《CSAPP》（第3版）答案（第二章）（三）

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

$A bit$	$A value$	$B bit$	$B value$
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 <stdio.h>
#include <math.h>
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 <stdio.h>
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 <stdio.h>
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 <stdio.h>
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 <stdio.h>
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 <stdio.h>
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<bias+0)
        val = 0;
    else if(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 <stdio.h>
#include <limits.h>
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<<length))
        length++;
    return length;
}
unsigned bits_mask(int l){
    return (unsigned)-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){
            //lalala
        }else 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));
}

第二章 完