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more floating point alternatives

there are many alternative ways to represent numbers

These are all implemented in software (not hardware) so they’re a lot slower, and different languages have different libraries.

alternative 1: decimal floating point

This is like regular floating point, but in base 10 instead of base 2. It’s also standardized in IEEE 754.

Examples: Python’s decimal module or Java’s BigDecimal

alternative 2: fractions

This lets you do exact calculations with fractions (110 + 210 = 310)

Examples: Python’s fractions module in the standard library, Lisps have first-class support

alternative 3: symbolic computation

For example, sqrt(2) instead of 1.414.

You’ll see this in computer algebra systems like Mathematica, Maple, or sympy.

alternative 4: interval arithmetic

The idea is to store every number as a range so that you can precisely track your error bars.

Probably the least mainstream of these alternatives.

alternative 5: binary-coded decimal

This is how floating point numbers (and integers) were stored on IBM computers in the 60s, and you can still occasionally see it today in old formats like ISO 8583 for financial transactions.

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