/* * CS:APP Data Lab * * <Please put your name and userid here> * * bits.c - Sou
ID: 3751788 • Letter: #
Question
/*
* CS:APP Data Lab
*
* <Please put your name and userid here>
*
* bits.c - Source file with your solutions to the Lab.
* This is the file you will hand in to your instructor.
*
* WARNING: Do not include the <stdio.h> header; it confuses the dlc
* compiler. You can still use printf for debugging without including
* <stdio.h>, although you might get a compiler warning. In general,
* it's not good practice to ignore compiler warnings, but in this
* case it's OK.
*/
#if 0
/*
* Instructions to Students:
*
* STEP 1: Read the following instructions carefully.
*/
You will provide your solution to the Data Lab by
editing the collection of functions in this source file.
INTEGER CODING RULES:
Replace the "return" statement in each function with one
or more lines of C code that implements the function. Your code
must conform to the following style:
int Funct(arg1, arg2, ...) {
/* brief description of how your implementation works */
int var1 = Expr1;
...
int varM = ExprM;
varJ = ExprJ;
...
varN = ExprN;
return ExprR;
}
Each "Expr" is an expression using ONLY the following:
1. Integer constants 0 through 255 (0xFF), inclusive. You are
not allowed to use big constants such as 0xffffffff.
2. Function arguments and local variables (no global variables).
3. Unary integer operations ! ~
4. Binary integer operations & ^ | + << >>
Some of the problems restrict the set of allowed operators even further.
Each "Expr" may consist of multiple operators. You are not restricted to
one operator per line.
You are expressly forbidden to:
1. Use any control constructs such as if, do, while, for, switch, etc.
2. Define or use any macros.
3. Define any additional functions in this file.
4. Call any functions.
5. Use any other operations, such as &&, ||, -, or ?:
6. Use any form of casting.
7. Use any data type other than int. This implies that you
cannot use arrays, structs, or unions.
You may assume that your machine:
1. Uses 2s complement, 32-bit representations of integers.
2. Performs right shifts arithmetically.
3. Has unpredictable behavior when shifting an integer by more
than the word size.
EXAMPLES OF ACCEPTABLE CODING STYLE:
/*
* pow2plus1 - returns 2^x + 1, where 0 <= x <= 31
*/
int pow2plus1(int x) {
/* exploit ability of shifts to compute powers of 2 */
return (1 << x) + 1;
}
/*
* pow2plus4 - returns 2^x + 4, where 0 <= x <= 31
*/
int pow2plus4(int x) {
/* exploit ability of shifts to compute powers of 2 */
int result = (1 << x);
result += 4;
return result;
}
FLOATING POINT CODING RULES
For the problems that require you to implent floating-point operations,
the coding rules are less strict. You are allowed to use looping and
conditional control. You are allowed to use both ints and unsigneds.
You can use arbitrary integer and unsigned constants.
You are expressly forbidden to:
1. Define or use any macros.
2. Define any additional functions in this file.
3. Call any functions.
4. Use any form of casting.
5. Use any data type other than int or unsigned. This means that you
cannot use arrays, structs, or unions.
6. Use any floating point data types, operations, or constants.
NOTES:
1. Use the dlc (data lab checker) compiler (described in the handout) to
check the legality of your solutions.
2. Each function has a maximum number of operators (! ~ & ^ | + << >>)
that you are allowed to use for your implementation of the function.
The max operator count is checked by dlc. Note that '=' is not
counted; you may use as many of these as you want without penalty.
3. Use the btest test harness to check your functions for correctness.
4. Use the BDD checker to formally verify your functions
5. The maximum number of ops for each function is given in the
header comment for each function. If there are any inconsistencies
between the maximum ops in the writeup and in this file, consider
this file the authoritative source.
/*
* STEP 2: Modify the following functions according the coding rules.
*
* IMPORTANT. TO AVOID GRADING SURPRISES:
* 1. Use the dlc compiler to check that your solutions conform
* to the coding rules.
* 2. Use the BDD checker to formally verify that your solutions produce
* the correct answers.
*/
#endif
/*
* bitAnd - x&y using only ~ and |
* Example: bitAnd(6, 5) = 4
* Legal ops: ~ |
* Max ops: 8
* Rating: 1
*/
int bitAnd(int x, int y) {
return 2;
}
/*
* allEvenBits - return 1 if all even-numbered bits in word set to 1
* Examples allEvenBits(0xFFFFFFFE) = 0, allEvenBits(0x55555555) = 1
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 12
* Rating: 2
*/
int allEvenBits(int x) {
return 2;
}
/*
* bitMask - Generate a mask consisting of all 1's
* lowbit and highbit
* Examples: bitMask(5,3) = 0x38
* Assume 0 <= lowbit <= 31, and 0 <= highbit <= 31
* If lowbit > highbit, then mask should be all 0's
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 16
* Rating: 3
*/
int bitMask(int highbit, int lowbit) {
return 2;
}
/*
* replaceByte(x,n,c) - Replace byte n in x with c
* Bytes numbered from 0 (LSB) to 3 (MSB)
* Examples: replaceByte(0x12345678,1,0xab) = 0x1234ab78
* You can assume 0 <= n <= 3 and 0 <= c <= 255
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 10
* Rating: 3
*/
int replaceByte(int x, int n, int c) {
return 2;
}
/*
* bitParity - returns 1 if x contains an odd number of 0's
* Examples: bitParity(5) = 0, bitParity(7) = 1
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 4
*/
int bitParity(int x) {
return 2;
}
/*
* tmin - return minimum two's complement integer
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 4
* Rating: 1
*/
int tmin(void) {
return 2;
}
/*
* isNegative - return 1 if x < 0, return 0 otherwise
* Example: isNegative(-1) = 1.
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 6
* Rating: 2
*/
int isNegative(int x) {
return 2;
}
/*
* addOK - Determine if can compute x+y without overflow
* Example: addOK(0x80000000,0x80000000) = 0,
* addOK(0x80000000,0x70000000) = 1,
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 3
*/
int addOK(int x, int y) {
return 2;
}
/*
* absVal - absolute value of x
* Example: absVal(-1) = 1.
* You may assume -TMax <= x <= TMax
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 10
* Rating: 4
*/
int absVal(int x) {
return 2;
}
/*
* float_neg - Return bit-level equivalent of expression -f for
* floating point argument f.
* Both the argument and result are passed as unsigned int's, but
* they are to be interpreted as the bit-level representations of
* single-precision floating point values.
* When argument is NaN, return argument.
* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
* Max ops: 10
* Rating: 2
*/
unsigned float_neg(unsigned uf) {
return 2;
}
/*
* float_half - Return bit-level equivalent of expression 0.5*f for
* floating point argument f.
* Both the argument and result are passed as unsigned int's, but
* they are to be interpreted as the bit-level representation of
* single-precision floating point values.
* When argument is NaN, return argument
* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
* Max ops: 30
* Rating: 4
*/
unsigned float_half(unsigned uf) {
return 2;
}
Explanation / Answer
/*Please Upvote*/
/*
* CS:APP Data Lab
*
* <Please put your name and userid here>
*
* bits.c - Source file with your solutions to the Lab.
* This is the file you will hand in to your instructor.
*
* WARNING: Do not include the <stdio.h> header; it confuses the dlc
* compiler. You can still use printf for debugging without including
* <stdio.h>, although you might get a compiler warning. In general,
* it's not good practice to ignore compiler warnings, but in this
* case it's OK.
*/
#if 0
/*
* Instructions to Students:
*
* STEP 1: Read the following instructions carefully.
*/
You will provide your solution to the Data Lab by
editing the collection of functions in this source file.
INTEGER CODING RULES:
Replace the "return" statement in each function with one
or more lines of C code that implements the function. Your code
must conform to the following style:
int Funct(arg1, arg2, ...) {
/* brief description of how your implementation works */
int var1 = Expr1;
...
int varM = ExprM;
varJ = ExprJ;
...
varN = ExprN;
return ExprR;
}
Each "Expr" is an expression using ONLY the following:
1. Integer constants 0 through 255 (0xFF), inclusive. You are
not allowed to use big constants such as 0xffffffff.
2. Function arguments and local variables (no global variables).
3. Unary integer operations ! ~
4. Binary integer operations & ^ | + << >>
Some of the problems restrict the set of allowed operators even further.
Each "Expr" may consist of multiple operators. You are not restricted to
one operator per line.
You are expressly forbidden to:
1. Use any control constructs such as if, do, while, for, switch, etc.
2. Define or use any macros.
3. Define any additional functions in this file.
4. Call any functions.
5. Use any other operations, such as &&, ||, -, or ?:
6. Use any form of casting.
7. Use any data type other than int. This implies that you
cannot use arrays, structs, or unions.
You may assume that your machine:
1. Uses 2s complement, 32-bit representations of integers.
2. Performs right shifts arithmetically.
3. Has unpredictable behavior when shifting an integer by more
than the word size.
EXAMPLES OF ACCEPTABLE CODING STYLE:
/*
* pow2plus1 - returns 2^x + 1, where 0 <= x <= 31
*/
int pow2plus1(int x) {
/* exploit ability of shifts to compute powers of 2 */
return (1 << x) + 1;
}
/*
* pow2plus4 - returns 2^x + 4, where 0 <= x <= 31
*/
int pow2plus4(int x) {
/* exploit ability of shifts to compute powers of 2 */
int result = (1 << x);
result += 4;
return result;
}
FLOATING POINT CODING RULES
For the problems that require you to implent floating-point operations,
the coding rules are less strict. You are allowed to use looping and
conditional control. You are allowed to use both ints and unsigneds.
You can use arbitrary integer and unsigned constants.
You are expressly forbidden to:
1. Define or use any macros.
2. Define any additional functions in this file.
3. Call any functions.
4. Use any form of casting.
5. Use any data type other than int or unsigned. This means that you
cannot use arrays, structs, or unions.
6. Use any floating point data types, operations, or constants.
NOTES:
1. Use the dlc (data lab checker) compiler (described in the handout) to
check the legality of your solutions.
2. Each function has a maximum number of operators (! ~ & ^ | + << >>)
that you are allowed to use for your implementation of the function.
The max operator count is checked by dlc. Note that '=' is not
counted; you may use as many of these as you want without penalty.
3. Use the btest test harness to check your functions for correctness.
4. Use the BDD checker to formally verify your functions
5. The maximum number of ops for each function is given in the
header comment for each function. If there are any inconsistencies
between the maximum ops in the writeup and in this file, consider
this file the authoritative source.
/*
* STEP 2: Modify the following functions according the coding rules.
*
* IMPORTANT. TO AVOID GRADING SURPRISES:
* 1. Use the dlc compiler to check that your solutions conform
* to the coding rules.
* 2. Use the BDD checker to formally verify that your solutions produce
* the correct answers.
*/
#endif
/*
* bitAnd - x&y using only ~ and |
* Example: bitAnd(6, 5) = 4
* Legal ops: ~ |
* Max ops: 8
* Rating: 1
*/
int bitAnd(int x, int y) {
/* docs */
return ~(~x | ~y);
}
/*
* allEvenBits - return 1 if all even-numbered bits in word set to 1
* Examples allEvenBits(0xFFFFFFFE) = 0, allEvenBits(0x55555555) = 1
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 12
* Rating: 2
*/
int allEvenBits(int x)
{
int everyBit;
int allOdd = (0xAA << 8) | 0xAA;
allOdd = allOdd | (allOdd << 16); /*int with all odd bits set to 1*/
everyBit = allOdd | x;
everyBit = ~everyBit; /*all 0's if x had each even bit at 1*/
return !everyBit;
}
/*
* bitMask - Generate a mask consisting of all 1's
* lowbit and highbit
* Examples: bitMask(5,3) = 0x38
* Assume 0 <= lowbit <= 31, and 0 <= highbit <= 31
* If lowbit > highbit, then mask should be all 0's
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 16
* Rating: 3
*/
int bitMask(int highbit, int lowbit) {
return ((2 << highbit) + ~0) >> lowbit << lowbit;
}
/*
* replaceByte(x,n,c) - Replace byte n in x with c
* Bytes numbered from 0 (LSB) to 3 (MSB)
* Examples: replaceByte(0x12345678,1,0xab) = 0x1234ab78
* You can assume 0 <= n <= 3 and 0 <= c <= 255
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 10
* Rating: 3
*/
int replaceByte(int x, int n, int c) {
int mask, shift;
mask = 255; // byte-wide mask of 1s
shift = n << 3; // == n*2^3 == n * 8
mask = ~(mask << shift); // shift byte-wide mask, flip to get byte-wide mask of 0s
c = c << shift; // shift bits of c into nth byte
return (x & mask) | c; // apply mask to x, zeroing x's nth byte, replacing it with byte given by c
}
/*
* bitParity - returns 1 if x contains an odd number of 0's
* Examples: bitParity(5) = 0, bitParity(7) = 1
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 4
*/
int bitParity(int x) {
x ^= x >> 16;
x ^= x >> 8;
x ^= x >> 4;
x ^= x >> 2;
x ^= x >> 1;
return x & 0x01;
}
* tmin - return minimum two's complement integer
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 4
* Rating: 1
*/
int tmin(void)
{
return 1 << 31; /*shift the '1' bit to get 0x80000000*/
}
/*
* isNegative - return 1 if x < 0, return 0 otherwise
* Example: isNegative(-1) = 1.
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 6
* Rating: 2
*/
int isNonNegative(int x) {
x = x >> 31; /*only keep the sign bit*/
return (~x & 1);
}
/*
* addOK - Determine if can compute x+y without overflow
* Example: addOK(0x80000000,0x80000000) = 0,
* addOK(0x80000000,0x70000000) = 1,
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 3
*/
int addOK(int x, int y) {
int xMSB = (x >> 31) & 1; /*tracks the most significant bit of x */
int yMSB = (y >> 31) & 1; /*y's MSB*/
int totalMSB = ((x + y) >> 31) & 1; /*the MSB of the total */
return ((xMSB ^ yMSB) | !((xMSB & yMSB) ^ totalMSB));
/*either the xMSB and yMSB are different, or if they are the same they
must be the same as the totalMSB (otherwise there was overflow */
}
/*
* absVal - absolute value of x
* Example: absVal(-1) = 1.
* You may assume -TMax <= x <= TMax
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 10
* Rating: 4
*/
int absVal(int x) {
int mask, ret;
mask = x >> 31;
ret = x + mask;
ret = ret ^ mask;
return ret;
}
/*
* float_neg - Return bit-level equivalent of expression -f for
* floating point argument f.
* Both the argument and result are passed as unsigned int's, but
* they are to be interpreted as the bit-level representations of
* single-precision floating point values.
* When argument is NaN, return argument.
* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
* Max ops: 10
* Rating: 2
*/
unsigned float_neg(unsigned uf)
{
int nanCheck = 0x000000FF << 23; /*1's in the 8 exponent bits*/
int frac = 0x7FFFFF & uf; /*contains just the fraction value*/
/*return argument if exp bits are all 1's and frac is not zero*/
if((nanCheck & uf) == nanCheck && frac)
return uf;
/*otherwise, just flip the sign bit*/
return uf ^ (1 << 31);
}
/*
* float_half - Return bit-level equivalent of expression 0.5*f for
* floating point argument f.
* Both the argument and result are passed as unsigned int's, but
* they are to be interpreted as the bit-level representation of
* single-precision floating point values.
* When argument is NaN, return argument
* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
* Max ops: 30
* Rating: 4
*/
unsigned float_half(unsigned uf) {
int round, S, E, maskE, maskM, maskS,maskEM, maskSM, tmp;
round = !((uf&3)^3);
maskS = 0x80000000;
maskE = 0x7F800000;
maskM = 0x007FFFFF;
maskEM= 0x7FFFFFFF;
maskSM= 0x807FFFFF;
E = uf&maskE;
S = uf&maskS;
//Nan or Infinity
if (E==0x7F800000) return uf;
//E=1 - specialcase
if (E==0x00800000){
return S | (round + ((uf & maskEM)>>1)) ;
}
//E=0 - denormalized
if (E==0x00000000) {
tmp = (uf&maskM)>>1;
return S | (tmp + round);
}
//normalized case
return (((E>>23)-1)<<23) | (uf & maskSM);
}
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