signifix

Number Formatter of Fixed Significance with Metric or Binary Prefix

Formats a given number in one of the three Signifix notations as defined below by determining

1. the appropriate metric or binary prefix and
2. the decimal mark position in such a way as to sustain a fixed number of four significant figures.

Contents

• Signifix Notations
  • With Metrix Prefix
  • With Binary Prefix
• Usage
• Examples
  1. The Notations
  2. Transfer Rate
  3. Measured Amps
  4. Filesize Diff
  5. Boundary Stat
  6. Localizations
  7. Customization
• License
• Contribution

Signifix Notations

Three notations are defined,

• two with metric prefix, a default and an alternate, and
• one with binary prefix, a default only.

With Metric Prefix

The two Signifix notations with metric prefix comprise

• a signed significand of four significant figures normalized from ±1.000 to ±999.9 to cover the three powers of ten of a particular metric prefix with the three different decimal mark positions between these four figures, and
• a metric prefix symbol or its placeholder in case of no prefix
  • either being appended along with a whitespace as in ±1.234␣k, that is the default notation,
  • or replacing the decimal mark of the significand as in ±1k234, that is the alternate notation.

In default notation the placeholder is another whitespace as in ±1.234␣␣ to align consistently, while in alternate notation it is a number sign as in ±1#234 to conspicuously separate the integer from the fractional part of the significand. The locale-sensitive decimal mark defaults to a decimal point. The plus sign of positive numbers is optional.

With Binary Prefix

The one Signifix notation with binary prefix comprises

• a signed significand of four significant figures normalized from ±1.000 over ±999.9 to ±1 023 to cover the four powers of ten of a particular binary prefix with the three different decimal mark positions between these four figures and a thousands separator, and
• a binary prefix symbol or its placeholder in case of no prefix being appended along with a whitespace as in ±1.234␣Ki.

To align consistently, the placeholder is another two whitespaces as in ±1.234␣␣␣. The locale-sensitive decimal mark defaults to a decimal point while the locale-sensitive thousands separator defaults to a whitespace as in ±1␣023␣Ki. The plus sign of positive numbers is optional.

Usage

This crate works since Rust 1.34 on stable channel. It is on crates.io and can be used by adding signifix to the dependencies in your project's Cargo.toml:

[dependencies]
signifix = "0.10"

Examples

The Notations

The Signifix notations result in a fixed number of characters preventing jumps to the left or right while making maximum use of their occupied space:

use std::convert::TryFrom;

use signifix::{metric, binary, Result};

let metric = |number| -> Result<(String, String)> {
	let number = metric::Signifix::try_from(number)?;
	Ok((format!("{}", number), format!("{:#}", number)))
};
let binary = |number| -> Result<String> {
	let number = binary::Signifix::try_from(number)?;
	Ok(format!("{}", number))
};

// Three different decimal mark positions covering the three powers of ten
// of a particular metric prefix.
assert_eq!(metric(1E-04), Ok(("100.0 µ".into(), "100µ0".into()))); // 3rd
assert_eq!(metric(1E-03), Ok(("1.000 m".into(), "1m000".into()))); // 1st
assert_eq!(metric(1E-02), Ok(("10.00 m".into(), "10m00".into()))); // 2nd
assert_eq!(metric(1E-01), Ok(("100.0 m".into(), "100m0".into()))); // 3rd
assert_eq!(metric(1E+00), Ok(("1.000  ".into(), "1#000".into()))); // 1st
assert_eq!(metric(1E+01), Ok(("10.00  ".into(), "10#00".into()))); // 2nd
assert_eq!(metric(1E+02), Ok(("100.0  ".into(), "100#0".into()))); // 3rd
assert_eq!(metric(1E+03), Ok(("1.000 k".into(), "1k000".into()))); // 1st
assert_eq!(metric(1E+04), Ok(("10.00 k".into(), "10k00".into()))); // 2nd
assert_eq!(metric(1E+05), Ok(("100.0 k".into(), "100k0".into()))); // 3rd
assert_eq!(metric(1E+06), Ok(("1.000 M".into(), "1M000".into()))); // 1st

// Three different decimal mark positions and a thousands separator covering
// the four powers of ten of a particular binary prefix.
assert_eq!(binary(1_024f64.powi(0) * 1E+00), Ok("1.000   ".into())); // 1st
assert_eq!(binary(1_024f64.powi(0) * 1E+01), Ok("10.00   ".into())); // 2nd
assert_eq!(binary(1_024f64.powi(0) * 1E+02), Ok("100.0   ".into())); // 3rd
assert_eq!(binary(1_024f64.powi(0) * 1E+03), Ok("1 000   ".into())); // 4th
assert_eq!(binary(1_024f64.powi(1) * 1E+00), Ok("1.000 Ki".into())); // 1st
assert_eq!(binary(1_024f64.powi(1) * 1E+01), Ok("10.00 Ki".into())); // 2nd
assert_eq!(binary(1_024f64.powi(1) * 1E+02), Ok("100.0 Ki".into())); // 3rd
assert_eq!(binary(1_024f64.powi(1) * 1E+03), Ok("1 000 Ki".into())); // 4th
assert_eq!(binary(1_024f64.powi(2) * 1E+00), Ok("1.000 Mi".into())); // 1st

// Rounding over prefixes is safe against floating-point inaccuracies.
assert_eq!(metric(999.949_999_999_999_8),
	Ok(("999.9  ".into(), "999#9".into())));
assert_eq!(metric(999.949_999_999_999_9),
	Ok(("1.000 k".into(), "1k000".into())));
assert_eq!(binary(1_023.499_999_999_999_94),
	Ok("1 023   ".into()));
assert_eq!(binary(1_023.499_999_999_999_95),
	Ok("1.000 Ki".into()));

Transfer Rate

This is useful to smoothly refresh a transfer rate within a terminal:

use std::convert::TryFrom;

use std::f64;
use std::time::Duration;
use signifix::metric::{Signifix, Error, DEF_MIN_LEN};

let transfer_rate = |bytes: u64, duration: Duration| -> String {
	let seconds = duration.as_secs() as f64
		+ duration.subsec_nanos() as f64 * 1E-09;
	let bytes_per_second = bytes as f64 / seconds;
	let unit = "B/s";
	let rate = match Signifix::try_from(bytes_per_second) {
		Ok(rate) => if rate.factor() < 1E+00 {
			" - slow - ".into() // instead of mB/s, µB/s, ...
		} else {
			format!("{}{}", rate, unit) // normal rate
		},
		Err(case) => match case {
			Error::OutOfLowerBound(rate) => if rate == 0f64 {
				" - idle - " // no progress at all
			} else {
				" - slow - " // almost no progress
			},
			Error::OutOfUpperBound(rate) => if rate == f64::INFINITY {
				" - ---- - " // zero nanoseconds
			} else {
				" - fast - " // awkwardly fast
			},
			Error::Nan => " - ---- - ", // zero bytes in zero nanoseconds
		}.into(),
	};
	debug_assert_eq!(rate.chars().count(),
		DEF_MIN_LEN + unit.chars().count());
	rate
};

assert_eq!(transfer_rate(42_667, Duration::from_secs(300)), "142.2  B/s");
assert_eq!(transfer_rate(42_667, Duration::from_secs(030)), "1.422 kB/s");
assert_eq!(transfer_rate(42_667, Duration::from_secs(003)), "14.22 kB/s");
assert_eq!(transfer_rate(00_001, Duration::from_secs(003)), " - slow - ");
assert_eq!(transfer_rate(00_000, Duration::from_secs(003)), " - idle - ");
assert_eq!(transfer_rate(42_667, Duration::from_secs(000)), " - ---- - ");

Measured Amps

Or to monitor a measured quantity like an electrical current including its direction with positive numbers being padded to align with negative ones:

use std::convert::TryFrom;

use signifix::metric::{Signifix, Result, DEF_MAX_LEN};

let measured_amps = |amps| -> Result<String> {
	if let Some(amps) = amps {
		Signifix::try_from(amps)
			.map(|amps| format!("{:>1$}A", amps, DEF_MAX_LEN))
	} else {
		Ok("     0  A".into())
	}
};

assert_eq!(measured_amps(Some( 1.476E-06)), Ok(" 1.476 µA".into()));
assert_eq!(measured_amps(None),             Ok("     0  A".into()));
assert_eq!(measured_amps(Some(-2.927E-06)), Ok("-2.927 µA".into()));

Filesize Diff

While to visualize a change in file size, a plus sign might be preferred for positive numbers:

use std::convert::TryFrom;

use signifix::metric::{Signifix, Error, Result};

let filesize_diff = |curr, prev| -> Result<String> {
	Signifix::try_from(curr - prev).map(|diff| format!("{:+#}", diff))
		.or_else(|case| if case == Error::OutOfLowerBound(0f64)
			{ Ok("=const".into()) } else { Err(case) })
};

assert_eq!(filesize_diff(78_346, 57_393), Ok("+20k95".into()));
assert_eq!(filesize_diff(93_837, 93_837), Ok("=const".into()));
assert_eq!(filesize_diff(27_473, 36_839), Ok("-9k366".into()));

Boundary Stat

The binary prefix instead suits well to visualize quantities being multiples of powers of two, such as memory boundaries due to binary addressing:

use std::convert::TryFrom;

use signifix::binary::{Signifix, Error, Result};

let boundary_stat = |used: u64, size: u64| -> Result<String> {
	if used == 0 {
		let size = Signifix::try_from(size)?;
		return Ok(format!("    0   B (    0 %) of {}B", size));
	}
	let p100 = Signifix::try_from(used as f64 / size as f64 * 100.0)
		.map(|p100| format!("{:.*} %", p100.exponent(), p100.significand()))
		.or_else(|error| if let Error::OutOfLowerBound(_) = error
			{ Ok("  < 1 %".into()) } else { Err(error) })?;
	let used = Signifix::try_from(used)?;
	let size = Signifix::try_from(size)?;
	Ok(format!("{}B ({}) of {}B", used, p100, size))
};

assert_eq!(boundary_stat(0_000u64.pow(1), 1_024u64.pow(3)),
	Ok("    0   B (    0 %) of 1.000 GiB".into()));
assert_eq!(boundary_stat(1_024u64.pow(2), 1_024u64.pow(3)),
	Ok("1.000 MiB (  < 1 %) of 1.000 GiB".into()));
assert_eq!(boundary_stat(3_292u64.pow(2), 1_024u64.pow(3)),
	Ok("10.34 MiB (1.009 %) of 1.000 GiB".into()));
assert_eq!(boundary_stat(8_192u64.pow(2), 1_024u64.pow(3)),
	Ok("64.00 MiB (6.250 %) of 1.000 GiB".into()));
assert_eq!(boundary_stat(1_000u64.pow(3), 1_024u64.pow(3)),
	Ok("953.7 MiB (93.13 %) of 1.000 GiB".into()));
assert_eq!(boundary_stat(1_024u64.pow(3), 1_024u64.pow(3)),
	Ok("1.000 GiB (100.0 %) of 1.000 GiB".into()));

Localizations

Until there is a recommended and possibly implicit localization system for Rust, explicit localization can be achieved by wrapping the Signifix type into a locale-sensitive newtype which implements the Display trait via the Signifix::fmt() method:

use std::convert::TryFrom;

use signifix::binary::{Signifix, Result};

struct SignifixSi(Signifix); // English SI style (default)
struct SignifixEn(Signifix); // English locale (whitespace -> comma)
struct SignifixDe(Signifix); // German locale (comma <-> point)

impl std::fmt::Display for SignifixSi {
	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
		std::fmt::Display::fmt(&self.0, f)
	}
}
impl std::fmt::Display for SignifixEn {
	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
		self.0.fmt(f, ".", ",")
	}
}
impl std::fmt::Display for SignifixDe {
	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
		self.0.fmt(f, ",", ".")
	}
}

let localizations = |number| -> Result<(String, String, String)> {
	Signifix::try_from(number).map(|number| (
		format!("{}", SignifixSi(number)),
		format!("{}", SignifixEn(number)),
		format!("{}", SignifixDe(number)),
	))
};

assert_eq!(localizations(999.9f64 * 1_024f64),
	Ok(("999.9 Ki".into(), "999.9 Ki".into(), "999,9 Ki".into())));
assert_eq!(localizations(1_000f64 * 1_024f64),
	Ok(("1 000 Ki".into(), "1,000 Ki".into(), "1.000 Ki".into())));

Customization

Customization can be achieved by extracting information from the Signifix type via its methods:

use std::convert::TryFrom;

use signifix::metric::{Signifix, Result};

struct SignifixTable<'a>(&'a[Signifix]);

impl<'a> std::fmt::Display for SignifixTable<'a> {
	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
		f.pad(" Int Fra   10³\n")?;
		f.pad("---- ---- ----\n")?;
		for entry in self.0 {
			let (integer, fractional) = entry.parts();
			f.pad(&format!("{:4} {:<3}    {:2}\n",
				integer, fractional, entry.prefix() as i32 - 8))?;
		}
		Ok(())
	}
}

let customization = |entries: &[_]| -> Result<String> {
	let mut table = Vec::with_capacity(entries.len());
	for entry in entries {
		table.push(Signifix::try_from(*entry)?);
	}
	Ok(SignifixTable(&table).to_string())
};

assert_eq!(customization(&[
	 1.234E-06,
	 12.34E+00,
	-123.4E+24,
]), Ok(concat!(
	" Int Fra   10³\n",
	"---- ---- ----\n",
	"   1 234    -2\n",
	"  12 34      0\n",
	"-123 4       8\n",
).into()));

License

Copyright (c) 2016-2019 Rouven Spreckels n3vu0r@qu1x.org

Usage of the works is permitted provided that this instrument is retained with the works, so that any entity that uses the works is notified of this instrument.

DISCLAIMER: THE WORKS ARE WITHOUT WARRANTY.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the works by you shall be licensed as above, without any additional terms or conditions.