/**
* Computes the value of this number raised to an integral power. Follows semantics of Java
* Math.pow as closely as possible.
*
* @param exp the integer exponent
* @return x raised to the integral power exp
*/
public WB_DoubleDouble pow(final int exp) {
if (exp == 0.0) {
return valueOf(1.0);
}
WB_DoubleDouble r = new WB_DoubleDouble(this);
WB_DoubleDouble s = valueOf(1.0);
int n = Math.abs(exp);
if (n > 1) {
/* Use binary exponentiation */
while (n > 0) {
if ((n % 2) == 1) {
s.selfMultiply(r);
}
n /= 2;
if (n > 0) {
r = r.sqr();
}
}
} else {
s = r;
}
/* Compute the reciprocal if n is negative. */
if (exp < 0) {
return s.reciprocal();
}
return s;
}
/**
* Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and
* taking the floor of the result. Special cases:
*
* <ul>
* <li>If this value is NaN, returns NaN.
* </ul>
*
* @return this value rounded to the nearest integer
*/
public WB_DoubleDouble rint() {
if (isNaN()) {
return this;
}
// may not be 100% correct
final WB_DoubleDouble plus5 = this.add(0.5);
return plus5.floor();
}
/**
* Computes the positive square root of this value. If the number is NaN or negative, NaN is
* returned.
*
* @return the positive square root of this number. If the argument is NaN or less than zero, the
* result is NaN.
*/
public WB_DoubleDouble sqrt() {
/*
* Strategy: Use Karp's trick: if x is an approximation to sqrt(a), then
*
* sqrt(a) = a*x + [a - (a*x)^2] * x / 2 (approx)
*
* The approximation is accurate to twice the accuracy of x. Also, the
* multiplication (a*x) and [-]*x can be done with only half the
* precision.
*/
if (isZero()) {
return valueOf(0.0);
}
if (isNegative()) {
return NaN;
}
final double x = 1.0 / Math.sqrt(hi);
final double ax = hi * x;
final WB_DoubleDouble axdd = valueOf(ax);
final WB_DoubleDouble diffSq = this.subtract(axdd.sqr());
final double d2 = diffSq.hi * (x * 0.5);
return axdd.add(d2);
}
/**
* Implements extended-precision floating-point numbers which maintain 106 bits (approximately 30
* decimal digits) of precision.
*
* <p>A DoubleDouble uses a representation containing two double-precision values. A number x is
* represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi +
* x.lo, where
*
* <p>|x.lo| <= 0.5*ulp(x.hi)
*
* <p>and ulp(y) means "unit in the last place of y". The basic arithmetic operations are
* implemented using convenient properties of IEEE-754 floating-point arithmetic.
*
* <p>The range of values which can be represented is the same as in IEEE-754. The precision of the
* representable numbers is twice as great as IEEE-754 double precision.
*
* <p>The correctness of the arithmetic algorithms relies on operations being performed with
* standard IEEE-754 double precision and rounding. This is the Java standard arithmetic model, but
* for performance reasons Java implementations are not constrained to using this standard by
* default. Some processors (notably the Intel Pentium architecure) perform floating point
* operations in (non-IEEE-754-standard) extended-precision. A JVM implementation may choose to use
* the non-standard extended-precision as its default arithmetic mode. To prevent this from
* happening, this code uses the Java <tt>strictfp</tt> modifier, which forces all operations to
* take place in the standard IEEE-754 rounding model.
*
* <p>The API provides both a set of value-oriented operations and a set of mutating operations.
* Value-oriented operations treat DoubleDouble values as immutable; operations on them return new
* objects carrying the result of the operation. This provides a simple and safe semantics for
* writing DoubleDouble expressions. However, there is a performance penalty for the object
* allocations required. The mutable interface updates object values in-place. It provides optimum
* memory performance, but requires care to ensure that aliasing errors are not created and constant
* values are not changed.
*
* <p>This implementation uses algorithms originally designed variously by Knuth, Kahan, Dekker, and
* Linnainmaa. Douglas Priest developed the first C implementation of these techniques. Other more
* recent C++ implementation are due to Keith M. Briggs and David Bailey et al.
*
* @author Martin Davis
*/
public final strictfp class WB_DoubleDouble implements Serializable, Comparable<Object>, Cloneable {
/** The Constant serialVersionUID. */
private static final long serialVersionUID = -2751466014056438637L;
/** The value nearest to the constant Pi. */
public static final WB_DoubleDouble PI =
new WB_DoubleDouble(3.141592653589793116e+00, 1.224646799147353207e-16);
/** The value nearest to the constant 2 * Pi. */
public static final WB_DoubleDouble TWO_PI =
new WB_DoubleDouble(6.283185307179586232e+00, 2.449293598294706414e-16);
/** The value nearest to the constant Pi / 2. */
public static final WB_DoubleDouble PI_2 =
new WB_DoubleDouble(1.570796326794896558e+00, 6.123233995736766036e-17);
/** The value nearest to the constant e (the natural logarithm base). */
public static final WB_DoubleDouble E =
new WB_DoubleDouble(2.718281828459045091e+00, 1.445646891729250158e-16);
/** A value representing the result of an operation which does not return a valid number. */
public static final WB_DoubleDouble NaN = new WB_DoubleDouble(Double.NaN, Double.NaN);
/** The smallest representable relative difference between two {link @ DoubleDouble} values. */
public static final double EPS = 1.23259516440783e-32; /* = 2^-106 */
/** The Constant ZERO. */
public static final WB_DoubleDouble ZERO = new WB_DoubleDouble(0.0, 0.0);
/**
* Creates the na n.
*
* @return the w b_ double double
*/
private static WB_DoubleDouble createNaN() {
return new WB_DoubleDouble(Double.NaN, Double.NaN);
}
/**
* Converts the string argument to a DoubleDouble number.
*
* @param str a string containing a representation of a numeric value
* @return the extended precision version of the value
* @throws NumberFormatException if <tt>s</tt> is not a valid representation of a number
*/
public static WB_DoubleDouble valueOf(final String str) throws NumberFormatException {
return parse(str);
}
/**
* Converts the <tt>double</tt> argument to a DoubleDouble number.
*
* @param x a numeric value
* @return the extended precision version of the value
*/
public static WB_DoubleDouble valueOf(final double x) {
return new WB_DoubleDouble(x);
}
/** The value to split a double-precision value on during multiplication. */
private static final double SPLIT = 134217729.0D; // 2^27+1, for IEEE double
/** The high-order component of the double-double precision value. */
private double hi = 0.0;
/** The low-order component of the double-double precision value. */
private double lo = 0.0;
/** Creates a new DoubleDouble with value 0.0. */
public WB_DoubleDouble() {
init(0.0);
}
/**
* Creates a new DoubleDouble with value x.
*
* @param x the value to initialize
*/
public WB_DoubleDouble(final double x) {
init(x);
}
/**
* Creates a new DoubleDouble with value (hi, lo).
*
* @param hi the high-order component
* @param lo the high-order component
*/
public WB_DoubleDouble(final double hi, final double lo) {
init(hi, lo);
}
/**
* Creates a new DoubleDouble with value equal to the argument.
*
* @param dd the value to initialize
*/
public WB_DoubleDouble(final WB_DoubleDouble dd) {
init(dd);
}
/**
* Creates a new DoubleDouble with value equal to the argument.
*
* @param str the value to initialize by
* @throws NumberFormatException if <tt>str</tt> is not a valid representation of a number
*/
public WB_DoubleDouble(final String str) throws NumberFormatException {
this(parse(str));
}
/**
* Creates a new DoubleDouble with the value of the argument.
*
* @param dd the DoubleDouble value to copy
* @return a copy of the input value
*/
public static WB_DoubleDouble copy(final WB_DoubleDouble dd) {
return new WB_DoubleDouble(dd);
}
/**
* Creates and returns a copy of this value.
*
* @return a copy of this value
*/
@Override
public Object clone() {
try {
return super.clone();
} catch (final CloneNotSupportedException ex) {
// should never reach here
return null;
}
}
/**
* Inits the.
*
* @param x the x
*/
private void init(final double x) {
init(x, 0.0);
}
/**
* Inits the.
*
* @param hi the hi
* @param lo the lo
*/
private void init(final double hi, final double lo) {
this.hi = hi;
this.lo = lo;
}
/**
* Inits the.
*
* @param dd the dd
*/
private void init(final WB_DoubleDouble dd) {
init(dd.hi, dd.lo);
}
/**
* Returns a DoubleDouble whose value is <tt>(this + y)</tt>.
*
* @param y the addend
* @return <tt>(this + y)</tt>
*/
public WB_DoubleDouble add(final WB_DoubleDouble y) {
return copy(this).selfAdd(y);
}
/**
* Returns a DoubleDouble whose value is <tt>(this + y)</tt>.
*
* @param y the addend
* @return <tt>(this + y)</tt>
*/
public WB_DoubleDouble add(final double y) {
return copy(this).selfAdd(y);
}
/**
* Adds the argument to the value of <tt>this</tt>. To prevent altering constants, this method
* <b>must only</b> be used on values known to be newly created.
*
* @param y the addend
* @return this object, increased by y
*/
public WB_DoubleDouble selfAdd(final WB_DoubleDouble y) {
return selfAdd(y.hi, y.lo);
}
/**
* Adds the argument to the value of <tt>this</tt>. To prevent altering constants, this method
* <b>must only</b> be used on values known to be newly created.
*
* @param y the addend
* @return this object, increased by y
*/
public WB_DoubleDouble selfAdd(final double y) {
return selfAdd(y, 0.0);
}
/**
* Self add.
*
* @param yhi the yhi
* @param ylo the ylo
* @return the w b_ double double
*/
private WB_DoubleDouble selfAdd(final double yhi, final double ylo) {
double H, h, T, t, S, s, e, f;
S = hi + yhi;
T = lo + ylo;
e = S - hi;
f = T - lo;
s = S - e;
t = T - f;
s = (yhi - e) + (hi - s);
t = (ylo - f) + (lo - t);
e = s + T;
H = S + e;
h = e + (S - H);
e = t + h;
final double zhi = H + e;
final double zlo = e + (H - zhi);
hi = zhi;
lo = zlo;
return this;
}
/**
* Computes a new DoubleDouble object whose value is <tt>(this - y)</tt>.
*
* @param y the subtrahend
* @return <tt>(this - y)</tt>
*/
public WB_DoubleDouble subtract(final WB_DoubleDouble y) {
return add(y.negate());
}
/**
* Computes a new DoubleDouble object whose value is <tt>(this - y)</tt>.
*
* @param y the subtrahend
* @return <tt>(this - y)</tt>
*/
public WB_DoubleDouble subtract(final double y) {
return add(-y);
}
/**
* Subtracts the argument from the value of <tt>this</tt>. To prevent altering constants, this
* method <b>must only</b> be used on values known to be newly created.
*
* @param y the addend
* @return this object, decreased by y
*/
public WB_DoubleDouble selfSubtract(final WB_DoubleDouble y) {
if (isNaN()) {
return this;
}
return selfAdd(-y.hi, -y.lo);
}
/**
* Subtracts the argument from the value of <tt>this</tt>. To prevent altering constants, this
* method <b>must only</b> be used on values known to be newly created.
*
* @param y the addend
* @return this object, decreased by y
*/
public WB_DoubleDouble selfSubtract(final double y) {
if (isNaN()) {
return this;
}
return selfAdd(-y, 0.0);
}
/**
* Returns a DoubleDouble whose value is <tt>-this</tt>.
*
* @return <tt>-this</tt>
*/
public WB_DoubleDouble negate() {
if (isNaN()) {
return this;
}
return new WB_DoubleDouble(-hi, -lo);
}
/**
* Returns a new DoubleDouble whose value is <tt>(this * y)</tt>.
*
* @param y the multiplicand
* @return <tt>(this * y)</tt>
*/
public WB_DoubleDouble multiply(final WB_DoubleDouble y) {
if (y.isNaN()) {
return createNaN();
}
return copy(this).selfMultiply(y);
}
/**
* Returns a new DoubleDouble whose value is <tt>(this * y)</tt>.
*
* @param y the multiplicand
* @return <tt>(this * y)</tt>
*/
public WB_DoubleDouble multiply(final double y) {
if (Double.isNaN(y)) {
return createNaN();
}
return copy(this).selfMultiply(y, 0.0);
}
/**
* Multiplies this object by the argument, returning <tt>this</tt>. To prevent altering constants,
* this method <b>must only</b> be used on values known to be newly created.
*
* @param y the value to multiply by
* @return this object, multiplied by y
*/
public WB_DoubleDouble selfMultiply(final WB_DoubleDouble y) {
return selfMultiply(y.hi, y.lo);
}
/**
* Multiplies this object by the argument, returning <tt>this</tt>. To prevent altering constants,
* this method <b>must only</b> be used on values known to be newly created.
*
* @param y the value to multiply by
* @return this object, multiplied by y
*/
public WB_DoubleDouble selfMultiply(final double y) {
return selfMultiply(y, 0.0);
}
/**
* Self multiply.
*
* @param yhi the yhi
* @param ylo the ylo
* @return the w b_ double double
*/
private WB_DoubleDouble selfMultiply(final double yhi, final double ylo) {
double hx, tx, hy, ty, C, c;
C = SPLIT * hi;
hx = C - hi;
c = SPLIT * yhi;
hx = C - hx;
tx = hi - hx;
hy = c - yhi;
C = hi * yhi;
hy = c - hy;
ty = yhi - hy;
c = (((((hx * hy) - C) + (hx * ty)) + (tx * hy)) + (tx * ty)) + ((hi * ylo) + (lo * yhi));
final double zhi = C + c;
hx = C - zhi;
final double zlo = c + hx;
hi = zhi;
lo = zlo;
return this;
}
/**
* Computes a new DoubleDouble whose value is <tt>(this / y)</tt>.
*
* @param y the divisor
* @return a new object with the value <tt>(this / y)</tt>
*/
public WB_DoubleDouble divide(final WB_DoubleDouble y) {
double hc, tc, hy, ty, C, c, U, u;
C = hi / y.hi;
c = SPLIT * C;
hc = c - C;
u = SPLIT * y.hi;
hc = c - hc;
tc = C - hc;
hy = u - y.hi;
U = C * y.hi;
hy = u - hy;
ty = y.hi - hy;
u = ((((hc * hy) - U) + (hc * ty)) + (tc * hy)) + (tc * ty);
c = ((((hi - U) - u) + lo) - (C * y.lo)) / y.hi;
u = C + c;
final double zhi = u;
final double zlo = (C - u) + c;
return new WB_DoubleDouble(zhi, zlo);
}
/**
* Computes a new DoubleDouble whose value is <tt>(this / y)</tt>.
*
* @param y the divisor
* @return a new object with the value <tt>(this / y)</tt>
*/
public WB_DoubleDouble divide(final double y) {
if (Double.isNaN(y)) {
return createNaN();
}
return copy(this).selfDivide(y, 0.0);
}
/**
* Divides this object by the argument, returning <tt>this</tt>. To prevent altering constants,
* this method <b>must only</b> be used on values known to be newly created.
*
* @param y the value to divide by
* @return this object, divided by y
*/
public WB_DoubleDouble selfDivide(final WB_DoubleDouble y) {
return selfDivide(y.hi, y.lo);
}
/**
* Divides this object by the argument, returning <tt>this</tt>. To prevent altering constants,
* this method <b>must only</b> be used on values known to be newly created.
*
* @param y the value to divide by
* @return this object, divided by y
*/
public WB_DoubleDouble selfDivide(final double y) {
return selfDivide(y, 0.0);
}
/**
* Self divide.
*
* @param yhi the yhi
* @param ylo the ylo
* @return the w b_ double double
*/
private WB_DoubleDouble selfDivide(final double yhi, final double ylo) {
double hc, tc, hy, ty, C, c, U, u;
C = hi / yhi;
c = SPLIT * C;
hc = c - C;
u = SPLIT * yhi;
hc = c - hc;
tc = C - hc;
hy = u - yhi;
U = C * yhi;
hy = u - hy;
ty = yhi - hy;
u = ((((hc * hy) - U) + (hc * ty)) + (tc * hy)) + (tc * ty);
c = ((((hi - U) - u) + lo) - (C * ylo)) / yhi;
u = C + c;
hi = u;
lo = (C - u) + c;
return this;
}
/**
* Returns a DoubleDouble whose value is <tt>1 / this</tt>.
*
* @return the reciprocal of this value
*/
public WB_DoubleDouble reciprocal() {
double hc, tc, hy, ty, C, c, U, u;
C = 1.0 / hi;
c = SPLIT * C;
hc = c - C;
u = SPLIT * hi;
hc = c - hc;
tc = C - hc;
hy = u - hi;
U = C * hi;
hy = u - hy;
ty = hi - hy;
u = ((((hc * hy) - U) + (hc * ty)) + (tc * hy)) + (tc * ty);
c = ((((1.0 - U) - u)) - (C * lo)) / hi;
final double zhi = C + c;
final double zlo = (C - zhi) + c;
return new WB_DoubleDouble(zhi, zlo);
}
/**
* Returns the largest (closest to positive infinity) value that is not greater than the argument
* and is equal to a mathematical integer. Special cases:
*
* <ul>
* <li>If this value is NaN, returns NaN.
* </ul>
*
* @return the largest (closest to positive infinity) value that is not greater than the argument
* and is equal to a mathematical integer.
*/
public WB_DoubleDouble floor() {
if (isNaN()) {
return NaN;
}
final double fhi = Math.floor(hi);
double flo = 0.0;
// Hi is already integral. Floor the low word
if (fhi == hi) {
flo = Math.floor(lo);
}
// do we need to renormalize here?
return new WB_DoubleDouble(fhi, flo);
}
/**
* Returns the smallest (closest to negative infinity) value that is not less than the argument
* and is equal to a mathematical integer. Special cases:
*
* <ul>
* <li>If this value is NaN, returns NaN.
* </ul>
*
* @return the smallest (closest to negative infinity) value that is not less than the argument
* and is equal to a mathematical integer.
*/
public WB_DoubleDouble ceil() {
if (isNaN()) {
return NaN;
}
final double fhi = Math.ceil(hi);
double flo = 0.0;
// Hi is already integral. Ceil the low word
if (fhi == hi) {
flo = Math.ceil(lo);
// do we need to renormalize here?
}
return new WB_DoubleDouble(fhi, flo);
}
/**
* Returns an integer indicating the sign of this value.
*
* <ul>
* <li>if this value is > 0, returns 1
* <li>if this value is < 0, returns -1
* <li>if this value is = 0, returns 0
* <li>if this value is NaN, returns 0
* </ul>
*
* @return an integer indicating the sign of this value
*/
public int signum() {
if (isPositive()) {
return 1;
}
if (isNegative()) {
return -1;
}
return 0;
}
/**
* Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and
* taking the floor of the result. Special cases:
*
* <ul>
* <li>If this value is NaN, returns NaN.
* </ul>
*
* @return this value rounded to the nearest integer
*/
public WB_DoubleDouble rint() {
if (isNaN()) {
return this;
}
// may not be 100% correct
final WB_DoubleDouble plus5 = this.add(0.5);
return plus5.floor();
}
/**
* Returns the integer which is largest in absolute value and not further from zero than this
* value. Special cases:
*
* <ul>
* <li>If this value is NaN, returns NaN.
* </ul>
*
* @return the integer which is largest in absolute value and not further from zero than this
* value
*/
public WB_DoubleDouble trunc() {
if (isNaN()) {
return NaN;
}
if (isPositive()) {
return floor();
} else {
return ceil();
}
}
/**
* Returns the absolute value of this value. Special cases:
*
* <ul>
* <li>If this value is NaN, it is returned.
* </ul>
*
* @return the absolute value of this value
*/
public WB_DoubleDouble abs() {
if (isNaN()) {
return NaN;
}
if (isNegative()) {
return negate();
}
return new WB_DoubleDouble(this);
}
/**
* Computes the square of this value.
*
* @return the square of this value.
*/
public WB_DoubleDouble sqr() {
return this.multiply(this);
}
/**
* Computes the square of this value.
*
* @param x the x
* @return the square of this value.
*/
public static WB_DoubleDouble sqr(final double x) {
return valueOf(x).selfMultiply(x);
}
/**
* Computes the positive square root of this value. If the number is NaN or negative, NaN is
* returned.
*
* @return the positive square root of this number. If the argument is NaN or less than zero, the
* result is NaN.
*/
public WB_DoubleDouble sqrt() {
/*
* Strategy: Use Karp's trick: if x is an approximation to sqrt(a), then
*
* sqrt(a) = a*x + [a - (a*x)^2] * x / 2 (approx)
*
* The approximation is accurate to twice the accuracy of x. Also, the
* multiplication (a*x) and [-]*x can be done with only half the
* precision.
*/
if (isZero()) {
return valueOf(0.0);
}
if (isNegative()) {
return NaN;
}
final double x = 1.0 / Math.sqrt(hi);
final double ax = hi * x;
final WB_DoubleDouble axdd = valueOf(ax);
final WB_DoubleDouble diffSq = this.subtract(axdd.sqr());
final double d2 = diffSq.hi * (x * 0.5);
return axdd.add(d2);
}
/**
* Sqrt.
*
* @param x the x
* @return the w b_ double double
*/
public static WB_DoubleDouble sqrt(final double x) {
return valueOf(x).sqrt();
}
/**
* Computes the value of this number raised to an integral power. Follows semantics of Java
* Math.pow as closely as possible.
*
* @param exp the integer exponent
* @return x raised to the integral power exp
*/
public WB_DoubleDouble pow(final int exp) {
if (exp == 0.0) {
return valueOf(1.0);
}
WB_DoubleDouble r = new WB_DoubleDouble(this);
WB_DoubleDouble s = valueOf(1.0);
int n = Math.abs(exp);
if (n > 1) {
/* Use binary exponentiation */
while (n > 0) {
if ((n % 2) == 1) {
s.selfMultiply(r);
}
n /= 2;
if (n > 0) {
r = r.sqr();
}
}
} else {
s = r;
}
/* Compute the reciprocal if n is negative. */
if (exp < 0) {
return s.reciprocal();
}
return s;
}
/*------------------------------------------------------------
* Conversion Functions
*------------------------------------------------------------
*/
/**
* Converts this value to the nearest double-precision number.
*
* @return the nearest double-precision number to this value
*/
public double doubleValue() {
return hi + lo;
}
/**
* Converts this value to the nearest integer.
*
* @return the nearest integer to this value
*/
public int intValue() {
return (int) hi;
}
/*------------------------------------------------------------
* Predicates
*------------------------------------------------------------
*/
/**
* Tests whether this value is equal to 0.
*
* @return true if this value is equal to 0
*/
public boolean isZero() {
return (hi == 0.0) && (lo == 0.0);
}
/**
* Tests whether this value is less than 0.
*
* @return true if this value is less than 0
*/
public boolean isNegative() {
return (hi < 0.0) || ((hi == 0.0) && (lo < 0.0));
}
/**
* Tests whether this value is greater than 0.
*
* @return true if this value is greater than 0
*/
public boolean isPositive() {
return (hi > 0.0) || ((hi == 0.0) && (lo > 0.0));
}
/**
* Tests whether this value is NaN.
*
* @return true if this value is NaN
*/
public boolean isNaN() {
return Double.isNaN(hi);
}
/**
* Tests whether this value is equal to another <tt>DoubleDouble</tt> value.
*
* @param y a DoubleDouble value
* @return true if this value = y
*/
public boolean equals(final WB_DoubleDouble y) {
return (hi == y.hi) && (lo == y.lo);
}
/**
* Tests whether this value is greater than another <tt>DoubleDouble</tt> value.
*
* @param y a DoubleDouble value
* @return true if this value > y
*/
public boolean gt(final WB_DoubleDouble y) {
return (hi > y.hi) || ((hi == y.hi) && (lo > y.lo));
}
/**
* Tests whether this value is greater than or equals to another <tt>DoubleDouble</tt> value.
*
* @param y a DoubleDouble value
* @return true if this value >= y
*/
public boolean ge(final WB_DoubleDouble y) {
return (hi > y.hi) || ((hi == y.hi) && (lo >= y.lo));
}
/**
* Tests whether this value is less than another <tt>DoubleDouble</tt> value.
*
* @param y a DoubleDouble value
* @return true if this value < y
*/
public boolean lt(final WB_DoubleDouble y) {
return (hi < y.hi) || ((hi == y.hi) && (lo < y.lo));
}
/**
* Tests whether this value is less than or equal to another <tt>DoubleDouble</tt> value.
*
* @param y a DoubleDouble value
* @return true if this value <= y
*/
public boolean le(final WB_DoubleDouble y) {
return (hi < y.hi) || ((hi == y.hi) && (lo <= y.lo));
}
/**
* Compares two DoubleDouble objects numerically.
*
* @param o the o
* @return -1,0 or 1 depending on whether this value is less than, equal to or greater than the
* value of <tt>o</tt>
*/
@Override
public int compareTo(final Object o) {
final WB_DoubleDouble other = (WB_DoubleDouble) o;
if (hi < other.hi) {
return -1;
}
if (hi > other.hi) {
return 1;
}
if (lo < other.lo) {
return -1;
}
if (lo > other.lo) {
return 1;
}
return 0;
}
/*------------------------------------------------------------
* Output
*------------------------------------------------------------
*/
/** The Constant MAX_PRINT_DIGITS. */
private static final int MAX_PRINT_DIGITS = 32;
/** The Constant TEN. */
private static final WB_DoubleDouble TEN = WB_DoubleDouble.valueOf(10.0);
/** The Constant ONE. */
private static final WB_DoubleDouble ONE = WB_DoubleDouble.valueOf(1.0);
/** The Constant SCI_NOT_EXPONENT_CHAR. */
private static final String SCI_NOT_EXPONENT_CHAR = "E";
/** The Constant SCI_NOT_ZERO. */
private static final String SCI_NOT_ZERO = "0.0E0";
/**
* Dumps the components of this number to a string.
*
* @return a string showing the components of the number
*/
public String dump() {
return "DD<" + hi + ", " + lo + ">";
}
/**
* Returns a string representation of this number, in either standard or scientific notation. If
* the magnitude of the number is in the range [ 10<sup>-3</sup>, 10<sup>8</sup> ] standard
* notation will be used. Otherwise, scientific notation will be used.
*
* @return a string representation of this number
*/
@Override
public String toString() {
final int mag = magnitude(hi);
if ((mag >= -3) && (mag <= 20)) {
return toStandardNotation();
}
return toSciNotation();
}
/**
* Returns the string representation of this value in standard notation.
*
* @return the string representation in standard notation
*/
public String toStandardNotation() {
final String specialStr = getSpecialNumberString();
if (specialStr != null) {
return specialStr;
}
final int[] magnitude = new int[1];
final String sigDigits = extractSignificantDigits(true, magnitude);
final int decimalPointPos = magnitude[0] + 1;
String num = sigDigits;
// add a leading 0 if the decimal point is the first char
if (sigDigits.charAt(0) == '.') {
num = "0" + sigDigits;
} else if (decimalPointPos < 0) {
num = "0." + stringOfChar('0', -decimalPointPos) + sigDigits;
} else if (sigDigits.indexOf('.') == -1) {
// no point inserted - sig digits must be smaller than magnitude of
// number
// add zeroes to end to make number the correct size
final int numZeroes = decimalPointPos - sigDigits.length();
final String zeroes = stringOfChar('0', numZeroes);
num = sigDigits + zeroes + ".0";
}
if (this.isNegative()) {
return "-" + num;
}
return num;
}
/**
* Returns the string representation of this value in scientific notation.
*
* @return the string representation in scientific notation
*/
public String toSciNotation() {
// special case zero, to allow as
if (isZero()) {
return SCI_NOT_ZERO;
}
final String specialStr = getSpecialNumberString();
if (specialStr != null) {
return specialStr;
}
final int[] magnitude = new int[1];
final String digits = extractSignificantDigits(false, magnitude);
final String expStr = SCI_NOT_EXPONENT_CHAR + magnitude[0];
// should never have leading zeroes
// MD - is this correct? Or should we simply strip them if they are
// present?
if (digits.charAt(0) == '0') {
throw new IllegalStateException("Found leading zero: " + digits);
}
// add decimal point
String trailingDigits = "";
if (digits.length() > 1) {
trailingDigits = digits.substring(1);
}
final String digitsWithDecimal = digits.charAt(0) + "." + trailingDigits;
if (this.isNegative()) {
return "-" + digitsWithDecimal + expStr;
}
return digitsWithDecimal + expStr;
}
/**
* Extracts the significant digits in the decimal representation of the argument. A decimal point
* may be optionally inserted in the string of digits (as long as its position lies within the
* extracted digits - if not, the caller must prepend or append the appropriate zeroes and decimal
* point).
*
* @param insertDecimalPoint the insert decimal point
* @param magnitude the magnitude
* @return the string containing the significant digits and possibly a decimal point
*/
private String extractSignificantDigits(final boolean insertDecimalPoint, final int[] magnitude) {
WB_DoubleDouble y = this.abs();
// compute *correct* magnitude of y
int mag = magnitude(y.hi);
final WB_DoubleDouble scale = TEN.pow(mag);
y = y.divide(scale);
// fix magnitude if off by one
if (y.gt(TEN)) {
y = y.divide(TEN);
mag += 1;
} else if (y.lt(ONE)) {
y = y.multiply(TEN);
mag -= 1;
}
final int decimalPointPos = mag + 1;
final StringBuffer buf = new StringBuffer();
final int numDigits = MAX_PRINT_DIGITS - 1;
for (int i = 0; i <= numDigits; i++) {
if (insertDecimalPoint && (i == decimalPointPos)) {
buf.append('.');
}
final int digit = (int) y.hi;
// System.out.println("printDump: [" + i + "] digit: " + digit +
// " y: " + y.dump() + " buf: " + buf);
/** This should never happen, due to heuristic checks on remainder below */
if ((digit < 0) || (digit > 9)) {
// System.out.println("digit > 10 : " + digit);
// throw new
// IllegalStateException("Internal errror: found digit = " +
// digit);
}
/**
* If a negative remainder is encountered, simply terminate the extraction. This is robust,
* but maybe slightly inaccurate. My current hypothesis is that negative remainders only occur
* for very small lo components, so the inaccuracy is tolerable
*/
if (digit < 0) {
break;
// throw new
// IllegalStateException("Internal errror: found digit = " +
// digit);
}
boolean rebiasBy10 = false;
char digitChar = 0;
if (digit > 9) {
// set flag to re-bias after next 10-shift
rebiasBy10 = true;
// output digit will end up being '9'
digitChar = '9';
} else {
digitChar = (char) ('0' + digit);
}
buf.append(digitChar);
y = (y.subtract(WB_DoubleDouble.valueOf(digit)).multiply(TEN));
if (rebiasBy10) {
y.selfAdd(TEN);
}
boolean continueExtractingDigits = true;
/**
* Heuristic check: if the remaining portion of y is non-positive, assume that output is
* complete
*/
// if (y.hi <= 0.0)
// if (y.hi < 0.0)
// continueExtractingDigits = false;
/**
* Check if remaining digits will be 0, and if so don't output them. Do this by comparing the
* magnitude of the remainder with the expected precision.
*/
final int remMag = magnitude(y.hi);
if ((remMag < 0) && (Math.abs(remMag) >= (numDigits - i))) {
continueExtractingDigits = false;
}
if (!continueExtractingDigits) {
break;
}
}
magnitude[0] = mag;
return buf.toString();
}
/**
* Creates a string of a given length containing the given character.
*
* @param ch the character to be repeated
* @param len the len of the desired string
* @return the string
*/
private static String stringOfChar(final char ch, final int len) {
final StringBuffer buf = new StringBuffer();
for (int i = 0; i < len; i++) {
buf.append(ch);
}
return buf.toString();
}
/**
* Returns the string for this value if it has a known representation. (E.g. NaN or 0.0)
*
* @return the string for this special number null if the number is not a special number
*/
private String getSpecialNumberString() {
if (isZero()) {
return "0.0";
}
if (isNaN()) {
return "NaN ";
}
return null;
}
/**
* Determines the decimal magnitude of a number. The magnitude is the exponent of the greatest
* power of 10 which is less than or equal to the number.
*
* @param x the number to find the magnitude of
* @return the decimal magnitude of x
*/
private static int magnitude(final double x) {
final double xAbs = Math.abs(x);
final double xLog10 = Math.log(xAbs) / Math.log(10);
int xMag = (int) Math.floor(xLog10);
/**
* Since log computation is inexact, there may be an off-by-one error in the computed magnitude.
* Following tests that magnitude is correct, and adjusts it if not
*/
final double xApprox = Math.pow(10, xMag);
if ((xApprox * 10) <= xAbs) {
xMag += 1;
}
return xMag;
}
/*------------------------------------------------------------
* Input
*------------------------------------------------------------
*/
/**
* Converts a string representation of a real number into a DoubleDouble value. The format
* accepted is similar to the standard Java real number syntax. It is defined by the following
* regular expression:
*
* <pre>
* [<tt>+</tt>|<tt>-</tt>] {<i>digit</i>} [ <tt>.</tt> {<i>digit</i>} ] [ ( <tt>e</tt> | <tt>E</tt> ) [<tt>+</tt>|<tt>-</tt>
* ] {<i>digit</i>}+
*
* </pre>
*
* @param str the string to parse
* @return the value of the parsed number
* @throws NumberFormatException if <tt>str</tt> is not a valid representation of a number
*/
public static WB_DoubleDouble parse(final String str) throws NumberFormatException {
int i = 0;
final int strlen = str.length();
// skip leading whitespace
while (Character.isWhitespace(str.charAt(i))) {
i++;
}
// check for sign
boolean isNegative = false;
if (i < strlen) {
final char signCh = str.charAt(i);
if ((signCh == '-') || (signCh == '+')) {
i++;
if (signCh == '-') {
isNegative = true;
}
}
}
// scan all digits and accumulate into an integral value
// Keep track of the location of the decimal point (if any) to allow
// scaling later
final WB_DoubleDouble val = new WB_DoubleDouble();
int numDigits = 0;
int numBeforeDec = 0;
int exp = 0;
while (true) {
if (i >= strlen) {
break;
}
final char ch = str.charAt(i);
i++;
if (Character.isDigit(ch)) {
final double d = ch - '0';
val.selfMultiply(TEN);
// MD: need to optimize this
val.selfAdd(d);
numDigits++;
continue;
}
if (ch == '.') {
numBeforeDec = numDigits;
continue;
}
if ((ch == 'e') || (ch == 'E')) {
final String expStr = str.substring(i);
// this should catch any format problems with the exponent
try {
exp = Integer.parseInt(expStr);
} catch (final NumberFormatException ex) {
throw new NumberFormatException("Invalid exponent " + expStr + " in string " + str);
}
break;
}
throw new NumberFormatException(
"Unexpected character '" + ch + "' at position " + i + " in string " + str);
}
WB_DoubleDouble val2 = val;
// scale the number correctly
final int numDecPlaces = numDigits - numBeforeDec - exp;
if (numDecPlaces == 0) {
val2 = val;
} else if (numDecPlaces > 0) {
final WB_DoubleDouble scale = TEN.pow(numDecPlaces);
val2 = val.divide(scale);
} else if (numDecPlaces < 0) {
final WB_DoubleDouble scale = TEN.pow(-numDecPlaces);
val2 = val.multiply(scale);
}
// apply leading sign, if any
if (isNegative) {
return val2.negate();
}
return val2;
}
}
/**
* Returns a new DoubleDouble whose value is <tt>(this * y)</tt>.
*
* @param y the multiplicand
* @return <tt>(this * y)</tt>
*/
public WB_DoubleDouble multiply(final WB_DoubleDouble y) {
if (y.isNaN()) {
return createNaN();
}
return copy(this).selfMultiply(y);
}
/**
* Computes a new DoubleDouble object whose value is <tt>(this - y)</tt>.
*
* @param y the subtrahend
* @return <tt>(this - y)</tt>
*/
public WB_DoubleDouble subtract(final WB_DoubleDouble y) {
return add(y.negate());
}
/**
* Converts a string representation of a real number into a DoubleDouble value. The format
* accepted is similar to the standard Java real number syntax. It is defined by the following
* regular expression:
*
* <pre>
* [<tt>+</tt>|<tt>-</tt>] {<i>digit</i>} [ <tt>.</tt> {<i>digit</i>} ] [ ( <tt>e</tt> | <tt>E</tt> ) [<tt>+</tt>|<tt>-</tt>
* ] {<i>digit</i>}+
*
* </pre>
*
* @param str the string to parse
* @return the value of the parsed number
* @throws NumberFormatException if <tt>str</tt> is not a valid representation of a number
*/
public static WB_DoubleDouble parse(final String str) throws NumberFormatException {
int i = 0;
final int strlen = str.length();
// skip leading whitespace
while (Character.isWhitespace(str.charAt(i))) {
i++;
}
// check for sign
boolean isNegative = false;
if (i < strlen) {
final char signCh = str.charAt(i);
if ((signCh == '-') || (signCh == '+')) {
i++;
if (signCh == '-') {
isNegative = true;
}
}
}
// scan all digits and accumulate into an integral value
// Keep track of the location of the decimal point (if any) to allow
// scaling later
final WB_DoubleDouble val = new WB_DoubleDouble();
int numDigits = 0;
int numBeforeDec = 0;
int exp = 0;
while (true) {
if (i >= strlen) {
break;
}
final char ch = str.charAt(i);
i++;
if (Character.isDigit(ch)) {
final double d = ch - '0';
val.selfMultiply(TEN);
// MD: need to optimize this
val.selfAdd(d);
numDigits++;
continue;
}
if (ch == '.') {
numBeforeDec = numDigits;
continue;
}
if ((ch == 'e') || (ch == 'E')) {
final String expStr = str.substring(i);
// this should catch any format problems with the exponent
try {
exp = Integer.parseInt(expStr);
} catch (final NumberFormatException ex) {
throw new NumberFormatException("Invalid exponent " + expStr + " in string " + str);
}
break;
}
throw new NumberFormatException(
"Unexpected character '" + ch + "' at position " + i + " in string " + str);
}
WB_DoubleDouble val2 = val;
// scale the number correctly
final int numDecPlaces = numDigits - numBeforeDec - exp;
if (numDecPlaces == 0) {
val2 = val;
} else if (numDecPlaces > 0) {
final WB_DoubleDouble scale = TEN.pow(numDecPlaces);
val2 = val.divide(scale);
} else if (numDecPlaces < 0) {
final WB_DoubleDouble scale = TEN.pow(-numDecPlaces);
val2 = val.multiply(scale);
}
// apply leading sign, if any
if (isNegative) {
return val2.negate();
}
return val2;
}
/**
* Extracts the significant digits in the decimal representation of the argument. A decimal point
* may be optionally inserted in the string of digits (as long as its position lies within the
* extracted digits - if not, the caller must prepend or append the appropriate zeroes and decimal
* point).
*
* @param insertDecimalPoint the insert decimal point
* @param magnitude the magnitude
* @return the string containing the significant digits and possibly a decimal point
*/
private String extractSignificantDigits(final boolean insertDecimalPoint, final int[] magnitude) {
WB_DoubleDouble y = this.abs();
// compute *correct* magnitude of y
int mag = magnitude(y.hi);
final WB_DoubleDouble scale = TEN.pow(mag);
y = y.divide(scale);
// fix magnitude if off by one
if (y.gt(TEN)) {
y = y.divide(TEN);
mag += 1;
} else if (y.lt(ONE)) {
y = y.multiply(TEN);
mag -= 1;
}
final int decimalPointPos = mag + 1;
final StringBuffer buf = new StringBuffer();
final int numDigits = MAX_PRINT_DIGITS - 1;
for (int i = 0; i <= numDigits; i++) {
if (insertDecimalPoint && (i == decimalPointPos)) {
buf.append('.');
}
final int digit = (int) y.hi;
// System.out.println("printDump: [" + i + "] digit: " + digit +
// " y: " + y.dump() + " buf: " + buf);
/** This should never happen, due to heuristic checks on remainder below */
if ((digit < 0) || (digit > 9)) {
// System.out.println("digit > 10 : " + digit);
// throw new
// IllegalStateException("Internal errror: found digit = " +
// digit);
}
/**
* If a negative remainder is encountered, simply terminate the extraction. This is robust,
* but maybe slightly inaccurate. My current hypothesis is that negative remainders only occur
* for very small lo components, so the inaccuracy is tolerable
*/
if (digit < 0) {
break;
// throw new
// IllegalStateException("Internal errror: found digit = " +
// digit);
}
boolean rebiasBy10 = false;
char digitChar = 0;
if (digit > 9) {
// set flag to re-bias after next 10-shift
rebiasBy10 = true;
// output digit will end up being '9'
digitChar = '9';
} else {
digitChar = (char) ('0' + digit);
}
buf.append(digitChar);
y = (y.subtract(WB_DoubleDouble.valueOf(digit)).multiply(TEN));
if (rebiasBy10) {
y.selfAdd(TEN);
}
boolean continueExtractingDigits = true;
/**
* Heuristic check: if the remaining portion of y is non-positive, assume that output is
* complete
*/
// if (y.hi <= 0.0)
// if (y.hi < 0.0)
// continueExtractingDigits = false;
/**
* Check if remaining digits will be 0, and if so don't output them. Do this by comparing the
* magnitude of the remainder with the expected precision.
*/
final int remMag = magnitude(y.hi);
if ((remMag < 0) && (Math.abs(remMag) >= (numDigits - i))) {
continueExtractingDigits = false;
}
if (!continueExtractingDigits) {
break;
}
}
magnitude[0] = mag;
return buf.toString();
}