/*
 * Copyright (c) 1998, 2017, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
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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)*2**20 */
 private static final int B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */

 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 = x*x + y*y
 * has error less than sqrt(2)/2 ulp, than
 * sqrt(z) has error less than 1 ulp (exercise).
 *
 * So, compute sqrt(x*x + y*y) 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
 * x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y
 * where x1 = x with lower 32 bits cleared, x2 = x - x1; else
 * 2. if x <= 2y use
 * t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y))
 * 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(t1*t1 - (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(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));
 }
 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 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.
 */
 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 =わ 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-2/3*s**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/(3*log2) = 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-2/3*s**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 = 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= 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 - 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;
 }
 }
 }
}