我知道Math.sqrt调用StrictMath.sqrt(double a)我想查看用于计算它的实际代码.
Joe*_*oey 32
安装JDK时,可以在里面找到标准库的源代码src.zip.StrictMath但是,这对您没有帮助,StrictMath.sqrt(double)如下所示:
public static native double sqrt(double a);
所以它实际上只是一个原生调用,并且可能在Java的不同平台上以不同的方式实现.
但是,作为StrictMath州的文件:
为了帮助确保Java程序的可移植性,此程序包中某些数字函数的定义要求它们产生与某些已发布算法相同的结果.这些算法可从知名网络库获得,
netlib作为"Freely Distributable Math Library" 包fdlibm.然后,这些以C编程语言编写的算法应理解为遵循Java浮点算法规则的所有浮点运算.Java数学库是根据fdlibm 5.3版定义的.其中fdlibm为函数提供了多个定义(例如acos),请使用"IEEE 754核心函数"版本(驻留在名称以字母e开头的文件中).需要fdlibm语义的方法是sin,cos,tan,asin,acos,atan,exp,log,log10,cbrt,atan2,pow,sinh,cosh,tanh,hypot,expm1和log1p.
因此,通过查找fdlibm源的适当版本,您还应该找到Java使用的确切实现(并且此处的规范强制要求).
使用的实现fdlibm是
static const double one = 1.0, tiny=1.0e-300;
double z;
int sign = (int) 0x80000000;
unsigned r, t1, s1, ix1, q1;
int ix0, s0, q, m, t, i;
ix0 = __HI(x); /* high word of x */
ix1 = __LO(x); /* low word of x */
/* take care of Inf and NaN */
if ((ix0 & 0x7ff00000) == 0x7ff00000) {
return x*x+x; /* sqrt(NaN) = NaN,
sqrt(+inf) = +inf,
sqrt(-inf) = sNaN */
}
/* take care of zero */
if (ix0 <= 0) {
if (((ix0&(~sign)) | ix1) == 0) {
return x; /* sqrt(+-0) = +-0 */
} else if (ix0 < 0) {
return (x-x) / (x-x); /* sqrt(-ve) = sNaN */
}
}
/* normalize x */
m = (ix0 >> 20);
if (m == 0) { /* subnormal x */
while (ix0==0) {
m -= 21;
ix0 |= (ix1 >> 11); ix1 <<= 21;
}
for (i=0; (ix0&0x00100000)==0; i++) {
ix0 <<= 1;
}
m -= i-1;
ix0 |= (ix1 >> (32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if (m&1) { /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign) >> 31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1 & sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
while (r != 0) {
t = s0 + r;
if (t <= ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
r = sign;
while (r != 0) {
t1 = s1+r;
t = s0;
if ((t<ix0) || ((t == ix0) && (t1 <= ix1))) {
s1 = t1+r;
if (((t1&sign) == sign) && (s1 & sign) == 0) {
s0 += 1;
}
ix0 -= t;
if (ix1 < t1) {
ix0 -= 1;
}
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign) >> 31);
ix1 += ix1;
r >>= 1;
}
/* use floating add to find out rounding direction */
if((ix0 | ix1) != 0) {
z = one - tiny; /* trigger inexact flag */
if (z >= one) {
z = one+tiny;
if (q1 == (unsigned) 0xffffffff) {
q1=0;
q += 1;
}
} else if (z > one) {
if (q1 == (unsigned) 0xfffffffe) {
q+=1;
}
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1) + 0x3fe00000;
ix1 = q 1>> 1;
if ((q&1) == 1) ix1 |= sign;
ix0 += (m <<20);
__HI(z) = ix0;
__LO(z) = ix1;
return z;
由于我碰巧有OpenJDK,我会在这里展示它的实现.
在jdk/src/share/native/java/lang/StrictMath.c中:
JNIEXPORT jdouble JNICALL
Java_java_lang_StrictMath_sqrt(JNIEnv *env, jclass unused, jdouble d)
{
return (jdouble) jsqrt((double)d);
}
jsqrt被定义为sqrt在JDK/SRC /共享/天然的/爪哇/郎/ fdlibm/SRC/w_sqrt.c(名字通过预处理器改变):
#ifdef __STDC__
double sqrt(double x) /* wrapper sqrt */
#else
double sqrt(x) /* wrapper sqrt */
double x;
#endif
{
#ifdef _IEEE_LIBM
return __ieee754_sqrt(x);
#else
double z;
z = __ieee754_sqrt(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<0.0) {
return __kernel_standard(x,x,26); /* sqrt(negative) */
} else
return z;
#endif
}
并__ieee754_sqrt在jdk/src/share/native/java/lang/fdlibm/src/e_sqrt.c中定义为:
#ifdef __STDC__
static const double one = 1.0, tiny=1.0e-300;
#else
static double one = 1.0, tiny=1.0e-300;
#endif
#ifdef __STDC__
double __ieee754_sqrt(double x)
#else
double __ieee754_sqrt(x)
double x;
#endif
{
double z;
int sign = (int)0x80000000;
unsigned r,t1,s1,ix1,q1;
int ix0,s0,q,m,t,i;
ix0 = __HI(x); /* high word of x */
ix1 = __LO(x); /* low word of x */
/* take care of Inf and NaN */
if((ix0&0x7ff00000)==0x7ff00000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix0<=0) {
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
else if(ix0<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix0>>20);
if(m==0) { /* subnormal x */
while(ix0==0) {
m -= 21;
ix0 |= (ix1>>11); ix1 <<= 21;
}
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
m -= i-1;
ix0 |= (ix1>>(32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if(m&1){ /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
while(r!=0) {
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
r = sign;
while(r!=0) {
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
if (ix1 < t1) ix0 -= 1;
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
/* use floating add to find out rounding direction */
if((ix0|ix1)!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(unsigned)0xfffffffe) q+=1;
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1)+0x3fe00000;
ix1 = q1>>1;
if ((q&1)==1) ix1 |= sign;
ix0 += (m <<20);
__HI(z) = ix0;
__LO(z) = ix1;
return z;
}
文件中有大量的注释解释了所使用的方法,我省略了(半)简洁.这是Mercurial中的文件(我希望这是链接到它的正确方法).
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