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title Data Lab

Resources

  • datalab.pdf
  • datalab-handout.tar
    1. Run tar xvf datalab-handout.tar to unpack the project.
    2. Modify bits.c to solve the puzzles.
    3. Run make to build the project.
      • Install gcc-multilib (once only) if fatal error: bits/libc-header-start.h: No such file or directory occurs.

Helpers

To make the working directory clean, it is recommended to add btest, fshow and ishow into a .gitignore file.

tests.c

tests.c expresses the correct behavior of your functions.

fshow, ishow

fshow (built from fshow.c) helps you understand the structure of floating point numbers.

btest

btest (built from btest.c) checks the functional correctness of the functions in bits.c.

./btest -f bitXor  # tests only a single function.

dlc

The executable dlc is an ANSI C compiler that you can use to check for compliance with the coding rules for each puzzle.

./dlc bits.c  # returns silently if there are no problems with your code.
./dlc -e bits.c  # prints the number of operators used by each function.

driver.pl

The Perl script driver.pl is a driver program that uses btest and dlc to compute the correctness and performance points for your solution.

## Grading:
./driver.pl
## Install required modules (once only):
apt install cpanminus  # if `cpan` is not found
cpan App::cpanminus  # recommended in CPAN docs
cpanm Getopt::Std  # redundant, use as a check

Hints

(x == y) ==   (!(x ^ y)) ;
(x != y) == (!(!(x ^ y)));
(-x) == (~x + 1);

bitXor

tmin

The minimum two's complement (32-bit) integer is

./ishow 0x80000000
Hex = 0x80000000,       Signed = -2147483648,   Unsigned = 2147483648

isTmax

The maximum two's complement (32-bit) integer is

./ishow 0x7FFFFFFF
Hex = 0x7fffffff,       Signed = 2147483647,    Unsigned = 2147483647

allOddBits

The binary representation of 0xAA is 10101010.

negate

x + y == 0 implies x + (y - 1) == 0xFFFFFFFF.

isAsciiDigit

  0x30 <= x && x <= 0x39
== (x & 0xFFFFFF00 == 0)
&& (x & 0xF0 == 0x30)
&& (x & 0xF + 6 < 16);

conditional

int x_is_0 = !x ;  /* x == 0 ? 0x00000001 : 0x00000000 */
x_is_0 = ~x_is_0;  /* x == 0 ? 0xFFFFFFFE : 0xFFFFFFFF */
x_is_0 += 1;       /* x == 0 ? 0xFFFFFFFF : 0x00000000 */

isLessOrEqual

  x <= y
== (x == 1 << 31)
|| (x < 0 && 0 <= y)
|| (!((x ^ y) & (1 << 31)) && 0 <= y - x)

logicalNeg

Compress all bits to the least significant one.

howManyBits

If x < 0, find the first 0. Else, find the first 0 in ~x.

floatScale2

If expotent == 0, a single operation fraction << 1 will handle both cases:

  • if the highest bit of fraction is 0, the last bit of expotent will still be 0.
  • if the highest bit of fraction is 1, it will naturally be the last bit of expotent.

floatFloat2Int

floatPower2

int x float(pow(2, x))
(INT_MIN, -149) 0
[-149, -127] 1 << (x + 149)
(-127, +127] (x + 127) << 23
[+128, INT_MAX) 0x7F800000