Power function in java

Table of Contents

Syntax
Internal working

Power function in java is used to get first argument’s power to 2nd argument.
For example:
Let’s say you want to calculate 2 to the power 4.

That will be 2*2*2*2=16
In java, you can do it by :
Math.pow(2,4) =16

Syntax


public static double pow(double x, double y)

public static double pow(double x, double y)

Example :
Let’s use power function in java.


import java.lang.*;

public class PowerMain {

public static void main(String[] args) {

// print 2 to the power 4
System.out.println("Math.pow(2 ,4)=" + Math.pow(2, 4));
// print 4.2 to the power 3
System.out.println("Math.pow(4.2,3)=" + Math.pow(4.2,3));
   }
}

import java.lang.*;

public class PowerMain {

public static void main(String[] args) {

// print 2 to the power 4

System.out.println("Math.pow(2 ,4)=" + Math.pow(2, 4));

// print 4.2 to the power 3

System.out.println("Math.pow(4.2,3)=" + Math.pow(4.2,3));

}

When you run above program, you will get below output:

Math.pow(2 ,4)=16.0
Math.pow(4.2,3)=74.08800000000001

If you want to return integer from power function, you need to explicitly cast it to Integer.


import java.lang.*;

public class PowerMain {

public static void main(String[] args) {

// print 2 to the power 
int i=(int)Math.pow(2,4);
System.out.println("Math.pow(2 ,4)=" + i);

  }
}

import java.lang.*;

public class PowerMain {

public static void main(String[] args) {

// print 2 to the power

int i=(int)Math.pow(2,4);

System.out.println("Math.pow(2 ,4)=" + i);

}

When you run above program, you will get below output:

Math.pow(2 ,4)=16

Internal working

Math.pow is native method in java and it is written in c.
Let me provide you source code for Math.pow method.

Math.java


public static double pow(double a, double b) {
return StrictMath.pow(a, b); // default impl. delegates to StrictMath
}

public static double pow(double a, double b) {

return StrictMath.pow(a, b); // default impl. delegates to StrictMath

}

So if you above code, Math.pow delegate call to StrictMath.
StrictMath.java


public static native double pow(double a, double b);

public static native double pow(double a, double b);

As you can see it calls native method.

jdk/src/share/native/java/lang/fdlibm/src/w_pow.c


#include "fdlibm.h"
#ifdef __STDC__
        double pow(double x, double y)  /* wrapper pow */
#else
        double pow(x,y)                 /* wrapper pow */
        double x,y;
#endif
{
#ifdef _IEEE_LIBM
        return  __ieee754_pow(x,y);
#else
        double z;
        z=__ieee754_pow(x,y);
        if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
        if(isnan(x)) {
            if(y==0.0)
                return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
            else
                return z;
        }
        if(x==0.0){
            if(y==0.0)
                return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
            if(finite(y)&&y<0.0)
                return __kernel_standard(x,y,23); /* pow(0.0,negative) */
            return z;
        }
        if(!finite(z)) {
            if(finite(x)&&finite(y)) {
                if(isnan(z))
                    return __kernel_standard(x,y,24); /* pow neg**non-int */
                else
                    return __kernel_standard(x,y,21); /* pow overflow */
            }
        }
        if(z==0.0&&finite(x)&&finite(y))
            return __kernel_standard(x,y,22); /* pow underflow */
        return z;
#endif
}

#include "fdlibm.h"

#ifdef __STDC__

double pow(double x, double y) /* wrapper pow */

#else

double pow(x,y) /* wrapper pow */

double x,y;

#endif

{

#ifdef _IEEE_LIBM

return __ieee754_pow(x,y);

#else

double z;

z=__ieee754_pow(x,y);

if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;

if(isnan(x)) {

if(y==0.0)

return __kernel_standard(x,y,42); /* pow(NaN,0.0) */

else

return z;

}

if(x==0.0){

if(y==0.0)

return __kernel_standard(x,y,20); /* pow(0.0,0.0) */

if(finite(y)&&y<0.0)

return __kernel_standard(x,y,23); /* pow(0.0,negative) */

return z;

}

if(!finite(z)) {

if(finite(x)&&finite(y)) {

if(isnan(z))

return __kernel_standard(x,y,24); /* pow neg**non-int */

else

return __kernel_standard(x,y,21); /* pow overflow */

}

if(z==0.0&&finite(x)&&finite(y))

return __kernel_standard(x,y,22); /* pow underflow */

return z;

#endif

}

jdk/src/share/native/java/lang/fdlibm/src/e_pow.c


#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero    =  0.0,
one     =  1.0,
two     =  2.0,
two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
huge    =  1.0e300,
tiny    =  1.0e-300,
        /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
#ifdef __STDC__
        double __ieee754_pow(double x, double y)
#else
        double __ieee754_pow(x,y)
        double x, y;
#endif
{
        double z,ax,z_h,z_l,p_h,p_l;
        double y1,t1,t2,r,s,t,u,v,w;
        int i0,i1,i,j,k,yisint,n;
        int hx,hy,ix,iy;
        unsigned lx,ly;
        i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
        hx = __HI(x); lx = __LO(x);
        hy = __HI(y); ly = __LO(y);
        ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
    /* y==zero: x**0 = 1 */
        if((iy|ly)==0) return one;
    /* +-NaN return x+y */
        if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
           iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
                return x+y;
    /* determine if y is an odd int when x < 0
     * yisint = 0       ... y is not an integer
     * yisint = 1       ... y is an odd int
     * yisint = 2       ... y is an even int
     */
        yisint  = 0;
        if(hx<0) {
            if(iy>=0x43400000) yisint = 2; /* even integer y */
            else if(iy>=0x3ff00000) {
                k = (iy>>20)-0x3ff;        /* exponent */
                if(k>20) {
                    j = ly>>(52-k);
                    if((j<<(52-k))==ly) yisint = 2-(j&1);
                } else if(ly==0) {
                    j = iy>>(20-k);
                    if((j<<(20-k))==iy) yisint = 2-(j&1);
                }
            }
        }
    /* special value of y */
        if(ly==0) {
            if (iy==0x7ff00000) {       /* y is +-inf */
                if(((ix-0x3ff00000)|lx)==0)
                    return  y - y;      /* inf**+-1 is NaN */
                else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
                    return (hy>=0)? y: zero;
                else                    /* (|x|<1)**-,+inf = inf,0 */
                    return (hy<0)?-y: zero;
            }
            if(iy==0x3ff00000) {        /* y is  +-1 */
                if(hy<0) return one/x; else return x;
            }
            if(hy==0x40000000) return x*x; /* y is  2 */
            if(hy==0x3fe00000) {        /* y is  0.5 */
                if(hx>=0)       /* x >= +0 */
                return sqrt(x);
            }
        }
        ax   = fabs(x);
    /* special value of x */
        if(lx==0) {
            if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
                z = ax;                 /*x is +-0,+-inf,+-1*/
                if(hy<0) z = one/z;     /* z = (1/|x|) */
                if(hx<0) {
                    if(((ix-0x3ff00000)|yisint)==0) {
                        z = (z-z)/(z-z); /* (-1)**non-int is NaN */
                    } else if(yisint==1)
                        z = -1.0*z;             /* (x<0)**odd = -(|x|**odd) */
                }
                return z;
            }
        }
        n = (hx>>31)+1;
    /* (x<0)**(non-int) is NaN */
        if((n|yisint)==0) return (x-x)/(x-x);
        s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
        if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
    /* |y| is huge */
        if(iy>0x41e00000) { /* if |y| > 2**31 */
            if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
                if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
                if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
            }
        /* over/underflow if x is not close to one */
            if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
            if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
        /* now |1-x| is tiny <= 2**-20, suffice to compute
           log(x) by x-x^2/2+x^3/3-x^4/4 */
            t = ax-one;         /* t has 20 trailing zeros */
            w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
            u = ivln2_h*t;      /* ivln2_h has 21 sig. bits */
            v = t*ivln2_l-w*ivln2;
            t1 = u+v;
            __LO(t1) = 0;
            t2 = v-(t1-u);
        } else {
            double ss,s2,s_h,s_l,t_h,t_l;
            n = 0;
        /* take care subnormal number */
            if(ix<0x00100000)
                {ax *= two53; n -= 53; ix = __HI(ax); }
            n  += ((ix)>>20)-0x3ff;
            j  = ix&0x000fffff;
        /* determine interval */
            ix = j|0x3ff00000;          /* normalize ix */
            if(j<=0x3988E) k=0;         /* |x|<sqrt else if k="1;" __hi ix compute ss="s_h+s_l" or u="ax-bp[k];" bp v="one/(ax+bp[k]);" s_h="ss;" __lo t_h="ax+bp[k]" high>>1)|0x20000000)+0x00080000+(k<<18);
            t_l = ax - (t_h-bp[k]);
            s_l = v*((u-s_h*t_h)-s_h*t_l);
        /* compute log(ax) */
            s2 = ss*ss;
            r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
            r += s_l*(s_h+ss);
            s2  = s_h*s_h;
            t_h = 3.0+s2+r;
            __LO(t_h) = 0;
            t_l = r-((t_h-3.0)-s2);
        /* u+v = ss*(1+...) */
            u = s_h*t_h;
            v = s_l*t_h+t_l*ss;
        /* 2/(3log2)*(ss+...) */
            p_h = u+v;
            __LO(p_h) = 0;
            p_l = v-(p_h-u);
            z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
            z_l = cp_l*p_h+p_l*cp+dp_l[k];
        /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
            t = (double)n;
            t1 = (((z_h+z_l)+dp_h[k])+t);
            __LO(t1) = 0;
            t2 = z_l-(((t1-t)-dp_h[k])-z_h);
        }
    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
        y1  = y;
        __LO(y1) = 0;
        p_l = (y-y1)*t1+y*t2;
        p_h = y1*t1;
        z = p_l+p_h;
        j = __HI(z);
        i = __LO(z);
        if (j>=0x40900000) {                            /* z >= 1024 */
            if(((j-0x40900000)|i)!=0)                   /* if z > 1024 */
                return s*huge*huge;                     /* overflow */
            else {
                if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
            }
        } else if((j&0x7fffffff)>=0x4090cc00 ) {        /* z <= -1075 */
            if(((j-0xc090cc00)|i)!=0)           /* z < -1075 */
                return s*tiny*tiny;             /* underflow */
            else {
                if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
            }
        }
    /*
     * compute 2**(p_h+p_l)
     */
        i = j&0x7fffffff;
        k = (i>>20)-0x3ff;
        n = 0;
        if(i>0x3fe00000) {              /* if |z| > 0.5, set n = [z+0.5] */
            n = j+(0x00100000>>(k+1));
            k = ((n&0x7fffffff)>>20)-0x3ff;     /* new k for n */
            t = zero;
            __HI(t) = (n&~(0x000fffff>>k));
            n = ((n&0x000fffff)|0x00100000)>>(20-k);
            if(j<0) n = -n;
            p_h -= t;
        }
        t = p_l+p_h;
        __LO(t) = 0;
        u = t*lg2_h;
        v = (p_l-(t-p_h))*lg2+t*lg2_l;
        z = u+v;
        w = v-(z-u);
        t  = z*z;
        t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
        r  = (z*t1)/(t1-two)-(w+z*w);
        z  = one-(r-z);
        j  = __HI(z);
        j += (n<<20);
        if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
        else __HI(z) += (n<<20);
        return s*z;
}
</sqrt>

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#include "fdlibm.h"

#ifdef __STDC__

static const double

#else

static double

#endif

bp[] = {1.0, 1.5,},

dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */

dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */

zero = 0.0,

one = 1.0,

two = 2.0,

two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */

huge = 1.0e300,

tiny = 1.0e-300,

/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */

L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */

L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */

L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */

L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */

L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */

L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */

P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */

P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */

P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */

P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */

P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */

lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */

lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */

lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */

ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */

cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */

cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */

cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/

ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */

ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/

ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

#ifdef __STDC__

double __ieee754_pow(double x, double y)

#else

double __ieee754_pow(x,y)

double x, y;

#endif

{

double z,ax,z_h,z_l,p_h,p_l;

double y1,t1,t2,r,s,t,u,v,w;

int i0,i1,i,j,k,yisint,n;

int hx,hy,ix,iy;

unsigned lx,ly;

i0 = ((*(int*)&one)>>29)^1; i1=1-i0;

hx = __HI(x); lx = __LO(x);

hy = __HI(y); ly = __LO(y);

ix = hx&0x7fffffff; iy = hy&0x7fffffff;

/* y==zero: x**0 = 1 */

if((iy|ly)==0) return one;

/* +-NaN return x+y */

if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||

iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))

return x+y;

/* determine if y is an odd int when x < 0

* yisint = 0 ... y is not an integer

* yisint = 1 ... y is an odd int

* yisint = 2 ... y is an even int

yisint = 0;

if(hx<0) {

if(iy>=0x43400000) yisint = 2; /* even integer y */

else if(iy>=0x3ff00000) {

k = (iy>>20)-0x3ff; /* exponent */

if(k>20) {

j = ly>>(52-k);

if((j<<(52-k))==ly) yisint = 2-(j&1);

} else if(ly==0) {

j = iy>>(20-k);

if((j<<(20-k))==iy) yisint = 2-(j&1);

}

/* special value of y */

if(ly==0) {

if (iy==0x7ff00000) { /* y is +-inf */

if(((ix-0x3ff00000)|lx)==0)

return y - y; /* inf**+-1 is NaN */

else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */

return (hy>=0)? y: zero;

else /* (|x|<1)**-,+inf = inf,0 */

return (hy<0)?-y: zero;

}

if(iy==0x3ff00000) { /* y is +-1 */

if(hy<0) return one/x; else return x;

}

if(hy==0x40000000) return x*x; /* y is 2 */

if(hy==0x3fe00000) { /* y is 0.5 */

if(hx>=0) /* x >= +0 */

return sqrt(x);

}

ax = fabs(x);

/* special value of x */

if(lx==0) {

if(ix==0x7ff00000||ix==0||ix==0x3ff00000){

z = ax; /*x is +-0,+-inf,+-1*/

if(hy<0) z = one/z; /* z = (1/|x|) */

if(hx<0) {

if(((ix-0x3ff00000)|yisint)==0) {

z = (z-z)/(z-z); /* (-1)**non-int is NaN */

} else if(yisint==1)

z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */

}

return z;

}

n = (hx>>31)+1;

/* (x<0)**(non-int) is NaN */

if((n|yisint)==0) return (x-x)/(x-x);

s = one; /* s (sign of result -ve**odd) = -1 else = 1 */

if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

/* |y| is huge */

if(iy>0x41e00000) { /* if |y| > 2**31 */

if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */

if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;

if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;

}

/* over/underflow if x is not close to one */

if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;

if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;

/* now |1-x| is tiny <= 2**-20, suffice to compute

log(x) by x-x^2/2+x^3/3-x^4/4 */

t = ax-one; /* t has 20 trailing zeros */

w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));

u = ivln2_h*t; /* ivln2_h has 21 sig. bits */

v = t*ivln2_l-w*ivln2;

t1 = u+v;

__LO(t1) = 0;

t2 = v-(t1-u);

} else {

double ss,s2,s_h,s_l,t_h,t_l;

n = 0;

/* take care subnormal number */

if(ix<0x00100000)

{ax *= two53; n -= 53; ix = __HI(ax); }

n += ((ix)>>20)-0x3ff;

j = ix&0x000fffff;

/* determine interval */

ix = j|0x3ff00000; /* normalize ix */

if(j<=0x3988E) k=0; /* |x|<sqrt else if k="1;" __hi ix compute ss="s_h+s_l" or u="ax-bp[k];" bp v="one/(ax+bp[k]);" s_h="ss;" __lo t_h="ax+bp[k]" high>>1)|0x20000000)+0x00080000+(k<<18);

t_l = ax - (t_h-bp[k]);

s_l = v*((u-s_h*t_h)-s_h*t_l);

/* compute log(ax) */

s2 = ss*ss;

r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));

r += s_l*(s_h+ss);

s2 = s_h*s_h;

t_h = 3.0+s2+r;

__LO(t_h) = 0;

t_l = r-((t_h-3.0)-s2);

/* u+v = ss*(1+...) */

u = s_h*t_h;

v = s_l*t_h+t_l*ss;

/* 2/(3log2)*(ss+...) */

p_h = u+v;

__LO(p_h) = 0;

p_l = v-(p_h-u);

z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */

z_l = cp_l*p_h+p_l*cp+dp_l[k];

/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */

t = (double)n;

t1 = (((z_h+z_l)+dp_h[k])+t);

__LO(t1) = 0;

t2 = z_l-(((t1-t)-dp_h[k])-z_h);

}

/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */

y1 = y;

__LO(y1) = 0;

p_l = (y-y1)*t1+y*t2;

p_h = y1*t1;

z = p_l+p_h;

j = __HI(z);

i = __LO(z);

if (j>=0x40900000) { /* z >= 1024 */

if(((j-0x40900000)|i)!=0) /* if z > 1024 */

return s*huge*huge; /* overflow */

else {

if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */

}

} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */

if(((j-0xc090cc00)|i)!=0) /* z < -1075 */

return s*tiny*tiny; /* underflow */

else {

if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */

}

* compute 2**(p_h+p_l)

i = j&0x7fffffff;

k = (i>>20)-0x3ff;

n = 0;

if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */

n = j+(0x00100000>>(k+1));

k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */

t = zero;

__HI(t) = (n&~(0x000fffff>>k));

n = ((n&0x000fffff)|0x00100000)>>(20-k);

if(j<0) n = -n;

p_h -= t;

}

t = p_l+p_h;

__LO(t) = 0;

u = t*lg2_h;

v = (p_l-(t-p_h))*lg2+t*lg2_l;

z = u+v;

w = v-(z-u);

t = z*z;

t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));

r = (z*t1)/(t1-two)-(w+z*w);

z = one-(r-z);

j = __HI(z);

j += (n<<20);

if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */

else __HI(z) += (n<<20);

return s*z;

}

</sqrt>

That’s all about power funcation in java.

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