Java中的Power函数
时间:2020-02-23 14:35:30 来源:igfitidea点击:
java中的Power函数用于获得第2个参数的第2个参数的幂。
例如:假设我们想计算2的4次方.
That will be 2*2*2*2=16 In java, you can do it by : Math.pow(2,4) =16
语法
public static double pow(double x, double y)
示例:让我们在Java中使用Power函数。
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)); } }
运行上面的程序时,我们将得到以下输出:
Math.Pow(2,4)= 16.0 Math.Pow(4.2,3)= 74.08800000000001
如果要从Power函数返回整数,则需要将其显式投递给整数。
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); } }
运行上面的程序时,我们将得到以下输出:
Math.pow(2 ,4)=16
内部工作
Math.Pow是Java中的本机方法,它是用C写入的。
让我为我们提供Math.pow方法的源代码。
math.java.
public static double pow(double a, double b) { return StrictMath.pow(a, b); //default impl. delegates to StrictMath }
因此,如果我们以上代码,Math.pow委派拨打strictmath。
strictmath.java.
public static native double pow(double a, double b);
正如我们可以看到它调用本机方法。
#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__ 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(3/2) */ else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ else {k=0;n+=1;ix -= 0x00100000;} __HI(ax) = ix; /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ v = one/(ax+bp[k]); ss = u*v; s_h = ss; __LO(s_h) = 0; /* t_h=ax+bp[k] High */ t_h = zero; __HI(t_h)=((ix>>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; }