Solved-Data Lab-: Floating Point Numbers -Solution

Description

• Introduction

The purpose of this assignment is to become more familiar with bit-level representations of floating point numbers. You’ll do this by solving a series of programming “puzzles.” Many of these puzzles are quite artificial, but you’ll find yourself thinking much more about bits in working your way through them.

• Logistics

This is an individual project. All handins are electronic. Clarifications and corrections will be posted on the course Web page.

• Handout Instructions

The only file you will be needing for this assignment is datalabFP-handout.tar file.

It is uploaded on lms under the assignments tab.

Start by copying datalabFP-handout.tar to a (protected) directory on a Linux machine in which you plan to do your work. Then give the command

unix> tar xvf datalabFP-handout.tar.

This will cause a number of files to be unpacked in the directory. The only file you will be modifying and turning in is bits.c.

The bits.c file contains a skeleton for each of the 4 Floating Point programming puzzles.

• The Puzzles

This section describes the puzzles that you will be solving in bits.c.

4.1 Floating-Point Operations

For this part of the assignment, you will implement some common single-precision floating-point opera-tions. In this section, you are allowed to use standard control structures (conditionals, loops), and you may use both int and unsigned data types, including arbitrary unsigned and integer constants. You may not use any unions, structs, or arrays. Most significantly, you may not use any floating point data types, operations, or constants. Instead, any floating-point operand will be passed to the function as having type unsigned, and any returned floating-point value will be of type unsigned. Your code should perform the bit manipulations that implement the specified floating point operations.

Table 1 describes a set of functions that operate on the bit-level representations of floating-point numbers.

Refer to the comments in bits.c and the reference versions in tests.c for more information.

Name	Description	Rating	Max Ops
float_f2i(x)	Compute (int) x	4	30
float_i2f(x)	Compute (float) x	4	30
float_neg(uf)	Compute -f	2	10
float_twice(uf)	Computer 2*f	4	30

Table 1: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.

Functions float_neg and float_twice must handle the full range of possible argument values, in-cluding not-a-number (NaN) and infinity. The IEEE standard does not specify precisely how to handle NaN’s, and the IA32 behavior is a bit obscure. We will follow a convention that for any function returning a NaN value, it will return the one with bit representation 0x7FC00000.

The included program fshow helps you understand the structure of floating point numbers. To compile fshow, switch to the handout directory and type:

unix> make

You can use fshow to see what an arbitrary pattern represents as a floating-point number:

unix> ./fshow 2080374784

Floating point value 2.658455992e+36

Bit Representation 0x7c000000, sign = 0, exponent = f8, fraction = 000000 Normalized. 1.0000000000 X 2ˆ(121)

You can also give fshow hexadecimal and floating point values, and it will decipher their bit structure.

• Evaluation

Your score will be computed out of a maximum of 14 points. The 4 puzzles you must solve have been given a difficulty rating between 1 and 4, such that their weighted sum totals to 14. We will evaluate your functions using the btest program, which is described in the next section. You will get full credit for a puzzle if it passes all of the tests performed by btest, and no credit otherwise.

Autograding your work

We have included some autograding tools in the handout directory — btest, dlc, and driver.pl — to help you check the correctness of your work.

btest: This program checks the functional correctness of the functions in bits.c. To build and use it, type the following two commands:

unix> make

unix> ./btest

Notice that you must rebuild btest each time you modify your bits.c file.

You’ll find it helpful to work through the functions one at a time, testing each one as you go. You can use the -f flag to instruct btest to test only a single function:

unix> ./btest -f float_i2f

Check the file README for documentation on running the btest program.

dlc: This is a modified version of an ANSI C compiler from the MIT CILK group that you can use to check for compliance with the coding rules for each puzzle. The typical usage is:

unix> ./dlc bits.c

The program runs silently unless it detects a problem, such as an illegal operator, too many operators, or non-straightline code in the integer puzzles. Running with the -e switch:

unix> ./dlc -e bits.c

causes dlc to print counts of the number of operators used by each function. Type ./dlc -help for a list of command line options.

driver.pl: This is a driver program that uses btest and dlc to compute the correctness and performance points for your solution. It takes no arguments:

unix> ./driver.pl

Your instructors will use driver.pl to evaluate your solution.

• Handin Instructions

Upload your assignments before the deadline on the lms tab. The only file you need to

submit is bits.c.

IMPORTANT:

The naming convention you must follow is s<roll-no>-bits.c for the file name. e.g., if your roll number is 21100180, the “bits.c” file you will be submitting should be renamed to “s21100180-bits.c” before submission. The submissions which don’t follow the naming conventions won’t be considered for grading.

• Advice

Don’t include the <stdio.h> header file in your bits.c file, as it confuses dlc and results in some non-intuitive error messages. You will still be able to use printf in your bits.c file for debugging without including the <stdio.h> header, although gcc will print a warning that you can ignore.

The dlc program enforces a stricter form of C declarations than is the case for C++ or that is enforced by gcc. In particular, any declaration must appear in a block (what you enclose in curly braces) before any statement that is not a declaration. For example, it will complain about the following code:

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