# chickadee » mpfi » make-ia-interval-empty

##### Identifier search
make-ia-interval-emptyprocedure
make-ia-interval-f64 LO HIprocedure

The following procedures are available:

Arithmetic:

```(ia+ A B)
(ia+f64 A F)
(ia+u64 A U)
(ia+s64 A S)
(ia- A B)
(ia-f64 A F)
(f64-ia F A)
(ia-u64 A U)
(u64-ia U A)
(ia-s64 A S)
(s64-ia S A)
(ia* A B)
(ia*f64 A F)
(ia*u64 A U)
(ia*s64 A S)
(ia/ A B)
(ia/f64 A F)
(f64/ia F A)
(ia/u64 A U)
(u64/ia U A)
(ia/s64 A S)
(s64/ia S A)```

The procedures ending with +, -, * and / operate on two intervals and give an interval as result. The procedures that have f64 in their name take one flonum argument.

Unary functions:

```(ia-neg A)
(ia-sqr A)  ;; square, (* x x)
(ia-inv A)  ;; inverse, (/ 1 x)
(ia-sqrt A) ;; square root
(ia-abs A)
(ia-log A)
(ia-exp A)
(ia-exp2 A)
(ia-log1p A)
(ia-expm1 A)
(ia-log2 A)
(ia-log10 A)```

Trigonometric functions:

```(ia-cos A)
(ia-sin A)
(ia-tan A)
(ia-acos A)
(ia-asin A)
(ia-atan A)
(ia-cosh A)
(ia-sinh A)
(ia-tanh A)
(ia-acosh A)
(ia-asinh A)
(ia-atanh A) ```

Constants:

```(ia-const-log2)
(ia-const-pi)
(ia-const-e)```

These procedures calculate e, pi and the logarithm of two and give back intervals representing them.

Comparisons:

```(ia< A B)
(ia> A B)```

Given two intervals A and B, A is considered greater than B is and only if all elements of A are greater than all elements of B.

`(ia-overlap? A B)`

Returns true if A overlap with or contains B.

```(ia-nan? A)
(ia-inf? A)
(ia-zero? A)
(ia-has-zero? A)
(ia-positive? A)
(ia-negative? A)
(ia-strictly-positive? A)
(ia-strictly-negative? A)
(ia-nonpositive? A)
(ia-nonnegative? A)
(ia-bounded? A)
(ia-empty? A)
(ia-inside?  A B)
(ia-f64-inside? A B)```

Procedures returning flonum:

```(ia-diameter A)
(ia-diameter-absolute A)
(ia-diameter-relative A)
(ia-magnitude A)
(ia-mignitude A)
(ia-random A)
(ia-middle A)```

Other procedures: