## Underflow and Overflow Logging Using fipref

### Logging Overflows and Underflows as Warnings

Overflows and underflows are logged as warnings for all assignment, plus, minus, and multiplication operations when the `fipref` `LoggingMode` property is set to `on`. For example, try the following:

1. Create a signed `fi` object that is a vector of values from 1 to 5, with 8-bit word length and 6-bit fraction length.

```a = fi(1:5,1,8,6); ```
2. Define the `fimath` object associated with `a`, and indicate that you will specify the sum and product word and fraction lengths.

```F = a.fimath; F.SumMode = 'SpecifyPrecision'; F.ProductMode = 'SpecifyPrecision'; a.fimath = F; ```
3. Define the `fipref` object and turn on overflow and underflow logging.

```P = fipref; P.LoggingMode = 'on'; ```
4. Suppress the `numerictype` and `fimath` displays.

```P.NumericTypeDisplay = 'none'; P.FimathDisplay = 'none'; ```
5. Specify the sum and product word and fraction lengths.

```a.SumWordLength = 16; a.SumFractionLength = 15; a.ProductWordLength = 16; a.ProductFractionLength = 15; ```
6. Warnings are displayed for overflows and underflows in assignment operations. For example, try:

```a(1) = pi Warning: 1 overflow occurred in the fi assignment operation. a = 1.9844 1.9844 1.9844 1.9844 1.9844 a(1) = double(eps(a))/10 Warning: 1 underflow occurred in the fi assignment operation. a = 0 1.9844 1.9844 1.9844 1.9844 ```
7. Warnings are displayed for overflows and underflows in addition and subtraction operations. For example, try:

```a+a Warning: 12 overflows occurred in the fi + operation. ans = 0 1.0000 1.0000 1.0000 1.0000 a-a Warning: 8 overflows occurred in the fi - operation. ans = 0 0 0 0 0 ```
8. Warnings are displayed for overflows and underflows in multiplication operations. For example, try:

```a.*a Warning: 4 product overflows occurred in the fi .* operation. ans = 0 1.0000 1.0000 1.0000 1.0000 a*a' Warning: 4 product overflows occurred in the fi * operation. Warning: 3 sum overflows occurred in the fi * operation. ans = 1.0000 ```

The final example above is a complex multiplication that requires both multiplication and addition operations. The warnings inform you of overflows and underflows in both.

Because overflows and underflows are logged as warnings, you can use the `dbstop` MATLAB® function with the syntax

```dbstop if warning ```

to find the exact lines in a file that are causing overflows or underflows.

Use

`dbstop if warning fi:underflow`

to stop only on lines that cause an underflow. Use

`dbstop if warning fi:overflow`

to stop only on lines that cause an overflow.

### Accessing Logged Information with Functions

When the `fipref` `LoggingMode` property is set to `on`, you can use the following functions to return logged information about assignment and creation operations to the MATLAB command line:

`LoggingMode` must be set to `on` before you perform any operation in order to log information about it. To clear the log, use the function `resetlog`.

For example, consider the following. First turn logging on, then perform operations, and then finally get information about the operations:

```fipref('LoggingMode','on'); x = fi([-1.5 eps 0.5], true, 16, 15); x(1) = 3.0; maxlog(x) ans = 1.0000 minlog(x) ans = -1 noverflows(x) ans = 2 nunderflows(x) ans = 1```

Next, reset the log and request the same information again. Note that the functions return empty [], because logging has been reset since the operations were run:

```resetlog(x) maxlog(x) ans = [] minlog(x) ans = [] noverflows(x) ans = [] nunderflows(x) ans = []```

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