package com.codename1.util;
/*
* Ported from the Sun Microsystems FDLIBM C-library.
* (Freely Distributable Library for Math)
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/**
* MathUtil for Java ME.
* This fills the gap in Java ME Math with a port of Sun's public FDLIBM C-library for IEEE-754.
*
* @author kmashint
*
* @see http://www.netlib.org/fdlibm/readme
* For the Freely Distributable C-library conforming to IEEE-754 floating point math.
* @see http://web.mit.edu/source/third/gcc/libjava/java/lang/
* For the GNU C variant of the same IEEE-754 routines.
* @see http://www.dclausen.net/projects/microfloat/
* Another take on the IEEE-754 routines.
* @see http://real-java.sourceforge.net/Real.html
* Yet another take on the IEEE-754 routines.
* @see http://today.java.net/pub/a/today/2007/11/06/creating-java-me-math-pow-method.html
* For other approximations.
* @see http://martin.ankerl.com/2007/10/04/optimized-pow-approximation-for-java-and-c-c/
* For fast but rough approximations.
* @see http://martin.ankerl.com/2007/02/11/optimized-exponential-functions-for-java/
* For more fast but rough approximations.
*/
public abstract class MathUtil {
/* Common constants. */
private static final double zero = 0.0,
one = 1.0,
two = 2.0,
tiny = 1.0e-300,
huge = 1.0e+300,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
private static final double pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
private static final double pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
private static final double log10 = 2.302585092994046D; /* Natural log(10.0D). */
private static final long HI_MASK = 0xffffffff00000000L,
LO_MASK = 0x00000000ffffffffL;
private static final int HI_SHIFT = 32;
/**
* Return Math.E to the exponent a.
* This in turn uses ieee7854_exp(double).
*/
public static final double exp(double a) {
return ieee754_exp(a);
}
/**
* Return the natural logarithm, ln(a), as it relates to Math.E.
* This in turn uses ieee7854_log(double).
*/
public static final double log(double a) {
return ieee754_log(a);
}
/**
* Return the common base-10 logarithm, log10(a).
* This in turn uses ieee7854_log(double)/ieee7854_log(10.0).
*/
public static final double log10(double a) {
return ieee754_log(a) / log10;
}
/**
* Return a to the power of b, sometimes written as a ** b
* but not to be confused with the bitwise ^ operator.
* This in turn uses ieee7854_log(double).
*/
public static final double pow(double a, double b) {
return ieee754_pow(a, b);
}
/**
* Return the arcsine of a.
*/
public static final double asin(double a) {
return ieee754_asin(a);
}
/**
* Return the arccosine of a.
*/
public static final double acos(double a) {
return ieee754_acos(a);
}
/**
* Return the arctangent of a, call it b, where a = tan(b).
*/
public static final double atan(double a) {
return ieee754_atan(a);
}
/**
* For any real arguments x and y not both equal to zero, atan2(y, x)
* is the angle in radians between the positive x-axis of a plane
* and the point given by the coordinates (x, y) on it.
* The angle is positive for counter-clockwise angles (upper half-plane, y > 0),
* and negative for clockwise angles (lower half-plane, y < 0).
* This in turn uses ieee7854_arctan2(double).
*/
public static final double atan2(double b, double a) {
return ieee754_atan2(a, b);
}
/* __ieee754_exp(x)
* 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 Remes 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.
*/
private static final double twom1000 = 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold = -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
invln2 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
private static final double[] halF = new double[]{0.5, -0.5},
ln2HI = new double[]{6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
-6.93147180369123816490e-01}, /* 0xbfe62e42, 0xfee00000 */
ln2LO = new double[]{1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
-1.90821492927058770002e-10}; /* 0xbdea39ef, 0x35793c76 */
private static final double ieee754_exp(double x) {
double y, c, t;
double hi = 0, lo = 0;
int k = 0;
int xsb, hx, lx;
long yl;
long xl = Double.doubleToLongBits(x);
hx = (int) ((long) xl >>> HI_SHIFT); /* 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) {
lx = (int) ((long) xl & LO_MASK); /* low word of x */
if (((hx & 0xfffff) | lx) != 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; // handled at declaration
/* 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);
}
yl = Double.doubleToLongBits(y);
if (k >= -1021) {
yl += ((long) k << (20 + HI_SHIFT)); /* add k to y's exponent */
return Double.longBitsToDouble(yl);
} else {
yl += ((long) (k + 1000) << (20 + HI_SHIFT));/* add k to y's exponent */
return Double.longBitsToDouble(yl) * twom1000;
}
}
/* __ieee754_log(x)
* Return the logrithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* 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.
*/
private static final double ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
private static final double ieee754_log(double x) {
double hfsq, f, s, z, R, w, t1, t2, dk;
int k, hx, lx, i, j;
long xl = Double.doubleToLongBits(x);
hx = (int) (xl >> HI_SHIFT); /* high word of x */
lx = (int) (xl & LO_MASK); /* low word of x */
k = 0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx & 0x7fffffff) | lx) == 0) {
return -two54 / zero; /* log(+-0)=-inf */
}
if (hx < 0) {
return (x - x) / zero; /* log(-#) = NaN */
}
k -= 54;
x *= two54; /* subnormal number, scale up x */
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT); /* high word of x */
}
if (hx >= 0x7ff00000) {
return x + x;
}
k += (hx >> 20) - 1023;
hx &= 0x000fffff;
i = (hx + 0x95f64) & 0x100000;
//__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
x = Double.longBitsToDouble(((long) (hx | (i ^ 0x3ff00000)) << HI_SHIFT) | (Double.doubleToLongBits(x) & LO_MASK));
k += (i >> 20);
f = x - 1.0;
if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
if (f == zero) {
if (k == 0) {
return zero;
} else {
dk = (double) k;
return dk * ln2_hi + dk * ln2_lo;
}
}
R = f * f * (0.5 - 0.33333333333333333 * f);
if (k == 0) {
return f - R;
} else {
dk = (double) k;
return dk * ln2_hi - ((R - dk * ln2_lo) - f);
}
}
s = f / (2.0 + f);
dk = (double) k;
z = s * s;
i = hx - 0x6147a;
w = z * z;
j = 0x6b851 - hx;
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
i |= j;
R = t2 + t1;
if (i > 0) {
hfsq = 0.5 * f * f;
if (k == 0) {
return f - (hfsq - s * (hfsq + R));
} else {
return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f);
}
} else {
if (k == 0) {
return f - s * (f - R);
} else {
return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
}
}
}
/* __ieee754_pow(x,y) return 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 muti-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.
*
* 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.
*/
private static final double bp[] = {1.0, 1.5,},
dp_h[] = {0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = {0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
private static final double ieee754_pow(double x, double y) {
double z, ax, z_h, z_l, p_h, p_l;
double y1, t1, t2, r, s, t, u, v, w;
//int i0,i1;
int i, j, k, yisint, n;
int hx, hy, ix, iy;
int lx, ly;
//i0 = (int)((Double.doubleToLongBits(one)) >>> (29+HI_SHIFT))^1;
//i1 = 1-i0;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
lx = (int) (Double.doubleToLongBits(x) & LO_MASK);
hy = (int) (Double.doubleToLongBits(y) >>> HI_SHIFT);
ly = (int) (Double.doubleToLongBits(y) & LO_MASK);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* y==zero: x**0 = 1 */
if ((iy | ly) == 0) {
return one;
}
/* +-NaN return x+y */
if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0))
|| iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) {
return x + y;
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if (hx < 0) {
if (iy >= 0x43400000) {
yisint = 2; /* even integer y */
} else if (iy >= 0x3ff00000) {
k = (iy >> 20) - 0x3ff; /* exponent */
if (k > 20) {
j = ly >> (52 - k);
if ((j << (52 - k)) == ly) {
yisint = 2 - (j & 1);
}
} else if (ly == 0) {
j = iy >> (20 - k);
if ((j << (20 - k)) == iy) {
yisint = 2 - (j & 1);
}
}
}
}
/* special value of y */
if (ly == 0) {
if (iy == 0x7ff00000) { /* y is +-inf */
if (((ix - 0x3ff00000) | lx) == 0) {
return y - y; /* inf**+-1 is NaN */
} else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ {
return (hy >= 0) ? y : zero;
} else /* (|x|<1)**-,+inf = inf,0 */ {
return (hy < 0) ? -y : zero;
}
}
if (iy == 0x3ff00000) { /* y is +-1 */
if (hy < 0) {
return one / x;
} else {
return x;
}
}
if (hy == 0x40000000) {
return x * x; /* y is 2 */
}
if (hy == 0x3fe00000) { /* y is 0.5 */
if (hx >= 0) /* x >= +0 */ {
return Math.sqrt(x);
}
}
}
ax = Math.abs(x);
/* special value of x */
if (lx == 0) {
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
z = ax; /*x is +-0,+-inf,+-1*/
if (hy < 0) {
z = one / z; /* z = (1/|x|) */
}
if (hx < 0) {
if (((ix - 0x3ff00000) | yisint) == 0) {
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
} else if (yisint == 1) {
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
}
return z;
}
}
n = (hx >>> 31) + 1;
/* (x<0)**(non-int) is NaN */
if ((n | yisint) == 0) {
return (x - x) / (x - x);
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if ((n | (yisint - 1)) == 0) {
s = -one;/* (-ve)**(odd int) */
}
/* |y| is huge */
if (iy > 0x41e00000) { /* if |y| > 2**31 */
if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
if (ix <= 0x3fefffff) {
return (hy < 0) ? huge * huge : tiny * tiny;
}
if (ix >= 0x3ff00000) {
return (hy > 0) ? huge * huge : tiny * tiny;
}
}
/* over/underflow if x is not close to one */
if (ix < 0x3fefffff) {
return (hy < 0) ? s * huge * huge : s * tiny * tiny;
}
if (ix > 0x3ff00000) {
return (hy > 0) ? s * huge * huge : s * tiny * tiny;
}
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = x - one; /* t has 20 trailing zeros */
w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
v = t * ivln2_l - w * ivln2;
t1 = u + v;
//__LO(t1) = 0; // keep high word
t1 = Double.longBitsToDouble(Double.doubleToLongBits(t1) & HI_MASK);
t2 = v - (t1 - u);
} else {
double ss, s2, s_h, s_l, t_h, t_l;
n = 0;
/* take care subnormal number */
if (ix < 0x00100000) {
ax *= two53;
n -= 53;
ix = (int) (Double.doubleToLongBits(ax) >>> HI_SHIFT);
}
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;
}
//__HI(ax) = ix;
ax = Double.longBitsToDouble(((long) ix << HI_SHIFT) | (Double.doubleToLongBits(ax) & LO_MASK));
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one / (ax + bp[k]);
ss = u * v;
s_h = ss;
//__LO(s_h) = 0; // keep high word
s_h = Double.longBitsToDouble(Double.doubleToLongBits(s_h) & HI_MASK);
/* t_h=ax+bp[k] High */
t_h = zero;
//__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
t_h = Double.longBitsToDouble(((long) ((int) ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)) << HI_SHIFT) | (Double.doubleToLongBits(t_h) & LO_MASK));
t_l = ax - (t_h - bp[k]);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
/* compute log(ax) */
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;
//__LO(t_h) = 0; // keep high word
t_h = Double.longBitsToDouble(Double.doubleToLongBits(t_h) & HI_MASK);
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;
//__LO(p_h) = 0; // keep high word
p_h = Double.longBitsToDouble(Double.doubleToLongBits(p_h) & HI_MASK);
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(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double) n;
t1 = (((z_h + z_l) + dp_h[k]) + t);
//__LO(t1) = 0; // keep high word
t1 = Double.longBitsToDouble(Double.doubleToLongBits(t1) & HI_MASK);
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
//__LO(y1) = 0; // keep high word
y1 = Double.longBitsToDouble(Double.doubleToLongBits(y1) & HI_MASK);
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
j = (int) (Double.doubleToLongBits(z) >>> HI_SHIFT);
i = (int) (Double.doubleToLongBits(z) & LO_MASK);
if (j >= 0x40900000) { /* z >= 1024 */
if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ {
return s * huge * huge; /* overflow */
} else {
if (p_l + ovt > z - p_h) {
return s * huge * huge; /* overflow */
}
}
} else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ {
return s * tiny * tiny; /* underflow */
} else {
if (p_l <= z - p_h) {
return s * tiny * tiny; /* underflow */
}
}
}
/*
* compute 2**(p_h+p_l)
*/
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 = zero;
//__HI(t) = (n&~(0x000fffff>>k));
t = Double.longBitsToDouble(((long) (n & ~(0x000fffff >> k)) << HI_SHIFT) | (Double.doubleToLongBits(t) & LO_MASK));
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
if (j < 0) {
n = -n;
}
p_h -= t;
}
t = p_l + p_h;
//__LO(t) = 0; // keep high word
t = Double.longBitsToDouble(Double.doubleToLongBits(t) & HI_MASK);
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 - two) - (w + z * w);
z = one - (r - z);
j = (int) ((long) Double.doubleToLongBits(z) >>> HI_SHIFT);
j += (n << 20);
if ((j >> 20) <= 0) {
z = scalb(z, n); /* subnormal output */
} else //__HI(z) = j;
{
z = Double.longBitsToDouble(((long) j << HI_SHIFT) | (Double.doubleToLongBits(z) & LO_MASK));
}
return s * z;
}
/* __ieee754_acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
private static final double ieee754_acos(double x) {
double z, p, q, r, w, s, c, df;
int hx, ix;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000) { /* |x| >= 1 */
if (((ix - 0x3ff00000) | (int) (Double.doubleToLongBits(x) & LO_MASK)) == 0) { /* |x|==1 */
if (hx > 0) {
return 0.0; /* acos(1) = 0 */
} else {
return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
}
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
}
if (ix < 0x3fe00000) { /* |x| < 0.5 */
if (ix <= 0x3c600000) {
return pio2_hi + pio2_lo;/*if|x|<2**-57*/
}
z = x * x;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
return pio2_hi - (x - (pio2_lo - x * r));
} else if (hx < 0) { /* x < -0.5 */
z = (one + x) * 0.5;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
s = Math.sqrt(z);
r = p / q;
w = r * s - pio2_lo;
return pi - 2.0 * (s + w);
} else { /* x > 0.5 */
z = (one - x) * 0.5;
s = Math.sqrt(z);
df = s;
//__LO(df) = 0; // keep high word
df = Double.longBitsToDouble(Double.doubleToLongBits(df) & HI_MASK);
c = (z - df * df) / (s + df);
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
w = r * s + c;
return 2.0 * (df + w);
}
}
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* where
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
* and its remez error is bounded by
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
*
* For x in [0.5,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
private static final double ieee754_asin(double x) {
double t, w, p, q, c, r, s;
int hx, ix;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000) { /* |x|>= 1 */
if (((ix - 0x3ff00000) | (int) (Double.doubleToLongBits(x) & LO_MASK)) == 0) /* asin(1)=+-pi/2 with inexact */ {
return x * pio2_hi + x * pio2_lo;
}
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
} else if (ix < 0x3fe00000) { /* |x|<0.5 */
if (ix < 0x3e400000) { /* if |x| < 2**-27 */
if (huge + x > one) {
return x;/* return x with inexact if x!=0*/
}
} else {
t = x * x;
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
w = p / q;
return x + x * w;
}
}
/* 1> |x|>= 0.5 */
w = one - Math.abs(x);
t = w * 0.5;
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
s = Math.sqrt(t);
if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
w = p / q;
t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
} else {
w = s;
//__LO(w) = 0; // keep the high word
w = Double.longBitsToDouble(Double.doubleToLongBits(w) & HI_MASK);
c = (t - w * w) / (s + w);
r = p / q;
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
q = pio4_hi - 2.0 * w;
t = pio4_hi - (p - q);
}
if (hx > 0) {
return t;
} else {
return -t;
}
}
/* atan(x)
* Method
* 1. Reduce x to positive by atan(x) = -atan(-x).
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
* is further reduced to one of the following intervals and the
* arctangent of t is evaluated by the corresponding formula:
*
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
*
* 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.
*/
private static final double atanhi[] = {
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */};
private static final double atanlo[] = {
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */};
private static final double aT[] = {
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */};
private static final double ieee754_atan(double x) {
double w, s1, s2, z;
int ix, hx, id;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
ix = hx & 0x7fffffff;
if (ix >= 0x44100000) { /* if |x| >= 2^66 */
if (ix > 0x7ff00000
|| (ix == 0x7ff00000 && ((int) (Double.doubleToLongBits(x) & LO_MASK) != 0))) {
return x + x; /* NaN */
}
if (hx > 0) {
return atanhi[3] + atanlo[3];
} else {
return -atanhi[3] - atanlo[3];
}
}
if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
if (ix < 0x3e200000) { /* |x| < 2^-29 */
if (huge + x > one) {
return x; /* raise inexact */
}
}
id = -1;
} else {
x = Math.abs(x);
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
id = 0;
x = (2.0 * x - one) / (2.0 + x);
} else { /* 11/16<=|x|< 19/16 */
id = 1;
x = (x - one) / (x + one);
}
} else {
if (ix < 0x40038000) { /* |x| < 2.4375 */
id = 2;
x = (x - 1.5) / (one + 1.5 * x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3;
x = -1.0 / x;
}
}
}
/* end of argument reduction */
z = x * x;
w = z * z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
if (id < 0) {
return x - x * (s1 + s2);
} else {
z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
return (hx < 0) ? -z : z;
}
}
/* __ieee754_atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* 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.
*/
private static final double ieee754_atan2(double x, double y) {
double z;
int k, m;
int hx, hy, ix, iy;
int lx, ly;
//i0 = (int)((Double.doubleToLongBits(one)) >> (29+HI_SHIFT))^1;
//i1 = 1-i0;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
lx = (int) (Double.doubleToLongBits(x) & LO_MASK);
hy = (int) (Double.doubleToLongBits(y) >>> HI_SHIFT);
ly = (int) (Double.doubleToLongBits(y) & LO_MASK);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000)
|| ((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* x or y is NaN */ {
return x + y;
}
if ((hx - 0x3ff00000 | lx) == 0) {
return ieee754_atan(y); /* x=1.0 */
}
m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if ((iy | ly) == 0) {
switch (m) {
case 0:
case 1:
return y; /* atan(+-0,+anything)=+-0 */
case 2:
return pi + tiny;/* atan(+0,-anything) = pi */
case 3:
return -pi - tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if ((ix | lx) == 0) {
return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
}
/* when x is INF */
if (ix == 0x7ff00000) {
if (iy == 0x7ff00000) {
switch (m) {
case 0:
return pi_o_4 + tiny;/* atan(+INF,+INF) */
case 1:
return -pi_o_4 - tiny;/* atan(-INF,+INF) */
case 2:
return 3.0 * pi_o_4 + tiny;/*atan(+INF,-INF)*/
case 3:
return -3.0 * pi_o_4 - tiny;/*atan(-INF,-INF)*/
}
} else {
switch (m) {
case 0:
return zero; /* atan(+...,+INF) */
case 1:
return -zero; /* atan(-...,+INF) */
case 2:
return pi + tiny; /* atan(+...,-INF) */
case 3:
return -pi - tiny; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if (iy == 0x7ff00000) {
return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
}
/* compute y/x */
k = (iy - ix) >> 20;
if (k > 60) {
z = pi_o_2 + 0.5 * pi_lo; /* |y/x| > 2**60 */
} else if (hx < 0 && k < -60) {
z = 0.0; /* |y|/x < -2**60 */
} else {
z = ieee754_atan(Math.abs(y / x)); /* safe to do y/x */
}
switch (m) {
case 0:
return z; /* atan(+,+) */
case 1:
return -z; /* atan(-,+) */
case 2:
return pi - (z - pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z - pi_lo) - pi;/* atan(-,-) */
}
}
/**
* scalbn (double x, int n)
* scalbn(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
public static final double scalb(double x, int n) {
int k, hx, lx;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
lx = (int) (Double.doubleToLongBits(x) & LO_MASK);
k = (hx & 0x7ff00000) >> 20; /* extract exponent */
if (k == 0) { /* 0 or subnormal x */
if ((lx | (hx & 0x7fffffff)) == 0) {
return x; /* +-0 */
}
x *= two54;
hx = (int) (Double.doubleToLongBits(x) >>> HI_SHIFT);
k = ((hx & 0x7ff00000) >> 20) - 54;
if (n < -50000) {
return tiny * x; /*underflow*/
}
}
if (k == 0x7ff) {
return x + x; /* NaN or Inf */
}
k = k + n;
if (k > 0x7fe) {
return huge * copySign(huge, x); /* overflow */
}
if (k > 0) /* normal result */ {
//__HI(x) = (hx&0x800fffff)|(k<<20);
x = Double.longBitsToDouble(((long) ((int) (hx & 0x800fffff) | (k << 20)) << HI_SHIFT) | (Double.doubleToLongBits(x) & LO_MASK));
return x;
}
if (k <= -54) {
if (n > 50000) /* in case integer overflow in n+k */ {
return huge * copySign(huge, x); /*overflow*/
} else {
return tiny * copySign(tiny, x); /*underflow*/
}
}
k += 54; /* subnormal result */
//__HI(x) = (hx&0x800fffff)|(k<<20);
x = Double.longBitsToDouble(((long) ((int) (hx & 0x800fffff) | (k << 20)) << HI_SHIFT) | (Double.doubleToLongBits(x) & LO_MASK));
return x * twom54;
}
/**
* Please update your code to use scalb
* @param x
* @param n
* @return scalb(x,n)
* @deprecated Please update your code to use scalb
*/
public static final double scalbn(double x, int n) {
return scalb(x, n);
}
/*
* copySign(double x, double y)
* copySign(x,y) returns a value with the magnitude of x and
* with the sign bit of y.
*/
public static final double copySign(final double x, final double y) {
//__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
// The below is actually about 30% faster than doing greater/less comparisons.
return Double.longBitsToDouble((Double.doubleToLongBits(x) & 0x7fffffffffffffffL)
| (Double.doubleToLongBits(y) & 0x8000000000000000L));
}
/**
* Please update your code to use copySign
* @param x
* @param y
* @return copySign(x,y)
* @deprecated Please update your code to use copySign
*/
public static final double copysign(final double x, final double y) {
return copySign(x, y);
}
/*
* fabs(x) returns the absolute value of x.
* This is already handled by Java ME.
public static final double fabs(double x)
{
//__HI(x) &= 0x7fffffff;
//return Double.longBitsToDouble(Double.doubleToLongBits(x) & 0x7fffffffffffffffL);
}
*/
/*
* use a precalculated value for the ulp of Double.MAX_VALUE
*/
private static final double MAX_ULP = 1.9958403095347198E292;
/**
* Returns the size of an ulp (units in the last place) of the argument.
* @param d value whose ulp is to be returned
* @return size of an ulp for the argument
*/
public static double ulp(double d) {
if (Double.isNaN(d)) {
// If the argument is NaN, then the result is NaN.
return Double.NaN;
}
if (Double.isInfinite(d)) {
// If the argument is positive or negative infinity, then the
// result is positive infinity.
return Double.POSITIVE_INFINITY;
}
if (d == 0.0) {
// If the argument is positive or negative zero, then the result is Double.MIN_VALUE.
return Double.MIN_VALUE;
}
d = Math.abs(d);
if (d == Double.MAX_VALUE) {
// If the argument is ±Double.MAX_VALUE, then the result is equal to 2^971.
return MAX_ULP;
}
return nextAfter(d, Double.MAX_VALUE) - d;
}
private static boolean isSameSign(double x, double y) {
return copySign(x, y) == x;
}
/**
* Returns the next representable floating point number after the first
* argument in the direction of the second argument.
*
* @param start starting value
* @param direction value indicating which of the neighboring representable
* floating point number to return
* @return The floating-point number next to {@code start} in the
* direction of {@direction}.
*/
public static double nextAfter(final double start, final double direction) {
if (Double.isNaN(start) || Double.isNaN(direction)) {
// If either argument is a NaN, then NaN is returned.
return Double.NaN;
}
if (start == direction) {
// If both arguments compare as equal the second argument is returned.
return direction;
}
final double absStart = Math.abs(start);
final double absDir = Math.abs(direction);
final boolean toZero = !isSameSign(start, direction) || absDir < absStart;
if (toZero) {
// we are reducing the magnitude, going toward zero.
if (absStart == Double.MIN_VALUE) {
return copySign(0.0, start);
}
if (Double.isInfinite(absStart)) {
return copySign(Double.MAX_VALUE, start);
}
return copySign(Double.longBitsToDouble(Double.doubleToLongBits(absStart) - 1L), start);
} else {
// we are increasing the magnitude, toward +-Infinity
if (start == 0.0) {
return copySign(Double.MIN_VALUE, direction);
}
if (absStart == Double.MAX_VALUE) {
return copySign(Double.POSITIVE_INFINITY, start);
}
return copySign(Double.longBitsToDouble(Double.doubleToLongBits(absStart) + 1L), start);
}
}
/**
* Rounds the number to the closest integer
* @param a the number
* @return the closest integer
*/
public static int round(float a) {
return Math.round(a);
}
/**
* Rounds the number to the closest integer
* @param a the number
* @return the closest integer
*/
public static long round(double a) {
return Math.round(a);
}
/**
* Rounds the number down
* @param a the number
* @return a rounded down number
*/
public static int floor(float a) {
return (int)a;
}
/**
* Rounds the number down
* @param a the number
* @return a rounded down number
*/
public static long floor(double a) {
return (long)a;
}
}