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363 lines
10 KiB
363 lines
10 KiB
/*
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* CS:APP Data Lab
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*
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* <GentleCold>
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*
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* bits.c - Source file with your solutions to the Lab.
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* This is the file you will hand in to your instructor.
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*
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* WARNING: Do not include the <stdio.h> header; it confuses the dlc
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* compiler. You can still use printf for debugging without including
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* <stdio.h>, although you might get a compiler warning. In general,
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* it's not good practice to ignore compiler warnings, but in this
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* case it's OK.
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*/
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#if 0
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/*
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* Instructions to Students:
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*
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* STEP 1: Read the following instructions carefully.
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*/
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You will provide your solution to the Data Lab by
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editing the collection of functions in this source file.
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INTEGER CODING RULES:
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Replace the "return" statement in each function with one
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or more lines of C code that implements the function. Your code
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must conform to the following style:
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int Funct(arg1, arg2, ...) {
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/* brief description of how your implementation works */
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int var1 = Expr1;
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...
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int varM = ExprM;
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varJ = ExprJ;
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...
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varN = ExprN;
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return ExprR;
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}
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Each "Expr" is an expression using ONLY the following:
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1. Integer constants 0 through 255 (0xFF), inclusive. You are
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not allowed to use big constants such as 0xffffffff.
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2. Function arguments and local variables (no global variables).
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3. Unary integer operations ! ~
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4. Binary integer operations & ^ | + << >>
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Some of the problems restrict the set of allowed operators even further.
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Each "Expr" may consist of multiple operators. You are not restricted to
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one operator per line.
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You are expressly forbidden to:
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1. Use any control constructs such as if, do, while, for, switch, etc.
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2. Define or use any macros.
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3. Define any additional functions in this file.
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4. Call any functions.
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5. Use any other operations, such as &&, ||, -, or ?:
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6. Use any form of casting.
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7. Use any data type other than int. This implies that you
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cannot use arrays, structs, or unions.
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You may assume that your machine:
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1. Uses 2s complement, 32-bit representations of integers.
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2. Performs right shifts arithmetically.
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3. Has unpredictable behavior when shifting if the shift amount
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is less than 0 or greater than 31.
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EXAMPLES OF ACCEPTABLE CODING STYLE:
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/*
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* pow2plus1 - returns 2^x + 1, where 0 <= x <= 31
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*/
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int pow2plus1(int x) {
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/* exploit ability of shifts to compute powers of 2 */
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return (1 << x) + 1;
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}
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/*
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* pow2plus4 - returns 2^x + 4, where 0 <= x <= 31
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*/
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int pow2plus4(int x) {
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/* exploit ability of shifts to compute powers of 2 */
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int result = (1 << x);
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result += 4;
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return result;
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}
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FLOATING POINT CODING RULES
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For the problems that require you to implement floating-point operations,
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the coding rules are less strict. You are allowed to use looping and
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conditional control. You are allowed to use both ints and unsigneds.
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You can use arbitrary integer and unsigned constants. You can use any arithmetic,
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logical, or comparison operations on int or unsigned data.
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You are expressly forbidden to:
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1. Define or use any macros.
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2. Define any additional functions in this file.
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3. Call any functions.
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4. Use any form of casting.
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5. Use any data type other than int or unsigned. This means that you
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cannot use arrays, structs, or unions.
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6. Use any floating point data types, operations, or constants.
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NOTES:
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1. Use the dlc (data lab checker) compiler (described in the handout) to
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check the legality of your solutions.
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2. Each function has a maximum number of operations (integer, logical,
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or comparison) that you are allowed to use for your implementation
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of the function. The max operator count is checked by dlc.
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Note that assignment ('=') is not counted; you may use as many of
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these as you want without penalty.
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3. Use the btest test harness to check your functions for correctness.
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4. Use the BDD checker to formally verify your functions
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5. The maximum number of ops for each function is given in the
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header comment for each function. If there are any inconsistencies
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between the maximum ops in the writeup and in this file, consider
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this file the authoritative source.
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/*
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* STEP 2: Modify the following functions according the coding rules.
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*
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* IMPORTANT. TO AVOID GRADING SURPRISES:
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* 1. Use the dlc compiler to check that your solutions conform
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* to the coding rules.
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* 2. Use the BDD checker to formally verify that your solutions produce
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* the correct answers.
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*/
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#endif
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//1
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/*
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* bitXor - x^y using only ~ and &
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* Example: bitXor(4, 5) = 1
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* Legal ops: ~ &
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* Max ops: 14
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* Rating: 1
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*/
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int bitXor(int x, int y) {
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// make 0 ^ 1 to 1 & 1 and 0 & 1 equal to 1 0
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// make 0 ^ 0 to 1 & 0 and 0 & 1 equal to 0 0
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// make 1 0 to ~(0 & 1) equal to 1
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// make 0 0 to ~(1 & 1) equal to 0
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return ~(~(~x & y) & ~(x & ~y));
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}
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/*
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* tmin - return minimum two's complement integer
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 4
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* Rating: 1
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*/
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int tmin(void) {
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return 1 << 31;
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}
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//2
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/*
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* isTmax - returns 1 if x is the maximum, two's complement number,
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* and 0 otherwise
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* Legal ops: ! ~ & ^ | +
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* Max ops: 10
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* Rating: 1
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*/
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int isTmax(int x) {
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x += 1;
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return !!(!!x & !((~x + 1) ^ x)); // attention to zero case
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}
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/*
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* allOddBits - return 1 if all odd-numbered bits in word set to 1
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* where bits are numbered from 0 (least significant) to 31 (most significant)
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* Examples allOddBits(0xFFFFFFFD) = 0, allOddBits(0xAAAAAAAA) = 1
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 12
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* Rating: 2
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*/
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int allOddBits(int x) {
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// 0101 is stored as 1010
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int mask = 0xAA + (0xAA << 8) + (0xAA << 16) + (0xAA << 24);
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return !((mask & x) ^ mask);
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}
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/*
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* negate - return -x
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* Example: negate(1) = -1.
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 5
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* Rating: 2
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*/
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int negate(int x) {
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return ~x + 1;
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}
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//3
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/*
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* isAsciiDigit - return 1 if 0x30 <= x <= 0x39 (ASCII codes for characters '0' to '9')
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* Example: isAsciiDigit(0x35) = 1.
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* isAsciiDigit(0x3a) = 0.
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* isAsciiDigit(0x05) = 0.
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 15
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* Rating: 3
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*/
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int isAsciiDigit(int x) {
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int i = !((1 << 31) & ((~0x30 + 1) + x));
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int j = !!((1 << 31) & ((~0x39) + x));
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return i & j;
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}
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/*
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* conditional - same as x ? y : z
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* Example: conditional(2,4,5) = 4
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 16
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* Rating: 3
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*/
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int conditional(int x, int y, int z) {
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int mask = ~(!x) + 1;
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y &= ~mask;
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z &= mask;
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return y + z;
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}
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/*
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* isLessOrEqual - if x <= y then return 1, else return 0
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* Example: isLessOrEqual(4,5) = 1.
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 24
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* Rating: 3
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*/
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int isLessOrEqual(int x, int y) {
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// judge if positive or negative
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int i = x >> 31 & 1;
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int j = y >> 31 & 1;
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// three cases
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return !(!i & j) & ((i ^ j) | !(((~x + 1) + y) & (1 << 31)));
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}
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//4
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/*
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* logicalNeg - implement the ! operator, using all of
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* the legal operators except !
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* Examples: logicalNeg(3) = 0, logicalNeg(0) = 1
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* Legal ops: ~ & ^ | + << >>
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* Max ops: 12
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* Rating: 4
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*/
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int logicalNeg(int x) {
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int i = (x >> 31) & 1;
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int j = ((~x + 1) >> 31) & 1;
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return ~(i | j) + 2;
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}
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/* howManyBits - return the minimum number of bits required to represent x in
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* two's complement
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* Examples: howManyBits(12) = 5
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* howManyBits(298) = 10
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* howManyBits(-5) = 4
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* howManyBits(0) = 1
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* howManyBits(-1) = 1
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* howManyBits(0x80000000) = 32
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* Legal ops: ! ~ & ^ | + << >>
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* Max ops: 90
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* Rating: 4
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*/
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int howManyBits(int x) {
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// TODO reference from https://zhuanlan.zhihu.com/p/59534845
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int s = x >> 31, a1, a2, a3, a4, a5; // c99
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x = ((~s) & x) + (s & (~x));
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a1 = !!(x >> 16) << 4;
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x >>= a1;
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a2 = !!(x >> 8) << 3;
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x >>= a2;
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a3 = !!(x >> 4) << 2;
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x >>= a3;
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a4 = !!(x >> 2) << 1;
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x >>= a4;
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a5 = !!(x >> 1);
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x >>= a5;
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return a1 + a2 + a3 + a4 + a5 + x + 1;
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}
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//float
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/*
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* floatScale2 - Return bit-level equivalent of expression 2*f for
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* floating point argument f.
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* Both the argument and result are passed as unsigned int's, but
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* they are to be interpreted as the bit-level representation of
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* single-precision floating point values.
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* When argument is NaN, return argument
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* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
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* Max ops: 30
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* Rating: 4
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*/
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unsigned floatScale2(unsigned uf) {
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int s = (uf >> 31) & 1;
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int e = ((uf >> 23) & 0x000000FF);
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int f = uf & 0x007FFFFF;
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if (e == 0) {
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if (f == 0) return uf; // 0.0 * 2
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return s << 31 | f << 1; // still non-formatted
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}
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e += 1; // formatted
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if ((e == 0x000000FF && f != 0) || e > 0x000000FF) return uf; // nan
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return (s << 31) | (e << 23) | f;
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}
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/*
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* floatFloat2Int - Return bit-level equivalent of expression (int) f
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* for floating point argument f.
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* Argument is passed as unsigned int, but
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* it is to be interpreted as the bit-level representation of a
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* single-precision floating point value.
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* Anything out of range (including NaN and infinity) should return
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* 0x80000000u.
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* Legal ops: Any integer/unsigned operations incl. ||, &&. also if, while
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* Max ops: 30
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* Rating: 4
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*/
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int floatFloat2Int(unsigned uf) {
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unsigned s = (uf >> 31) & 1;
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unsigned e = ((uf >> 23) & 0x000000FF);
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unsigned f = uf & 0x007FFFFF;
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if (e < 0x7F) return 0;
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if (e > 0x7F + 31) return 0x80000000u; // nan
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e -= 0x7F;
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if (s)
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return ~((((f << e) & (~0x007FFFFF)) >> 23) + (1 << e)) + 1;
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else
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return ((((f << e) & (~0x007FFFFF)) >> 23) + (1 << e));
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}
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/*
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* floatPower2 - Return bit-level equivalent of the expression 2.0^x
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* (2.0 raised to the power x) for any 32-bit integer x.
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*
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* The unsigned value that is returned should have the identical bit
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* representation as the single-precision floating-point number 2.0^x.
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* If the result is too small to be represented as a denorm, return
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* 0. If too large, return +INF.
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*
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* Legal ops: Any integer/unsigned operations incl. ||, &&. Also if, while
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* Max ops: 30
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* Rating: 4
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*/
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unsigned floatPower2(int x) {
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unsigned s = 0;
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unsigned e = 0x7F;
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unsigned f = 0;
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if (x >= 0x80) return 0x7F800000; // nan
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if (x < 0) {
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if (x == 0x80000000) return 0;
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x = ~x + 1;
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if (x >= 0x7F) return 0;
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e -= x;
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} else {
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e += x;
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}
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return (s << 31) | (e << 23) | f;
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}
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