Some people have mentioned that this above code doesnt pass all test cases. I realized, that the rules in the question dont actually match rules used by programming languages on what qualifies as an integer or float. For example, the rules say that 1e3 is not a float, but in reality it is:

Some people have mentioned that the code above doesn't pass all test cases. I realized that the rules in the question don't actually match rules used by programming languages on what qualifies as an integer or float. For example, the rules say that 1e3 is not a float, but in reality it is:

Go, 135 bytes

Responding to this comment:

Your code doesn't compile on it's own either though? It lacks a main.

You can save the code to a file, and test like this:

go build file.go

Also, countless Go packages exist without a main, many in the standard library, for example:

https://github.com/golang/go/blob/go1.17.8/src/fmt/print.go

Go, 135 bytes

Go, 418 bytes

Some people have mentioned that this above code doesnt pass all test cases. I realized, that the rules in the question dont actually match rules used by programming languages on what qualifies as an integer or float. For example, the rules say that 1e3 is not a float, but in reality it is:

package main

import (
   "fmt"
   "strconv"
)

func main() {
   f, err := strconv.ParseFloat("1e3", 64)
   fmt.Println(f, err) // 1000 <nil>
}

So I made an edit to handle these rules:

package n
import."strconv"
func f(s string)byte{if s[0]=='0'&&s[1]!='.'{return'n'}
if len(s)>=3&&s[:2]=="-0"&&s[2]!='.'{return'n'}
if s[0]=='-'{}else if s[0]>='0'&&s[0]<='9'{}else{return'n'}
if s[len(s)-1]>='0'&&s[len(s)-1]<='9'{}else{return'n'}
for _,r:=range s{if r=='-'{}else if r=='.'{}else if r>='0'&&r<='9'{}else{return'n'}}
if _,e:=Atoi(s);e==nil{return'i'}
if _,e:=ParseFloat(s,64);e==nil{return'f'}
return'n'}

Test:

package n

import (
   "fmt"
   "testing"
)

type testType struct {
   in string
   out byte
}

var tests = []testType{
   {"+1.0", 'n'}, {"--1.0", 'n'}, {"-0", 'i'}, {"-0.0", 'f'}, {"-001.1", 'n'},
   {"-1e3", 'n'}, {"-2", 'i'}, {".1", 'n'}, {"00", 'n'}, {"042", 'n'},
   {"1.", 'n'}, {"1.0", 'f'}, {"1.0.0", 'n'}, {"1.00", 'f'}, {"1.0ec3", 'n'},
   {"123", 'i'}, {"1e+3", 'n'}, {"1e-3", 'n'}, {"1e3", 'n'}, {"42", 'i'},
   {"62727.0033", 'f'}, {"644c.33", 'n'}, {"NaN", 'n'},
}

func TestNumber(t *testing.T) {
   for _, test := range tests {
      out := f(test.in)
      if out != test.out {
         fmt.Printf("%v %c %c\n", test.in, test.out, out)
      }
   }
}

Go, 135 bytes

package n
import."strconv"
func f(s string)byte{if _,e:=Atoi(s)
e==nil{return'i'}
if _,e:=ParseFloat(s,64)
e==nil{return'f'}
return'n'}

Update. Since someone thinks this is not a valid program, you can save the code to a file, and test like this:

go build file.go

Go, 135 bytes

package n
import."strconv"
func f(s string)byte{if _,e:=Atoi(s)
e==nil{return'i'}
if _,e:=ParseFloat(s,64)
e==nil{return'f'}
return'n'}

Responding to this comment:

Your code doesn't compile on it's own either though? It lacks a main.

You can save the code to a file, and test like this:

go build file.go

Also, countless Go packages exist without a main, many in the standard library, for example:

https://github.com/golang/go/blob/go1.17.8/src/fmt/print.go