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### 12.7 Performance of numeric operations

Kawa can generally do a pretty good job of generating efficient code for numeric operations, at least when it knows or can figure out the types of the operands.

The basic operations `+`, `-`, and `*` are compiled to single-instruction bytecode if both operands are `int` or `long`. Likewise, if both operands are floating-point (or one is floating-point and the other is rational), then single-instruction `double` or `float` instructions are emitted.

A binary operation involving an infinite-precision `integer` and a fixed-size `int` or `long` is normally evaluated by expanding the latter to `integer` and using `integer` arithmetic. An exception is an integer literal whose value fits in an `int` or `long` - in that case the operation is done using `int` or `long` arithmetic.

In general, integer literals have amorphous type. When used to infer the type of a variable, they have `integer` type:

```(let ((v1 0))
... v1 has type integer ... )
```

However, a literal whose value fits in the `int` or `long` range is implicitly viewed `int` or `long` in certain contexts, primarily method overload resolution and binary arithmetic (as mentioned above).

The comparison functions `<`, `<=`, `=`, `>`, and `=>` are also optimized to single instriction operations if the operands have appropriate type. However, the functions `zero?`, `positive?`, and `negative?` have not yet been optimized. Instead of `(positive? x)` write `(> x 0)`.

There are a number of integer division and modulo operations. If the operands are `int` or `long`, it is faster to use `quotient` and `remainder` rather than `div` and `mod` (or `modulo`). If you know the first operand is non-negative and the second is positive, then use `quotient` and `remainder`. (If an operand is an arbitrary-precision `integer`, then it dosn’t really matter.)

The logical operations `bitwise-and`, `bitwise-ior`, `bitwise-xor`, `bitwise-not`, `bitwise-arithmetic-shift-left`, `bitwise-arithmetic-shift-right` are compiled to single bitcode instructions if the operands are `int` or `long`. Avoid `bitwise-arithmetic-shift` if the sign of the shift is known. If the operands are arbitrary-precision `integer`, a library call is needed, but run-time type dispatch is avoided.

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