duke@435: /* lfoltan@7000: * Copyright (c) 2005, 2014, Oracle and/or its affiliates. All rights reserved. duke@435: * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. duke@435: * duke@435: * This code is free software; you can redistribute it and/or modify it duke@435: * under the terms of the GNU General Public License version 2 only, as duke@435: * published by the Free Software Foundation. duke@435: * duke@435: * This code is distributed in the hope that it will be useful, but WITHOUT duke@435: * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or duke@435: * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License duke@435: * version 2 for more details (a copy is included in the LICENSE file that duke@435: * accompanied this code). duke@435: * duke@435: * You should have received a copy of the GNU General Public License version duke@435: * 2 along with this work; if not, write to the Free Software Foundation, duke@435: * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. duke@435: * trims@1907: * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA trims@1907: * or visit www.oracle.com if you need additional information or have any trims@1907: * questions. duke@435: * duke@435: */ duke@435: stefank@2314: #include "precompiled.hpp" stefank@2314: #include "prims/jni.h" stefank@2314: #include "runtime/interfaceSupport.hpp" stefank@2314: #include "runtime/sharedRuntime.hpp" duke@435: duke@435: // This file contains copies of the fdlibm routines used by duke@435: // StrictMath. It turns out that it is almost always required to use duke@435: // these runtime routines; the Intel CPU doesn't meet the Java duke@435: // specification for sin/cos outside a certain limited argument range, duke@435: // and the SPARC CPU doesn't appear to have sin/cos instructions. It duke@435: // also turns out that avoiding the indirect call through function duke@435: // pointer out to libjava.so in SharedRuntime speeds these routines up duke@435: // by roughly 15% on both Win32/x86 and Solaris/SPARC. duke@435: duke@435: // Enabling optimizations in this file causes incorrect code to be duke@435: // generated; can not figure out how to turn down optimization for one duke@435: // file in the IDE on Windows duke@435: #ifdef WIN32 thartmann@7002: # pragma warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function duke@435: # pragma optimize ( "", off ) duke@435: #endif duke@435: lfoltan@7000: #include "runtime/sharedRuntimeMath.hpp" duke@435: duke@435: /* __ieee754_log(x) duke@435: * Return the logrithm of x duke@435: * duke@435: * Method : duke@435: * 1. Argument Reduction: find k and f such that duke@435: * x = 2^k * (1+f), duke@435: * where sqrt(2)/2 < 1+f < sqrt(2) . duke@435: * duke@435: * 2. Approximation of log(1+f). duke@435: * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) duke@435: * = 2s + 2/3 s**3 + 2/5 s**5 + ....., duke@435: * = 2s + s*R duke@435: * We use a special Reme algorithm on [0,0.1716] to generate duke@435: * a polynomial of degree 14 to approximate R The maximum error duke@435: * of this polynomial approximation is bounded by 2**-58.45. In duke@435: * other words, duke@435: * 2 4 6 8 10 12 14 duke@435: * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s duke@435: * (the values of Lg1 to Lg7 are listed in the program) duke@435: * and duke@435: * | 2 14 | -58.45 duke@435: * | Lg1*s +...+Lg7*s - R(z) | <= 2 duke@435: * | | duke@435: * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. duke@435: * In order to guarantee error in log below 1ulp, we compute log duke@435: * by duke@435: * log(1+f) = f - s*(f - R) (if f is not too large) duke@435: * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) duke@435: * duke@435: * 3. Finally, log(x) = k*ln2 + log(1+f). duke@435: * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) duke@435: * Here ln2 is split into two floating point number: duke@435: * ln2_hi + ln2_lo, duke@435: * where n*ln2_hi is always exact for |n| < 2000. duke@435: * duke@435: * Special cases: duke@435: * log(x) is NaN with signal if x < 0 (including -INF) ; duke@435: * log(+INF) is +INF; log(0) is -INF with signal; duke@435: * log(NaN) is that NaN with no signal. duke@435: * duke@435: * Accuracy: duke@435: * according to an error analysis, the error is always less than duke@435: * 1 ulp (unit in the last place). duke@435: * duke@435: * Constants: duke@435: * The hexadecimal values are the intended ones for the following duke@435: * constants. The decimal values may be used, provided that the duke@435: * compiler will convert from decimal to binary accurately enough duke@435: * to produce the hexadecimal values shown. duke@435: */ duke@435: duke@435: static const double duke@435: ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ duke@435: ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ duke@435: Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ duke@435: Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ duke@435: Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ duke@435: Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ duke@435: Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ duke@435: Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ duke@435: Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ duke@435: duke@435: static double zero = 0.0; duke@435: duke@435: static double __ieee754_log(double x) { duke@435: double hfsq,f,s,z,R,w,t1,t2,dk; duke@435: int k,hx,i,j; duke@435: unsigned lx; duke@435: thartmann@7002: hx = high(x); /* high word of x */ thartmann@7002: lx = low(x); /* low word of x */ duke@435: duke@435: k=0; duke@435: if (hx < 0x00100000) { /* x < 2**-1022 */ duke@435: if (((hx&0x7fffffff)|lx)==0) duke@435: return -two54/zero; /* log(+-0)=-inf */ duke@435: if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ duke@435: k -= 54; x *= two54; /* subnormal number, scale up x */ thartmann@7002: hx = high(x); /* high word of x */ duke@435: } duke@435: if (hx >= 0x7ff00000) return x+x; duke@435: k += (hx>>20)-1023; duke@435: hx &= 0x000fffff; duke@435: i = (hx+0x95f64)&0x100000; thartmann@7002: set_high(&x, hx|(i^0x3ff00000)); /* normalize x or x/2 */ duke@435: k += (i>>20); duke@435: f = x-1.0; duke@435: if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ duke@435: if(f==zero) { duke@435: if (k==0) return zero; duke@435: else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} duke@435: } duke@435: R = f*f*(0.5-0.33333333333333333*f); duke@435: if(k==0) return f-R; else {dk=(double)k; duke@435: return dk*ln2_hi-((R-dk*ln2_lo)-f);} duke@435: } duke@435: s = f/(2.0+f); duke@435: dk = (double)k; duke@435: z = s*s; duke@435: i = hx-0x6147a; duke@435: w = z*z; duke@435: j = 0x6b851-hx; duke@435: t1= w*(Lg2+w*(Lg4+w*Lg6)); duke@435: t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); duke@435: i |= j; duke@435: R = t2+t1; duke@435: if(i>0) { duke@435: hfsq=0.5*f*f; duke@435: if(k==0) return f-(hfsq-s*(hfsq+R)); else duke@435: return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); duke@435: } else { duke@435: if(k==0) return f-s*(f-R); else duke@435: return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); duke@435: } duke@435: } duke@435: duke@435: JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) duke@435: return __ieee754_log(x); duke@435: JRT_END duke@435: duke@435: /* __ieee754_log10(x) duke@435: * Return the base 10 logarithm of x duke@435: * duke@435: * Method : duke@435: * Let log10_2hi = leading 40 bits of log10(2) and duke@435: * log10_2lo = log10(2) - log10_2hi, duke@435: * ivln10 = 1/log(10) rounded. duke@435: * Then duke@435: * n = ilogb(x), duke@435: * if(n<0) n = n+1; duke@435: * x = scalbn(x,-n); duke@435: * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) duke@435: * duke@435: * Note 1: duke@435: * To guarantee log10(10**n)=n, where 10**n is normal, the rounding duke@435: * mode must set to Round-to-Nearest. duke@435: * Note 2: duke@435: * [1/log(10)] rounded to 53 bits has error .198 ulps; duke@435: * log10 is monotonic at all binary break points. duke@435: * duke@435: * Special cases: duke@435: * log10(x) is NaN with signal if x < 0; duke@435: * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; duke@435: * log10(NaN) is that NaN with no signal; duke@435: * log10(10**N) = N for N=0,1,...,22. duke@435: * duke@435: * Constants: duke@435: * The hexadecimal values are the intended ones for the following constants. duke@435: * The decimal values may be used, provided that the compiler will convert duke@435: * from decimal to binary accurately enough to produce the hexadecimal values duke@435: * shown. duke@435: */ duke@435: duke@435: static const double duke@435: ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ duke@435: log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ duke@435: log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ duke@435: duke@435: static double __ieee754_log10(double x) { duke@435: double y,z; duke@435: int i,k,hx; duke@435: unsigned lx; duke@435: thartmann@7002: hx = high(x); /* high word of x */ thartmann@7002: lx = low(x); /* low word of x */ duke@435: duke@435: k=0; duke@435: if (hx < 0x00100000) { /* x < 2**-1022 */ duke@435: if (((hx&0x7fffffff)|lx)==0) duke@435: return -two54/zero; /* log(+-0)=-inf */ duke@435: if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ duke@435: k -= 54; x *= two54; /* subnormal number, scale up x */ thartmann@7002: hx = high(x); /* high word of x */ duke@435: } duke@435: if (hx >= 0x7ff00000) return x+x; duke@435: k += (hx>>20)-1023; duke@435: i = ((unsigned)k&0x80000000)>>31; duke@435: hx = (hx&0x000fffff)|((0x3ff-i)<<20); duke@435: y = (double)(k+i); thartmann@7002: set_high(&x, hx); duke@435: z = y*log10_2lo + ivln10*__ieee754_log(x); duke@435: return z+y*log10_2hi; duke@435: } duke@435: duke@435: JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) duke@435: return __ieee754_log10(x); duke@435: JRT_END duke@435: duke@435: duke@435: /* __ieee754_exp(x) duke@435: * Returns the exponential of x. duke@435: * duke@435: * Method duke@435: * 1. Argument reduction: duke@435: * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. duke@435: * Given x, find r and integer k such that duke@435: * duke@435: * x = k*ln2 + r, |r| <= 0.5*ln2. duke@435: * duke@435: * Here r will be represented as r = hi-lo for better duke@435: * accuracy. duke@435: * duke@435: * 2. Approximation of exp(r) by a special rational function on duke@435: * the interval [0,0.34658]: duke@435: * Write duke@435: * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... duke@435: * We use a special Reme algorithm on [0,0.34658] to generate duke@435: * a polynomial of degree 5 to approximate R. The maximum error duke@435: * of this polynomial approximation is bounded by 2**-59. In duke@435: * other words, duke@435: * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 duke@435: * (where z=r*r, and the values of P1 to P5 are listed below) duke@435: * and duke@435: * | 5 | -59 duke@435: * | 2.0+P1*z+...+P5*z - R(z) | <= 2 duke@435: * | | duke@435: * The computation of exp(r) thus becomes duke@435: * 2*r duke@435: * exp(r) = 1 + ------- duke@435: * R - r duke@435: * r*R1(r) duke@435: * = 1 + r + ----------- (for better accuracy) duke@435: * 2 - R1(r) duke@435: * where duke@435: * 2 4 10 duke@435: * R1(r) = r - (P1*r + P2*r + ... + P5*r ). duke@435: * duke@435: * 3. Scale back to obtain exp(x): duke@435: * From step 1, we have duke@435: * exp(x) = 2^k * exp(r) duke@435: * duke@435: * Special cases: duke@435: * exp(INF) is INF, exp(NaN) is NaN; duke@435: * exp(-INF) is 0, and duke@435: * for finite argument, only exp(0)=1 is exact. duke@435: * duke@435: * Accuracy: duke@435: * according to an error analysis, the error is always less than duke@435: * 1 ulp (unit in the last place). duke@435: * duke@435: * Misc. info. duke@435: * For IEEE double duke@435: * if x > 7.09782712893383973096e+02 then exp(x) overflow duke@435: * if x < -7.45133219101941108420e+02 then exp(x) underflow duke@435: * duke@435: * Constants: duke@435: * The hexadecimal values are the intended ones for the following duke@435: * constants. The decimal values may be used, provided that the duke@435: * compiler will convert from decimal to binary accurately enough duke@435: * to produce the hexadecimal values shown. duke@435: */ duke@435: duke@435: static const double duke@435: one = 1.0, duke@435: halF[2] = {0.5,-0.5,}, duke@435: twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ duke@435: o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ duke@435: u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ duke@435: ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ duke@435: -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ duke@435: ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ duke@435: -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ duke@435: invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ duke@435: P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ duke@435: P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ duke@435: P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ duke@435: P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ duke@435: P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ duke@435: duke@435: static double __ieee754_exp(double x) { duke@435: double y,hi=0,lo=0,c,t; duke@435: int k=0,xsb; duke@435: unsigned hx; duke@435: thartmann@7002: hx = high(x); /* high word of x */ duke@435: xsb = (hx>>31)&1; /* sign bit of x */ duke@435: hx &= 0x7fffffff; /* high word of |x| */ duke@435: duke@435: /* filter out non-finite argument */ duke@435: if(hx >= 0x40862E42) { /* if |x|>=709.78... */ duke@435: if(hx>=0x7ff00000) { thartmann@7002: if(((hx&0xfffff)|low(x))!=0) duke@435: return x+x; /* NaN */ duke@435: else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ duke@435: } duke@435: if(x > o_threshold) return hugeX*hugeX; /* overflow */ duke@435: if(x < u_threshold) return twom1000*twom1000; /* underflow */ duke@435: } duke@435: duke@435: /* argument reduction */ duke@435: if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ duke@435: if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ duke@435: hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; duke@435: } else { duke@435: k = (int)(invln2*x+halF[xsb]); duke@435: t = k; duke@435: hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ duke@435: lo = t*ln2LO[0]; duke@435: } duke@435: x = hi - lo; duke@435: } duke@435: else if(hx < 0x3e300000) { /* when |x|<2**-28 */ duke@435: if(hugeX+x>one) return one+x;/* trigger inexact */ duke@435: } duke@435: else k = 0; duke@435: duke@435: /* x is now in primary range */ duke@435: t = x*x; duke@435: c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); duke@435: if(k==0) return one-((x*c)/(c-2.0)-x); duke@435: else y = one-((lo-(x*c)/(2.0-c))-hi); duke@435: if(k >= -1021) { thartmann@7002: set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */ duke@435: return y; duke@435: } else { thartmann@7002: set_high(&y, high(y) + ((k+1000)<<20)); /* add k to y's exponent */ duke@435: return y*twom1000; duke@435: } duke@435: } duke@435: duke@435: JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) duke@435: return __ieee754_exp(x); duke@435: JRT_END duke@435: duke@435: /* __ieee754_pow(x,y) return x**y duke@435: * duke@435: * n duke@435: * Method: Let x = 2 * (1+f) duke@435: * 1. Compute and return log2(x) in two pieces: duke@435: * log2(x) = w1 + w2, duke@435: * where w1 has 53-24 = 29 bit trailing zeros. duke@435: * 2. Perform y*log2(x) = n+y' by simulating muti-precision duke@435: * arithmetic, where |y'|<=0.5. duke@435: * 3. Return x**y = 2**n*exp(y'*log2) duke@435: * duke@435: * Special cases: duke@435: * 1. (anything) ** 0 is 1 duke@435: * 2. (anything) ** 1 is itself duke@435: * 3. (anything) ** NAN is NAN duke@435: * 4. NAN ** (anything except 0) is NAN duke@435: * 5. +-(|x| > 1) ** +INF is +INF duke@435: * 6. +-(|x| > 1) ** -INF is +0 duke@435: * 7. +-(|x| < 1) ** +INF is +0 duke@435: * 8. +-(|x| < 1) ** -INF is +INF duke@435: * 9. +-1 ** +-INF is NAN duke@435: * 10. +0 ** (+anything except 0, NAN) is +0 duke@435: * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 duke@435: * 12. +0 ** (-anything except 0, NAN) is +INF duke@435: * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF duke@435: * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) duke@435: * 15. +INF ** (+anything except 0,NAN) is +INF duke@435: * 16. +INF ** (-anything except 0,NAN) is +0 duke@435: * 17. -INF ** (anything) = -0 ** (-anything) duke@435: * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) duke@435: * 19. (-anything except 0 and inf) ** (non-integer) is NAN duke@435: * duke@435: * Accuracy: duke@435: * pow(x,y) returns x**y nearly rounded. In particular duke@435: * pow(integer,integer) duke@435: * always returns the correct integer provided it is duke@435: * representable. duke@435: * duke@435: * Constants : duke@435: * The hexadecimal values are the intended ones for the following duke@435: * constants. The decimal values may be used, provided that the duke@435: * compiler will convert from decimal to binary accurately enough duke@435: * to produce the hexadecimal values shown. duke@435: */ duke@435: duke@435: static const double duke@435: bp[] = {1.0, 1.5,}, duke@435: dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ duke@435: dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ duke@435: zeroX = 0.0, duke@435: two = 2.0, duke@435: two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ duke@435: /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ duke@435: L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ duke@435: L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ duke@435: L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ duke@435: L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ duke@435: L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ duke@435: L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ duke@435: lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ duke@435: lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ duke@435: lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ duke@435: ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ duke@435: cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ duke@435: cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ duke@435: cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ duke@435: ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ duke@435: ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ duke@435: ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ duke@435: duke@435: double __ieee754_pow(double x, double y) { duke@435: double z,ax,z_h,z_l,p_h,p_l; duke@435: double y1,t1,t2,r,s,t,u,v,w; duke@435: int i0,i1,i,j,k,yisint,n; duke@435: int hx,hy,ix,iy; duke@435: unsigned lx,ly; duke@435: duke@435: i0 = ((*(int*)&one)>>29)^1; i1=1-i0; thartmann@7002: hx = high(x); lx = low(x); thartmann@7002: hy = high(y); ly = low(y); duke@435: ix = hx&0x7fffffff; iy = hy&0x7fffffff; duke@435: duke@435: /* y==zero: x**0 = 1 */ duke@435: if((iy|ly)==0) return one; duke@435: duke@435: /* +-NaN return x+y */ duke@435: if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || duke@435: iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) duke@435: return x+y; duke@435: duke@435: /* determine if y is an odd int when x < 0 duke@435: * yisint = 0 ... y is not an integer duke@435: * yisint = 1 ... y is an odd int duke@435: * yisint = 2 ... y is an even int duke@435: */ duke@435: yisint = 0; duke@435: if(hx<0) { duke@435: if(iy>=0x43400000) yisint = 2; /* even integer y */ duke@435: else if(iy>=0x3ff00000) { duke@435: k = (iy>>20)-0x3ff; /* exponent */ duke@435: if(k>20) { duke@435: j = ly>>(52-k); duke@435: if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); duke@435: } else if(ly==0) { duke@435: j = iy>>(20-k); duke@435: if((j<<(20-k))==iy) yisint = 2-(j&1); duke@435: } duke@435: } duke@435: } duke@435: duke@435: /* special value of y */ duke@435: if(ly==0) { duke@435: if (iy==0x7ff00000) { /* y is +-inf */ duke@435: if(((ix-0x3ff00000)|lx)==0) duke@435: return y - y; /* inf**+-1 is NaN */ duke@435: else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ duke@435: return (hy>=0)? y: zeroX; duke@435: else /* (|x|<1)**-,+inf = inf,0 */ duke@435: return (hy<0)?-y: zeroX; duke@435: } duke@435: if(iy==0x3ff00000) { /* y is +-1 */ duke@435: if(hy<0) return one/x; else return x; duke@435: } duke@435: if(hy==0x40000000) return x*x; /* y is 2 */ duke@435: if(hy==0x3fe00000) { /* y is 0.5 */ duke@435: if(hx>=0) /* x >= +0 */ duke@435: return sqrt(x); duke@435: } duke@435: } duke@435: duke@435: ax = fabsd(x); duke@435: /* special value of x */ duke@435: if(lx==0) { duke@435: if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ duke@435: z = ax; /*x is +-0,+-inf,+-1*/ duke@435: if(hy<0) z = one/z; /* z = (1/|x|) */ duke@435: if(hx<0) { duke@435: if(((ix-0x3ff00000)|yisint)==0) { bobv@2036: #ifdef CAN_USE_NAN_DEFINE bobv@2036: z = NAN; bobv@2036: #else duke@435: z = (z-z)/(z-z); /* (-1)**non-int is NaN */ bobv@2036: #endif duke@435: } else if(yisint==1) duke@435: z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ duke@435: } duke@435: return z; duke@435: } duke@435: } duke@435: duke@435: n = (hx>>31)+1; duke@435: duke@435: /* (x<0)**(non-int) is NaN */ bobv@2036: if((n|yisint)==0) bobv@2036: #ifdef CAN_USE_NAN_DEFINE bobv@2036: return NAN; bobv@2036: #else bobv@2036: return (x-x)/(x-x); bobv@2036: #endif duke@435: duke@435: s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ duke@435: if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ duke@435: duke@435: /* |y| is huge */ duke@435: if(iy>0x41e00000) { /* if |y| > 2**31 */ duke@435: if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ duke@435: if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; duke@435: if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; duke@435: } duke@435: /* over/underflow if x is not close to one */ duke@435: if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; duke@435: if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; duke@435: /* now |1-x| is tiny <= 2**-20, suffice to compute duke@435: log(x) by x-x^2/2+x^3/3-x^4/4 */ duke@435: t = ax-one; /* t has 20 trailing zeros */ duke@435: w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); duke@435: u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ duke@435: v = t*ivln2_l-w*ivln2; duke@435: t1 = u+v; thartmann@7002: set_low(&t1, 0); duke@435: t2 = v-(t1-u); duke@435: } else { duke@435: double ss,s2,s_h,s_l,t_h,t_l; duke@435: n = 0; duke@435: /* take care subnormal number */ duke@435: if(ix<0x00100000) thartmann@7002: {ax *= two53; n -= 53; ix = high(ax); } duke@435: n += ((ix)>>20)-0x3ff; duke@435: j = ix&0x000fffff; duke@435: /* determine interval */ duke@435: ix = j|0x3ff00000; /* normalize ix */ duke@435: if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); duke@435: t_l = ax - (t_h-bp[k]); duke@435: s_l = v*((u-s_h*t_h)-s_h*t_l); duke@435: /* compute log(ax) */ duke@435: s2 = ss*ss; duke@435: r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); duke@435: r += s_l*(s_h+ss); duke@435: s2 = s_h*s_h; duke@435: t_h = 3.0+s2+r; thartmann@7002: set_low(&t_h, 0); duke@435: t_l = r-((t_h-3.0)-s2); duke@435: /* u+v = ss*(1+...) */ duke@435: u = s_h*t_h; duke@435: v = s_l*t_h+t_l*ss; duke@435: /* 2/(3log2)*(ss+...) */ duke@435: p_h = u+v; thartmann@7002: set_low(&p_h, 0); duke@435: p_l = v-(p_h-u); duke@435: z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ duke@435: z_l = cp_l*p_h+p_l*cp+dp_l[k]; duke@435: /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ duke@435: t = (double)n; duke@435: t1 = (((z_h+z_l)+dp_h[k])+t); thartmann@7002: set_low(&t1, 0); duke@435: t2 = z_l-(((t1-t)-dp_h[k])-z_h); duke@435: } duke@435: duke@435: /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ duke@435: y1 = y; thartmann@7002: set_low(&y1, 0); duke@435: p_l = (y-y1)*t1+y*t2; duke@435: p_h = y1*t1; duke@435: z = p_l+p_h; thartmann@7002: j = high(z); thartmann@7002: i = low(z); duke@435: if (j>=0x40900000) { /* z >= 1024 */ duke@435: if(((j-0x40900000)|i)!=0) /* if z > 1024 */ duke@435: return s*hugeX*hugeX; /* overflow */ duke@435: else { duke@435: if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ duke@435: } duke@435: } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ duke@435: if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ duke@435: return s*tiny*tiny; /* underflow */ duke@435: else { duke@435: if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ duke@435: } duke@435: } duke@435: /* duke@435: * compute 2**(p_h+p_l) duke@435: */ duke@435: i = j&0x7fffffff; duke@435: k = (i>>20)-0x3ff; duke@435: n = 0; duke@435: if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ duke@435: n = j+(0x00100000>>(k+1)); duke@435: k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ duke@435: t = zeroX; thartmann@7002: set_high(&t, (n&~(0x000fffff>>k))); duke@435: n = ((n&0x000fffff)|0x00100000)>>(20-k); duke@435: if(j<0) n = -n; duke@435: p_h -= t; duke@435: } duke@435: t = p_l+p_h; thartmann@7002: set_low(&t, 0); duke@435: u = t*lg2_h; duke@435: v = (p_l-(t-p_h))*lg2+t*lg2_l; duke@435: z = u+v; duke@435: w = v-(z-u); duke@435: t = z*z; duke@435: t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); duke@435: r = (z*t1)/(t1-two)-(w+z*w); duke@435: z = one-(r-z); thartmann@7002: j = high(z); duke@435: j += (n<<20); lfoltan@7000: if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */ thartmann@7002: else set_high(&z, high(z) + (n<<20)); duke@435: return s*z; duke@435: } duke@435: duke@435: duke@435: JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) duke@435: return __ieee754_pow(x, y); duke@435: JRT_END duke@435: duke@435: #ifdef WIN32 duke@435: # pragma optimize ( "", on ) duke@435: #endif