**What is Floating Point Coprocessor?**

A floating point coprocessor refers to the part of a computer system or the dedicated logic unit that is specially designed to execute floating point or non-integer calculations.

In simple terms, a floating point coprocessor refers to an integrated circuit that is meant to handle all mathematical calculations that involve floating point numbers or fractions.

**Understanding Floating Point Coprocessor**

Ideally, the floating point coprocessors help the processors to carry out different mathematical calculations faster, which adds to the overall performance of the CPU or Central Processing Unit.

This is a specialized coprocessor that can perform different mathematical operations such as addition, subtraction, multiplication, division of integers and fractions, along with square roots and several complex transcendental functions.

It can manipulate numbers much quicker than the central microprocessor circuitry itself.

The floating point coprocessor is also known by different names such as:

- A math coprocessor
- A numeric coprocessor
- A Floating Point Unit or FPU

Today, there is a floating point coprocessor integrated into the computer processor, much unlike the earlier processors where this was a separate add-on feature.

In the architecture of a general-purpose computer, there may be one or more of these numeric processors integrated.

These work in tandem as the execution units within the CPU.

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Ideally, the modern CPUs can carry out a floating point operation when needed in three different ways such as:

- A floating point library or floating point unit emulator
- An add-on unit
- An integrated unit

However, there are several embedded processors that do not have these units integrated due to a lack of or inadequate hardware support to perform floating point operations separately.

There may not be a hardware FPU in all computer systems as well. In that case, these systems can only imitate its functions.

It can be done in different ways such as:

- In the operating system as an inherent function
- In the CPU as a micro-program or a microcode
- In user code, which is actually referred to as software emulation

Typically, a CPU does not necessarily need to have or use a dedicated math processor to make the calculations involving integers and non-integers since it is capable enough to perform these operations itself.

However, if it has to do so, the final outcome may be slow. This is because the integer operations are notably different from the floating point or non-integer operations due to the significant difference in logic.

This is the basic reason that it is pretty inefficient and unreasonable to use the same processor to handle both diverse types of mathematical operations.

It will slow down the process, especially while dealing with the floating point numbers.

**Floating Point Coprocessor Architecture**

**The architecture of the floating point coprocessors is quite different from what it was before when it was used as a standalone processor within a computer system.**

**Typically, the architecture of the floating point arithmetic unit uses two fixed-point data path units that are loosely united. One of the paths is dedicated for the exponent and the other is for the mantissa.**

These days, these coprocessors are more like a set of VLSI or Very Large Scale Integration Central Processing Units that are tied closely with the primary CPU.

In a math coprocessor, the operations are often pipelined which results in faster processing of the given data.

Once again, it is the modular architecture of these special FPUs that helps with implementing simultaneous multithreading.

The floating-point coprocessors typically come with three particular interface registers apart from the COSTAT register, shared with other coprocessors. These are:

- Coprocessor Status Register
- Floating-Point-Low Register
- Floating-Point Accumulators, both in short and long formats

These three 32-bit registers are usually referenced by the COSET and COGET instructions. These registers allow direct access to the two floating point accumulators of 64 bits.

In a few current architectures of these numeric coprocessors, their functionality is shared with the SIMD units.

This specific aspect of the architecture allows the floating point coprocessors to perform Single Instruction, Multiple Data or SIMD computations as well.

The architecture of the add-on FPUs, however, makes them independent of the host processor.

They have all the necessary programming requirements for them such as instruction sets, operations, and more.

In addition to that, these add-on numeric coprocessors are also sometimes provided with their own IDEs or Integrated Development Environments.

**How Does a Floating Point Coprocessor Work?**

**A floating point coprocessor handles mathematical operations and works with the floating point numbers. These numbers can be whole numbers, fractions or decimal points.**

**It typically accesses the necessary data by similar addressing means as the rest of the CPU and uses its own registers to perform.**

Ideally, the operations of these coprocessors include floating point calculations that may range from simple additions and multiplications to more complex mathematical processes such as exponential and trigonometric calculations.

This is done as follows:

- When the CPU needs to perform a mathematical operation involving simple integers, say, for example, to calculate the value of 125 x 16, the instruction is sent to the integer processing unit for calculation.
- When the CPU needs to perform a bit more complex calculation involving fractions, such as calculating the value of 5.051 x 11.0003 for example, this specific instruction is sent to the Floating Point Coprocessor.

There are a few prerequisites for different types of floating point calculations such as:

- In the case of addition operation, which is pretty much the same as integer addition, the two numbers should necessarily be aligned. The smaller number can be moved to the left if required in order to align it with the larger number.
- In the case of a subtraction operation, it is usually done by using two’s complement.
- In the case of multiplication operations, clever methods, such as the Schönhage and Strassen method, are followed in order to produce the results faster than humans can calculate.
- It is the same with division operations, wherein clever methods are used as well to come up with the answer quickly.

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Ideally, the floating point numbers in computers are represented according to the Institute of Electrical and Electronics Engineers or IEEE standard by using three specific variables such as:

- s – This represents the sign bit which is usually 1 bit in length.
- e – This represents the exponent which is usually negative and 11 bits in length for a 64-bit representation.
- m – This represents the significand which is 52 bits in length for a 64-bit representation.

Based on the above variables, the floating point coprocessor puts different elements together and represents each operation differently using different formulas.

For example, for a division operation, the formula would be (-1)^s * 2^e * m.

**Why is the Floating Point Coprocessor Important?**

The floating point coprocessor is important because it will offer a much better and faster means to perform several calculations involving non-integer numbers.

It will also offer the flexibility to handle any mathematical operation such as addition, subtraction, multiplication, or division either by itself or by the integer processing unit.

**Conclusion**

The math coprocessor is a small but an integral part of the computing system that handles all the calculations involving floating point numbers.

It is typically employed through hardware but all computer systems may not have it implemented due to several reasons such as power, space and price.