有关fixed point number和floating point number的问题
fixed point number:存贮是按下图所示：
|8 7 6 5 4 3 2 1|
|X8 X9 X10 X11 X12 |第一字节
|S X1 X2 X3 X4 X5 X6 X7|第二字节
其中S为符号位，X1...X12表示2的负1次方到负12次方，剩余几位是别的用途。这样表示数的范围是-1 ... 1-（2的负12次方）,当符号位为1表示负数，此时如果X1到X13都为零，那么表示数是-1。
我现在的问题是，如果写一个函数来把这两个字节中的数转化为float型数直接可以用。或者给你一个float型的数，写一个函数把它存储到两个字节的空间去，我花了不少时间仍想不出一种比较简便快捷的方法，如果有人能给出一个比较完美的算法，我不会吝啬分数的。呵呵，多谢了！
按照上面所说的方式存放到一个字节数组里去，在数组里面占连续的两个元素。还有就是一个相反的过程。
nSign = (short)uFixed > 0; 写错了，应该是 nSign = (short)uFixed < 0; 重贴一下：
分别用位域和移位来实现，这样写是为了让你看清楚float的构成，还提供了最简单的方法
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#include "stdafx.h"
#include <stdio.h>
#include <assert.h>
#include <math.h>
typedef struct
{
unsigned short uSpare : 3; // 为了对齐
unsigned short uSignificand : 12;
short nSign : 1;
}FIXED_BIT;
typedef union
{
unsigned short uFixed;
FIXED_BIT tFixedBit;
}FIXED;
typedef struct
{
unsigned int uSignificand : 23;
int nExponent : 8;
int nSign : 1;
}FLOAT_BIT;
typedef union
{
float fFloat;
FLOAT_BIT tFloatBit;
unsigned int uFloat;
}FLOAT;
unsigned short FloatToFixed( float fFloat ); // 部分用位域实现
float FixedToFloat( unsigned short uFixed ); // 部分用位域实现
unsigned short FloatToFixedEx( float fFloat ); // 全部用移位实现
float FixedToFloatEx( unsigned short uFixed ); // 全部用移位实现
unsigned short FloatToFixedSimple( float fFloat ); // 最简单实现
float FixedToFloatSimple( unsigned short uFixed ); // 最简单实现
int main()
{
float x = (float)-0.175;
unsigned short y;
printf( "x = %f\n",x );
y = FloatToFixed( x );
printf( "fixed = 0x%x\n",y );
printf( "float = %f\n",FixedToFloat(y) );
y = FloatToFixedEx( x );
printf( "fixed = 0x%x\n",y );
printf( "float = %f\n",FixedToFloatEx(y) );
y = FloatToFixedSimple( x );
printf( "fixed = 0x%x\n",y );
printf( "float = %f\n",FixedToFloatSimple(y) );
return 0;
}
unsigned short FloatToFixed( float fFloat )
{
FLOAT unFloat;
FIXED unFixed;
int nExponent;
unFloat.fFloat = fFloat;
nExponent = (int)unFloat.tFloatBit.nExponent - 0x7f;
// float的significand表示1~2之间的数，expoent=0x7f表示指数0
// 不太清楚你对溢出有什么要求
// 指数是否溢出
assert( (nExponent >= -12) && (nExponent <= 0) );
unFixed.tFixedBit.uSpare = 0;
unFixed.tFixedBit.nSign = unFloat.tFloatBit.nSign;
unFixed.tFixedBit.uSignificand = ((int)unFloat.tFloatBit.uSignificand + 0x800000)
>> (11 - nExponent);
return unFixed.uFixed;
}
float FixedToFloat( unsigned short uFixed )
{
FLOAT unFloat;
FIXED unFixed;
unsigned int uSignificand;
unFixed.uFixed = uFixed;
uSignificand = unFixed.tFixedBit.uSignificand << 11;
unFloat.tFloatBit.nExponent = 0x7f;
while( (uSignificand & 0x800000)==0 )
{
uSignificand <<= 1;
unFloat.tFloatBit.nExponent--;
}
uSignificand -= 0x800000;
unFloat.tFloatBit.uSignificand = uSignificand;
unFloat.tFloatBit.nSign = unFixed.tFixedBit.nSign;
return unFloat.fFloat;
}
unsigned short FloatToFixedEx( float fFloat )
{
FLOAT unFloat;
unsigned int uFloat;
int nSign;
int nExponent;
int nSignificand;
unFloat.fFloat = fFloat;
uFloat = unFloat.uFloat;
nSign = (int)uFloat < 0;
nExponent = ((uFloat & 0x7fffffff) >> 23) - 0x7f;
nSignificand = (uFloat & 0x7fffff) + 0x800000;
// float的significand表示1~2之间的数，expoent=0x7f表示指数0
// 不太清楚你对溢出有什么要求
// 指数是否溢出
assert( (nExponent >= -12) && (nExponent <= 0) );
nSignificand >>= (8 - nExponent);
nSignificand &= 0xfffff8; // 清除低3位
if( nSign==0 )
{
return (unsigned short)nSignificand;
}
else
{
return (unsigned short)nSignificand | 0x8000;
}
//return (unsigned short)( (nSign << 15) | nSignificand );
}
float FixedToFloatEx( unsigned short uFixed )
{
FLOAT unFloat;
int nSign;
int nExponent;
int nSignificand;
nSign = (short)uFixed < 0;
nExponent = 0x7f;
nSignificand = (uFixed & 0x7fff) << 8;
while( (nSignificand & 0x800000)==0 )
{
nSignificand <<= 1;
nExponent--;
}
nSignificand -= 0x800000;
unFloat.uFloat = (nSign << 31) | (nExponent << 23) | nSignificand;
return unFloat.fFloat;
}
unsigned short FloatToFixedSimple( float fFloat )
{
int nSign = fFloat<0.0;
int nSignificand;
if( nSign==0 )
{
nSignificand = (int)(fFloat * 4096);
assert( nSignificand<4096 );
return (unsigned short)(nSignificand << 3);
}
else
{
nSignificand = (int)(-fFloat * 4096);
assert( nSignificand<4096 );
return (unsigned short)(nSignificand << 3) | 0x8000;
}
}
float FixedToFloatSimple( unsigned short uFixed )
{
int nSign;
int nSignificand;
nSign = (short)uFixed < 0;
nSignificand = ( (int)uFixed & 0x7fff) >> 3;
if( nSign==0 )
{
return (float)(nSignificand/4096.0);
}
else
{
return -(float)(nSignificand/4096.0);
}
}
运行结果：
x = -0.175000
fixed = 0x9660
float = -0.174805
fixed = 0x9660
float = -0.174805
fixed = 0x9660
float = -0.174805
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