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| @ -1,140 +1,153 @@ | |||
| *********************** | |||
| The CS:APP Data Lab | |||
| Directions to Students | |||
| *********************** | |||
| 1. bitXor思路 | |||
| Your goal is to modify your copy of bits.c so that it passes all the | |||
| tests in btest without violating any of the coding guidelines. | |||
| 根据德摩根定律,A^B = (A&~B)|(~A&B) | |||
| 2. tmin思路 | |||
| ********* | |||
| 0. Files: | |||
| ********* | |||
| 最小的INT类即首位1，末31位全为0，故TMIN = 0x1<<31 | |||
| Makefile - Makes btest, fshow, and ishow | |||
| README - This file | |||
| bits.c - The file you will be modifying and handing in | |||
| bits.h - Header file | |||
| btest.c - The main btest program | |||
| btest.h - Used to build btest | |||
| decl.c - Used to build btest | |||
| tests.c - Used to build btest | |||
| tests-header.c- Used to build btest | |||
| dlc* - Rule checking compiler binary (data lab compiler) | |||
| driver.pl* - Driver program that uses btest and dlc to autograde bits.c | |||
| Driverhdrs.pm - Header file for optional "Beat the Prof" contest | |||
| fshow.c - Utility for examining floating-point representations | |||
| ishow.c - Utility for examining integer representations | |||
| 3. isTmax思路 | |||
| *********************************************************** | |||
| 1. Modifying bits.c and checking it for compliance with dlc | |||
| *********************************************************** | |||
| 设置掩码y = 0x7fffffff | |||
| 构造掩码方式为 y = (0x7f<<24)+(0xff<<16)+(0xff<<8)+0xff | |||
| x^y只有在x = Tmax时才为0，其余情况非0 | |||
| 取反返回即可 | |||
| IMPORTANT: Carefully read the instructions in the bits.c file before | |||
| you start. These give the coding rules that you will need to follow if | |||
| you want full credit. | |||
| 4. allOddBits思路 | |||
| Use the dlc compiler (./dlc) to automatically check your version of | |||
| bits.c for compliance with the coding guidelines: | |||
| 设置掩码y = 0xaaaaaaaa | |||
| 构造掩码方式为 y = (0xaa<<24)+(0xaa<<16)+(0xaa<<8)+0xaa | |||
| 由于只看奇数次幂 | |||
| 故得过滤掉偶数次幂,即x&y使得偶数次幂均为0，奇数次幂不变 | |||
| 随后 (x&y)^y即可 | |||
| 只有奇数次幂全为1才可输出为0，其余非0 | |||
| 取反返回即可 | |||
| unix> ./dlc bits.c | |||
| 5. negate思路 | |||
| dlc returns silently if there are no problems with your code. | |||
| Otherwise it prints messages that flag any problems. Running dlc with | |||
| the -e switch: | |||
| 补码规则 负数取反加一即可 | |||
| unix> ./dlc -e bits.c | |||
| causes dlc to print counts of the number of operators used by each function. | |||
| Once you have a legal solution, you can test it for correctness using | |||
| the ./btest program. | |||
| ********************* | |||
| 2. Testing with btest | |||
| ********************* | |||
| The Makefile in this directory compiles your version of bits.c with | |||
| additional code to create a program (or test harness) named btest. | |||
| To compile and run the btest program, type: | |||
| unix> make btest | |||
| unix> ./btest [optional cmd line args] | |||
| You will need to recompile btest each time you change your bits.c | |||
| program. When moving from one platform to another, you will want to | |||
| get rid of the old version of btest and generate a new one. Use the | |||
| commands: | |||
| unix> make clean | |||
| unix> make btest | |||
| Btest tests your code for correctness by running millions of test | |||
| cases on each function. It tests wide swaths around well known corner | |||
| cases such as Tmin and zero for integer puzzles, and zero, inf, and | |||
| the boundary between denormalized and normalized numbers for floating | |||
| point puzzles. When btest detects an error in one of your functions, | |||
| it prints out the test that failed, the incorrect result, and the | |||
| expected result, and then terminates the testing for that function. | |||
| Here are the command line options for btest: | |||
| unix> ./btest -h | |||
| Usage: ./btest [-hg] [-r <n>] [-f <name> [-1|-2|-3 <val>]*] [-T <time limit>] | |||
| -1 <val> Specify first function argument | |||
| -2 <val> Specify second function argument | |||
| -3 <val> Specify third function argument | |||
| -f <name> Test only the named function | |||
| -g Format output for autograding with no error messages | |||
| -h Print this message | |||
| -r <n> Give uniform weight of n for all problems | |||
| -T <lim> Set timeout limit to lim | |||
| Examples: | |||
| Test all functions for correctness and print out error messages: | |||
| unix> ./btest | |||
| Test all functions in a compact form with no error messages: | |||
| unix> ./btest -g | |||
| Test function foo for correctness: | |||
| unix> ./btest -f foo | |||
| Test function foo for correctness with specific arguments: | |||
| unix> ./btest -f foo -1 27 -2 0xf | |||
| Btest does not check your code for compliance with the coding | |||
| guidelines. Use dlc to do that. | |||
| ******************* | |||
| 3. Helper Programs | |||
| ******************* | |||
| We have included the ishow and fshow programs to help you decipher | |||
| integer and floating point representations respectively. Each takes a | |||
| single decimal or hex number as an argument. To build them type: | |||
| unix> make | |||
| Example usages: | |||
| unix> ./ishow 0x27 | |||
| Hex = 0x00000027, Signed = 39, Unsigned = 39 | |||
| unix> ./ishow 27 | |||
| Hex = 0x0000001b, Signed = 27, Unsigned = 27 | |||
| unix> ./fshow 0x15213243 | |||
| Floating point value 3.255334057e-26 | |||
| Bit Representation 0x15213243, sign = 0, exponent = 0x2a, fraction = 0x213243 | |||
| Normalized. +1.2593463659 X 2^(-85) | |||
| linux> ./fshow 15213243 | |||
| Floating point value 2.131829405e-38 | |||
| Bit Representation 0x00e822bb, sign = 0, exponent = 0x01, fraction = 0x6822bb | |||
| Normalized. +1.8135598898 X 2^(-126) | |||
| 6. isAsciiDigit思路 | |||
| 上界为0x39 下届为0x30 | |||
| 各取补码 | |||
| 将x各与其补码相加 | |||
| 结果符号位为0 表示x大于等于该界限 | |||
| 结果符号位为1 表示x小于该界限 | |||
| 故为了满足 0x30 <=x <=0x39 | |||
| 则上界调整为0x3a | |||
| 提取出符号位右移31位即可 | |||
| 满足结果为1，则{![(~down+1+x)>>31]}&[!!(~up+1+x)>>31] | |||
| 7. conditional思路 | |||
| x为非0输出y | |||
| x为0输出z | |||
| 则令x = !!x;x = ~x+1 | |||
| 当x为非0时，最终x全为1 | |||
| 当x为0时,最终x全为0 | |||
| 输出(x&y)|(~x&z)即可 | |||
| 8. isLessOrEqual思路 | |||
| 取y的补码 | |||
| x+(~y+1) | |||
| 此时x大于等于y,结果符号位为0 | |||
| x小于y，结果符号位为1 | |||
| 为了变成小于等于,式子改为x+(~y+1)-1 | |||
| 右移31位取反再取反返回即可 | |||
| 9. logicalNeg思路 | |||
| 利用0的补码仍然为0的特点 | |||
| x = x|(~x+1) | |||
| 显然对于0,最高位为0 | |||
| 对于非0，其最高位必定1(正数补码为负数，负数补码为正数，取并必定有1) | |||
| 右移31位提取最高位即可 | |||
| 为了让0输出1,非0输出0，再加1返回 | |||
| 10. howManyBits思路 | |||
| 运用二分查找的思想 | |||
| 为了方便查找,应让负数也变成符号位为0，即应取反 | |||
| x = ((~(x>>31))&x)|(x>>31&~x) 即可完成该操作，正数保持原样,负数取反 | |||
| 二分，查找有没有超过16位 | |||
| tf = !!(x>>16) 如果小于等于16位，则为0，否则为1 | |||
| 如果超过了，二分超过的16位，没超过，二分没超过的16位 | |||
| int b16 = tf << 4 长度超过16位，记录值b16为16，否则为0，代表至少16位 | |||
| x = x>>b16 右移动b16位，超过16位则探讨16位以上的，少于16位则探讨16位以下的 | |||
| b8 b4 b2 b1 同理 | |||
| 值得注意的是 | |||
| 当经过x = x>>b1操作后 | |||
| x只会剩下一个原表达式中的数字 | |||
| 应该令b0 = x,如果该数字为1，则b0为1，否则为0 | |||
| 最终位数结果为 b16+b8+b4+b2+b1+b0+1 正数多一位补码最高位，负数因为取反未+1，理应再加1，故两个输出表达式一致 | |||
| 11. floatScale2思路 | |||
| unsigned sign = (0x80<<24)&uf; | |||
| unsigned exp = ((0x7f<<24)+(0x80<<16))&uf; | |||
| unsigned frac = ((0x7f<<16)+(0xff<<8)+0xff)&uf; | |||
| 使用三个掩码分别提取出sign exp frac | |||
| 应注意非规格化数 | |||
| if(exp == ((0x7f<<24)+(0x80<<16))) | |||
| return uf; //如果是exp全为255,frac全是0就是无穷，不是就是NaN，都直接return | |||
| if(exp == 0x0){ | |||
| if(frac == 0x0) | |||
| return uf; //exp全为0,frac全为0，则为0，0*2=0，原样不动 | |||
| return (frac<<1)|sign|exp;//exp全为0,frac不全为0，注意到非规格化极小和规格化之间是连续的，即frac第一位为1时，左移会把exp变为非全0，回到规格化 | |||
| } | |||
| 剩下的情况就是规格化数 | |||
| 乘以2后exp应多加一，加完后按原来float数规则复原即可 | |||
| return (exp+(0x80<<16))|sign|frac; | |||
| 12. floatFloat2Int思路 | |||
| 使用三个掩码提取出各部分，为了方便计算，sign和exp复原到最简单的int | |||
| unsigned sign = ((0x80<<24)&uf)>>31; | |||
| unsigned exp = (((0x7f<<24)+(0x80<<16))&uf)>>23; | |||
| unsigned frac = ((0x7f<<16)+(0xff<<8)+0xff)&uf; | |||
| 同时再定义一个不满足题干要求时应输出的数值 | |||
| unsigned notpermit = 0x80 << 24; | |||
| 对于常规数，根据规则，应为1+frac代表的小数 | |||
| 复原至float的frac | |||
| unsigned base = (frac+(0x80<<16)) | |||
| 同时，2的幂是经过偏移后的，求出该幂，并应对后面base左移需求，额外再减23 | |||
| int bias = (exp-127)-23;//真实需要左移的 | |||
| 解析sign,让其在乘法时正确使用 | |||
| if(sign==0) | |||
| sign = 1; | |||
| else | |||
| sign = -1; | |||
| 排除非规格数 | |||
| if(exp == 255) | |||
| return notpermit;//足够大 | |||
| if(exp == 0) | |||
| return 0;//足够小 | |||
| 如果bias <= 0 则右移，否则左移 | |||
| base有效数字只有24位，故还应判断bias是否小于等于24 如果小于,显然已经偏移到足够小了，换成int一定会是0，故设置bias为恒定-24即可 | |||
| 如果bias >0 则左移 | |||
| 当bias>=9时，将超过int表达范围，此时返回规定的数即可 | |||
| 综上，为 | |||
| if(bias <=0){ | |||
| if(bias<=-24) | |||
| bias = -24; | |||
| return sign*(base>>(-bias)); | |||
| } | |||
| else{ | |||
| if(bias>=9) | |||
| return notpermit; | |||
| return sign*(base<<bias); | |||
| } | |||