/* java.lang.StrictMath -- common mathematical functions, strict Java
- Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
+ Copyright (C) 1998, 2001, 2002, 2003, 2006 Free Software Foundation, Inc.
This file is part of GNU Classpath.
}
/**
+ * Returns the hyperbolic sine of <code>x</code> which is defined as
+ * (exp(x) - exp(-x)) / 2.
+ *
+ * Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN</li>
+ * <li>If the argument is positive infinity, the result is positive
+ * infinity.</li>
+ * <li>If the argument is negative infinity, the result is negative
+ * infinity.</li>
+ * <li>If the argument is zero, the result is zero.</li>
+ * </ul>
+ *
+ * @param x the argument to <em>sinh</em>
+ * @return the hyperbolic sine of <code>x</code>
+ *
+ * @since 1.5
+ */
+ public static double sinh(double x)
+ {
+ // Method :
+ // mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ // 1. Replace x by |x| (sinh(-x) = -sinh(x)).
+ // 2.
+ // E + E/(E+1)
+ // 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
+ // 2
+ //
+ // 22 <= x <= lnovft : sinh(x) := exp(x)/2
+ // lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
+ // ln2ovft < x : sinh(x) := +inf (overflow)
+
+ double t, w, h;
+
+ long bits;
+ long h_bits;
+ long l_bits;
+
+ // handle special cases
+ if (x != x)
+ return x;
+ if (x == Double.POSITIVE_INFINITY)
+ return Double.POSITIVE_INFINITY;
+ if (x == Double.NEGATIVE_INFINITY)
+ return Double.NEGATIVE_INFINITY;
+
+ if (x < 0)
+ h = - 0.5;
+ else
+ h = 0.5;
+
+ bits = Double.doubleToLongBits(x);
+ h_bits = getHighDWord(bits) & 0x7fffffffL; // ignore sign
+ l_bits = getLowDWord(bits);
+
+ // |x| in [0, 22], return sign(x) * 0.5 * (E+E/(E+1))
+ if (h_bits < 0x40360000L) // |x| < 22
+ {
+ if (h_bits < 0x3e300000L) // |x| < 2^-28
+ return x; // for tiny arguments return x
+
+ t = expm1(abs(x));
+
+ if (h_bits < 0x3ff00000L)
+ return h * (2.0 * t - t * t / (t + 1.0));
+
+ return h * (t + t / (t + 1.0));
+ }
+
+ // |x| in [22, log(Double.MAX_VALUE)], return 0.5 * exp(|x|)
+ if (h_bits < 0x40862e42L)
+ return h * exp(abs(x));
+
+ // |x| in [log(Double.MAX_VALUE), overflowthreshold]
+ if ((h_bits < 0x408633ceL)
+ || ((h_bits == 0x408633ceL) && (l_bits <= 0x8fb9f87dL)))
+ {
+ w = exp(0.5 * abs(x));
+ t = h * w;
+
+ return t * w;
+ }
+
+ // |x| > overflowthershold
+ return h * Double.POSITIVE_INFINITY;
+ }
+
+ /**
+ * Returns the hyperbolic cosine of <code>x</code>, which is defined as
+ * (exp(x) + exp(-x)) / 2.
+ *
+ * Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN</li>
+ * <li>If the argument is positive infinity, the result is positive
+ * infinity.</li>
+ * <li>If the argument is negative infinity, the result is positive
+ * infinity.</li>
+ * <li>If the argument is zero, the result is one.</li>
+ * </ul>
+ *
+ * @param x the argument to <em>cosh</em>
+ * @return the hyperbolic cosine of <code>x</code>
+ *
+ * @since 1.5
+ */
+ public static double cosh(double x)
+ {
+ // Method :
+ // mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ // 1. Replace x by |x| (cosh(x) = cosh(-x)).
+ // 2.
+ // [ exp(x) - 1 ]^2
+ // 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
+ // 2*exp(x)
+ //
+ // exp(x) + 1/exp(x)
+ // ln2/2 <= x <= 22 : cosh(x) := ------------------
+ // 2
+ // 22 <= x <= lnovft : cosh(x) := exp(x)/2
+ // lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
+ // ln2ovft < x : cosh(x) := +inf (overflow)
+
+ double t, w;
+ long bits;
+ long hx;
+ long lx;
+
+ // handle special cases
+ if (x != x)
+ return x;
+ if (x == Double.POSITIVE_INFINITY)
+ return Double.POSITIVE_INFINITY;
+ if (x == Double.NEGATIVE_INFINITY)
+ return Double.POSITIVE_INFINITY;
+
+ bits = Double.doubleToLongBits(x);
+ hx = getHighDWord(bits) & 0x7fffffffL; // ignore sign
+ lx = getLowDWord(bits);
+
+ // |x| in [0, 0.5 * ln(2)], return 1 + expm1(|x|)^2 / (2 * exp(|x|))
+ if (hx < 0x3fd62e43L)
+ {
+ t = expm1(abs(x));
+ w = 1.0 + t;
+
+ // for tiny arguments return 1.
+ if (hx < 0x3c800000L)
+ return w;
+
+ return 1.0 + (t * t) / (w + w);
+ }
+
+ // |x| in [0.5 * ln(2), 22], return exp(|x|)/2 + 1 / (2 * exp(|x|))
+ if (hx < 0x40360000L)
+ {
+ t = exp(abs(x));
+
+ return 0.5 * t + 0.5 / t;
+ }
+
+ // |x| in [22, log(Double.MAX_VALUE)], return 0.5 * exp(|x|)
+ if (hx < 0x40862e42L)
+ return 0.5 * exp(abs(x));
+
+ // |x| in [log(Double.MAX_VALUE), overflowthreshold],
+ // return exp(x/2)/2 * exp(x/2)
+ if ((hx < 0x408633ceL)
+ || ((hx == 0x408633ceL) && (lx <= 0x8fb9f87dL)))
+ {
+ w = exp(0.5 * abs(x));
+ t = 0.5 * w;
+
+ return t * w;
+ }
+
+ // |x| > overflowthreshold
+ return Double.POSITIVE_INFINITY;
+ }
+
+ /**
+ * Returns the hyperbolic tangent of <code>x</code>, which is defined as
+ * (exp(x) - exp(-x)) / (exp(x) + exp(-x)), i.e. sinh(x) / cosh(x).
+ *
+ Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN</li>
+ * <li>If the argument is positive infinity, the result is 1.</li>
+ * <li>If the argument is negative infinity, the result is -1.</li>
+ * <li>If the argument is zero, the result is zero.</li>
+ * </ul>
+ *
+ * @param x the argument to <em>tanh</em>
+ * @return the hyperbolic tagent of <code>x</code>
+ *
+ * @since 1.5
+ */
+ public static double tanh(double x)
+ {
+ // Method :
+ // 0. tanh(x) is defined to be (exp(x) - exp(-x)) / (exp(x) + exp(-x))
+ // 1. reduce x to non-negative by tanh(-x) = -tanh(x).
+ // 2. 0 <= x <= 2^-55 : tanh(x) := x * (1.0 + x)
+ // -t
+ // 2^-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
+ // t + 2
+ // 2
+ // 1 <= x <= 22.0 : tanh(x) := 1 - ----- ; t=expm1(2x)
+ // t + 2
+ // 22.0 < x <= INF : tanh(x) := 1.
+
+ double t, z;
+
+ long bits;
+ long h_bits;
+
+ // handle special cases
+ if (x != x)
+ return x;
+ if (x == Double.POSITIVE_INFINITY)
+ return 1.0;
+ if (x == Double.NEGATIVE_INFINITY)
+ return -1.0;
+
+ bits = Double.doubleToLongBits(x);
+ h_bits = getHighDWord(bits) & 0x7fffffffL; // ingnore sign
+
+ if (h_bits < 0x40360000L) // |x| < 22
+ {
+ if (h_bits < 0x3c800000L) // |x| < 2^-55
+ return x * (1.0 + x);
+
+ if (h_bits >= 0x3ff00000L) // |x| >= 1
+ {
+ t = expm1(2.0 * abs(x));
+ z = 1.0 - 2.0 / (t + 2.0);
+ }
+ else // |x| < 1
+ {
+ t = expm1(-2.0 * abs(x));
+ z = -t / (t + 2.0);
+ }
+ }
+ else // |x| >= 22
+ z = 1.0;
+
+ return (x >= 0) ? z : -z;
+ }
+
+ /**
+ * Returns the lower two words of a long. This is intended to be
+ * used like this:
+ * <code>getLowDWord(Double.doubleToLongBits(x))</code>.
+ */
+ private static long getLowDWord(long x)
+ {
+ return x & 0x00000000ffffffffL;
+ }
+
+ /**
+ * Returns the higher two words of a long. This is intended to be
+ * used like this:
+ * <code>getHighDWord(Double.doubleToLongBits(x))</code>.
+ */
+ private static long getHighDWord(long x)
+ {
+ return (x & 0xffffffff00000000L) >> 32;
+ }
+
+ /**
+ * Returns a double with the IEEE754 bit pattern given in the lower
+ * and higher two words <code>lowDWord</code> and <code>highDWord</code>.
+ */
+ private static double buildDouble(long lowDWord, long highDWord)
+ {
+ return Double.longBitsToDouble(((highDWord & 0xffffffffL) << 32)
+ | (lowDWord & 0xffffffffL));
+ }
+
+ /**
+ * Returns the cube root of <code>x</code>. The sign of the cube root
+ * is equal to the sign of <code>x</code>.
+ *
+ * Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN</li>
+ * <li>If the argument is positive infinity, the result is positive
+ * infinity.</li>
+ * <li>If the argument is negative infinity, the result is negative
+ * infinity.</li>
+ * <li>If the argument is zero, the result is zero with the same
+ * sign as the argument.</li>
+ * </ul>
+ *
+ * @param x the number to take the cube root of
+ * @return the cube root of <code>x</code>
+ * @see #sqrt(double)
+ *
+ * @since 1.5
+ */
+ public static double cbrt(double x)
+ {
+ boolean negative = (x < 0);
+ double r;
+ double s;
+ double t;
+ double w;
+
+ long bits;
+ long l;
+ long h;
+
+ // handle the special cases
+ if (x != x)
+ return x;
+ if (x == Double.POSITIVE_INFINITY)
+ return Double.POSITIVE_INFINITY;
+ if (x == Double.NEGATIVE_INFINITY)
+ return Double.NEGATIVE_INFINITY;
+ if (x == 0)
+ return x;
+
+ x = abs(x);
+ bits = Double.doubleToLongBits(x);
+
+ if (bits < 0x0010000000000000L) // subnormal number
+ {
+ t = TWO_54;
+ t *= x;
+
+ // __HI(t)=__HI(t)/3+B2;
+ bits = Double.doubleToLongBits(t);
+ h = getHighDWord(bits);
+ l = getLowDWord(bits);
+
+ h = h / 3 + CBRT_B2;
+
+ t = buildDouble(l, h);
+ }
+ else
+ {
+ // __HI(t)=__HI(x)/3+B1;
+ h = getHighDWord(bits);
+ l = 0;
+
+ h = h / 3 + CBRT_B1;
+ t = buildDouble(l, h);
+ }
+
+ // new cbrt to 23 bits
+ r = t * t / x;
+ s = CBRT_C + r * t;
+ t *= CBRT_G + CBRT_F / (s + CBRT_E + CBRT_D / s);
+
+ // chopped to 20 bits and make it larger than cbrt(x)
+ bits = Double.doubleToLongBits(t);
+ h = getHighDWord(bits);
+
+ // __LO(t)=0;
+ // __HI(t)+=0x00000001;
+ l = 0;
+ h += 1;
+ t = buildDouble(l, h);
+
+ // 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 - t is exact
+ t = t + t * r;
+
+ return negative ? -t : t;
+ }
+
+ /**
* Take <em>e</em><sup>a</sup>. The opposite of <code>log()</code>. If the
* argument is NaN, the result is NaN; if the argument is positive infinity,
* the result is positive infinity; and if the argument is negative
}
/**
+ * Returns <em>e</em><sup>x</sup> - 1.
+ * Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN.</li>
+ * <li>If the argument is positive infinity, the result is positive
+ * infinity</li>
+ * <li>If the argument is negative infinity, the result is -1.</li>
+ * <li>If the argument is zero, the result is zero.</li>
+ * </ul>
+ *
+ * @param x the argument to <em>e</em><sup>x</sup> - 1.
+ * @return <em>e</em> raised to the power <code>x</code> minus one.
+ * @see #exp(double)
+ */
+ public static double expm1(double x)
+ {
+ // Method
+ // 1. Argument reduction:
+ // Given x, find r and integer k such that
+ //
+ // x = k * ln(2) + r, |r| <= 0.5 * ln(2)
+ //
+ // Here a correction term c will be computed to compensate
+ // the error in r when rounded to a floating-point number.
+ //
+ // 2. Approximating expm1(r) by a special rational function on
+ // the interval [0, 0.5 * ln(2)]:
+ // Since
+ // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 - r^4/360 + ...
+ // we define R1(r*r) by
+ // r*(exp(r)+1)/(exp(r)-1) = 2 + r^2/6 * R1(r*r)
+ // That is,
+ // R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ // = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
+ // = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+ // We use a special Remes algorithm on [0, 0.347] to generate
+ // a polynomial of degree 5 in r*r to approximate R1. The
+ // maximum error of this polynomial approximation is bounded
+ // by 2**-61. In other words,
+ // R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
+ // where Q1 = -1.6666666666666567384E-2,
+ // Q2 = 3.9682539681370365873E-4,
+ // Q3 = -9.9206344733435987357E-6,
+ // Q4 = 2.5051361420808517002E-7,
+ // Q5 = -6.2843505682382617102E-9;
+ // (where z=r*r, and Q1 to Q5 are called EXPM1_Qx in the source)
+ // with error bounded by
+ // | 5 | -61
+ // | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
+ // | |
+ //
+ // expm1(r) = exp(r)-1 is then computed by the following
+ // specific way which minimize the accumulation rounding error:
+ // 2 3
+ // r r [ 3 - (R1 + R1*r/2) ]
+ // expm1(r) = r + --- + --- * [--------------------]
+ // 2 2 [ 6 - r*(3 - R1*r/2) ]
+ //
+ // To compensate the error in the argument reduction, we use
+ // expm1(r+c) = expm1(r) + c + expm1(r)*c
+ // ~ expm1(r) + c + r*c
+ // Thus c+r*c will be added in as the correction terms for
+ // expm1(r+c). Now rearrange the term to avoid optimization
+ // screw up:
+ // ( 2 2 )
+ // ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
+ // expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ // ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
+ // ( )
+ //
+ // = r - E
+ // 3. Scale back to obtain expm1(x):
+ // From step 1, we have
+ // expm1(x) = either 2^k*[expm1(r)+1] - 1
+ // = or 2^k*[expm1(r) + (1-2^-k)]
+ // 4. Implementation notes:
+ // (A). To save one multiplication, we scale the coefficient Qi
+ // to Qi*2^i, and replace z by (x^2)/2.
+ // (B). To achieve maximum accuracy, we compute expm1(x) by
+ // (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ // (ii) if k=0, return r-E
+ // (iii) if k=-1, return 0.5*(r-E)-0.5
+ // (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
+ // else return 1.0+2.0*(r-E);
+ // (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
+ // (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
+ // (vii) return 2^k(1-((E+2^-k)-r))
+
+ boolean negative = (x < 0);
+ double y, hi, lo, c, t, e, hxs, hfx, r1;
+ int k;
+
+ long bits;
+ long h_bits;
+ long l_bits;
+
+ c = 0.0;
+ y = abs(x);
+
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
+
+ // handle special cases and large arguments
+ if (h_bits >= 0x4043687aL) // if |x| >= 56 * ln(2)
+ {
+ if (h_bits >= 0x40862e42L) // if |x| >= EXP_LIMIT_H
+ {
+ if (h_bits >= 0x7ff00000L)
+ {
+ if (((h_bits & 0x000fffffL) | (l_bits & 0xffffffffL)) != 0)
+ return x; // exp(NaN) = NaN
+ else
+ return negative ? -1.0 : x; // exp({+-inf}) = {+inf, -1}
+ }
+
+ if (x > EXP_LIMIT_H)
+ return Double.POSITIVE_INFINITY; // overflow
+ }
+
+ if (negative) // x <= -56 * ln(2)
+ return -1.0;
+ }
+
+ // argument reduction
+ if (h_bits > 0x3fd62e42L) // |x| > 0.5 * ln(2)
+ {
+ if (h_bits < 0x3ff0a2b2L) // |x| < 1.5 * ln(2)
+ {
+ if (negative)
+ {
+ hi = x + LN2_H;
+ lo = -LN2_L;
+ k = -1;
+ }
+ else
+ {
+ hi = x - LN2_H;
+ lo = LN2_L;
+ k = 1;
+ }
+ }
+ else
+ {
+ k = (int) (INV_LN2 * x + (negative ? - 0.5 : 0.5));
+ t = k;
+ hi = x - t * LN2_H;
+ lo = t * LN2_L;
+ }
+
+ x = hi - lo;
+ c = (hi - x) - lo;
+
+ }
+ else if (h_bits < 0x3c900000L) // |x| < 2^-54 return x
+ return x;
+ else
+ k = 0;
+
+ // x is now in primary range
+ hfx = 0.5 * x;
+ hxs = x * hfx;
+ r1 = 1.0 + hxs * (EXPM1_Q1
+ + hxs * (EXPM1_Q2
+ + hxs * (EXPM1_Q3
+ + hxs * (EXPM1_Q4
+ + hxs * EXPM1_Q5))));
+ t = 3.0 - r1 * hfx;
+ e = hxs * ((r1 - t) / (6.0 - x * t));
+
+ if (k == 0)
+ {
+ return x - (x * e - hxs); // c == 0
+ }
+ else
+ {
+ e = x * (e - c) - c;
+ e -= hxs;
+
+ if (k == -1)
+ return 0.5 * (x - e) - 0.5;
+
+ if (k == 1)
+ {
+ if (x < - 0.25)
+ return -2.0 * (e - (x + 0.5));
+ else
+ return 1.0 + 2.0 * (x - e);
+ }
+
+ if (k <= -2 || k > 56) // sufficient to return exp(x) - 1
+ {
+ y = 1.0 - (e - x);
+
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
+
+ h_bits += (k << 20); // add k to y's exponent
+
+ y = buildDouble(l_bits, h_bits);
+
+ return y - 1.0;
+ }
+
+ t = 1.0;
+ if (k < 20)
+ {
+ bits = Double.doubleToLongBits(t);
+ h_bits = 0x3ff00000L - (0x00200000L >> k);
+ l_bits = getLowDWord(bits);
+
+ t = buildDouble(l_bits, h_bits); // t = 1 - 2^(-k)
+ y = t - (e - x);
+
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
+
+ h_bits += (k << 20); // add k to y's exponent
+
+ y = buildDouble(l_bits, h_bits);
+ }
+ else
+ {
+ bits = Double.doubleToLongBits(t);
+ h_bits = (0x000003ffL - k) << 20;
+ l_bits = getLowDWord(bits);
+
+ t = buildDouble(l_bits, h_bits); // t = 2^(-k)
+
+ y = x - (e + t);
+ y += 1.0;
+
+ bits = Double.doubleToLongBits(y);
+ h_bits = getHighDWord(bits);
+ l_bits = getLowDWord(bits);
+
+ h_bits += (k << 20); // add k to y's exponent
+
+ y = buildDouble(l_bits, h_bits);
+ }
+ }
+
+ return y;
+ }
+
+ /**
* Take ln(a) (the natural log). The opposite of <code>exp()</code>. If the
* argument is NaN or negative, the result is NaN; if the argument is
* positive infinity, the result is positive infinity; and if the argument
/**
* Super precision for 2/pi in 24-bit chunks, for use in
- * {@link #remPiOver2()}.
+ * {@link #remPiOver2(double, double[])}.
*/
private static final int TWO_OVER_PI[] = {
0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62,
/**
* Super precision for pi/2 in 24-bit chunks, for use in
- * {@link #remPiOver2()}.
+ * {@link #remPiOver2(double, double[])}.
*/
private static final double PI_OVER_TWO[] = {
1.570796251296997, // Long bits 0x3ff921fb40000000L.
};
/**
- * More constants related to pi, used in {@link #remPiOver2()} and
- * elsewhere.
+ * More constants related to pi, used in
+ * {@link #remPiOver2(double, double[])} and elsewhere.
*/
private static final double
PI_L = 1.2246467991473532e-16, // Long bits 0x3ca1a62633145c07L.
/**
* Natural log and square root constants, for calculation of
* {@link #exp(double)}, {@link #log(double)} and
- * {@link #power(double, double)}. CP is 2/(3*ln(2)).
+ * {@link #pow(double, double)}. CP is 2/(3*ln(2)).
*/
private static final double
SQRT_1_5 = 1.224744871391589, // Long bits 0x3ff3988e1409212eL.
AT10 = 0.016285820115365782; // Long bits 0x3f90ad3ae322da11L.
/**
+ * Constants for computing {@link #cbrt(double)}.
+ */
+ private static final int
+ CBRT_B1 = 715094163, // B1 = (682-0.03306235651)*2**20
+ CBRT_B2 = 696219795; // B2 = (664-0.03306235651)*2**20
+
+ /**
+ * Constants for computing {@link #cbrt(double)}.
+ */
+ private static final double
+ CBRT_C = 5.42857142857142815906e-01, // Long bits 0x3fe15f15f15f15f1L
+ CBRT_D = -7.05306122448979611050e-01, // Long bits 0xbfe691de2532c834L
+ CBRT_E = 1.41428571428571436819e+00, // Long bits 0x3ff6a0ea0ea0ea0fL
+ CBRT_F = 1.60714285714285720630e+00, // Long bits 0x3ff9b6db6db6db6eL
+ CBRT_G = 3.57142857142857150787e-01; // Long bits 0x3fd6db6db6db6db7L
+
+ /**
+ * Constants for computing {@link #expm1(double)}
+ */
+ private static final double
+ EXPM1_Q1 = -3.33333333333331316428e-02, // Long bits 0xbfa11111111110f4L
+ EXPM1_Q2 = 1.58730158725481460165e-03, // Long bits 0x3f5a01a019fe5585L
+ EXPM1_Q3 = -7.93650757867487942473e-05, // Long bits 0xbf14ce199eaadbb7L
+ EXPM1_Q4 = 4.00821782732936239552e-06, // Long bits 0x3ed0cfca86e65239L
+ EXPM1_Q5 = -2.01099218183624371326e-07; // Long bits 0xbe8afdb76e09c32dL
+
+ /**
* Helper function for reducing an angle to a multiple of pi/2 within
* [-pi/4, pi/4].
*
j |= iq[i];
if (j == 0) // Need recomputation.
{
- int k;
- for (k = 1; iq[jk - k] == 0; k++); // k = no. of terms needed.
+ int k; // k = no. of terms needed.
+ for (k = 1; iq[jk - k] == 0; k++)
+ ;
for (i = jz + 1; i <= jz + k; i++) // Add q[jz+1] to q[jz+k].
{
double t = (float) a;
return t + a * (1 + t * z + t * v);
}
+
+ /**
+ * <p>
+ * Returns the sign of the argument as follows:
+ * </p>
+ * <ul>
+ * <li>If <code>a</code> is greater than zero, the result is 1.0.</li>
+ * <li>If <code>a</code> is less than zero, the result is -1.0.</li>
+ * <li>If <code>a</code> is <code>NaN</code>, the result is <code>NaN</code>.
+ * <li>If <code>a</code> is positive or negative zero, the result is the
+ * same.</li>
+ * </ul>
+ *
+ * @param a the numeric argument.
+ * @return the sign of the argument.
+ * @since 1.5.
+ */
+ public static double signum(double a)
+ {
+ // There's no difference.
+ return Math.signum(a);
+ }
+
+ /**
+ * <p>
+ * Returns the sign of the argument as follows:
+ * </p>
+ * <ul>
+ * <li>If <code>a</code> is greater than zero, the result is 1.0f.</li>
+ * <li>If <code>a</code> is less than zero, the result is -1.0f.</li>
+ * <li>If <code>a</code> is <code>NaN</code>, the result is <code>NaN</code>.
+ * <li>If <code>a</code> is positive or negative zero, the result is the
+ * same.</li>
+ * </ul>
+ *
+ * @param a the numeric argument.
+ * @return the sign of the argument.
+ * @since 1.5.
+ */
+ public static float signum(float a)
+ {
+ // There's no difference.
+ return Math.signum(a);
+ }
+
+ /**
+ * Return the ulp for the given double argument. The ulp is the
+ * difference between the argument and the next larger double. Note
+ * that the sign of the double argument is ignored, that is,
+ * ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned.
+ * If the argument is an infinity, then +Inf is returned. If the
+ * argument is zero (either positive or negative), then
+ * {@link Double#MIN_VALUE} is returned.
+ * @param d the double whose ulp should be returned
+ * @return the difference between the argument and the next larger double
+ * @since 1.5
+ */
+ public static double ulp(double d)
+ {
+ // There's no difference.
+ return Math.ulp(d);
+ }
+
+ /**
+ * Return the ulp for the given float argument. The ulp is the
+ * difference between the argument and the next larger float. Note
+ * that the sign of the float argument is ignored, that is,
+ * ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned.
+ * If the argument is an infinity, then +Inf is returned. If the
+ * argument is zero (either positive or negative), then
+ * {@link Float#MIN_VALUE} is returned.
+ * @param f the float whose ulp should be returned
+ * @return the difference between the argument and the next larger float
+ * @since 1.5
+ */
+ public static float ulp(float f)
+ {
+ // There's no difference.
+ return Math.ulp(f);
+ }
}
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