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test/java/lang/StrictMath/FdlibmTranslit.java
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@@ -63,11 +63,12 @@
* Return a double with its high-order bits of the second argument
* and the low-order bits of the first argument..
*/
private static double __HI(double x, int high) {
long transX = Double.doubleToRawLongBits(x);
- return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
+ return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) |
+ ( ((long)high)) << 32 );
}
public static double hypot(double x, double y) {
return Hypot.compute(x, y);
}
@@ -248,6 +249,138 @@
return t1 * w;
} else
return w;
}
}
+
+ /**
+ * 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 class Exp {
+ private static final double one = 1.0;
+ private static final double[] halF = {0.5,-0.5,};
+ private static final double huge = 1.0e+300;
+ private static final double twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/
+ private static final double o_threshold= 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
+ private static final double u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
+ private static final double[] ln2HI ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ -6.93147180369123816490e-01}; /* 0xbfe62e42, 0xfee00000 */
+ private static final double[] ln2LO ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ -1.90821492927058770002e-10,}; /* 0xbdea39ef, 0x35793c76 */
+ private static final double invln2 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
+ private static final double P1 = 1.66666666666666019037e-01; /* 0x3FC55555, 0x5555553E */
+ private static final double P2 = -2.77777777770155933842e-03; /* 0xBF66C16C, 0x16BEBD93 */
+ private static final double P3 = 6.61375632143793436117e-05; /* 0x3F11566A, 0xAF25DE2C */
+ private static final double P4 = -1.65339022054652515390e-06; /* 0xBEBBBD41, 0xC5D26BF1 */
+ private static final double P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+ public static strictfp double compute(double x) {
+ double y,hi=0,lo=0,c,t;
+ int k=0,xsb;
+ /*unsigned*/ int 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 huge*huge; /* 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(huge+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) {
+ y = __HI(y, __HI(y) + (k<<20)); /* add k to y's exponent */
+ return y;
+ } else {
+ y = __HI(y, __HI(y) + ((k+1000)<<20));/* add k to y's exponent */
+ return y*twom1000;
+ }
+ }
+ }
}
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