The ‘bc’ command is an arbitrary precision calculator language that can be used to perform mathematical calculations. It allows users to perform calculations with arbitrary precision, which is especially useful when working with large numbers or when precision is important. The ‘bc’ command can be used interactively or to execute scripts.

Use case 1: Start an interactive session

Code:

bc

Motivation: Starting an interactive session allows users to perform calculations directly in the terminal without the need for a script. This is useful for quick calculations or when experimenting with different mathematical expressions.

Explanation: The command ‘bc’ without any arguments starts an interactive session of the ‘bc’ calculator. Once the session is started, users can enter mathematical expressions and the ‘bc’ calculator will evaluate them.

Example output:

bc 1.07.1
> 

Use case 2: Start an interactive session with the standard math library enabled

Code:

bc --mathlib

Motivation: Enabling the standard math library provides additional mathematical functions and constants that can be used in calculations. This is useful for more advanced mathematical calculations that require functions like sine, cosine, or logarithm.

Explanation: The argument ‘–mathlib’ enables the standard math library when starting the interactive session of ‘bc’. This library adds additional mathematical functions and constants that can be accessed and used in calculations.

Example output:

bc 1.07.1
> 

Use case 3: Calculate an expression

Code:

echo '5 / 3' | bc

Motivation: Performing a calculation using ‘bc’ is useful when precision is important or when working with numbers that cannot be accurately represented using standard floating-point arithmetic.

Explanation: The ’echo’ command is used to send the mathematical expression ‘5 / 3’ as input to ‘bc’. The pipe symbol ‘|’ is used to redirect the output of ’echo’ as input to ‘bc’. ‘bc’ then evaluates the expression and returns the result.

Example output:

1

Use case 4: Execute a script

Code:

bc path/to/script.bc

Motivation: Executing a script allows users to perform a series of calculations or complex mathematical operations without the need to enter each calculation manually in an interactive session. This is useful for automating repetitive calculations or performing more advanced calculations.

Explanation: The command ‘bc’ is used to execute a script file located at ‘path/to/script.bc’. The script file contains a series of mathematical expressions or operations that ‘bc’ will evaluate in order.

Example output:

Output of the script

Use case 5: Calculate an expression with the specified scale

Code:

echo 'scale = 10; 5 / 3' | bc

Motivation: Specifying the scale allows users to control the precision of the calculation. This is useful when working with floating-point numbers and the desired precision is higher than the default scale of ‘bc’.

Explanation: The ’echo’ command is used to send the mathematical expression ‘scale = 10; 5 / 3’ as input to ‘bc’. The ‘scale’ variable is set to 10, which means that the calculation will be performed with a precision of 10 decimal places. ‘bc’ then evaluates the expression and returns the result with the specified scale.

Example output:

1.6666666666

Use case 6: Calculate a sine/cosine/arctangent/natural logarithm/exponential function using mathlib

Code:

echo 's|c|a|l|e(1)' | bc --mathlib

Motivation: Using the ‘mathlib’ enables the use of additional mathematical functions such as sine, cosine, arctangent, natural logarithm, and exponential functions. This is useful when performing more advanced mathematical calculations that involve trigonometric or exponential operations.

Explanation: The ’echo’ command is used to send the string ’s|c|a|l|e(1)’ as input to ‘bc –mathlib’. The ’s|c|a|l|e(1)’ is not a valid mathematical expression but rather a trick to trigger the display of the available mathematical functions in ‘mathlib’. ‘bc’ then shows the list of available functions and constants.

Example output:

The `mathlib` functions are not available in the output, but the user will see a list of mathematical functions and constants provided by the standard math library when executing this command.

Conclusion:

The ‘bc’ command is a powerful arbitrary precision calculator language that can be used to perform precise mathematical calculations. It supports interactive sessions, script execution, and provides a standard math library with additional functions and constants. Whether you need to perform simple or complex calculations, ‘bc’ is a versatile tool that can help you achieve accurate results.