/**
* Returns the largest power of 10 that is less than or equal to the
* the specified positive value.
*
* @param d the <code>double</code> number.
* @return <code>floor(Log10(abs(d)))</code>
* @throws ArithmeticException if <code>d <= 0<code> or <code>d</code>
* is <code>NaN</code> or <code>Infinity</code>.
**/
public static int floorLog10(double d) {
int guess = (int) (LOG2_DIV_LOG10 * MathLib.floorLog2(d));
double pow10 = MathLib.toDoublePow10(1, guess);
if ((pow10 <= d) && (pow10 * 10 > d)) return guess;
if (pow10 > d) return guess - 1;
return guess + 1;
}
private CGAffineTransform nodeToParentTransform() {
if (isTransformDirty_) {
transform_.setToIdentity();
if (!isRelativeAnchorPoint_ && !CGPoint.equalToPoint(anchorPointInPixels_, zero)) {
transform_.translate(anchorPointInPixels_.x, anchorPointInPixels_.y);
}
if (!CGPoint.equalToPoint(position_, zero)) transform_.translate(position_.x, position_.y);
if (rotation_ != 0) transform_.rotate(-ccMacros.CC_DEGREES_TO_RADIANS(rotation_));
if (skewX_ != 0 || skewY_ != 0) {
/** create a skewed coordinate system and apply the skew to the transform */
transform_ =
transform_.getTransformConcat(
CGAffineTransform.make(
1.0f,
MathLib.tan(ccMacros.CC_DEGREES_TO_RADIANS(skewY_)),
MathLib.tan(ccMacros.CC_DEGREES_TO_RADIANS(skewX_)),
1.0f,
0.0f,
0.0f));
}
if (!(scaleX_ == 1 && scaleY_ == 1)) transform_.scale(scaleX_, scaleY_);
if (!CGPoint.equalToPoint(anchorPointInPixels_, zero))
transform_.translate(-anchorPointInPixels_.x, -anchorPointInPixels_.y);
isTransformDirty_ = false;
}
return transform_;
}
/**
* Returns the angle theta such that <code>(x == cos(theta)) && (y == sin(theta))</code>.
*
* @param y the y value.
* @param x the x value.
* @return the angle theta in radians.
*/
public static double atan2(double y, double x) {
final double epsilon = 1E-128;
if (MathLib.abs(x) > epsilon) {
double temp = MathLib.atan(MathLib.abs(y) / MathLib.abs(x));
if (x < 0.0) temp = PI - temp;
if (y < 0.0) temp = TWO_PI - temp;
return temp;
} else if (y > epsilon) return HALF_PI;
else if (y < -epsilon) return 3 * HALF_PI;
else return 0.0;
}
/**
* Returns a pseudo random <code>long</code> value in the range <code>[min, max]</code> (fast and
* thread-safe without synchronization).
*
* @param min the minimum value inclusive.
* @param max the maximum value inclusive.
* @return a pseudo random number in the range <code>[min, max]</code>.
*/
public static long random(long min, long max) {
long next = RANDOM.nextLong();
if ((next >= min) && (next <= max)) return next;
next += Long.MIN_VALUE;
if ((next >= min) && (next <= max)) return next;
// We should not have interval overflow as the interval has to be less
// or equal to Long.MAX_VALUE (otherwise we would have exited before).
final long interval = 1L + max - min; // Positive.
if (interval <= 0) throw new Error("Interval error"); // Sanity check.
return MathLib.abs(next % interval) + min;
}
/**
* Returns a pseudo random <code>int</code> value in the range <code>[min, max]</code> (fast and
* thread-safe without synchronization).
*
* @param min the minimum value inclusive.
* @param max the maximum value exclusive.
* @return a pseudo random number in the range <code>[min, max]</code>.
*/
public static int random(int min, int max) {
int next = RANDOM.nextInt();
if ((next >= min) && (next <= max)) return next;
next += Integer.MIN_VALUE;
if ((next >= min) && (next <= max)) return next;
// We should not have interval overflow as the interval has to be less
// or equal to Integer.MAX_VALUE (otherwise we would have exited before).
final int interval = 1 + max - min; // Positive.
if (interval <= 0) throw new Error("Interval [" + min + ".." + max + "] error"); // In case.
return MathLib.abs(next % interval) + min;
}
static double _atan(double x) {
double w, s1, s2, z;
int ix, hx, id;
long xBits = Double.doubleToLongBits(x);
int __HIx = (int) (xBits >> 32);
int __LOx = (int) xBits;
hx = __HIx;
ix = hx & 0x7fffffff;
if (ix >= 0x44100000) { // if |x| >= 2^66
if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (__LOx != 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;
id = -1;
} else {
x = MathLib.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;
}
}
/**
* Returns the closest <code>double</code> representation of the specified <code>long</code>
* number multiplied by a power of two.
*
* @param m the <code>long</code> multiplier.
* @param n the power of two exponent.
* @return <code>m * 2<sup>n</sup></code>.
*/
public static double toDoublePow2(long m, int n) {
if (m == 0) return 0.0;
if (m == Long.MIN_VALUE) return toDoublePow2(Long.MIN_VALUE >> 1, n + 1);
if (m < 0) return -toDoublePow2(-m, n);
int bitLength = MathLib.bitLength(m);
int shift = bitLength - 53;
long exp = 1023L + 52 + n + shift; // Use long to avoid overflow.
if (exp >= 0x7FF) return Double.POSITIVE_INFINITY;
if (exp <= 0) { // Degenerated number (subnormal, assume 0 for bit 52)
if (exp <= -54) return 0.0;
return toDoublePow2(m, n + 54) / 18014398509481984L; // 2^54 Exact.
}
// Normal number.
long bits =
(shift > 0)
? (m >> shift) + ((m >> (shift - 1)) & 1)
: // Rounding.
m << -shift;
if (((bits >> 52) != 1) && (++exp >= 0x7FF)) return Double.POSITIVE_INFINITY;
bits &= 0x000fffffffffffffL; // Clears MSB (bit 52)
bits |= exp << 52;
return Double.longBitsToDouble(bits);
}
/**
* Returns the hyperbolic tangent of x.
*
* @param x the value for which the hyperbolic tangent is calculated.
* @return <code>(exp(2 * x) - 1) / (exp(2 * x) + 1)</code>
*/
public static double tanh(double x) {
return (MathLib.exp(2 * x) - 1) / (MathLib.exp(2 * x) + 1);
}
/**
* Returns the hyperbolic cosine of x.
*
* @param x the value for which the hyperbolic cosine is calculated.
* @return <code>(exp(x) + exp(-x)) / 2</code>
*/
public static double cosh(double x) {
return (MathLib.exp(x) + MathLib.exp(-x)) * 0.5;
}
/**
* Returns the hyperbolic sine of x.
*
* @param x the value for which the hyperbolic sine is calculated.
* @return <code>(exp(x) - exp(-x)) / 2</code>
*/
public static double sinh(double x) {
return (MathLib.exp(x) - MathLib.exp(-x)) * 0.5;
}
/**
* Returns the arc tangent of the specified value, in the range of -<i>pi</i>/2 through
* <i>pi</i>/2.
*
* @param x the value whose arc tangent is to be returned.
* @return the arc tangent in radians for the specified value.
* @see <a href="http://mathworld.wolfram.com/InverseTangent.html">Inverse Tangent -- from
* MathWorld</a>
*/
public static double atan(double x) {
return MathLib._atan(x);
}
/**
* Returns the arc cosine of the specified value, in the range of 0.0 through <i>pi</i>.
*
* @param x the value whose arc cosine is to be returned.
* @return the arc cosine in radians for the specified value.
*/
public static double acos(double x) {
return HALF_PI - MathLib.asin(x);
}
/**
* Returns the remainder of the division of the specified two arguments.
*
* @param x the dividend.
* @param y the divisor.
* @return <code>x - round(x / y) * y</code>
*/
public static double rem(double x, double y) {
double tmp = x / y;
if (MathLib.abs(tmp) <= Long.MAX_VALUE) return x - MathLib.round(tmp) * y;
else return NaN;
}
/**
* Returns the closest <code>long</code> representation of the specified <code>double</code>
* number multiplied by a power of ten.
*
* @param d the <code>double</code> multiplier.
* @param n the power of two exponent.
* @return <code>d * 10<sup>n</sup></code>.
*/
public static long toLongPow10(double d, int n) {
long bits = Double.doubleToLongBits(d);
boolean isNegative = (bits >> 63) != 0;
int exp = ((int) (bits >> 52)) & 0x7FF;
long m = bits & 0x000fffffffffffffL;
if (exp == 0x7FF) throw new ArithmeticException("Cannot convert to long (Infinity or NaN)");
if (exp == 0) {
if (m == 0) return 0L;
return toLongPow10(d * 1E16, n - 16);
}
m |= 0x0010000000000000L; // Sets MSB (bit 52)
int pow2 = exp - 1023 - 52;
// Retrieves 63 bits m with n == 0.
if (n >= 0) {
// Works with 4 x 32 bits registers (x3:x2:x1:x0)
long x0 = 0; // 32 bits.
long x1 = 0; // 32 bits.
long x2 = m & MASK_32; // 32 bits.
long x3 = m >>> 32; // 32 bits.
while (n != 0) {
int i = (n >= POW5_INT.length) ? POW5_INT.length - 1 : n;
int coef = POW5_INT[i]; // 31 bits max.
if (((int) x0) != 0) x0 *= coef; // 63 bits max.
if (((int) x1) != 0) x1 *= coef; // 63 bits max.
x2 *= coef; // 63 bits max.
x3 *= coef; // 63 bits max.
x1 += x0 >>> 32;
x0 &= MASK_32;
x2 += x1 >>> 32;
x1 &= MASK_32;
x3 += x2 >>> 32;
x2 &= MASK_32;
// Adjusts powers.
pow2 += i;
n -= i;
// Normalizes (x3 should be 32 bits max).
long carry = x3 >>> 32;
if (carry != 0) { // Shift.
x0 = x1;
x1 = x2;
x2 = x3 & MASK_32;
x3 = carry;
pow2 += 32;
}
}
// Merges registers to a 63 bits mantissa.
int shift = 31 - MathLib.bitLength(x3); // -1..30
pow2 -= shift;
m =
(shift < 0)
? (x3 << 31) | (x2 >>> 1)
: // x3 is 32 bits.
(((x3 << 32) | x2) << shift) | (x1 >>> (32 - shift));
} else { // n < 0
// Works with x1:x0 126 bits register.
long x1 = m; // 63 bits.
long x0 = 0; // 63 bits.
while (true) {
// Normalizes x1:x0
int shift = 63 - MathLib.bitLength(x1);
x1 <<= shift;
x1 |= x0 >>> (63 - shift);
x0 = (x0 << shift) & MASK_63;
pow2 -= shift;
// Checks if division has to be performed.
if (n == 0) break; // Done.
// Retrieves power of 5 divisor.
int i = (-n >= POW5_INT.length) ? POW5_INT.length - 1 : -n;
int divisor = POW5_INT[i];
// Performs the division (126 bits by 31 bits).
long wh = (x1 >>> 32);
long qh = wh / divisor;
long r = wh - qh * divisor;
long wl = (r << 32) | (x1 & MASK_32);
long ql = wl / divisor;
r = wl - ql * divisor;
x1 = (qh << 32) | ql;
wh = (r << 31) | (x0 >>> 32);
qh = wh / divisor;
r = wh - qh * divisor;
wl = (r << 32) | (x0 & MASK_32);
ql = wl / divisor;
x0 = (qh << 32) | ql;
// Adjusts powers.
n += i;
pow2 -= i;
}
m = x1;
}
if (pow2 > 0) throw new ArithmeticException("Overflow");
if (pow2 < -63) return 0;
m = (m >> -pow2) + ((m >> -(pow2 + 1)) & 1); // Rounding.
return isNegative ? -m : m;
}
/**
* Returns the closest <code>double</code> representation of the specified <code>long</code>
* number multiplied by a power of ten.
*
* @param m the <code>long</code> multiplier.
* @param n the power of ten exponent.
* @return <code>multiplier * 10<sup>n</sup></code>.
*/
public static double toDoublePow10(long m, int n) {
if (m == 0) return 0.0;
if (m == Long.MIN_VALUE) return toDoublePow10(Long.MIN_VALUE / 10, n + 1);
if (m < 0) return -toDoublePow10(-m, n);
if (n >= 0) { // Positive power.
if (n > 308) return Double.POSITIVE_INFINITY;
// Works with 4 x 32 bits registers (x3:x2:x1:x0)
long x0 = 0; // 32 bits.
long x1 = 0; // 32 bits.
long x2 = m & MASK_32; // 32 bits.
long x3 = m >>> 32; // 32 bits.
int pow2 = 0;
while (n != 0) {
int i = (n >= POW5_INT.length) ? POW5_INT.length - 1 : n;
int coef = POW5_INT[i]; // 31 bits max.
if (((int) x0) != 0) x0 *= coef; // 63 bits max.
if (((int) x1) != 0) x1 *= coef; // 63 bits max.
x2 *= coef; // 63 bits max.
x3 *= coef; // 63 bits max.
x1 += x0 >>> 32;
x0 &= MASK_32;
x2 += x1 >>> 32;
x1 &= MASK_32;
x3 += x2 >>> 32;
x2 &= MASK_32;
// Adjusts powers.
pow2 += i;
n -= i;
// Normalizes (x3 should be 32 bits max).
long carry = x3 >>> 32;
if (carry != 0) { // Shift.
x0 = x1;
x1 = x2;
x2 = x3 & MASK_32;
x3 = carry;
pow2 += 32;
}
}
// Merges registers to a 63 bits mantissa.
int shift = 31 - MathLib.bitLength(x3); // -1..30
pow2 -= shift;
long mantissa =
(shift < 0)
? (x3 << 31) | (x2 >>> 1)
: // x3 is 32 bits.
(((x3 << 32) | x2) << shift) | (x1 >>> (32 - shift));
return toDoublePow2(mantissa, pow2);
} else { // n < 0
if (n < -324 - 20) return 0.0;
// Works with x1:x0 126 bits register.
long x1 = m; // 63 bits.
long x0 = 0; // 63 bits.
int pow2 = 0;
while (true) {
// Normalizes x1:x0
int shift = 63 - MathLib.bitLength(x1);
x1 <<= shift;
x1 |= x0 >>> (63 - shift);
x0 = (x0 << shift) & MASK_63;
pow2 -= shift;
// Checks if division has to be performed.
if (n == 0) break; // Done.
// Retrieves power of 5 divisor.
int i = (-n >= POW5_INT.length) ? POW5_INT.length - 1 : -n;
int divisor = POW5_INT[i];
// Performs the division (126 bits by 31 bits).
long wh = (x1 >>> 32);
long qh = wh / divisor;
long r = wh - qh * divisor;
long wl = (r << 32) | (x1 & MASK_32);
long ql = wl / divisor;
r = wl - ql * divisor;
x1 = (qh << 32) | ql;
wh = (r << 31) | (x0 >>> 32);
qh = wh / divisor;
r = wh - qh * divisor;
wl = (r << 32) | (x0 & MASK_32);
ql = wl / divisor;
x0 = (qh << 32) | ql;
// Adjusts powers.
n += i;
pow2 -= i;
}
return toDoublePow2(x1, pow2);
}
}
/**
* Returns <i>{@link #E e}</i> raised to the specified power.
*
* @param x the exponent.
* @return <code><i>e</i><sup>x</sup></code>
* @see <a href="http://mathworld.wolfram.com/ExponentialFunction.html">Exponential Function --
* from MathWorld</a>
*/
public static double exp(double x) {
return MathLib._ieee754_exp(x);
}
/**
* Returns the natural logarithm (base <i>{@link #E e}</i>) of the specified value.
*
* @param x the value greater than <code>0.0</code>.
* @return the value y such as <code><i>e</i><sup>y</sup> == x</code>
*/
public static double log(double x) {
return MathLib._ieee754_log(x);
}
/**
* Returns the arc sine of the specified value, in the range of -<i>pi</i>/2 through <i>pi</i>/2.
*
* @param x the value whose arc sine is to be returned.
* @return the arc sine in radians for the specified value.
*/
public static double asin(double x) {
if (x < -1.0 || x > 1.0) return MathLib.NaN;
if (x == -1.0) return -HALF_PI;
if (x == 1.0) return HALF_PI;
return MathLib.atan(x / MathLib.sqrt(1.0 - x * x));
}