Find position of first non-zero decimal - regex

Question

Suppose I have the following local macro:
loc a = 12.000923
I would like to get the decimal position of the first non-zero decimal (4 in this example).
There are many ways to achieve this. One is to treat a as a string and to find the position of .:
loc a = 12.000923
loc b = strpos(string(`a'), ".")
di "`b'"
From here one could further loop through the decimals and count since I get the first non-zero element. Of course this doesn't seem to be a very elegant approach.
Can you suggest a better way to deal with this? Regular expressions perhaps?

Answer 1

Well, I don't know Stata, but according to the documentation, \.(0+)? is suported and it shouldn't be hard to convert this 2 lines JavaScript function in Stata.
It returns the position of the first nonzero decimal or -1 if there is no decimal.
function getNonZeroDecimalPosition(v) {
var v2 = v.replace(/\.(0+)?/, "")
return v2.length !== v.length ? v.length - v2.length : -1
}
Explanation
We remove from input string a dot followed by optional consecutive zeros.
The difference between the lengths of original input string and this new string gives the position of the first nonzero decimal
Demo
Sample Snippet
function getNonZeroDecimalPosition(v) {
var v2 = v.replace(/\.(0+)?/, "")
return v2.length !== v.length ? v.length - v2.length : -1
}
var samples = [
"loc a = 12.00012",
"loc b = 12",
"loc c = 12.012",
"loc d = 1.000012",
"loc e = -10.00012",
"loc f = -10.05012",
"loc g = 0.0012"
]
samples.forEach(function(sample) {
console.log(getNonZeroDecimalPosition(sample))
})

Answer 2

You can do this in mata in one line and without using regular expressions:
foreach x in 124.000923 65.020923 1.000022030 0.0090843 .00000425 {
mata: selectindex(tokens(tokens(st_local("x"), ".")[selectindex(tokens(st_local("x"), ".") :== ".") + 1], "0") :!= "0")[1]
}
4
2
5
3
6
Below, you can see the steps in detail:
. local x = 124.000823
. mata:
: /* Step 1: break Stata's local macro x in tokens using . as a parsing char */
: a = tokens(st_local("x"), ".")
: a
1 2 3
+----------------------------+
1 | 124 . 000823 |
+----------------------------+
: /* Step 2: tokenize the string in a[1,3] using 0 as a parsing char */
: b = tokens(a[3], "0")
: b
1 2 3 4
+-------------------------+
1 | 0 0 0 823 |
+-------------------------+
: /* Step 3: find which values are different from zero */
: c = b :!= "0"
: c
1 2 3 4
+-----------------+
1 | 0 0 0 1 |
+-----------------+
: /* Step 4: find the first index position where this is true */
: d = selectindex(c :!= 0)[1]
: d
4
: end
You can also find the position of the string of interest in Step 2 using the
same logic.
This is the index value after the one for .:
. mata:
: k = selectindex(a :== ".") + 1
: k
3
: end
In which case, Step 2 becomes:
. mata:
:
: b = tokens(a[k], "0")
: b
1 2 3 4
+-------------------------+
1 | 0 0 0 823 |
+-------------------------+
: end
For unexpected cases without decimal:
foreach x in 124.000923 65.020923 1.000022030 12 0.0090843 .00000425 {
if strmatch("`x'", "*.*") mata: selectindex(tokens(tokens(st_local("x"), ".")[selectindex(tokens(st_local("x"), ".") :== ".") + 1], "0") :!= "0")[1]
else display " 0"
}
4
2
5
0
3
6

Answer 3

A straighforward answer uses regular expressions and commands to work with strings.
One can select all decimals, find the first non 0 decimal, and finally find its position:
loc v = "123.000923"
loc v2 = regexr("`v'", "^[0-9]*[/.]", "") // 000923
loc v3 = regexr("`v'", "^[0-9]*[/.][0]*", "") // 923
loc first = substr("`v3'", 1, 1) // 9
loc first_pos = strpos("`v2'", "`first'") // 4: position of 9 in 000923
di "`v2'"
di "`v3'"
di "`first'"
di "`first_pos'"
Which in one step is equivalent to:
loc first_pos2 = strpos(regexr("`v'", "^[0-9]*[/.]", ""), substr(regexr("`v'", "^[0-9]*[/.][0]*", ""), 1, 1))
di "`first_pos2'"
An alternative suggested in another answer is to compare the lenght of the decimals block cleaned from the 0s with that not cleaned.
In one step this is:
loc first_pos3 = strlen(regexr("`v'", "^[0-9]*[/.]", "")) - strlen(regexr("`v'", "^[0-9]*[/.][0]*", "")) + 1
di "`first_pos3'"

Answer 4

Not using regex but log10 instead (which treats a number like a number), this function will:
For numbers >= 1 or numbers <= -1, return with a positive number the number of digits to the left of the decimal.
Or (and more specifically to what you were asking), for numbers between 1 and -1, return with a negative number the number of digits to the right of the decimal where the first non-zero number occurs.
digitsFromDecimal = (n) => {
dFD = Math.log10(Math.abs(n)) | 0;
if (n >= 1 || n <= -1) { dFD++; }
return dFD;
}
var x = [118.8161330, 11.10501660, 9.254180571, -1.245501523, 1, 0, 0.864931613, 0.097007836, -0.010880074, 0.009066729];
x.forEach(element => {
console.log(`${element}, Digits from Decimal: ${digitsFromDecimal(element)}`);
});
// Output
// 118.816133, Digits from Decimal: 3
// 11.1050166, Digits from Decimal: 2
// 9.254180571, Digits from Decimal: 1
// -1.245501523, Digits from Decimal: 1
// 1, Digits from Decimal: 1
// 0, Digits from Decimal: 0
// 0.864931613, Digits from Decimal: 0
// 0.097007836, Digits from Decimal: -1
// -0.010880074, Digits from Decimal: -1
// 0.009066729, Digits from Decimal: -2

Answer 5

Mata solution of Pearly is very likable, but notice should be paid for "unexpected" cases of "no decimal at all".
Besides, the regular expression is not a too bad choice when it could be made in a memorable 1-line.
loc v = "123.000923"
capture local x = regexm("`v'","(\.0*)")*length(regexs(0))
Below code tests with more values of v.
foreach v in 124.000923 605.20923 1.10022030 0.0090843 .00000425 12 .000125 {
capture local x = regexm("`v'","(\.0*)")*length(regexs(0))
di "`v': The wanted number = `x'"
}