This project implements a set of arithmetic and casting operations for the bfloat16 floating-point format in C, focusing on bit-level manipulations without the use of floating-point data types and their arithmetic operations. The bfloat16 format is a 16-bit floating point that represents a subset of the IEEE 754 single-precision floating-point standard, offering reduced precision while maintaining the same exponent range.

• Conversion Functions: Converts integers and standard float data types to bfloat16, and vice versa, ensuring accurate representation within the bfloat16 format's constraints.
• Arithmetic Operations: Implements basic arithmetic operations (addition, multiplication) between two bfloat16 numbers, utilizing bit-level manipulation to handle the operations.

The implementation is structured around the bf16.c file, which includes detailed implementations of the following functions:

• int2bf16: Converts an integer to bfloat16.
• bf162int: Converts a bfloat16 value back to an integer.
• float2bf16: Converts a standard IEEE 754 single-precision floating point number to bfloat16.
• bf162float: Converts a bfloat16 number back to a standard float.
• bf16_add: Performs addition between two bfloat16 numbers.
• bf16_mul: Performs multiplication between two bfloat16 numbers.

Through this project, I deepened my understanding of:

• The binary representation of integers and floating-point numbers.
• Bitwise operations in C for manipulating data at the bit level.
• The intricacies of floating-point arithmetic and precision trade-offs in computer systems.