- NAME
- VERSION
- DESCRIPTION
- TYPES
- AUTHOR
- COPYRIGHT AND LICENSE

# NAME

Types::Numbers - Type constraints for numbers

# VERSION

version v1.0.0

# DESCRIPTION

Because we deal with numbers every day in our programs and modules, this is an extensive Type::Tiny library of number validations. Like Type::Tiny, these types work with all modern OO platforms and as a standalone type system.

# TYPES

## Overview

All of these types strive for the accurate storage and validation of many different types of numbers, including some storage types that Perl doesn't natively support.

The hierarchy of the types is as follows:

```
(T:S = From Types::Standard)
(~T:C:N = Based on Types::Common::Numeric types)
Item (T:S)
Defined (T:S)
NumLike
NumRange[`n, `p] (~T:C:N)
PositiveNum (~T:C:N)
PositiveOrZeroNum (~T:C:N)
NegativeNum (~T:C:N)
NegativeOrZeroNum (~T:C:N)
IntLike
SignedInt[`b]
UnsignedInt[`b]
IntRange[`n, `p] (~T:C:N)
PositiveInt (~T:C:N)
PositiveOrZeroInt (~T:C:N)
NegativeInt (~T:C:N)
NegativeOrZeroInt (~T:C:N)
SingleDigit (~T:C:N)
PerlNum
PerlSafeInt
PerlSafeFloat
BlessedNum[`d]
BlessedInt[`d]
BlessedFloat[`d]
NaN
Inf[`s]
FloatSafeNum
FloatBinary[`b, `e]
FloatDecimal[`d, `e]
RealNum
RealSafeNum
FixedBinary[`b, `s]
FixedDecimal[`d, `s]
Value (T:S)
Str (T:S)
Char[`b]
```

## Basic types

### NumLike

Behaves like `LaxNum`

from Types::Standard, but will also accept blessed number types. Unlike `StrictNum`

, it will accept `NaN`

and `Inf`

numbers.

### NumRange[`n, `p]

Only accepts numbers within a certain range. By default, the two parameters are the minimums and maximums, inclusive. However, this type is also compatible with a few different parameter styles, a la Types::Common::Numeric.

The minimum/maximums can be omitted or undefined. Or two extra boolean parameters can be added to specify exclusivity:

```
NumRange[0.1, 10.0, 0, 0] # both inclusive
NumRange[0.1, 10.0, 0, 1] # exclusive maximum, so 10.0 is invalid
NumRange[0.1, 10.0, 1, 0] # exclusive minimum, so 0.1 is invalid
NumRange[0.1, 10.0, 1, 1] # both exclusive
NumRange[0.1] # lower bound check only
NumRange[undef, 10.0] # upper bound check only
NumRange[0.1, undef, 1] # lower bound check only, exclusively
NumRange[undef, 10.0, 1, 1] # upper bound check only, exclusively (third param ignored)
```

### PerlNum

Exactly like `LaxNum`

, but with a different parent. Only accepts unblessed numbers.

### BlessedNum

Only accepts blessed numbers. A blessed number would be using something like Math::BigInt or Math::BigFloat. It doesn't directly `isa`

check those classes, just that the number is blessed.

### BlessedNum[`d]

A blessed number that supports at least certain amount of digit accuracy. The blessed number must support the `accuracy`

or `div_scale`

method.

For example, `BlessedNum[40]`

would work for the default settings of Math::BigInt, and supports numbers at least as big as 128-bit integers.

### NaN

A "not-a-number" value, either embedded into the Perl native float or a blessed `NaN`

, checked via `is_nan`

.

### Inf

An infinity value, either embedded into the Perl native float or a blessed `Inf`

, checked via `is_inf`

.

### Inf[`s]

```
Inf['+']
Inf['-']
```

An infinity value with a certain sign, either embedded into the Perl native float or a blessed `Inf`

, checked via `is_inf`

. The parameter must be a plus or minus character.

### RealNum

Like "NumLike", but does not accept NaN or Inf. Closer to the spirit of `StrictNum`

, but accepts blessed numbers as well.

## Integers

### IntLike

Behaves like `Int`

from Types::Standard, but will also accept blessed number types and integers in E notation. There are no expectations of storage limitations here. (See "SignedInt" for that.)

### IntRange[`n, `p]

Only accepts integers within a certain range. By default, the two parameters are the minimums and maximums, inclusive. Though, the minimum/maximums can be omitted or undefined.

### PerlSafeInt

A Perl (unblessed) integer number than can safely hold the integer presented. This varies between 32-bit and 64-bit versions of Perl.

For example, for most 32-bit versions of Perl, the largest integer than can be safely held in a 4-byte NV (floating point number) is `9007199254740992`

. Numbers can go higher than that, but due to the NV's mantissa length (accuracy), information is lost beyond this point.

In this case, `...992`

would pass and `...993`

would fail.

(Technically, the max integer is `...993`

, but we can't tell the difference between `...993`

and `...994`

, so the cut off point is `...992`

, inclusive.)

Be aware that Perls compiled with "long doubles" have a unique problem with storage and information loss: their number form maintains accuracy while their (default) stringified form loses information. For example, take the max safe integer for a long double:

```
$num = 18446744073709551615;
say $num; # 1.84467440737095516e+19
say $num == 18446744073709551615; # true, so the full number is still there
say sprintf('%u', $num); # 18446744073709551615
```

These numbers are considered safe for storage. If this is not preferred, consider a simple `/e/`

check for stringified E notation.

### BlessedInt

A blessed number than is holding an integer. (A Math::BigFloat with an integer value would still pass.)

### BlessedInt[`d]

A blessed number holding an integer of at most ``d`

digits (inclusive). The blessed number container must also have digit accuracy to support this number. (See "BlessedNum[`d]".)

### SignedInt

A signed integer (blessed or otherwise) that can safely hold its own number. This is different than "IntLike", which doesn't check for storage limitations.

### SignedInt[`b]

A signed integer that can hold a ``b`

bit number and is within those boundaries. One bit is reserved for the sign, so the max limit on a 32-bit integer is actually `2**31-1`

or `2147483647`

.

### UnsignedInt

Like "SignedInt", but with a minimum boundary of zero.

### UnsignedInt[`b]

Like "SignedInt[`b]", but for unsigned integers. Also, unsigned integers gain their extra bit, so the maximum is twice as high.

## Floating-point numbers

### PerlSafeFloat

A Perl native float that is in the "integer safe" range, or is a NaN/Inf value.

This doesn't guarantee that every single fractional number is going to retain all of its information here. It only guarantees that the whole number will be retained, even if the fractional part is partly or completely lost.

### BlessedFloat

A blessed number that will support fractional numbers. A Math::BigFloat number will pass, whereas a Math::BigInt number will fail. However, if that Math::BigInt number is capable of upgrading to a Math::BigFloat, it will pass.

### BlessedFloat[`d]

A float-capable blessed number that supports at least certain amount of digit accuracy. The number itself is not boundary checked, as it is excessively difficult to figure out the exact dimensions of a floating point number. It would also not be useful for numbers like `0.333333...`

to fail checks.

### FloatSafeNum

A Union of "PerlSafeFloat" and "BlessedFloat". In other words, a float-capable number with some basic checks to make sure information is retained.

### FloatBinary[`b, `e]

A floating-point number that can hold a ``b`

bit number with ``e`

bits of exponent, and is within those boundaries (or is NaN/Inf). The bit breakdown follows traditional IEEE 754 floating point standards. For example:

```
FloatBinary[32, 8] =
32 bits total (`b)
23 bit mantissa (significand precision)
8 bit exponent (`e)
1 bit sign (+/-)
```

Unlike the `*Int`

types, if Perl's native NV cannot support all dimensions of the floating-point number without losing information, then unblessed numbers are completely off the table. For example, assuming a 32-bit machine:

```
(UnsignedInt[64])->check( 0 ) # pass
(UnsignedInt[64])->check( 2 ** 30 ) # pass
(UnsignedInt[64])->check( 2 ** 60 ) # fail, because 32-bit NVs can't safely hold it
(FloatBinary[64, 11])->check( 0 ) # fail
(FloatBinary[64, 11])->check( $any_unblessed_number ) # fail
```

### FloatDecimal[`d, `e]

A floating-point number that can hold a ``d`

digit number with ``e`

digits of exponent. Modeled after the IEEE 754 "decimal" float. Rejects all Perl NVs that won't support the dimensions. (See "FloatBinary[`b, `e]".)

## Fixed-point numbers

### RealSafeNum

Like "FloatSafeNum", but rejects any NaN/Inf.

### FixedBinary[`b, `s]

A fixed-point number, represented as a ``b`

bit integer than has been shifted by ``s`

digits. For example, a `FixedBinary[32, 4]`

has a max of `2**31-1 / 10**4 = 214748.3647`

. Because integers do not hold NaN/Inf, this type fails on those.

Otherwise, it has the same properties and caveats as the parameterized `Float*`

types.

### FixedDecimal[`d, `s]

Like "FixedBinary[`b, `s]", but for a ``d`

digit integer. Or, you could think of ``d`

and ``s`

as accuracy (significant figures) and decimal precision, respectively.

## Characters

Characters are basically encoded numbers, so there's a few types here. If you need types that handle multi-length strings, you're better off using Types::Encodings.

### Char

A single character. Unicode is supported, but it must be decoded first. A multi-byte character that Perl thinks is two separate characters will fail this type.

### Char[`b]

A single character that fits within ``b`

bits. Unicode is supported, but it must be decoded first.

## Types::Common::Numeric analogues

The Types::Common::Numeric module has a lot of useful types, but none of them are compatible with blessed numbers. This module re-implements them to be grandchildren of "NumLike" and "IntLike", which allows blessed numbers.

Furthermore, the "NumRange" and "IntRange" checks are already implemented and described above.

### PositiveNum

Accepts non-zero numbers in the positive range.

### PositiveOrZeroNum

Accepts numbers in the positive range, or zero.

### PositiveInt

Accepts non-zero integers in the positive range.

### PositiveOrZeroInt

Accepts integers in the positive range, or zero.

### NegativeNum

Accepts non-zero numbers in the negative range.

### NegativeOrZeroNum

Accepts numbers in the negative range, or zero.

### NegativeInt

Accepts non-zero integers in the negative range.

### NegativeOrZeroInt

Accepts integers in the negative range, or zero.

### SingleDigit

Accepts integers between -9 and 9.

# AUTHOR

Grant Street Group <developers@grantstreet.com>

# COPYRIGHT AND LICENSE

This software is Copyright (c) 2013 - 2021 by Grant Street Group.

This is free software, licensed under:

` The Artistic License 2.0 (GPL Compatible)`