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Jython is an implementation of the high-level, dynamic, object-oriented
language Python written in 100% Pure Java, and seamlessly integrated with
the Java platform. It thus allows you to run Python on any Java platform.
// Copyright (c) Corporation for National Research Initiatives
package org.python.modules;
import java.math.BigInteger;
import org.python.core.ClassDictInit;
import org.python.core.Py;
import org.python.core.PyException;
import org.python.core.PyFloat;
import org.python.core.PyInteger;
import org.python.core.PyLong;
import org.python.core.PyObject;
import org.python.core.PyTuple;
import org.python.core.__builtin__;
public class math implements ClassDictInit {
public static PyFloat pi = new PyFloat(Math.PI);
public static PyFloat e = new PyFloat(Math.E);
private static final double ZERO = 0.0;
private static final double MINUS_ZERO = -0.0;
private static final double ONE = 1.0;
private static final double MINUS_ONE = -1.0;
private static final double TWO = 2.0;
private static final double EIGHT = 8.0;
static final double LN2 = 0.693147180559945309417232121458; // Ref OEIS A002162
private static final double INF = Double.POSITIVE_INFINITY;
private static final double NINF = Double.NEGATIVE_INFINITY;
private static final double NAN = Double.NaN;
private static final BigInteger MAX_LONG_BIGINTEGER = new BigInteger(
String.valueOf(Long.MAX_VALUE));
private static final BigInteger MIN_LONG_BIGINTEGER = new BigInteger(
String.valueOf(Long.MIN_VALUE));
public static void classDictInit(@SuppressWarnings("unused") PyObject dict) {}
public static double gamma(double v) {
return math_gamma.gamma(v);
}
public static double lgamma(double v) {
return math_gamma.lgamma(v);
}
public static double erf(double v) {
return math_erf.erf(v);
}
public static double erfc(double v) {
return math_erf.erfc(v);
}
public static double expm1(double v) {
if (Double.POSITIVE_INFINITY == v) {
return v;
}
double result = Math.expm1(v);
if (Double.isInfinite(result)) {
throw Py.OverflowError(Double.toString(v));
}
return result;
}
public static double acos(double v) {
return exceptNaN(Math.acos(v), v);
}
/**
* Compute cosh-1y.
*
* @param y
* @return x such that cosh x = y
*/
public static double acosh(double y) {
if (y < 1.0) {
throw mathDomainError();
} else {
// acosh(y) = ln[y + sqrt(y**2 - 1)]
if (y < 2.) {
// Rearrange as acosh(1+u) = ln[1 + u + sqrt(u(2+u))]
final double u = y - 1.;
double s = Math.sqrt(u * (2. + u));
return Math.log1p(u + s);
} else if (y < 0x1p27) {
// Rearrange as acosh(y) = ln[ y ( 1 + sqrt[1-(1/y)**2] )]
final double u = 1. / y;
double t = Math.sqrt((1. + u) * (1. - u));
return Math.log(y * (1. + t));
} else {
// As above but t indistinguishable from 1.0 so ...
return Math.log(y) + LN2;
}
}
}
public static double asin(double v) {
return exceptNaN(Math.asin(v), v);
}
public static double asinh(double v) {
if (isnan(v) || isinf(v)) {
return v;
}
final double ln2 = 6.93147180559945286227e-01;
final double large = 1 << 28;
final double small = 1.0 / (1 << 28);
boolean sign = false;
if (v < 0) {
v = -v;
sign = true;
}
double temp;
if (v > large) {
temp = log(v) + ln2;
} else if (v > 2) {
temp = log(2 * v + 1 / (sqrt(v * v + 1) + v));
} else if (v < small) {
temp = v;
} else {
temp = log1p(v + v * v / (1 + sqrt(1 + v * v)));
}
return sign ? -temp : temp;
}
public static double atan(double v) {
return exceptNaN(Math.atan(v), v);
}
/**
* Compute tanh-1y.
*
* @param y
* @return x such that tanh x = y
*/
public static double atanh(double y) {
double absy = Math.abs(y);
if (absy >= 1.0) {
throw mathDomainError();
} else {
// 2x = ln[(1+y)/(1-y)] = ln[1 + 2y/(1-y)]
double u = (absy + absy) / (1. - absy);
double x = 0.5 * Math.log1p(u);
return Math.copySign(x, y);
}
}
public static double atan2(double v, double w) {
return Math.atan2(v, w);
}
public static double ceil(PyObject v) {
return ceil(v.asDouble());
}
public static double ceil(double v) {
return Math.ceil(v);
}
public static double cos(double v) {
return exceptNaN(Math.cos(v), v);
}
public static double cosh(double v) {
return exceptInf(Math.cosh(v), v);
}
public static double exp(double v) {
return exceptInf(Math.exp(v), v);
}
public static double floor(PyObject v) {
return floor(v.asDouble());
}
public static double floor(double v) {
return Math.floor(v);
}
public static double log(PyObject v) {
return log(v, null);
}
public static double log(PyObject v, PyObject base) {
double doubleValue;
if (v instanceof PyLong) {
doubleValue = calculateLongLog((PyLong)v);
} else {
doubleValue = log(v.asDouble());
}
return (base == null) ? doubleValue : applyLoggedBase(doubleValue, base);
}
public static double pow(double v, double w) {
if (w == ZERO) {
return ONE;
}
if (v == ONE) {
return v;
}
if (isnan(v) || isnan(w)) {
return NAN;
}
if (v == ZERO) {
if (w == ZERO) {
return ONE;
} else if (w > ZERO || ispinf(w)) {
return ZERO;
} else {
throw mathDomainError();
}
}
if (isninf(v)) {
if (isninf(w)) {
return ZERO;
}
if (isinf(w)) {
return INF;
}
if (w == ZERO) {
return ONE;
}
if (w > ZERO) {
if (isOdd(w)) {
return NINF;
}
return INF;
}
if (isOdd(w)) {
return MINUS_ZERO;
}
return ZERO;
}
if (isninf(w)) {
if (v < ZERO) {
if (v == MINUS_ONE) {
return ONE;
}
if (v < MINUS_ONE) {
return ZERO;
}
return INF;
}
}
if (ispinf(w)) {
if (v < ZERO) {
if (v == MINUS_ONE) {
return ONE;
}
if (v < MINUS_ONE) {
return INF;
}
return ZERO;
}
}
if (v < ZERO && !isIntegral(w)) {
throw mathDomainError();
}
return Math.pow(v, w);
}
public static double sin(PyObject v) {
return sin(v.asDouble());
}
public static double sin(double v) {
return exceptNaN(Math.sin(v), v);
}
public static double sqrt(PyObject v) {
return sqrt(v.asDouble());
}
public static double sqrt(double v) {
return exceptNaN(Math.sqrt(v), v);
}
public static double tan(double v) {
return exceptNaN(Math.tan(v), v);
}
public static double log10(PyObject v) {
if (v instanceof PyLong) {
int exp[] = new int[1];
double x = ((PyLong)v).scaledDoubleValue(exp);
if (x <= ZERO) {
throw mathDomainError();
}
return log10(x) + (exp[0] * EIGHT) * log10(TWO);
}
return log10(v.asDouble());
}
public static double sinh(double v) {
return exceptInf(Math.sinh(v), v);
}
public static double tanh(double v) {
return exceptInf(Math.tanh(v), v);
}
public static double fabs(double v) {
return Math.abs(v);
}
public static double fmod(double v, double w) {
if (isnan(v) || isnan(w)) {
return NAN;
}
if (isinf(w)) {
return v;
}
if (w == ZERO) {
throw mathDomainError();
}
if (isinf(v) && w == ONE) {
throw mathDomainError();
}
return v % w;
}
public static PyTuple modf(double v) {
if (isnan(v)) {
return new PyTuple(new PyFloat(v), new PyFloat(v));
}
if (isinf(v)) {
double first = ZERO;
if (isninf(v)) {
first = MINUS_ZERO;
}
return new PyTuple(new PyFloat(first), new PyFloat(v));
}
double w = v % ONE;
v -= w;
return new PyTuple(new PyFloat(w), new PyFloat(v));
}
public static PyTuple frexp(double x) {
int exponent;
double mantissa;
switch (exponent = Math.getExponent(x)) {
default:
// x = m * 2**exponent and 1 <=abs(m) <2
exponent = exponent + 1;
// x = m * 2**exponent and 0.5 <=abs(m) <1
mantissa = Math.scalb(x, -exponent);
break;
case 1024: // nan or inf
mantissa = x;
exponent = 0;
break;
case -1023:
if (x == 0.) { // , 0.0 or -0.0
mantissa = x;
exponent = 0;
} else { // denormalised value
// x = m * 2**exponent but 0 < abs(m) < 1
exponent = Math.getExponent(x * 0x1p52) - 51;
mantissa = Math.scalb(x, -exponent);
}
break;
}
return new PyTuple(new PyFloat(mantissa), new PyInteger(exponent));
}
public static PyObject trunc(PyObject number) {
return number.__getattr__("__trunc__").__call__();
}
public static double ldexp(double v, PyObject wObj) {
long w = getLong(wObj);
if (w < Integer.MIN_VALUE) {
w = Integer.MIN_VALUE;
} else if (w > Integer.MAX_VALUE) {
w = Integer.MAX_VALUE;
}
return exceptInf(Math.scalb(v, (int)w), v);
}
/**
* Returns (x2 +y2)½ without intermediate overflow or
* underflow. If either argument is infinite, the result is infinite, but overflow during the
* calculation is detected as an error.
*
* @param x
* @param y
* @return (x2 +y2)½
*/
public static double hypot(double x, double y) {
double mag = Math.hypot(x, y);
if (Double.isInfinite(mag) && !(Double.isInfinite(x) || Double.isInfinite(y))) {
// In these circumstances Math.hypot quietly returns inf, but CPython should raise.
throw mathRangeError();
}
return mag;
}
public static double radians(double v) {
return Math.toRadians(v);
}
public static double degrees(double v) {
// Note that this does not raise overflow in Python: 1e307 -> inf as in Java.
return Math.toDegrees(v);
}
public static boolean isnan(double v) {
return Double.isNaN(v);
}
/**
* @param v
*
* @return true if v is positive or negative infinity
*/
public static boolean isinf(double v) {
return Double.isInfinite(v);
}
public static double copysign(double v, double w) {
return Math.copySign(v, w);
}
public static PyLong factorial(double v) {
if (v == ZERO || v == ONE) {
return new PyLong(1);
} else if (v < ZERO || isnan(v) || isinf(v)) {
throw mathDomainError();
} else if (!isIntegral(v)) {
throw mathDomainError();
} else {
// long input should be big enough :-)
long value = (long)v;
BigInteger bi = new BigInteger(Long.toString(value));
for (long l = value - 1; l > 1; l--) {
bi = bi.multiply(new BigInteger(Long.toString(l)));
}
return new PyLong(bi);
}
}
public static double log1p(double v) {
if (v <= -1.) {
throw mathDomainError();
} else {
return Math.log1p(v);
}
}
public static double fsum(final PyObject iterable) {
PyFloat result = (PyFloat)__builtin__.__import__("_fsum").invoke("fsum", iterable);
return result.asDouble();
}
private static double calculateLongLog(PyLong v) {
int exp[] = new int[1];
double x = v.scaledDoubleValue(exp);
if (x <= ZERO) {
throw mathDomainError();
}
return log(x) + (exp[0] * EIGHT) * log(TWO);
}
private static double applyLoggedBase(double loggedValue, PyObject base) {
double loggedBase;
if (base instanceof PyLong) {
loggedBase = calculateLongLog((PyLong)base);
} else {
loggedBase = log(base.asDouble());
}
return loggedValue / loggedBase;
}
private static double log(double v) {
if (v <= 0.) {
throw mathDomainError();
} else {
return Math.log(v);
}
}
private static double log10(double v) {
if (v <= 0.) {
throw mathDomainError();
} else {
return Math.log10(v);
}
}
private static boolean isninf(double v) {
return v == NINF;
}
private static boolean ispinf(double v) {
return v == INF;
}
/**
* Returns a ValueError("math domain error"), ready to throw from the client code.
*
* @return ValueError("math domain error")
*/
static PyException mathDomainError() {
return Py.ValueError("math domain error");
}
/**
* Returns a OverflowError("math range error"), ready to throw from the client code.
*
* @return OverflowError("math range error")
*/
static PyException mathRangeError() {
return Py.OverflowError("math range error");
}
/**
* Turn a NaN result into a thrown ValueError, a math domain error, if
* the original argument was not itself NaN. Use as:
*
*
* public static double asin(double v) { return exceptNaN(Math.asin(v), v); }
*
*
* Note that the original function argument is also supplied to this method. Most Java math
* library methods do exactly what we need for Python, but some return {@value Double#NaN} when
* Python should raise ValueError. This is a brief way to change that.
*
* @param result to return (if we return)
* @param arg to include in check
* @return result if arg was NaN or result was not
* NaN
* @throws PyException (ValueError) if result was NaN and
* arg was not NaN
*/
private static double exceptNaN(double result, double arg) throws PyException {
if (Double.isNaN(result) && !Double.isNaN(arg)) {
throw mathDomainError();
} else {
return result;
}
}
/**
* Turn an infinite result into a thrown OverflowError, a math range error, if the
* original argument was not itself infinite. Use as:
*
*
* public static double cosh(double v) { return exceptInf( Math.cosh(v), v); }
*
*
* Note that the original function argument is also supplied to this method. Most Java math
* library methods do exactly what we need for Python, but some return an infinity when Python
* should raise OverflowError. This is a brief way to change that.
*
* @param result to return (if we return)
* @param arg to include in check
* @return result if arg was infinite or result was not infinite
* @throws PyException (ValueError) if result was infinite and arg was
* not infinite
*/
private static double exceptInf(double result, double arg) {
if (Double.isInfinite(result) && !Double.isInfinite(arg)) {
throw mathRangeError();
} else {
return result;
}
}
/**
* convert a PyObject into a long between Long.MIN_VALUE and Long.MAX_VALUE
*/
private static long getLong(PyObject pyo) {
if (pyo instanceof PyLong) {
return getLong(((PyLong)pyo));
}
return pyo.asLong();
}
/**
* convert a PyLong into a long between Long.MIN_VALUE and Long.MAX_VALUE
*/
private static long getLong(PyLong pyLong) {
BigInteger value = pyLong.getValue();
if (value.compareTo(MAX_LONG_BIGINTEGER) > 0) {
return Long.MAX_VALUE;
}
if (value.compareTo(MIN_LONG_BIGINTEGER) < 0) {
return Long.MIN_VALUE;
}
return value.longValue();
}
private static boolean isIntegral(double v) {
return ceil(v) - v == ZERO;
}
private static boolean isOdd(double v) {
return isIntegral(v) && v % TWO != ZERO;
}
}