《CSAPP》（第3版）答案（第二章）（三）-白红宇

《CSAPP》（第3版）答案（第二章）（三）

阅读量：4170 次

发布时间：2019-05-26

本文共 5697 字，大约阅读时间需要 18 分钟。

P85

$V=2^{E}* M$

bias = 2^{k-1}-1

A
7=111.000…;
M=1.11;
f=0.11;
E=2;
V=7.0;

B
M=1.11…;
f=0.11…(n个1);
E=n;
V= $2^{n+1}-1$ ;

C
M=1.00…;
f=0.00…
E=bias-1;
V= $2^{bias-1}$

P86

description	binary	decimal
least positive unstandard	0 0000…(15) 0 000…(62)1	$2^{1-(2^{15-1}-1)-63}$
least positive standard	0 000…(14)1 1 000…(63)	$2^{1-(2^{15-1}-1)}$
bigest standard	0 111…(14)0 1 111…(63)	$2^{2^{15-1}-1 }* (2-2^{-63})$

P87

Desc	Hex	$M$	$E$	$V$	$D$
-0	0x8000	0	-14	-0	-0.0
>2 least	0x4001	$\frac{1025}{1024}$	1	$\frac{1025}{512}$	2.00195312
512	0x6000	1	9	512	512.0
bigest denormalized	0x03FF	$\frac{1023}{1024}$	-14	$\frac{1023}{2^{24}}$	6.09755516e-5
- $\infin$	0xFC00	-	-	- $\infin$	- $\infin$
ox3BB0	0x3BB0	$\frac{123}{64}$	-1	$\frac{123}{128}$	0.9609375

P88

$A b i t$	$A v a l u e$	$B b i t$	$B v a l u e$
1 01110 001	- $\frac{9}{16}$	1 0110 0010	- $\frac{9}{16}$
0 10110 101	$13*2^4$	0 1110 1010	$13*2^4$
1 00111 110	- $\frac{7}{2^{10}}$	1 0000 0111	- $\frac{7}{2^{10}}$
0 00000 101	$\frac{5}{2^{11}}$	0 0000 0001	$\frac{1}{2^{10}}$
1 11011 000	- $2^{12}$	1 1110 1111	- $31*2^3$
0 11000 100	$3*2^8$	0 1111 0000	+ $\infin$

P89

A
是

B
否，y=INT_MIN;

C
是

D
否，-1，-1，INT_MIN

E
否。z==0;

P90

#include 
   
    #include 
    
     float u2f(unsigned x) {
     return *(float*) &x;}float fpwr2(int x) {
     unsigned exp, frac;  unsigned u;  if (x < 2-pow(2,7)-23) {
       exp = 0;    frac = 0;  } else if (x < 2-pow(2,7)) {
       exp = 0;    frac = 1 << (unsigned)(x - (2-pow(2,7)-23));  } else if (x < pow(2,7)-1+1) {
       exp = pow(2,7)-1+x;    frac = 0;  } else {
       exp = 0xFF;    frac = 0;  }  u = exp << 23 | frac;  return u2f(u);}

P91

A
11.0010010000111111011011

B
11.001001(001循环)…

C
第9位

P92

#include 
   
    typedef unsigned float_bits;float_bits float_negate(float_bits f){
       unsigned sig = f>>31;    unsigned e = (f>>23)&0xff;    unsigned frac = f&0x7fffff;    unsigned res = (e<<23)|frac;    if(e==0xff&&frac)        res = f;    return res;}int main(){
       printf("%x\n",float_negate(114514));}

P93

#include 
   
    typedef unsigned float_bits;float_bits float_absval(float_bits f){
       unsigned sig = f>>31;    unsigned e = (f>>23)&0xff;    unsigned frac = f & 0x7FFFFF;  if ((e == 0xFF) && (frac != 0)) {
       return f;  }  return 0 << 31 | e << 23 | frac;}int main(){
       printf("%u\n",float_absval(-1919810));}

P94

#include 
   
    typedef unsigned float_bits;float_bits float_twice(float_bits f) {
     unsigned sig = f >> 31;  unsigned e = f >> 23 & 0xFF;  unsigned frac = f & 0x7FFFFF;  if (e == 0xFF) {
       return f;  }  if (e == 0) {
       frac <<= 1;  } else if (e == (0xFF - 1)) {
       e = 0xFF;    frac = 0;  } else {
       e += 1;  }  return sig << 31 | e << 23 | frac;}int main(){
       printf("%f\n",float_twice(0x11451419));}

P95

#include 
   
    typedef unsigned float_bits;float_bits float_half(float_bits f){
       unsigned sig = f>>31;    unsigned e = (f>>23)&0xff;    unsigned frac = f&0x7fffff;    unsigned tail = f&0x7ffffffff;    if(e==0xff)        return f;    int ass = (frac&0x3)==0x3;    if(e==0){
           frac=frac>>1;        frac=frac+ass;    }    else if(e==1){
           tail=tail>>1;        tail=tail+ass;        e=(tail>>23)&0xff;        frac=tail&0x7fffff;    }    else    {
           e=e-1;    }    return sig<<31|e<<23|frac;}int main(){
       printf("%f\n",float_half(114514.1919810));}

P96

#include 
   
    typedef unsigned float_bits;int float_f2i(float_bits f){
       unsigned sig = f>>31;    unsigned e = (f>>23)&0xff;    unsigned frac = f&0x7fffff;    unsigned bias = 0x7f;    int val;//num    unsigned E;    unsigned M;    if(e>=0&&e
    
     =31+bias)        val = 0x80000000;    else{
           E = e-bias;        M = frac|0x800000;        if(E>23){
               val = M<<(E-23);        }else{
               val = M>>(23-E);        }    }    if(sig)        return -val;    else        return val;}int main(){
       printf("%f\n",float_f2i(0xffaaffaa));}

P97

#include 
   
    #include 
    
     typedef unsigned float_bits;int bits_length(int i){
       if((i&INT_MIN)!=0)        return 32;    unsigned u = (unsigned)i;    int length = 0;    while(u>=(1<
     
      >(32-1);}float_bits float_i2f(int i){
       unsigned sig,exp,rest,frac,exp_sig,round_part;    unsigned bits,fbits;    unsigned bias = 0x7f;    if(i==0){
           sig=0;        exp=0;        frac=0;        return sig<<31|exp<<23|frac;    }    if(i==INT_MIN){
           sig=1;        exp=bias+31;        frac=0;        return sig<<31|exp<<23|frac;    }    sig=0;    if(i<0){
           sig=1;        i=-i;    }    bits=bits_length(i);    fbits=bits-1;    exp=bias+fbits;    rest=i&bits_mask(fbits);    if(fbits<=23){
           frac=rest<<(23-fbits);        exp_sig=exp<<23|frac;    }    else{
           int offset=fbits-23;        int round_mid=1<<(offset-1);        round_part=rest&bits_mask(offset);        frac=rest>>offset;        exp_sig=exp<<23|frac;        if(round_part
      
       round_mid){
               exp_sig=exp_sig+1;        }else{
               if((frac&0x1)==1){
                   exp_sig=exp_sig+1;            }        }    }    return sig<<31|exp_sig;}int main(){
       printf("%f\n",float_i2f(114.514));}