| /* |
| * Copyright (c) 2005, 2014, 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 "precompiled.hpp" |
| #include "prims/jni.h" |
| #include "runtime/interfaceSupport.hpp" |
| #include "runtime/sharedRuntime.hpp" |
| |
| // 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 warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function |
| # pragma optimize ( "", off ) |
| #endif |
| |
| #include "runtime/sharedRuntimeMath.hpp" |
| |
| /* __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 = high(x); /* high word of x */ |
| lx = low(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 = high(x); /* high word of x */ |
| } |
| if (hx >= 0x7ff00000) return x+x; |
| k += (hx>>20)-1023; |
| hx &= 0x000fffff; |
| i = (hx+0x95f64)&0x100000; |
| set_high(&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 = high(x); /* high word of x */ |
| lx = low(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 = high(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); |
| set_high(&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 = high(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)|low(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) { |
| set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */ |
| return y; |
| } else { |
| set_high(&y, high(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 = high(x); lx = low(x); |
| hy = high(y); ly = low(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) { |
| #ifdef CAN_USE_NAN_DEFINE |
| z = NAN; |
| #else |
| z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
| #endif |
| } 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) |
| #ifdef CAN_USE_NAN_DEFINE |
| return NAN; |
| #else |
| return (x-x)/(x-x); |
| #endif |
| |
| 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; |
| set_low(&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 = high(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;} |
| set_high(&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; |
| set_low(&s_h, 0); |
| /* t_h=ax+bp[k] High */ |
| t_h = zeroX; |
| set_high(&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; |
| set_low(&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; |
| set_low(&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); |
| set_low(&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; |
| set_low(&y1, 0); |
| p_l = (y-y1)*t1+y*t2; |
| p_h = y1*t1; |
| z = p_l+p_h; |
| j = high(z); |
| i = low(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; |
| set_high(&t, (n&~(0x000fffff>>k))); |
| n = ((n&0x000fffff)|0x00100000)>>(20-k); |
| if(j<0) n = -n; |
| p_h -= t; |
| } |
| t = p_l+p_h; |
| set_low(&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 = high(z); |
| j += (n<<20); |
| if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */ |
| else set_high(&z, high(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 |
