUBLE_PLUS_ZERO = u64(0x0000000000000000)
// DOUBLE_MINUS_ZERO = 0x8000000000000000
// DOUBLE_PLUS_INFINITY = 0x7FF0000000000000
// DOUBLE_MINUS_INFINITY = 0xFFF0000000000000
const(
DOUBLE_PLUS_ZERO = u64(0x0000000000000000)
DOUBLE_MINUS_ZERO = 0x8000000000000000
DOUBLE_PLUS_INFINITY = 0x7FF0000000000000
DOUBLE_MINUS_INFINITY = 0xFFF0000000000000
)
union Float64u {
mut:
f f64
u u64 = u64(0)
}
// atof_quick return a f64 number from a string in a quick way
pub fn atof_quick(s string) f64 {
mut f := f64(0.0) // result
mut f := Float64u{} // result
mut sign := f64(1.0) // result sign
mut i := 0 // index
// skip white spaces
@ -47,34 +53,32 @@ pub fn atof_quick(s string) f64 {
}
// infinite
if s[i] == `i` && i + 2 < s.len && s[i + 1] == `n` && s[i + 2] == `f` {
mut d := *u64(&f)
if sign > 0.0 {
*d = strconv.DOUBLE_PLUS_INFINITY
f.u = DOUBLE_PLUS_INFINITY
}
else {
*d = strconv.DOUBLE_MINUS_INFINITY
f.u = DOUBLE_MINUS_INFINITY
}
return f
return f.f
}
// skip zeros
for i < s.len && s[i] == `0` {
i++
// we have a zero, manage it
if i >= s.len {
mut d := *u64(&f)
if sign > 0.0 {
*d = strconv.DOUBLE_PLUS_ZERO
f.u = DOUBLE_PLUS_ZERO
}
else {
*d = strconv.DOUBLE_MINUS_ZERO
f.u = DOUBLE_MINUS_ZERO
}
return f
return f.f
}
}
// integer part
for i < s.len && (s[i] >= `0` && s[i] <= `9`) {
f *= f64(10.0)
f += f64(s[i] - `0`)
f.f *= f64(10.0)
f.f += f64(s[i] - `0`)
i++
}
// decimal point
@ -82,7 +86,7 @@ pub fn atof_quick(s string) f64 {
i++
mut frac_mul := f64(0.1)
for i < s.len && (s[i] >= `0` && s[i] <= `9`) {
f += f64(s[i] - `0`) * frac_mul
f.f += f64(s[i] - `0`) * frac_mul
frac_mul *= f64(0.1)
i++
}
@ -113,41 +117,36 @@ pub fn atof_quick(s string) f64 {
}
if exp_sign == 1 {
if exp > pos_exp.len {
mut d := *u64(&f)
if sign > 0 {
*d = strconv.DOUBLE_PLUS_INFINITY
f.u = DOUBLE_PLUS_INFINITY
}
else {
*d = strconv.DOUBLE_MINUS_INFINITY
f.u = DOUBLE_MINUS_INFINITY
}
return f
return f.f
}
tmp_mul := f64(0.0)
mut ptr_d := *u64(&tmp_mul)
*ptr_d = pos_exp[exp]
tmp_mul := Float64u{u: pos_exp[exp]}
// C.printf("exp: %d [0x%016llx] %f,",exp,pos_exp[exp],tmp_mul)
f = f * tmp_mul
f.f = f.f * tmp_mul.f
}
else {
if exp > neg_exp.len {
mut d := *u64(&f)
if (sign > 0) {
*d = strconv.DOUBLE_PLUS_ZERO
f.u = DOUBLE_PLUS_ZERO
}
else {
*d = strconv.DOUBLE_MINUS_ZERO
f.u = DOUBLE_MINUS_ZERO
}
return f
return f.f
}
tmp_mul := f64(0.0)
mut ptr_d := *u64(&tmp_mul)
*ptr_d = neg_exp[exp]
tmp_mul := Float64u{u: neg_exp[exp]}
// C.printf("exp: %d [0x%016llx] %f,",exp,pos_exp[exp],tmp_mul)
f = f * tmp_mul
f.f = f.f * tmp_mul.f
}
}
f = f * sign
return f
f.f = f.f * sign
return f.f
}
const (

View File

@ -59,8 +59,8 @@ test_cases_f32 = [
exp_result_f32 = [
"0e+00",
"-0e+00",
"NaN",
"NaN",
"nan",
"nan",
"+inf",
"-inf",
"1.e+00",
@ -111,8 +111,8 @@ test_cases_f64 = [
exp_result_f64 = [
"0e+00",
"-0e+00",
"NaN",
"NaN",
"nan",
"nan",
"+inf",
"-inf",
"1.e+00",
@ -141,7 +141,7 @@ exp_result_f64 = [
fn test_float_to_str(){
// test f32
for c,x in test_cases_f32 {
s := ftoa.f32_to_str(x,8)
s := f32_to_str(x,8)
s1 := exp_result_f32[c]
//println("$s1 $s")
assert s == s1
@ -149,7 +149,7 @@ fn test_float_to_str(){
// test f64
for c,x in test_cases_f64 {
s := ftoa.f64_to_str(x,17)
s := f64_to_str(x,17)
s1 := exp_result_f64[c]
//println("$s1 $s")
assert s == s1
@ -157,11 +157,11 @@ fn test_float_to_str(){
// test long format
for exp := 1 ; exp < 120 ; exp++ {
a :=ftoa.f64_to_str_l(("1e"+exp.str()).f64())
a := f64_to_str_l(("1e"+exp.str()).f64())
//println(a)
assert a.len == exp + 1
b :=ftoa.f64_to_str_l(("1e-"+exp.str()).f64())
b := f64_to_str_l(("1e-"+exp.str()).f64())
//println(b)
assert b.len == exp + 2
}

View File

@ -58,7 +58,7 @@ fn bool_to_u64(b bool) u64 {
fn get_string_special(neg bool, expZero bool, mantZero bool) string {
if !mantZero {
return "NaN"
return "nan"
}
if !expZero {
if neg {
@ -230,7 +230,7 @@ pub fn f32_to_str_l(f f64) string {
// f64_to_str_l return a string with the f64 converted in a strign in decimal notation
pub fn f64_to_str_l(f f64) string {
s := ftoa.f64_to_str(f,18)
s := f64_to_str(f,18)
// check for +inf -inf Nan
if s.len > 2 && (s[0] == `N` || s[1] == `i`) {
@ -239,7 +239,7 @@ pub fn f64_to_str_l(f f64) string {
m_sgn_flag := false
mut sgn := 1
mut b := [32]byte
mut b := [18+8]byte
mut d_pos := 1
mut i := 0
mut i1 := 0