Format number by rounding up - rust

Question

I have a number which I want to print with a fixed precision, rounded up. I know I can use {:.3} to truncate it.
assert_eq!("0.0123", format!("{:.3}", 0.0123456))
Is there a simple way to "ceil" it instead?
assert_eq!("0.0124", format!("{:magic}", 0.012301))
assert_eq!("0.0124", format!("{:magic}", 0.012399))
assert_eq!("0.0124", format!("{:magic}", 0.0124))
I can do something like
let x = format!("{:.3}", (((y * 1000.0).ceil() + 0.5) as i64) as f64 / 1000.0)
which is pretty unreadable. It also gives me would give me 3 digits after the decimal point, not three digits of precision, so I need to figure out the scale the number, probably with something like -log10(y) as i64
In case it's not clear, I want a string to show the user, not an f64.
More examples
assert_eq!("1.24e-42", format!("{:magic}", 1.234e-42))
assert_eq!("1240", format!("{:magic}", 1234.5)) // "1240." also works
If the f64 representing 0.123 is slightly larger than the real number 0.123, displaying "0.124" is acceptable.
The two requirements are:
The string, when converted back to an f64, is greater than or equal to the original f64 (so 0.123 -> "0.124" is acceptable)
The string has 3 significant digits (although dropping trailing zeros is acceptable, so 0.5 -> "0.5" and "0.5 -> "0.500" both work)
In case it comes up, the input number will always be positive.

Answer 1

This is harder than it seems because there is no way to tell the formatting machinery to change the rounding strategy. Also, format precision works on the number of digits after the decimal point, not on the number of significant digits. (AFAIK there is no equivalent to the printf("%.3g", n), and even if there were, it wouldn't round up.)
You can use a decimal arithmetic crate such as rust_decimal to do the heavy-lifting - something like:
use rust_decimal::prelude::*;
pub fn fmtup(n: f64, ndigits: u32) -> String {
let d = Decimal::from_f64_retain(n).unwrap();
d.round_sf_with_strategy(ndigits, RoundingStrategy::AwayFromZero)
.unwrap()
.normalize()
.to_string()
}
EDIT: The answer originally included a manual implementation of the rounding due to issues in rust_decimal which have since been fixed. As of Oct 24 2021 the above snippet using rust_decimal is the recommended solution. The only exception is if you need to handle numbers that are very large or very close to zero (such as 1.234e-42 or 1.234e42), which are approximated to zero or rejected by rust_decimal.
To manually round to significant digits, one can scale the number until it has the desired number of digits before the decimal point, and then round it up. In case of 3 digits, scaling would multiply or divide it by 10 until it falls between 100 and 1000. After rounding the number, format the resulting whole number as string, and insert the . at the position determined by the amount of scaling done in the first step.
To avoid inexactness of floating-point division by ten, the number can be first converted to a fraction, and then all operations can proceed on the fraction. Here is an implementation that uses the ubiquitous num crate to provide fractions:
use num::{rational::BigRational, FromPrimitive};
/// Format `n` to `ndigits` significant digits, rounding away from zero.
pub fn fmtup(n: f64, ndigits: i32) -> String {
// Pass 0 (which we can't scale), infinities and NaN to f64::to_string()
if n == 0.0 || !n.is_finite() {
return n.to_string();
}
// Handle negative numbers the easy way.
if n < 0.0 {
return format!("-{}", fmtup(-n, ndigits));
}
// Convert the input to a fraction. From this point onward, we are only doing exact
// arithmetic.
let mut n = BigRational::from_float(n).unwrap();
// Scale N so its whole part is ndigits long, meaning truncating it will result in an
// integer ndigits long. If ndigits is 3, we'd want N to be in (100, 1000] range, so
// that e.g. 0.012345 would be scaled to 123.45, and then rounded up to 124.
let mut scale = 0i16;
let ten = BigRational::from_u8(10).unwrap();
let lower_bound = ten.pow(ndigits - 1);
if n < lower_bound {
while n < lower_bound {
n *= &ten;
scale -= 1;
}
} else {
let upper_bound = lower_bound * &ten;
while n >= upper_bound {
n /= &ten;
scale += 1;
}
}
// Round N up
n = n.ceil();
// Format the number as integer and place the decimal point at the right position.
let mut s = n.to_string();
// multiply N with 10**scale, i.e. append zeros if SCALE is positve, otherwise
// insert the point inside or before the number
if scale > 0 {
s.extend(std::iter::repeat('0').take(scale as _));
} else if scale < 0 {
// Find where to place the decimal point in the string.
let point_pos = s.len() as i16 + scale;
if point_pos <= 0 {
// Negative position means before beginning of the string, so we have
// to pad with zeros. E.g. s == "123" and point_pos == -2 means we
// want "0.00123", and with point_pos == 0 we'd want "0.123".
let mut pad = "0.".to_string();
pad.extend(std::iter::repeat('0').take(-point_pos as _));
pad.push_str(&s);
s = pad;
// Trim trailing zeros after decimal point. E.g. 0.25 gets scaled to
// 250 and then ends up "0.250".
s.truncate(s.trim_end_matches('0').len());
} else {
// Insert the decimal point in the middle of string. E.g. s == "123"
// and point_pos == 1 would result in "1.23".
let point_pos = point_pos as usize;
if s.as_bytes()[point_pos..].iter().all(|&digit| digit == b'0') {
// if only zeros are after the decimal point, e.g. "10.000", omit those
// digits instead of placing the decimal point.
s.truncate(point_pos);
} else {
s.insert(point_pos, '.');
}
}
}
s
}
Playground
Here are some test cases:
fn main() {
let fmt3up = |n| fmtup(n, 3);
assert_eq!("12400", fmt3up(12301.));
assert_eq!("1240", fmt3up(1234.5));
assert_eq!("124", fmt3up(123.01));
assert_eq!("1000", fmt3up(1000.));
assert_eq!("999", fmt3up(999.));
assert_eq!("1010", fmt3up(1001.));
assert_eq!("100", fmt3up(100.));
assert_eq!("10", fmt3up(10.));
assert_eq!("99", fmt3up(99.));
assert_eq!("101", fmt3up(101.));
assert_eq!("0.25", fmt3up(0.25));
assert_eq!("12400", fmt3up(12301.0));
assert_eq!("0.0124", fmt3up(0.0123)); // because 0.0123 is slightly above 123/10_000
assert_eq!("0.0124", fmt3up(0.012301));
assert_eq!("0.00124", fmt3up(0.0012301));
assert_eq!("0.0124", fmt3up(0.012399));
assert_eq!("0.0124", fmt3up(0.0124));
assert_eq!("0.124", fmt3up(0.12301));
assert_eq!("1.24", fmt3up(1.2301));
assert_eq!("1.24", fmt3up(1.234));
}
Note that this will display 1.234e-42 as 0.00000000000000000000000000000000000000000124, but an improvement that to switch to exponential notation should be fairly straightforward.