zero

Advanced scientific number formatting.

• Introduction
• Quick Demo
• Documentation
• Table alignment
• Zero for third-party packages

Introduction

Proper number formatting requires some love for detail to guarantee a readable and clear output. This package provides tools to ensure consistent formatting and to simplify the process of following established publication practices. Key features are

• standardized formatting,
• digit grouping, e.g., $299\,792\,458$ instead of $299792458$,
• plug-and-play number alignment in tables,
• quick scientific notation, e.g., "2e4" becomes $2\times10^4$,
• symmetric and asymmetric uncertainties,
• rounding in various modes,
• and some specials for package authors.

A number in scientific notation consists of three parts of which the latter two are optional. The first part is the mantissa that may consist of an integer and a fractional part. In many fields of science, values are not known exactly and the corresponding uncertainty is then given along with the mantissa. Lastly, to facilitate reading very large or small numbers, the mantissa may be multiplied with a power of 10 (or another base).

The anatomy of a formatted number is shown in the following figure.

Quick Demo

Documentation

• Function num
• Grouping
• Rounding
• Uncertainties
• Table alignment

num

The function num() is the heart of Zero. It provides a wide range of number formatting utilities and its default values are configurable via set-num() which takes the same named arguments as num().

#let num(
  number:                 str | content | int | float | dictionary | array,
  digits:                 auto | int = auto,
  fixed:                  none | int = none,

  decimal-separator:      str = ".",
  product:                content = sym.times,
  tight:                  boolean = false,
  omit-unity-mantissa:    boolean = true,
  positive-sign:          boolean = false,
  positive-sign-exponent: boolean = false,
  base:                   int | content = 10,
  uncertainty-mode:       str = "separate",
  rounding:               dictionary,
  grouping:               dictionary,
)

• number: str | content | int | float | array : Number input; str is preferred. If the input is content, it may only contain text nodes. Numeric types int and float are supported but not encouraged because of information loss (e.g., the number of trailing “0” digits or the exponent). The remaining types dictionary and array are intended for advanced use, see below.
• digits: auto | int = auto : Truncates the number at a given (positive) number of decimal places or pads the number with zeros if necessary. This is independent of rounding.
• fixed: none | int = none : If not none, forces a fixed exponent. Additional exponents given in the number input are taken into account.
• decimal-separator: str = "." : Specifies the marker that is used for separating integer and decimal part.
• product: content = sym.times : Specifies the multiplication symbol used for scientific notation.
• tight: boolean = false : If true, tight spacing is applied between operands (applies to $\times$ and $\pm$).
• omit-unity-mantissa: boolean = false : Determines whether a mantissa of 1 is omitted in scientific notation, e.g., $10^4$ instead of $1\cdot 10^4$.
• positive-sign: boolean = false : If set to true, positive coefficients are shown with a $+$ sign.
• positive-sign-exponent: boolean = false : If set to true, positive exponents are shown with a $+$ sign.
• base: int | content = 10 : The base used for scientific power notation.
• uncertainty-mode: str = "separate" : Selects one of the modes "separate", "compact", or "compact-separator" for displaying uncertainties. The different behaviors are shown below:

• rounding: dictionary : You can provide one or more rounding options in a dictionary. Also see rounding.
• grouping: dictionary : You can provide one or more grouping options in a dictionary. Also see grouping.

Configuration example:

#set-num(product: math.dot, tight: true)

Grouping

Digit grouping is important for keeping large figures readable. It is customary to separate thousands with a thin space, a period, comma, or an apostrophe (however, we discourage using a period or a comma to avoid confusion since both are used for decimal separators in various countries).

Digit grouping can be configured with the set-group() function.

#let set-group(
  size:       int = 3, 
  separator:  content = sym.space.thin,
  threshold:  int = 5
)

• size: int = 3 : Determines the size of the groups.
• separator: content = sym.space.thin : Separator between groups.
• threshold: int = 5 : Necessary number of digits needed for digit grouping to kick in. Four-digit numbers for example are usually not grouped at all since they can still be read easily.

Configuration example:

#set-group(separator: "'", threshold: 4)

Grouping can be turned off altogether by setting the threshold to calc.inf.

Rounding

Rounding can be configured with the set-round() function.

#let set-round(
  mode:       none | str = none,
  precision:  int = 2,
  pad:        boolean = true,
  direction:  str = "nearest",
)

• mode: none | str = none : Sets the rounding mode. The possible options are
  • none : Rounding is turned off.
  • "places" : The number is rounded to the number of decimal places given by the precision parameter.
  • "figures" : The number is rounded to a number of significant figures given by the precision parameter.
  • "uncertainty" : Requires giving an uncertainty value. The uncertainty is rounded to significant figures according to the precision argument and then the number is rounded to the same number of decimal places as the uncertainty.
• precision: int = 2 : The precision to round to. Also see parameter mode.
• pad: boolean = true : Whether to pad the number with zeros if the number has fewer digits than the rounding precision.
• direction: str = "nearest" : Sets the rounding direction.
  • "nearest": Rounding takes place in the usual fashion, rounding to the nearer number, e.g., 2.34 → 2.3 and 2.36 → 2.4.
  • "down": Always rounds down, e.g., 2.38 → 2.3 and 2.30 → 2.3.
  • "up": Always rounds up, e.g., 2.32 → 2.4 and 2.30 → 2.3.

Specifying uncertainties

There are two ways of specifying uncertainties:

• Applying an uncertainty to the least significant digits using parentheses, e.g., 2.3(4),
• Denoting an absolute uncertainty, e.g., 2.3+-0.4 becomes $2.3\pm0.4$.

Zero supports both and can convert between these two, so that you can pick the displayed style (configured via uncertainty-mode, see above) independently of the input style.

How do uncertainties interplay with exponents? The uncertainty needs to come first, and the exponent applies to both the mantissa and the uncertainty, e.g., num("1.23+-.04e2") becomes

$$ (1.23\pm0.04)\times 10^2. $$

Note that the mantissa is now put in parentheses to disambiguate the application of the power.

In some cases, the uncertainty is asymmetric which can be expressed via num("1.23+0.02-0.01")

$$ 1.23^{+0.02}_{-0.01}. $$

Table alignment

In scientific publication, presenting many numbers in a readable fashion can be a difficult discipline. A good starting point is to align numbers in a table at the decimal separator. With Zero, this can be accomplished by using ztable, a wrapper for the built-in table function. It features an additional parameter format which takes an array of none, auto, or dictionary values to turn on number alignment for specific columns.

#ztable(
  columns: 3,
  align: center,
  format: (none, auto, auto),
  $n$, $α$, $β$,
  [1], [3.45], [-11.1],
  ..
)

Non-number entries (e.g., in the header) are automatically recognized in some cases and will not be aligned. In ambiguous cases, adding a leading or trailing space tells Zero not to apply alignment to this cell, e.g., [Angle ] instead of [Angle].

Zero not only aligns numbers at the decimal point but also at the uncertainty and exponent part. Moreover, by passing a dictionary instead of auto, a set of num() arguments to apply to all numbers in a column can be specified.

#ztable(
  columns: 4,
  align: center,
  format: (none, auto, auto, (digits: 1)),
  $n$, $α$, $β$, $γ$,
  [1], [3.45e2], [-11.1+-3], [0],
  ..
)

Zero for third-party packages

This package provides some useful extras for third-party packages that generate formatted numbers (for example graphics libraries).

Instead of passing a str to num(), it is also possible to pass a dictionary of the form

(
  mantissa:  str | int | float,
  e:         none | str,
  pm:        none | array
)

This way, parsing the number can be avoided which makes especially sense for packages that generate numbers (e.g., tick labels for a diagram axis) with independent mantissa and exponent.

Furthermore, num() also allows array arguments for number which allows for more efficient batch-processing of numbers with the same setup. In this case, the caller of the function needs to provide context.