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	/*
	* Copyright (c) 1998, 2017, 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. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* 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.
	*/

	package java.lang;

	/**
	* Port of the "Freely Distributable Math Library", version 5.3, from
	* C to Java.
	*
	* <p>The C version of fdlibm relied on the idiom of pointer aliasing
	* a 64-bit double floating-point value as a two-element array of
	* 32-bit integers and reading and writing the two halves of the
	* double independently. This coding pattern was problematic to C
	* optimizers and not directly expressible in Java. Therefore, rather
	* than a memory level overlay, if portions of a double need to be
	* operated on as integer values, the standard library methods for
	* bitwise floating-point to integer conversion,
	* Double.longBitsToDouble and Double.doubleToRawLongBits, are directly
	* or indirectly used.
	*
	* <p>The C version of fdlibm also took some pains to signal the
	* correct IEEE 754 exceptional conditions divide by zero, invalid,
	* overflow and underflow. For example, overflow would be signaled by
	* {@code huge * huge} where {@code huge} was a large constant that
	* would overflow when squared. Since IEEE floating-point exceptional
	* handling is not supported natively in the JVM, such coding patterns
	* have been omitted from this port. For example, rather than {@code
	* return huge * huge}, this port will use {@code return INFINITY}.
	*
	* <p>Various comparison and arithmetic operations in fdlibm could be
	* done either based on the integer view of a value or directly on the
	* floating-point representation. Which idiom is faster may depend on
	* platform specific factors. However, for code clarity if no other
	* reason, this port will favor expressing the semantics of those
	* operations in terms of floating-point operations when convenient to
	* do so.
	*/
	class FdLibm {
	// Constants used by multiple algorithms
	private static final double INFINITY = Double.POSITIVE_INFINITY;

	private FdLibm() {
	throw new UnsupportedOperationException("No FdLibm instances for you.");
	}

	/**
	* Return the low-order 32 bits of the double argument as an int.
	*/
	private static int __LO(double x) {
	long transducer = Double.doubleToRawLongBits(x);
	return (int)transducer;
	}

	/**
	* Return a double with its low-order bits of the second argument
	* and the high-order bits of the first argument..
	*/
	private static double __LO(double x, int low) {
	long transX = Double.doubleToRawLongBits(x);
	return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) \|
	(low & 0x0000_0000_FFFF_FFFFL));
	}

	/**
	* Return the high-order 32 bits of the double argument as an int.
	*/
	private static int __HI(double x) {
	long transducer = Double.doubleToRawLongBits(x);
	return (int)(transducer >> 32);
	}

	/**
	* 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 );
	}

	/**
	* cbrt(x)
	* Return cube root of x
	*/
	public static class Cbrt {
	// unsigned
	private static final int B1 = 715094163; /* B1 = (682-0.03306235651)220 /
	private static final int B2 = 696219795; /* B2 = (664-0.03306235651)220 /

	private static final double C = 0x1.15f15f15f15f1p-1; // 19/35 ~= 5.42857142857142815906e-01
	private static final double D = -0x1.691de2532c834p-1; // -864/1225 ~= 7.05306122448979611050e-01
	private static final double E = 0x1.6a0ea0ea0ea0fp0; // 99/70 ~= 1.41428571428571436819e+00
	private static final double F = 0x1.9b6db6db6db6ep0; // 45/28 ~= 1.60714285714285720630e+00
	private static final double G = 0x1.6db6db6db6db7p-2; // 5/14 ~= 3.57142857142857150787e-01

	private Cbrt() {
	throw new UnsupportedOperationException();
	}

	public static strictfp double compute(double x) {
	double t = 0.0;
	double sign;

	if (x == 0.0 \|\| !Double.isFinite(x))
	return x; // Handles signed zeros properly

	sign = (x < 0.0) ? -1.0: 1.0;

	x = Math.abs(x); // x <- \|x\|

	// Rough cbrt to 5 bits
	if (x < 0x1.0p-1022) { // subnormal number
	t = 0x1.0p54; // set t= 2**54
	t *= x;
	t = __HI(t, __HI(t)/3 + B2);
	} else {
	int hx = __HI(x); // high word of x
	t = __HI(t, hx/3 + B1);
	}

	// New cbrt to 23 bits, may be implemented in single precision
	double r, s, w;
	r = t * t/x;
	s = C + r*t;
	t *= G + F/(s + E + D/s);

	// Chopped to 20 bits and make it larger than cbrt(x)
	t = __LO(t, 0);
	t = __HI(t, __HI(t) + 0x00000001);

	// One step newton iteration to 53 bits with error less than 0.667 ulps
	s = t * t; // t*t is exact
	r = x / s;
	w = t + t;
	r = (r - t)/(w + r); // r-s is exact
	t = t + t*r;

	// Restore the original sign bit
	return sign * t;
	}
	}

	/**
	* hypot(x,y)
	*
	* Method :
	* If (assume round-to-nearest) z = xx + yy
	* has error less than sqrt(2)/2 ulp, than
	* sqrt(z) has error less than 1 ulp (exercise).
	*
	* So, compute sqrt(xx + yy) with some care as
	* follows to get the error below 1 ulp:
	*
	* Assume x > y > 0;
	* (if possible, set rounding to round-to-nearest)
	* 1. if x > 2y use
	* x1x1 + (yy + (x2(x + x1))) for xx + y*y
	* where x1 = x with lower 32 bits cleared, x2 = x - x1; else
	* 2. if x <= 2y use
	* t1y1 + ((x-y) (x-y) + (t1y2 + t2y))
	* where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1,
	* y1= y with lower 32 bits chopped, y2 = y - y1.
	*
	* NOTE: scaling may be necessary if some argument is too
	* large or too tiny
	*
	* Special cases:
	* hypot(x,y) is INF if x or y is +INF or -INF; else
	* hypot(x,y) is NAN if x or y is NAN.
	*
	* Accuracy:
	* hypot(x,y) returns sqrt(x^2 + y^2) with error less
	* than 1 ulp (unit in the last place)
	*/
	public static class Hypot {
	public static final double TWO_MINUS_600 = 0x1.0p-600;
	public static final double TWO_PLUS_600 = 0x1.0p+600;

	private Hypot() {
	throw new UnsupportedOperationException();
	}

	public static strictfp double compute(double x, double y) {
	double a = Math.abs(x);
	double b = Math.abs(y);

	if (!Double.isFinite(a) \|\| !Double.isFinite(b)) {
	if (a == INFINITY \|\| b == INFINITY)
	return INFINITY;
	else
	return a + b; // Propagate NaN significand bits
	}

	if (b > a) {
	double tmp = a;
	a = b;
	b = tmp;
	}
	assert a >= b;

	// Doing bitwise conversion after screening for NaN allows
	// the code to not worry about the possibility of
	// "negative" NaN values.

	// Note: the ha and hb variables are the high-order
	// 32-bits of a and b stored as integer values. The ha and
	// hb values are used first for a rough magnitude
	// comparison of a and b and second for simulating higher
	// precision by allowing a and b, respectively, to be
	// decomposed into non-overlapping portions. Both of these
	// uses could be eliminated. The magnitude comparison
	// could be eliminated by extracting and comparing the
	// exponents of a and b or just be performing a
	// floating-point divide. Splitting a floating-point
	// number into non-overlapping portions can be
	// accomplished by judicious use of multiplies and
	// additions. For details see T. J. Dekker, A Floating
	// Point Technique for Extending the Available Precision ,
	// Numerische Mathematik, vol. 18, 1971, pp.224-242 and
	// subsequent work.

	int ha = __HI(a); // high word of a
	int hb = __HI(b); // high word of b

	if ((ha - hb) > 0x3c00000) {
	return a + b; // x / y > 2**60
	}

	int k = 0;
	if (a > 0x1.00000_ffff_ffffp500) { // a > ~2**500
	// scale a and b by 2**-600
	ha -= 0x25800000;
	hb -= 0x25800000;
	a = a * TWO_MINUS_600;
	b = b * TWO_MINUS_600;
	k += 600;
	}
	double t1, t2;
	if (b < 0x1.0p-500) { // b < 2**-500
	if (b < Double.MIN_NORMAL) { // subnormal b or 0 */
	if (b == 0.0)
	return a;
	t1 = 0x1.0p1022; // t1 = 2^1022
	b *= t1;
	a *= t1;
	k -= 1022;
	} else { // scale a and b by 2^600
	ha += 0x25800000; // a *= 2^600
	hb += 0x25800000; // b *= 2^600
	a = a * TWO_PLUS_600;
	b = b * TWO_PLUS_600;
	k -= 600;
	}
	}
	// medium size a and b
	double w = a - b;
	if (w > b) {
	t1 = 0;
	t1 = __HI(t1, ha);
	t2 = a - t1;
	w = Math.sqrt(t1t1 - (b(-b) - t2 * (a + t1)));
	} else {
	double y1, y2;
	a = a + a;
	y1 = 0;
	y1 = __HI(y1, hb);
	y2 = b - y1;
	t1 = 0;
	t1 = __HI(t1, ha + 0x00100000);
	t2 = a - t1;
	w = Math.sqrt(t1y1 - (w(-w) - (t1y2 + t2b)));
	}
	if (k != 0) {
	return Math.powerOfTwoD(k) * w;
	} else
	return w;
	}
	}

	/**
	* Compute 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 multi-precision
	* arithmetic, where \|y'\| <= 0.5.
	* 3. Return xy = 2nexp(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.
	*/
	public static class Pow {
	private Pow() {
	throw new UnsupportedOperationException();
	}

	public static strictfp double compute(final double x, final double y) {
	double z;
	double r, s, t, u, v, w;
	int i, j, k, n;

	// y == zero: x**0 = 1
	if (y == 0.0)
	return 1.0;

	// +/-NaN return x + y to propagate NaN significands
	if (Double.isNaN(x) \|\| Double.isNaN(y))
	return x + y;

	final double y_abs = Math.abs(y);
	double x_abs = Math.abs(x);
	// Special values of y
	if (y == 2.0) {
	return x * x;
	} else if (y == 0.5) {
	if (x >= -Double.MAX_VALUE) // Handle x == -infinity later
	return Math.sqrt(x + 0.0); // Add 0.0 to properly handle x == -0.0
	} else if (y_abs == 1.0) { // y is +/-1
	return (y == 1.0) ? x : 1.0 / x;
	} else if (y_abs == INFINITY) { // y is +/-infinity
	if (x_abs == 1.0)
	return y - y; // inf**+/-1 is NaN
	else if (x_abs > 1.0) // (\|x\| > 1)**+/-inf = inf, 0
	return (y >= 0) ? y : 0.0;
	else // (\|x\| < 1)**-/+inf = inf, 0
	return (y < 0) ? -y : 0.0;
	}

	final int hx = __HI(x);
	int ix = hx & 0x7fffffff;

	/*
	* When x < 0, determine if y is an odd integer:
	* y_is_int = 0 ... y is not an integer
	* y_is_int = 1 ... y is an odd int
	* y_is_int = 2 ... y is an even int
	*/
	int y_is_int = 0;
	if (hx < 0) {
	if (y_abs >= 0x1.0p53) // \|y\| >= 2^53 = 9.007199254740992E15
	y_is_int = 2; // y is an even integer since ulp(2^53) = 2.0
	else if (y_abs >= 1.0) { // \|y\| >= 1.0
	long y_abs_as_long = (long) y_abs;
	if ( ((double) y_abs_as_long) == y_abs) {
	y_is_int = 2 - (int)(y_abs_as_long & 0x1L);
	}
	}
	}

	// Special value of x
	if (x_abs == 0.0 \|\|
	x_abs == INFINITY \|\|
	x_abs == 1.0) {
	z = x_abs; // x is +/-0, +/-inf, +/-1
	if (y < 0.0)
	z = 1.0/z; // z = (1/\|x\|)
	if (hx < 0) {
	if (((ix - 0x3ff00000) \| y_is_int) == 0) {
	z = (z-z)/(z-z); // (-1)**non-int is NaN
	} else if (y_is_int == 1)
	z = -1.0 * z; // (x < 0)odd = -(\|x\|odd)
	}
	return z;
	}

	n = (hx >> 31) + 1;

	// (x < 0)**(non-int) is NaN
	if ((n \| y_is_int) == 0)
	return (x-x)/(x-x);

	s = 1.0; // s (sign of result -ve**odd) = -1 else = 1
	if ( (n \| (y_is_int - 1)) == 0)
	s = -1.0; // (-ve)**(odd int)

	double p_h, p_l, t1, t2;
	// \|y\| is huge
	if (y_abs > 0x1.00000_ffff_ffffp31) { // if \|y\| > ~2**31
	final double INV_LN2 = 0x1.7154_7652_b82fep0; // 1.44269504088896338700e+00 = 1/ln2
	final double INV_LN2_H = 0x1.715476p0; // 1.44269502162933349609e+00 = 24 bits of 1/ln2
	final double INV_LN2_L = 0x1.4ae0_bf85_ddf44p-26; // 1.92596299112661746887e-08 = 1/ln2 tail

	// Over/underflow if x is not close to one
	if (x_abs < 0x1.fffff_0000_0000p-1) // \|x\| < ~0.9999995231628418
	return (y < 0.0) ? s * INFINITY : s * 0.0;
	if (x_abs > 0x1.00000_ffff_ffffp0) // \|x\| > ~1.0
	return (y > 0.0) ? s * INFINITY : s * 0.0;
	/*
	* now \|1-x\| is tiny <= 2**-20, sufficient to compute
	* log(x) by x - x^2/2 + x^3/3 - x^4/4
	*/
	t = x_abs - 1.0; // t has 20 trailing zeros
	w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
	u = INV_LN2_H * t; // INV_LN2_H has 21 sig. bits
	v = t * INV_LN2_L - w * INV_LN2;
	t1 = u + v;
	t1 =__LO(t1, 0);
	t2 = v - (t1 - u);
	} else {
	final double CP = 0x1.ec70_9dc3_a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2)
	final double CP_H = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp
	final double CP_L = -0x1.e2fe_0145_b01f5p-28; // -7.02846165095275826516e-09 = tail of CP_H

	double z_h, z_l, ss, s2, s_h, s_l, t_h, t_l;
	n = 0;
	// Take care of subnormal numbers
	if (ix < 0x00100000) {
	x_abs *= 0x1.0p53; // 2^53 = 9007199254740992.0
	n -= 53;
	ix = __HI(x_abs);
	}
	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;
	}
	x_abs = __HI(x_abs, ix);

	// Compute ss = s_h + s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)

	final double BP[] = {1.0,
	1.5};
	final double DP_H[] = {0.0,
	0x1.2b80_34p-1}; // 5.84962487220764160156e-01
	final double DP_L[] = {0.0,
	0x1.cfde_b43c_fd006p-27};// 1.35003920212974897128e-08

	// Poly coefs for (3/2)(log(x)-2s-2/3s**3
	final double L1 = 0x1.3333_3333_33303p-1; // 5.99999999999994648725e-01
	final double L2 = 0x1.b6db_6db6_fabffp-2; // 4.28571428578550184252e-01
	final double L3 = 0x1.5555_5518_f264dp-2; // 3.33333329818377432918e-01
	final double L4 = 0x1.1746_0a91_d4101p-2; // 2.72728123808534006489e-01
	final double L5 = 0x1.d864_a93c_9db65p-3; // 2.30660745775561754067e-01
	final double L6 = 0x1.a7e2_84a4_54eefp-3; // 2.06975017800338417784e-01
	u = x_abs - BP[k]; // BP[0]=1.0, BP[1]=1.5
	v = 1.0 / (x_abs + BP[k]);
	ss = u * v;
	s_h = ss;
	s_h = __LO(s_h, 0);
	// t_h=x_abs + BP[k] High
	t_h = 0.0;
	t_h = __HI(t_h, ((ix >> 1) \| 0x20000000) + 0x00080000 + (k << 18) );
	t_l = x_abs - (t_h - BP[k]);
	s_l = v * ((u - s_h * t_h) - s_h * t_l);
	// Compute log(x_abs)
	s2 = ss * ss;
	r = s2 * s2* (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
	r += s_l * (s_h + ss);
	s2 = s_h * s_h;
	t_h = 3.0 + s2 + r;
	t_h = __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;
	p_h = __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(x_abs) = (ss + ..)2/(3log2) = n + DP_H + z_h + z_l
	t = (double)n;
	t1 = (((z_h + z_l) + DP_H[k]) + t);
	t1 = __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)
	double y1 = y;
	y1 = __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 * INFINITY; // Overflow
	else {
	final double OVT = 8.0085662595372944372e-0017; // -(1024-log2(ovfl+.5ulp))
	if (p_l + OVT > z - p_h)
	return s * INFINITY; // Overflow
	}
	} else if ((j & 0x7fffffff) >= 0x4090cc00 ) { // z <= -1075
	if (((j - 0xc090cc00) \| i)!=0) // z < -1075
	return s * 0.0; // Underflow
	else {
	if (p_l <= z - p_h)
	return s * 0.0; // Underflow
	}
	}
	/*
	* Compute 2**(p_h+p_l)
	*/
	// Poly coefs for (3/2)(log(x)-2s-2/3s**3
	final double P1 = 0x1.5555_5555_5553ep-3; // 1.66666666666666019037e-01
	final double P2 = -0x1.6c16_c16b_ebd93p-9; // -2.77777777770155933842e-03
	final double P3 = 0x1.1566_aaf2_5de2cp-14; // 6.61375632143793436117e-05
	final double P4 = -0x1.bbd4_1c5d_26bf1p-20; // -1.65339022054652515390e-06
	final double P5 = 0x1.6376_972b_ea4d0p-25; // 4.13813679705723846039e-08
	final double LG2 = 0x1.62e4_2fef_a39efp-1; // 6.93147180559945286227e-01
	final double LG2_H = 0x1.62e43p-1; // 6.93147182464599609375e-01
	final double LG2_L = -0x1.05c6_10ca_86c39p-29; // -1.90465429995776804525e-09
	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 = 0.0;
	t = __HI(t, (n & ~(0x000fffff >> k)) );
	n = ((n & 0x000fffff) \| 0x00100000) >> (20 - k);
	if (j < 0)
	n = -n;
	p_h -= t;
	}
	t = p_l + p_h;
	t = __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 - 2.0) - (w + z * w);
	z = 1.0 - (r - z);
	j = __HI(z);
	j += (n << 20);
	if ((j >> 20) <= 0)
	z = Math.scalb(z, n); // subnormal output
	else {
	int z_hi = __HI(z);
	z_hi += (n << 20);
	z = __HI(z, z_hi);
	}
	return s * z;
	}
	}

	/**
	* 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 = kln2 + r, \|r\| <= 0.5ln2.
	*
	* 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 + rr/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 + P1z + P2z*2 + P3z*3 + P4z*4 + P5z**5
	* (where z=r*r, and the values of P1 to P5 are listed below)
	* and
	* \| 5 \| -59
	* \| 2.0+P1z+...+P5z - 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 - (P1r + P2r + ... + 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= 0x1.0p-1000; // 9.33263618503218878990e-302 = 2^-1000
	private static final double o_threshold= 0x1.62e42fefa39efp9; // 7.09782712893383973096e+02
	private static final double u_threshold= -0x1.74910d52d3051p9; // -7.45133219101941108420e+02;
	private static final double[] ln2HI ={ 0x1.62e42feep-1, // 6.93147180369123816490e-01
	-0x1.62e42feep-1}; // -6.93147180369123816490e-01
	private static final double[] ln2LO ={ 0x1.a39ef35793c76p-33, // 1.90821492927058770002e-10
	-0x1.a39ef35793c76p-33}; // -1.90821492927058770002e-10
	private static final double invln2 = 0x1.71547652b82fep0; // 1.44269504088896338700e+00

	private static final double P1 = 0x1.555555555553ep-3; // 1.66666666666666019037e-01
	private static final double P2 = -0x1.6c16c16bebd93p-9; // -2.77777777770155933842e-03
	private static final double P3 = 0x1.1566aaf25de2cp-14; // 6.61375632143793436117e-05
	private static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06
	private static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08

	private Exp() {
	throw new UnsupportedOperationException();
	}

	// should be able to forgo strictfp due to controlled over/underflow
	public static strictfp double compute(double x) {
	double y;
	double hi = 0.0;
	double lo = 0.0;
	double c;
	double t;
	int k = 0;
	int 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) // unsigned compare needed here?
	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 - tln2HI[0]; / tln2HI 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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