jdk8-mips64-public/hotspot: src/share/vm/runtime/sharedRuntimeTrans.cpp@c18cbe5936b8 (annotated)

src/share/vm/runtime/sharedRuntimeTrans.cpp@c18cbe5936b8 (annotated)

src/share/vm/runtime/sharedRuntimeTrans.cpp

Thu, 27 May 2010 19:08:38 -0700

author: trims
date: Thu, 27 May 2010 19:08:38 -0700
changeset 1907: c18cbe5936b8
parent 435: a61af66fc99e
child 2036: 126ea7725993
permissions: -rw-r--r--

6941466: Oracle rebranding changes for Hotspot repositories
Summary: Change all the Sun copyrights to Oracle copyright
Reviewed-by: ohair

 /*
  * Copyright (c) 2005, Oracle and/or its affiliates. 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 Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  * or visit www.oracle.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 <math.h>
 // 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 Oracle and/or its affiliates. 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|<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 = zeroX;
     __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*(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

Mercurial > jdk8-mips64-public > hotspot / annotate

src/share/vm/runtime/sharedRuntimeTrans.cpp@c18cbe5936b8 (annotated)

src/share/vm/runtime/sharedRuntimeTrans.cpp