diff -r 000000000000 -r a61af66fc99e src/share/vm/runtime/sharedRuntimeTrans.cpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/share/vm/runtime/sharedRuntimeTrans.cpp Sat Dec 01 00:00:00 2007 +0000 @@ -0,0 +1,719 @@ +/* + * Copyright 2005 Sun Microsystems, Inc. All Rights Reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, + * CA 95054 USA or visit www.sun.com if you need additional information or + * have any questions. + * + */ + +#include "incls/_precompiled.incl" +#include "incls/_sharedRuntimeTrans.cpp.incl" + +// This file contains copies of the fdlibm routines used by +// StrictMath. It turns out that it is almost always required to use +// these runtime routines; the Intel CPU doesn't meet the Java +// specification for sin/cos outside a certain limited argument range, +// and the SPARC CPU doesn't appear to have sin/cos instructions. It +// also turns out that avoiding the indirect call through function +// pointer out to libjava.so in SharedRuntime speeds these routines up +// by roughly 15% on both Win32/x86 and Solaris/SPARC. + +// Enabling optimizations in this file causes incorrect code to be +// generated; can not figure out how to turn down optimization for one +// file in the IDE on Windows +#ifdef WIN32 +# pragma optimize ( "", off ) +#endif + +#include + +// VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles +// [jk] this is not 100% correct because the float word order may different +// from the byte order (e.g. on ARM) +#ifdef VM_LITTLE_ENDIAN +# define __HI(x) *(1+(int*)&x) +# define __LO(x) *(int*)&x +#else +# define __HI(x) *(int*)&x +# define __LO(x) *(1+(int*)&x) +#endif + +double copysign(double x, double y) { + __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); + return x; +} + +/* + * ==================================================== + * Copyright (C) 1998 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + hugeX = 1.0e+300, + tiny = 1.0e-300; + +double scalbn (double x, int n) { + int k,hx,lx; + hx = __HI(x); + lx = __LO(x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + hx = __HI(x); + k = ((hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return hugeX*copysign(hugeX,x); /* overflow */ + if (k > 0) /* normal result */ + {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return hugeX*copysign(hugeX,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 54; /* subnormal result */ + __HI(x) = (hx&0x800fffff)|(k<<20); + return x*twom54; +} + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ + Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ + Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static double zero = 0.0; + +static double __ieee754_log(double x) { + double hfsq,f,s,z,R,w,t1,t2,dk; + int k,hx,i,j; + unsigned lx; + + hx = __HI(x); /* high word of x */ + lx = __LO(x); /* low word of x */ + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + hx = __HI(x); /* high word of x */ + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) { + if (k==0) return zero; + else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} + +JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) + return __ieee754_log(x); +JRT_END + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +static const double +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ + log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ + log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +static double __ieee754_log10(double x) { + double y,z; + int i,k,hx; + unsigned lx; + + hx = __HI(x); /* high word of x */ + lx = __LO(x); /* low word of x */ + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + hx = __HI(x); /* high word of x */ + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + i = ((unsigned)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + __HI(x) = hx; + z = y*log10_2lo + ivln10*__ieee754_log(x); + return z+y*log10_2hi; +} + +JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) + return __ieee754_log10(x); +JRT_END + + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +static const double +one = 1.0, + halF[2] = {0.5,-0.5,}, + twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ + o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ + u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ + ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ + ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ + invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ + 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 */ + +static double __ieee754_exp(double x) { + double y,hi=0,lo=0,c,t; + int k=0,xsb; + unsigned hx; + + hx = __HI(x); /* high word of x */ + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + if(((hx&0xfffff)|__LO(x))!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return hugeX*hugeX; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = (int)(invln2*x+halF[xsb]); + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(hugeX+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + __HI(y) += (k<<20); /* add k to y's exponent */ + return y; + } else { + __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ + return y*twom1000; + } +} + +JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) + return __ieee754_exp(x); +JRT_END + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +static const double +bp[] = {1.0, 1.5,}, + dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ + dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ + zeroX = 0.0, + two = 2.0, + two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ + L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ + L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ + L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ + L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ + L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ + L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ + 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*/ + +double __ieee754_pow(double x, double y) { + 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((unsigned)(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: zeroX; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zeroX; + } + 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 = fabsd(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)? hugeX*hugeX:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX: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|>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*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); + 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*hugeX*hugeX; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* 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 = zeroX; + __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; +} + + +JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) + return __ieee754_pow(x, y); +JRT_END + +#ifdef WIN32 +# pragma optimize ( "", on ) +#endif