自己动手写C语言浮点数转换字符串函数
前几天，应一个小友要求，写了几个字符串转换函数帮助其进行语言学习，自觉其中的几个函数还比较满意，故发布在此，可供初学者参考。
浮点数转换字符串函数说简单也简单，说麻烦，也够烦心的，关键看你如何写了。简单点的几十行代码就行，复杂点的恐怕就的几百行代码了。如果还要考虑移植性、可读性甚至可维护性等就更麻烦的了。我一贯认为，一些事务性的项目应着重考虑移植性、可读性和可维护性等，而常用的带点系统性质的函数代码就应该以执行效率为主。
本文的浮点数转换字符串函数还是比较复杂的，基本可算得上较低层次的转换。由于我已经习惯了用BCB写C/C++代码，因此我写的浮点数转换字符串函数是80位扩展精度浮点数的，但那个小友拿回去试了一下，说他用的VC不支持80位扩展精度浮点数，虽然能定义long double变量，但实际上还是64位的，我只好又重写了一个64位双精度浮点数的，2个版本使用条件编译，这也算得上是移植性吧，呵呵。
下面是浮点数转换字符串函数的全部代码：
#define USE_EXTENDED
/***************************************************************************
* 定义浮点数转换字符串结构 *
***************************************************************************/
typedef struct
{
SHORT exponent; /* 指数（整数位数） */
BYTE negative; /* 负数（0正，1负）*/
CHAR digits[21]; /* 十进制整数字串 */
}FloatRec;
#define F_DEFDECIMALS 6
#define F_MAXDECIMALS 100
#ifdef USE_EXTENDED
#define F_MAXPRECISION 19
#define F_CONEXPONENT 0x3fff
typedef long double EXTENDED, *PExtended, *PEXTENDED;
#include <pshpack2.h>
typedef struct
{
UINT64 mantissa;
USHORT exponent;
}_Extended;
#include <poppack.h>
static CONST _Extended _tab0[] =
{
{0x8000000000000000, 0x3FFF}, /* 10**0 */
{0xA000000000000000, 0x4002}, /* 10**1 */
{0xC800000000000000, 0x4005}, /* 10**2 */
{0xFA00000000000000, 0x4008}, /* 10**3 */
{0x9C40000000000000, 0x400C}, /* 10**4 */
{0xC350000000000000, 0x400F}, /* 10**5 */
{0xF424000000000000, 0x4012}, /* 10**6 */
{0x9896800000000000, 0x4016}, /* 10**7 */
{0xBEBC200000000000, 0x4019}, /* 10**8 */
{0xEE6B280000000000, 0x401C}, /* 10**9 */
{0x9502F90000000000, 0x4020}, /* 10**10 */
{0xBA43B74000000000, 0x4023}, /* 10**11 */
{0xE8D4A51000000000, 0x4026}, /* 10**12 */
{0x9184E72A00000000, 0x402A}, /* 10**13 */
{0xB5E620F480000000, 0x402D}, /* 10**14 */
{0xE35FA931A0000000, 0x4030}, /* 10**15 */
{0x8E1BC9BF04000000, 0x4034}, /* 10**16 */
{0xB1A2BC2EC5000000, 0x4037}, /* 10**17 */
{0xDE0B6B3A76400000, 0x403A}, /* 10**18 */
{0x8AC7230489E80000, 0x403E}, /* 10**19 */
{0xAD78EBC5AC620000, 0x4041}, /* 10**20 */
{0xD8D726B7177A8000, 0x4044}, /* 10**21 */
{0x878678326EAC9000, 0x4048}, /* 10**22 */
{0xA968163F0A57B400, 0x404B}, /* 10**23 */
{0xD3C21BCECCEDA100, 0x404E}, /* 10**24 */
{0x84595161401484A0, 0x4052}, /* 10**25 */
{0xA56FA5B99019A5C8, 0x4055}, /* 10**26 */
{0xCECB8F27F4200F3A, 0x4058}, /* 10**27 */
{0x813F3978F8940984, 0x405C}, /* 10**28 */
{0xA18F07D736B90BE5, 0x405F}, /* 10**29 */
{0xC9F2C9CD04674EDF, 0x4062}, /* 10**30 */
{0xFC6F7C4045812296, 0x4065} /* 10**31 */
};
static CONST _Extended _tab1[] =
{
{0x9DC5ADA82B70B59E, 0x4069}, /* 10**32 */
{0xC2781F49FFCFA6D5, 0x40D3}, /* 10**64 */
{0xEFB3AB16C59B14A3, 0x413D}, /* 10**96 */
{0x93BA47C980E98CE0, 0x41A8}, /* 10**128 */
{0xB616A12B7FE617AA, 0x4212}, /* 10**160 */
{0xE070F78D3927556B, 0x427C}, /* 10**192 */
{0x8A5296FFE33CC930, 0x42E7}, /* 10**224 */
{0xAA7EEBFB9DF9DE8E, 0x4351}, /* 10**256 */
{0xD226FC195C6A2F8C, 0x43BB}, /* 10**288 */
{0x81842F29F2CCE376, 0x4426}, /* 10**320 */
{0x9FA42700DB900AD2, 0x4490}, /* 10**352 */
{0xC4C5E310AEF8AA17, 0x44FA}, /* 10**384 */
{0xF28A9C07E9B09C59, 0x4564}, /* 10**416 */
{0x957A4AE1EBF7F3D4, 0x45CF}, /* 10**448 */
{0xB83ED8DC0795A262, 0x4639} /* 10**480 */
};
static CONST _Extended _tab2[] =
{
{0xE319A0AEA60E91C7, 0x46A3}, /* 10**512 */
{0xC976758681750C17, 0x4D48}, /* 10**1024 */
{0xB2B8353B3993A7E4, 0x53ED}, /* 10**1536 */
{0x9E8B3B5DC53D5DE5, 0x5A92}, /* 10**2048 */
{0x8CA554C020A1F0A6, 0x6137}, /* 10**2560 */
{0xF9895D25D88B5A8B, 0x67DB}, /* 10**3072 */
{0xDD5DC8A2BF27F3F8, 0x6E80}, /* 10**3584 */
{0xC46052028A20979B, 0x7525}, /* 10**4096 */
{0xAE3511626ED559F0, 0x7BCA} /* 10**4608 */
};
static CONST EXTENDED _conPrec = 1E19;
#else // USE_EXTENDED
#define F_MAXPRECISION 17
#define F_CONEXPONENT 0x03ff
typedef double EXTENDED, *PExtended, *PEXTENDED;
static CONST UINT64 _tab0[] =
{
{0x3FF0000000000000}, /* 10**0 */
{0x4024000000000000}, /* 10**1 */
{0x4059000000000000}, /* 10**2 */
{0x408F400000000000}, /* 10**3 */
{0x40C3880000000000}, /* 10**4 */
{0x40F86A0000000000}, /* 10**5 */
{0x412E848000000000}, /* 10**6 */
{0x416312D000000000}, /* 10**7 */
{0x4197D78400000000}, /* 10**8 */
{0x41CDCD6500000000}, /* 10**9 */
{0x4202A05F20000000}, /* 10**10 */
{0x42374876E8000000}, /* 10**11 */
{0x426D1A94A2000000}, /* 10**12 */
{0x42A2309CE5400000}, /* 10**13 */
{0x42D6BCC41E900000}, /* 10**14 */
{0x430C6BF526340000}, /* 10**15 */
{0x4341C37937E08000}, /* 10**16 */
{0x4376345785D8A000}, /* 10**17 */
{0x43ABC16D674EC800}, /* 10**18 */
{0x43E158E460913D00}, /* 10**19 */
{0x4415AF1D78B58C40}, /* 10**20 */
{0x444B1AE4D6E2EF50}, /* 10**21 */
{0x4480F0CF064DD592}, /* 10**22 */
{0x44B52D02C7E14AF7}, /* 10**23 */
{0x44EA784379D99DB4}, /* 10**24 */
{0x45208B2A2C280291}, /* 10**25 */
{0x4554ADF4B7320335}, /* 10**26 */
{0x4589D971E4FE8402}, /* 10**27 */
{0x45C027E72F1F1281}, /* 10**28 */
{0x45F431E0FAE6D722}, /* 10**29 */
{0x46293E5939A08CEA}, /* 10**30 */
{0x465F8DEF8808B024} /* 10**31 */
};
static CONST UINT64 _tab1[] =
{
{0x4693B8B5B5056E17}, /* 10**32 */
{0x4D384F03E93FF9F5}, /* 10**64 */
{0x53DDF67562D8B363}, /* 10**96 */
{0x5A827748F9301D32}, /* 10**128 */
{0x6126C2D4256FFCC3}, /* 10**160 */
{0x67CC0E1EF1A724EB}, /* 10**192 */
{0x6E714A52DFFC679A}, /* 10**224 */
{0x75154FDD7F73BF3C}, /* 10**256 */
{0x7BBA44DF832B8D46}, /* 10**288 */
};
static CONST EXTENDED _conPrec = 1E17;
#endif // !USE_EXTENDED
static CONST UINT64 _cvttab[F_MAXPRECISION] =
{
#ifdef USE_EXTENDED
0xDE0B6B3A7640000, 0x16345785D8A0000,
#endif
0x02386F26FC10000, 0x0038D7EA4C68000, 0x0005AF3107A4000, 0x00009184E72A000,
0x00000E8D4A51000, 0x00000174876E800, 0x0000002540BE400, 0x00000003B9ACA00,
0x000000005F5E100, 0x000000000989680, 0x0000000000F4240, 0x0000000000186A0,
0x000000000002710, 0x0000000000003E8, 0x000000000000064, 0x00000000000000A,
0x000000000000001
};
#define DECIMAL_EXP(exponent) ((((exponent - F_CONEXPONENT) * 0x4d10) >> 16) + 1)
static VOID AdjFloatDigits(UINT64 value, INT precision, INT decimals, FloatRec *rec)
{
INT i;
// value是F_MAXPRECISION位十进制整数，故从最高位开始转换为数字串
for (i = 0; value; i ++)
{
rec->digits[i] = (CHAR)((value / _cvttab[i]) | 0x30);
value %= _cvttab[i];
}
memset(rec->digits + i, 0, F_MAXPRECISION - i);
// 下面对数字串作精度处理
// 如果总的精度小于0，数字串为空串，该数字转换为'0'
if ((i = (rec->exponent + decimals)) < 0)
{
rec->exponent = rec->negative = rec->digits[0] = 0;
return;
}
if (i > precision) i = precision;
// 如果精度位数小于18，同时该位大于等于'5'，四舍五入
if (i < F_MAXPRECISION && rec->digits[i] >= '5')
{
do
{
rec->digits[i --] = 0;
rec->digits[i] ++;
}while (i >= 0 && rec->digits[i] > '9');
if (i < 0)
{
rec->digits[0] = '1';
rec->exponent ++;
}
}
// 否则，去掉数字串尾部多余的'0'
else
{
if (i > F_MAXPRECISION) i = F_MAXPRECISION;
do rec->digits[i --] = 0;
while (i >= 0 && rec->digits[i] == '0');
if (i < 0) rec->negative = 0;
}
}
#ifdef USE_EXTENDED
// 解析扩展精度浮点数为十进制字符串，并存入浮点数记录中
// 参数：浮点数指针，精度，小数位，浮点数记录
VOID FloatResolve(PEXTENDED pvalue, INT precision, INT decimals, FloatRec *rec)
{
INT power;
EXTENDED val;
// 79位：扩展精度浮点数符号位
rec->negative = ((_Extended*)pvalue)->exponent >> 15;
// 64-78位：扩展精度浮点数阶码(阶码 - 0x3fff = 二进制指数)
rec->exponent = ((_Extended*)pvalue)->exponent & 0x7fff;
if (!rec->exponent) // *pvalue = 0
{
rec->negative = rec->digits[0] = 0;
return;
}
if (rec->exponent == 0x7fff)// *pvalue = nan or inf
{
if (!((*(LPBYTE)pvalue + 7) & 0x80) || !(*(PUINT64)pvalue & 0x7fffffffffffffff))
{
lstrcpyA(rec->digits, "INF");
}
else
{
rec->exponent ++;
rec->negative = 0;
lstrcpyA(rec->digits, "NAN");
}
return;
}
// 阶码转换为十进制指数
rec->exponent = DECIMAL_EXP(rec->exponent);
// 0-63位：扩展精度浮点数尾数转换成F_MAXPRECISION位十进制浮点整数格式
val = *pvalue;
*((LPBYTE)&val + 9) &= 0x7f;// val = fabs(*pvalue)
power = F_MAXPRECISION - rec->exponent;
if (power > 0) // if (power > 0) val *= (10**power)
{
val *= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
{
if (power & 15)
val *= *(PEXTENDED)&_tab1[(power & 15) - 1];
power >>= 4; // power /= 16;
if (power)
val *= *(PEXTENDED)&_tab2[power - 1];
}
}
else if (power < 0) // if (power < 0) val /= (10**power)
{
power = -power;
val /= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
{
if (power & 15)
val /= *(PEXTENDED)&_tab1[(power & 15) - 1];
power >>= 4; // power /= 16;
if (power)
val /= *(PEXTENDED)&_tab2[power - 1];
}
}
val += 0.5; // 四舍五入
if (val >= _conPrec)
{
val /= 10;
rec->exponent ++;
}
// 调整并转换扩展精度浮点数尾数的整数部分rec->digits
AdjFloatDigits(*(PUINT64)&val >> ((((_Extended*)&val)->exponent - 0x3fff) ^ 0x3f),
precision, decimals, rec);
}
#else // USE_EXTENDED
// 解析双精度浮点数为十进制字符串，并存入浮点数记录中
// 参数：浮点数指针，精度，小数位，浮点数记录
VOID FloatResolve(PEXTENDED pvalue, INT precision, INT decimals, FloatRec *rec)
{
INT power;
EXTENDED val;
// 63位：双精度浮点数符号位
rec->negative = *((LPBYTE)pvalue + 7) >> 7;
// 52-62位：双精度浮点数阶码(阶码 - 0x3ff = 二进制指数)
rec->exponent = (*(PUINT64)pvalue >> 52) & 0x7ff;
if (!rec->exponent) // *pvalue = 0
{
rec->negative = rec->digits[0] = 0;
return;
}
if (rec->exponent == 0x7ff)// *pvalue = nan or inf
{
if ((*(PUINT64)pvalue & 0xfffffffffffff) == 0)
{
lstrcpyA(rec->digits, "INF");
}
else
{
rec->exponent ++;
rec->negative = 0;
lstrcpyA(rec->digits, "NAN");
}
return;
}
// 阶码转换为十进制指数
rec->exponent = DECIMAL_EXP(rec->exponent);
// 0-51位：双精度浮点数尾数转换成F_MAXPRECISION位十进制浮点整数格式
val = *pvalue;
*((LPBYTE)&val + 7) &= 0x7f;// val = fabs(*pvalue)
power = F_MAXPRECISION - rec->exponent;
if (power > 0) // if (power > 0) val *= (10**power)
{
val *= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
val *= *(PEXTENDED)&_tab1[power - 1];
}
else if (power < 0) // if (power < 0) val /= (10**power)
{
power = -power;
val /= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
val /= *(PEXTENDED)&_tab1[power - 1];
}
// 16位十进制浮点整数四舍五入
val += 0.5;
if (val >= _conPrec)
{
val /= 10;
rec->exponent ++;
}
// 调整并转换扩展精度浮点数尾数的整数部分rec->digits
// 清除52-63位，加隐藏的高位，F_MAXPRECISION=17，高位超过52位，所以左移
AdjFloatDigits(((*(PUINT64)&val & 0x000fffffffffffff) | 0x0010000000000000) <<
-(52 - ((*(PUINT64)&val >> 52) - 0x3ff)), precision, decimals, rec);
}
#endif // !USE_EXTENDED
// 输出指数字符串到buffer，返回指数字符串长度
INT PutExponent(LPSTR buffer, CONST FloatRec *rec)
{
LPSTR p = buffer;
INT e, exp = rec->digits[0]? rec->exponent - 1 : 0;
*p ++ = rec->negative & 0x80? 'E' : 'e';
if (exp < 0)
{
exp = -exp;
*p ++ = '-';
}
else *p ++ = '+';
if ((e = (exp / 1000)) != 0)
{
*p ++ = e + 0x30;
exp %= 1000;
}
*p ++ = exp / 100 + 0x30;
exp %= 100;
*(PUSHORT)p = (((exp % 10) << 8) | (exp / 10)) + 0x3030;
return (INT)(p - buffer + 2);
}
// 浮点数转换为字符串。参数：字符串，浮点数
LPSTR FloatToStr(LPSTR str, EXTENDED value)
{
INT exp;
FloatRec rec;
LPSTR pd = rec.digits;
LPSTR ps = str;
// 解析浮点数，并将信息保存在rec
FloatResolve(&value, 15, 9999, &rec);
// 打印负数符号
if (rec.negative) *ps ++ = '-';
// NAN or INF
if (*pd > '9')
{
memcpy(ps, pd, 4);
return str;
}
exp = rec.exponent;
// 如果十进制指数大于15或者小于-3，转换为指数形式
if (exp > 15 || exp < -3)
{
*ps ++ = *pd ++;
if (*pd)
for (*ps ++ = '.'; *pd; *ps ++ = *pd ++);
ps += PutExponent(ps, &rec);
*ps = 0;
return str;
}
// 否则，转换为小数形式
if (exp <= 0)
{
*ps ++ = '0';
if (*pd)
{
for (*ps ++ = '.'; exp < 0; *ps ++ = '0', exp ++);
while (*ps ++ = *pd ++);
}
else *ps = 0;
}
else
{
for (; exp > 0 && *pd; *ps ++ = *pd ++, exp --);
if (*pd)
{
*ps ++ = '.';
while (*ps ++ = *pd ++);
}
else
{
memset(ps, '0', exp);
ps[exp] = 0;
}
}
return str;
/***************************************************************************
* 定义浮点数转换字符串结构 *
***************************************************************************/
typedef struct
{
SHORT exponent; /* 指数（整数位数） */
BYTE negative; /* 负数（0正，1负）*/
CHAR digits[21]; /* 十进制整数字串 */
}FloatRec;
#define F_DEFDECIMALS 6
#define F_MAXDECIMALS 100
#ifdef USE_EXTENDED
#define F_MAXPRECISION 19
#define F_CONEXPONENT 0x3fff
typedef long double EXTENDED, *PExtended, *PEXTENDED;
#include <pshpack2.h>
typedef struct
{
UINT64 mantissa;
USHORT exponent;
}_Extended;
#include <poppack.h>
static CONST _Extended _tab0[] =
{
{0x8000000000000000, 0x3FFF}, /* 10**0 */
{0xA000000000000000, 0x4002}, /* 10**1 */
{0xC800000000000000, 0x4005}, /* 10**2 */
{0xFA00000000000000, 0x4008}, /* 10**3 */
{0x9C40000000000000, 0x400C}, /* 10**4 */
{0xC350000000000000, 0x400F}, /* 10**5 */
{0xF424000000000000, 0x4012}, /* 10**6 */
{0x9896800000000000, 0x4016}, /* 10**7 */
{0xBEBC200000000000, 0x4019}, /* 10**8 */
{0xEE6B280000000000, 0x401C}, /* 10**9 */
{0x9502F90000000000, 0x4020}, /* 10**10 */
{0xBA43B74000000000, 0x4023}, /* 10**11 */
{0xE8D4A51000000000, 0x4026}, /* 10**12 */
{0x9184E72A00000000, 0x402A}, /* 10**13 */
{0xB5E620F480000000, 0x402D}, /* 10**14 */
{0xE35FA931A0000000, 0x4030}, /* 10**15 */
{0x8E1BC9BF04000000, 0x4034}, /* 10**16 */
{0xB1A2BC2EC5000000, 0x4037}, /* 10**17 */
{0xDE0B6B3A76400000, 0x403A}, /* 10**18 */
{0x8AC7230489E80000, 0x403E}, /* 10**19 */
{0xAD78EBC5AC620000, 0x4041}, /* 10**20 */
{0xD8D726B7177A8000, 0x4044}, /* 10**21 */
{0x878678326EAC9000, 0x4048}, /* 10**22 */
{0xA968163F0A57B400, 0x404B}, /* 10**23 */
{0xD3C21BCECCEDA100, 0x404E}, /* 10**24 */
{0x84595161401484A0, 0x4052}, /* 10**25 */
{0xA56FA5B99019A5C8, 0x4055}, /* 10**26 */
{0xCECB8F27F4200F3A, 0x4058}, /* 10**27 */
{0x813F3978F8940984, 0x405C}, /* 10**28 */
{0xA18F07D736B90BE5, 0x405F}, /* 10**29 */
{0xC9F2C9CD04674EDF, 0x4062}, /* 10**30 */
{0xFC6F7C4045812296, 0x4065} /* 10**31 */
};
static CONST _Extended _tab1[] =
{
{0x9DC5ADA82B70B59E, 0x4069}, /* 10**32 */
{0xC2781F49FFCFA6D5, 0x40D3}, /* 10**64 */
{0xEFB3AB16C59B14A3, 0x413D}, /* 10**96 */
{0x93BA47C980E98CE0, 0x41A8}, /* 10**128 */
{0xB616A12B7FE617AA, 0x4212}, /* 10**160 */
{0xE070F78D3927556B, 0x427C}, /* 10**192 */
{0x8A5296FFE33CC930, 0x42E7}, /* 10**224 */
{0xAA7EEBFB9DF9DE8E, 0x4351}, /* 10**256 */
{0xD226FC195C6A2F8C, 0x43BB}, /* 10**288 */
{0x81842F29F2CCE376, 0x4426}, /* 10**320 */
{0x9FA42700DB900AD2, 0x4490}, /* 10**352 */
{0xC4C5E310AEF8AA17, 0x44FA}, /* 10**384 */
{0xF28A9C07E9B09C59, 0x4564}, /* 10**416 */
{0x957A4AE1EBF7F3D4, 0x45CF}, /* 10**448 */
{0xB83ED8DC0795A262, 0x4639} /* 10**480 */
};
static CONST _Extended _tab2[] =
{
{0xE319A0AEA60E91C7, 0x46A3}, /* 10**512 */
{0xC976758681750C17, 0x4D48}, /* 10**1024 */
{0xB2B8353B3993A7E4, 0x53ED}, /* 10**1536 */
{0x9E8B3B5DC53D5DE5, 0x5A92}, /* 10**2048 */
{0x8CA554C020A1F0A6, 0x6137}, /* 10**2560 */
{0xF9895D25D88B5A8B, 0x67DB}, /* 10**3072 */
{0xDD5DC8A2BF27F3F8, 0x6E80}, /* 10**3584 */
{0xC46052028A20979B, 0x7525}, /* 10**4096 */
{0xAE3511626ED559F0, 0x7BCA} /* 10**4608 */
};
static CONST EXTENDED _conPrec = 1E19;
#else // USE_EXTENDED
#define F_MAXPRECISION 17
#define F_CONEXPONENT 0x03ff
typedef double EXTENDED, *PExtended, *PEXTENDED;
static CONST UINT64 _tab0[] =
{
{0x3FF0000000000000}, /* 10**0 */
{0x4024000000000000}, /* 10**1 */
{0x4059000000000000}, /* 10**2 */
{0x408F400000000000}, /* 10**3 */
{0x40C3880000000000}, /* 10**4 */
{0x40F86A0000000000}, /* 10**5 */
{0x412E848000000000}, /* 10**6 */
{0x416312D000000000}, /* 10**7 */
{0x4197D78400000000}, /* 10**8 */
{0x41CDCD6500000000}, /* 10**9 */
{0x4202A05F20000000}, /* 10**10 */
{0x42374876E8000000}, /* 10**11 */
{0x426D1A94A2000000}, /* 10**12 */
{0x42A2309CE5400000}, /* 10**13 */
{0x42D6BCC41E900000}, /* 10**14 */
{0x430C6BF526340000}, /* 10**15 */
{0x4341C37937E08000}, /* 10**16 */
{0x4376345785D8A000}, /* 10**17 */
{0x43ABC16D674EC800}, /* 10**18 */
{0x43E158E460913D00}, /* 10**19 */
{0x4415AF1D78B58C40}, /* 10**20 */
{0x444B1AE4D6E2EF50}, /* 10**21 */
{0x4480F0CF064DD592}, /* 10**22 */
{0x44B52D02C7E14AF7}, /* 10**23 */
{0x44EA784379D99DB4}, /* 10**24 */
{0x45208B2A2C280291}, /* 10**25 */
{0x4554ADF4B7320335}, /* 10**26 */
{0x4589D971E4FE8402}, /* 10**27 */
{0x45C027E72F1F1281}, /* 10**28 */
{0x45F431E0FAE6D722}, /* 10**29 */
{0x46293E5939A08CEA}, /* 10**30 */
{0x465F8DEF8808B024} /* 10**31 */
};
static CONST UINT64 _tab1[] =
{
{0x4693B8B5B5056E17}, /* 10**32 */
{0x4D384F03E93FF9F5}, /* 10**64 */
{0x53DDF67562D8B363}, /* 10**96 */
{0x5A827748F9301D32}, /* 10**128 */
{0x6126C2D4256FFCC3}, /* 10**160 */
{0x67CC0E1EF1A724EB}, /* 10**192 */
{0x6E714A52DFFC679A}, /* 10**224 */
{0x75154FDD7F73BF3C}, /* 10**256 */
{0x7BBA44DF832B8D46}, /* 10**288 */
};
static CONST EXTENDED _conPrec = 1E17;
#endif // !USE_EXTENDED
static CONST UINT64 _cvttab[F_MAXPRECISION] =
{
#ifdef USE_EXTENDED
0xDE0B6B3A7640000, 0x16345785D8A0000,
#endif
0x02386F26FC10000, 0x0038D7EA4C68000, 0x0005AF3107A4000, 0x00009184E72A000,
0x00000E8D4A51000, 0x00000174876E800, 0x0000002540BE400, 0x00000003B9ACA00,
0x000000005F5E100, 0x000000000989680, 0x0000000000F4240, 0x0000000000186A0,
0x000000000002710, 0x0000000000003E8, 0x000000000000064, 0x00000000000000A,
0x000000000000001
};
#define DECIMAL_EXP(exponent) ((((exponent - F_CONEXPONENT) * 0x4d10) >> 16) + 1)
static VOID AdjFloatDigits(UINT64 value, INT precision, INT decimals, FloatRec *rec)
{
INT i;
// value是F_MAXPRECISION位十进制整数，故从最高位开始转换为数字串
for (i = 0; value; i ++)
{
rec->digits[i] = (CHAR)((value / _cvttab[i]) | 0x30);
value %= _cvttab[i];
}
memset(rec->digits + i, 0, F_MAXPRECISION - i);
// 下面对数字串作精度处理
// 如果总的精度小于0，数字串为空串，该数字转换为'0'
if ((i = (rec->exponent + decimals)) < 0)
{
rec->exponent = rec->negative = rec->digits[0] = 0;
return;
}
if (i > precision) i = precision;
// 如果精度位数小于18，同时该位大于等于'5'，四舍五入
if (i < F_MAXPRECISION && rec->digits[i] >= '5')
{
do
{
rec->digits[i --] = 0;
rec->digits[i] ++;
}while (i >= 0 && rec->digits[i] > '9');
if (i < 0)
{
rec->digits[0] = '1';
rec->exponent ++;
}
}
// 否则，去掉数字串尾部多余的'0'
else
{
if (i > F_MAXPRECISION) i = F_MAXPRECISION;
do rec->digits[i --] = 0;
while (i >= 0 && rec->digits[i] == '0');
if (i < 0) rec->negative = 0;
}
}
#ifdef USE_EXTENDED
// 解析扩展精度浮点数为十进制字符串，并存入浮点数记录中
// 参数：浮点数指针，精度，小数位，浮点数记录
VOID FloatResolve(PEXTENDED pvalue, INT precision, INT decimals, FloatRec *rec)
{
INT power;
EXTENDED val;
// 79位：扩展精度浮点数符号位
rec->negative = ((_Extended*)pvalue)->exponent >> 15;
// 64-78位：扩展精度浮点数阶码(阶码 - 0x3fff = 二进制指数)
rec->exponent = ((_Extended*)pvalue)->exponent & 0x7fff;
if (!rec->exponent) // *pvalue = 0
{
rec->negative = rec->digits[0] = 0;
return;
}
if (rec->exponent == 0x7fff)// *pvalue = nan or inf
{
if (!((*(LPBYTE)pvalue + 7) & 0x80) || !(*(PUINT64)pvalue & 0x7fffffffffffffff))
{
lstrcpyA(rec->digits, "INF");
}
else
{
rec->exponent ++;
rec->negative = 0;
lstrcpyA(rec->digits, "NAN");
}
return;
}
// 阶码转换为十进制指数
rec->exponent = DECIMAL_EXP(rec->exponent);
// 0-63位：扩展精度浮点数尾数转换成F_MAXPRECISION位十进制浮点整数格式
val = *pvalue;
*((LPBYTE)&val + 9) &= 0x7f;// val = fabs(*pvalue)
power = F_MAXPRECISION - rec->exponent;
if (power > 0) // if (power > 0) val *= (10**power)
{
val *= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
{
if (power & 15)
val *= *(PEXTENDED)&_tab1[(power & 15) - 1];
power >>= 4; // power /= 16;
if (power)
val *= *(PEXTENDED)&_tab2[power - 1];
}
}
else if (power < 0) // if (power < 0) val /= (10**power)
{
power = -power;
val /= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
{
if (power & 15)
val /= *(PEXTENDED)&_tab1[(power & 15) - 1];
power >>= 4; // power /= 16;
if (power)
val /= *(PEXTENDED)&_tab2[power - 1];
}
}
val += 0.5; // 四舍五入
if (val >= _conPrec)
{
val /= 10;
rec->exponent ++;
}
// 调整并转换扩展精度浮点数尾数的整数部分rec->digits
AdjFloatDigits(*(PUINT64)&val >> ((((_Extended*)&val)->exponent - 0x3fff) ^ 0x3f),
precision, decimals, rec);
}
#else // USE_EXTENDED
// 解析双精度浮点数为十进制字符串，并存入浮点数记录中
// 参数：浮点数指针，精度，小数位，浮点数记录
VOID FloatResolve(PEXTENDED pvalue, INT precision, INT decimals, FloatRec *rec)
{
INT power;
EXTENDED val;
// 63位：双精度浮点数符号位
rec->negative = *((LPBYTE)pvalue + 7) >> 7;
// 52-62位：双精度浮点数阶码(阶码 - 0x3ff = 二进制指数)
rec->exponent = (*(PUINT64)pvalue >> 52) & 0x7ff;
if (!rec->exponent) // *pvalue = 0
{
rec->negative = rec->digits[0] = 0;
return;
}
if (rec->exponent == 0x7ff)// *pvalue = nan or inf
{
if ((*(PUINT64)pvalue & 0xfffffffffffff) == 0)
{
lstrcpyA(rec->digits, "INF");
}
else
{
rec->exponent ++;
rec->negative = 0;
lstrcpyA(rec->digits, "NAN");
}
return;
}
// 阶码转换为十进制指数
rec->exponent = DECIMAL_EXP(rec->exponent);
// 0-51位：双精度浮点数尾数转换成F_MAXPRECISION位十进制浮点整数格式
val = *pvalue;
*((LPBYTE)&val + 7) &= 0x7f;// val = fabs(*pvalue)
power = F_MAXPRECISION - rec->exponent;
if (power > 0) // if (power > 0) val *= (10**power)
{
val *= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
val *= *(PEXTENDED)&_tab1[power - 1];
}
else if (power < 0) // if (power < 0) val /= (10**power)
{
power = -power;
val /= *(PEXTENDED)&_tab0[power & 31];
power >>= 5; // power /= 32;
if (power)
val /= *(PEXTENDED)&_tab1[power - 1];
}
// 16位十进制浮点整数四舍五入
val += 0.5;
if (val >= _conPrec)
{
val /= 10;
rec->exponent ++;
}
// 调整并转换扩展精度浮点数尾数的整数部分rec->digits
// 清除52-63位，加隐藏的高位，F_MAXPRECISION=17，高位超过52位，所以左移
AdjFloatDigits(((*(PUINT64)&val & 0x000fffffffffffff) | 0x0010000000000000) <<
-(52 - ((*(PUINT64)&val >> 52) - 0x3ff)), precision, decimals, rec);
}
#endif // !USE_EXTENDED
// 输出指数字符串到buffer，返回指数字符串长度
INT PutExponent(LPSTR buffer, CONST FloatRec *rec)
{
LPSTR p = buffer;
INT e, exp = rec->digits[0]? rec->exponent - 1 : 0;
*p ++ = rec->negative & 0x80? 'E' : 'e';
if (exp < 0)
{
exp = -exp;
*p ++ = '-';
}
else *p ++ = '+';
if ((e = (exp / 1000)) != 0)
{
*p ++ = e + 0x30;
exp %= 1000;
}
*p ++ = exp / 100 + 0x30;
exp %= 100;
*(PUSHORT)p = (((exp % 10) << 8) | (exp / 10)) + 0x3030;
return (INT)(p - buffer + 2);
}
// 浮点数转换为字符串。参数：字符串，浮点数
LPSTR FloatToStr(LPSTR str, EXTENDED value)
{
INT exp;
FloatRec rec;
LPSTR pd = rec.digits;
LPSTR ps = str;
// 解析浮点数，并将信息保存在rec
FloatResolve(&value, 15, 9999, &rec);
// 打印负数符号
if (rec.negative) *ps ++ = '-';
// NAN or INF
if (*pd > '9')
{
memcpy(ps, pd, 4);
return str;
}
exp = rec.exponent;
// 如果十进制指数大于15或者小于-3，转换为指数形式
if (exp > 15 || exp < -3)
{
*ps ++ = *pd ++;
if (*pd)
for (*ps ++ = '.'; *pd; *ps ++ = *pd ++);
ps += PutExponent(ps, &rec);
*ps = 0;
return str;
}
// 否则，转换为小数形式
if (exp <= 0)
{
*ps ++ = '0';
if (*pd)
{
for (*ps ++ = '.'; exp < 0; *ps ++ = '0', exp ++);
while (*ps ++ = *pd ++);
}
else *ps = 0;
}
else
{
for (; exp > 0 && *pd; *ps ++ = *pd ++, exp --);
if (*pd)
{
*ps ++ = '.';
while (*ps ++ = *pd ++);
}
else
{
memset(ps, '0', exp);
ps[exp] = 0;
}
}
return str;
}
2个版本的代码加起来很长，但还有个自写的springf函数（下篇文章开始介绍）也要用到本文除FloatToSt函数外的全部代码。
代码开头的USE_EXTENDED为编译条件，如果你的编译系统不支持80位扩展精度浮点数，可将该定义注释掉。
前面说了，由于该代码主要是学习用的，因此数据转换层次较低，涉及到的有关浮点数格式的知识，可在网上搜索到。当然，知道是一回事，而具体怎样去操作则又是另一回事了，一些关键地方，我都作了较详细的注释，相信能对初学者正确理解浮点数格式有所帮助。例如，如何在不调用C有关函数，不使用汇编而快速的求一个浮点数的绝对值？本文代码就直接对浮点数进行操作：*((LPBYTE)&val + 7) &= 0x7f;（双精度浮点数）和*((LPBYTE)&val + 9) &= 0x7f;（扩展精度浮点数），也就是直接将浮点数的最高位置零，这当然比什么if (val < 0) val = -val语句快多了。不过，如果你要说后者的可移植性好，那我就无话可说了。要说可移植性，前者也可办到的，修改一下：*((LPBYTE)&val + sizeof(val) - 1) &= 0x7f;不就行了么，除非浮点数格式规则改变。只不过本文代码主要用来学习，用显式的方式更有意义。
80位扩展精度浮点数的有效数字为19位，而64位双精度浮点数有效数字为15 - 16位，本文的解析函数FloatResolve分别用了19位和17位的最大转换精度，尽可能的多显示几位，这主要是为自写的sprintf函数（另文介绍）做准备的，本文的浮点数转换字符串函数FloatToStr只用了最大15位的精度。
下面是个很简单的调用例子：
int main(int argc, char* argv[])
{
CHAR s[32];
UINT64 inf = 0x7ff0000000000000;
double v = -1.230E45;
INT a, b;
puts(FloatToStr(s, -10000));
puts(FloatToStr(s, 123456789012345678));
puts(FloatToStr(s, 1234567890.12345678));
puts(FloatToStr(s, 0.0001234567890));
puts(FloatToStr(s, -0.00001234567890));
puts(FloatToStr(s, v));
puts(FloatToStr(s, 0));
puts(FloatToStr(s, *(double*)&inf));
system("pause");
return 0;
{
CHAR s[32];
UINT64 inf = 0x7ff0000000000000;
double v = -1.230E45;
INT a, b;
puts(FloatToStr(s, -10000));
puts(FloatToStr(s, 123456789012345678));
puts(FloatToStr(s, 1234567890.12345678));
puts(FloatToStr(s, 0.0001234567890));
puts(FloatToStr(s, -0.00001234567890));
puts(FloatToStr(s, v));
puts(FloatToStr(s, 0));
puts(FloatToStr(s, *(double*)&inf));
system("pause");
return 0;
}
下面是运行结果：
-10000
1.23456789012346e+017
1234567890.12346
0.000123456789
-1.23456789e-005
-1.23e+045
0
INF
1.23456789012346e+017
1234567890.12346
0.000123456789
-1.23456789e-005
-1.23e+045
0
INF
请按任意键继续. . .
再次声明：本文代码主要供学习使用，如作其它用途，出问题慨不负责。
水平有限，错误在所难免，欢迎指正和指导。邮箱地址：maozefa@hotmail.com
