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// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the Apache 2.0 License.
// See the LICENSE file in the project root for more information.
using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Numerics;
using Microsoft.Scripting;
using Microsoft.Scripting.Utils;
using IronPython.Runtime;
using IronPython.Runtime.Operations;
using IronPython.Runtime.Types;
[assembly: PythonModule("math", typeof(IronPython.Modules.PythonMath))]
namespace IronPython.Modules {
public static partial class PythonMath {
public const string __doc__ = "Provides common mathematical functions.";
#if NET
public const double tau = Math.Tau;
#else
public const double tau = 2 * Math.PI;
#endif
public const double pi = Math.PI;
public const double e = Math.E;
private const double degreesToRadians = Math.PI / 180.0;
private const int Bias = 0x3FE;
public static double degrees(double radians) {
return Check(radians, radians / degreesToRadians);
}
public static double radians(double degrees) {
return Check(degrees, degrees * degreesToRadians);
}
public static double fmod(double v, double w) {
return Check(v, w, v % w);
}
private static double sum(List<double> partials) {
// sum the partials the same was as CPython does
var n = partials.Count;
var hi = 0.0;
if (n == 0) return hi;
var lo = 0.0;
// sum exact
while (n > 0) {
var x = hi;
var y = partials[--n];
hi = x + y;
lo = y - (hi - x);
if (lo != 0.0)
break;
}
if (n == 0) return hi;
// half-even rounding
if (lo < 0.0 && partials[n - 1] < 0.0 || lo > 0.0 && partials[n - 1] > 0.0) {
var y = lo * 2.0;
var x = hi + y;
var yr = x - hi;
if (y == yr)
hi = x;
}
return hi;
}
public static double fsum(IEnumerable e) {
// msum from https://code.activestate.com/recipes/393090/
var partials = new List<double>();
foreach (var v in e.Cast<object>().Select(o => Converter.ConvertToDouble(o))) {
var x = v;
var i = 0;
for (var j = 0; j < partials.Count; j++) {
var y = partials[j];
if (Math.Abs(x) < Math.Abs(y)) {
var t = x;
x = y;
y = t;
}
var hi = x + y;
var lo = y - (hi - x);
if (lo != 0) {
partials[i++] = lo;
}
x = hi;
}
partials.RemoveRange(i, partials.Count - i);
partials.Add(x);
}
return sum(partials);
}
public static PythonTuple frexp(double v) {
if (Double.IsInfinity(v) || Double.IsNaN(v)) {
return PythonTuple.MakeTuple(v, 0.0);
}
int exponent = 0;
double mantissa = 0;
if (v == 0) {
mantissa = 0;
exponent = 0;
} else {
byte[] vb = BitConverter.GetBytes(v);
if (BitConverter.IsLittleEndian) {
DecomposeLe(vb, out mantissa, out exponent);
} else {
throw new NotImplementedException();
}
}
return PythonTuple.MakeTuple(mantissa, exponent);
}
public static PythonTuple modf(double v) {
if (double.IsInfinity(v)) {
return PythonTuple.MakeTuple(0.0, v);
}
double w = v % 1.0;
v -= w;
return PythonTuple.MakeTuple(w, v);
}
public static double ldexp(double v, BigInteger w) {
if (v == 0.0 || double.IsInfinity(v)) {
return v;
}
return Check(v, v * Math.Pow(2.0, (double)w));
}
public static double hypot(double v, double w) {
if (double.IsInfinity(v) || double.IsInfinity(w)) {
return double.PositiveInfinity;
}
return Check(v, w, MathUtils.Hypot(v, w));
}
public static double pow(double v, double exp) {
if (v == 1.0 || exp == 0.0) {
return 1.0;
} else if (double.IsNaN(v) || double.IsNaN(exp)) {
return double.NaN;
} else if (v == 0.0) {
if (exp > 0.0) {
return 0.0;
}
throw PythonOps.ValueError("math domain error");
} else if (double.IsPositiveInfinity(exp)) {
if (v > 1.0 || v < -1.0) {
return double.PositiveInfinity;
} else if (v == -1.0) {
return 1.0;
} else {
return 0.0;
}
} else if (double.IsNegativeInfinity(exp)) {
if (v > 1.0 || v < -1.0) {
return 0.0;
} else if (v == -1.0) {
return 1.0;
} else {
return double.PositiveInfinity;
}
}
return Check(v, exp, Math.Pow(v, exp));
}
public static double log(double v0) {
if (v0 <= 0.0) {
throw PythonOps.ValueError("math domain error");
}
return Check(v0, Math.Log(v0));
}
public static double log(double v0, double v1) {
if (v0 <= 0.0 || v1 == 0.0) {
throw PythonOps.ValueError("math domain error");
} else if (v1 == 1.0) {
throw PythonOps.ZeroDivisionError("float division");
} else if (v1 == Double.PositiveInfinity) {
return 0.0;
}
return Check(Math.Log(v0, v1));
}
public static double log(BigInteger value) {
if (value.Sign <= 0) {
throw PythonOps.ValueError("math domain error");
}
return value.Log();
}
public static double log(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return log(val);
} else {
return log(Converter.ConvertToBigInteger(value));
}
}
public static double log(BigInteger value, double newBase) {
if (newBase <= 0.0 || value <= 0) {
throw PythonOps.ValueError("math domain error");
} else if (newBase == 1.0) {
throw PythonOps.ZeroDivisionError("float division");
} else if (newBase == Double.PositiveInfinity) {
return 0.0;
}
return Check(value.Log(newBase));
}
public static double log(object value, double newBase) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return log(val, newBase);
} else {
return log(Converter.ConvertToBigInteger(value), newBase);
}
}
public static double log2(double x) {
if (x <= 0) throw PythonOps.ValueError("math domain error");
if (double.IsPositiveInfinity(x) || double.IsNaN(x)) return x;
if (!BitConverter.IsLittleEndian) return Math.Log(x, 2);
int exponent = 0;
double mantissa = 0;
byte[] vb = BitConverter.GetBytes(x);
DecomposeLe(vb, out mantissa, out exponent);
if (x >= 1)
return Math.Log(mantissa * 2, 2) + (exponent - 1); // similar to CPython for precision
else
return Math.Log(mantissa, 2) + exponent;
}
public static double log2(BigInteger x) {
if (x <= 0) throw PythonOps.ValueError("math domain error");
// cast to double if we can
var d = (double)x;
if (!double.IsPositiveInfinity(d)) return log2(d);
// bring to into double range and try again
var y = BigInteger.Log(x, 2);
var z = (int)Math.Ceiling(y) - 1023;
x >>= z;
Debug.Assert(!double.IsPositiveInfinity((double)x));
return log2((double)x) + z;
}
public static double log10(double v0) {
if (v0 <= 0.0) {
throw PythonOps.ValueError("math domain error");
}
return Check(v0, Math.Log10(v0));
}
public static double log10(BigInteger value) {
if (value.Sign <= 0) {
throw PythonOps.ValueError("math domain error");
}
return value.Log10();
}
public static double log10(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return log10(val);
} else {
return log10(Converter.ConvertToBigInteger(value));
}
}
public static double log1p(double v0) {
// Calculate log(1.0 + v0) using William Kahan's algorithm for numerical precision
if (double.IsPositiveInfinity(v0)) {
return double.PositiveInfinity;
}
double v1 = v0 + 1.0;
// Linear approximation for very small v0
if (v1 == 1.0) {
return v0;
}
// Apply correction factor
return log(v1) * (v0 / (v1 - 1.0));
}
public static double log1p(BigInteger value) {
return log(value + BigInteger.One);
}
public static double log1p(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return log1p(val);
} else {
return log1p(Converter.ConvertToBigInteger(value));
}
}
public static double expm1(double v0) {
return Check(v0, Math.Tanh(v0 / 2.0) * (Math.Exp(v0) + 1.0));
}
public static double asinh(double v0) {
if (v0 == 0.0 || double.IsInfinity(v0)) {
return v0;
}
// rewrote ln(v0 + sqrt(v0**2 + 1)) for precision
if (Math.Abs(v0) > 1.0) {
return Math.Sign(v0) * (Math.Log(Math.Abs(v0)) + Math.Log(1.0 + MathUtils.Hypot(1.0, 1.0 / v0)));
} else {
return Math.Log(v0 + MathUtils.Hypot(1.0, v0));
}
}
public static double asinh(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return asinh(val);
} else {
return asinh(Converter.ConvertToBigInteger(value));
}
}
public static double acosh(double v0) {
if (v0 < 1.0) {
throw PythonOps.ValueError("math domain error");
} else if (double.IsPositiveInfinity(v0)) {
return double.PositiveInfinity;
}
// rewrote ln(v0 + sqrt(v0**2 - 1)) for precision
double c = Math.Sqrt(v0 + 1.0);
return Math.Log(c) + Math.Log(v0 / c + Math.Sqrt(v0 - 1.0));
}
public static double acosh(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return acosh(val);
} else {
return acosh(Converter.ConvertToBigInteger(value));
}
}
public static double atanh(double v0) {
if (v0 >= 1.0 || v0 <= -1.0) {
throw PythonOps.ValueError("math domain error");
} else if (v0 == 0.0) {
// preserve +/-0.0
return v0;
}
return Math.Log((1.0 + v0) / (1.0 - v0)) * 0.5;
}
public static double atanh(BigInteger value) {
if (value == 0) {
return 0;
} else {
throw PythonOps.ValueError("math domain error");
}
}
public static double atanh(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return atanh(val);
} else {
return atanh(Converter.ConvertToBigInteger(value));
}
}
public static double atan2(double v0, double v1) {
if (double.IsNaN(v0) || double.IsNaN(v1)) {
return double.NaN;
} else if (double.IsInfinity(v0)) {
if (double.IsPositiveInfinity(v1)) {
return pi * 0.25 * Math.Sign(v0);
} else if (double.IsNegativeInfinity(v1)) {
return pi * 0.75 * Math.Sign(v0);
} else {
return pi * 0.5 * Math.Sign(v0);
}
} else if (double.IsInfinity(v1)) {
return v1 > 0.0 ? 0.0 : pi * DoubleOps.Sign(v0);
}
return Math.Atan2(v0, v1);
}
public static object ceil(CodeContext context, object x) {
object val;
if (PythonTypeOps.TryInvokeUnaryOperator(context, x, "__ceil__", out val)) {
return val;
}
throw PythonOps.TypeError("a float is required");
}
public static object ceil(double v0) {
if (double.IsInfinity(v0)) throw PythonOps.OverflowError("cannot convert float infinity to integer");
if (double.IsNaN(v0)) throw PythonOps.ValueError("cannot convert float NaN to integer");
var res = Math.Ceiling(v0);
if (res < int.MinValue || res > int.MaxValue) {
return (BigInteger)res;
}
return (int)res;
}
/// <summary>
/// Error function on real values
/// </summary>
public static double erf(double v0) {
return MathUtils.Erf(v0);
}
/// <summary>
/// Complementary error function on real values: erfc(x) = 1 - erf(x)
/// </summary>
public static double erfc(double v0) {
return MathUtils.ErfComplement(v0);
}
public static object factorial(double v0) {
if (v0 % 1.0 != 0.0) {
throw PythonOps.ValueError("factorial() only accepts integral values");
}
return factorial((BigInteger)v0);
}
public static object factorial(BigInteger value) {
if (value < 0) {
throw PythonOps.ValueError("factorial() not defined for negative values");
}
if (value > SysModule.maxsize) {
throw PythonOps.OverflowError("factorial() argument should not exceed {0}", SysModule.maxsize);
}
BigInteger val = 1;
for (BigInteger mul = value; mul > BigInteger.One; mul -= BigInteger.One) {
val *= mul;
}
if (val > int.MaxValue) {
return val;
}
return (int)val;
}
public static object factorial(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return factorial(val);
} else {
return factorial(Converter.ConvertToBigInteger(value));
}
}
public static object floor(CodeContext context, object x) {
object val;
if (PythonTypeOps.TryInvokeUnaryOperator(context, x, "__floor__", out val)) {
return val;
}
throw PythonOps.TypeError("a float is required");
}
public static object floor(double v0) {
if (double.IsInfinity(v0)) throw PythonOps.OverflowError("cannot convert float infinity to integer");
if (double.IsNaN(v0)) throw PythonOps.ValueError("cannot convert float NaN to integer");
var res = Math.Floor(v0);
if (res < int.MinValue || res > int.MaxValue) {
return (BigInteger)res;
}
return (int)res;
}
/// <summary>
/// Gamma function on real values
/// </summary>
public static double gamma(double v0) {
return Check(v0, MathUtils.Gamma(v0));
}
/// <summary>
/// Natural log of absolute value of Gamma function
/// </summary>
public static double lgamma(double v0) {
return Check(v0, MathUtils.LogGamma(v0));
}
public static object trunc(CodeContext/*!*/ context, object value) {
object func;
if (PythonOps.TryGetBoundAttr(value, "__trunc__", out func)) {
return PythonOps.CallWithContext(context, func);
} else {
throw PythonOps.TypeError("type {0} doesn't define __trunc__ method", PythonOps.GetPythonTypeName(value));
}
}
public static bool isfinite(double x) {
return !double.IsInfinity(x) && !double.IsNaN(x);
}
public static bool isinf(double v0) {
return double.IsInfinity(v0);
}
public static bool isinf(BigInteger value) {
return false;
}
public static bool isinf(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return isinf(val);
}
return false;
}
public static bool isnan(double v0) {
return double.IsNaN(v0);
}
public static bool isnan(BigInteger value) {
return false;
}
public static bool isnan(object value) {
// CPython tries float first, then double, so we need
// an explicit overload which properly matches the order here
double val;
if (Converter.TryConvertToDouble(value, out val)) {
return isnan(val);
}
return false;
}
public static double copysign(double x, double y) {
return DoubleOps.CopySign(x, y);
}
public static double copysign(object x, object y) {
double val, sign;
if (!Converter.TryConvertToDouble(x, out val) ||
!Converter.TryConvertToDouble(y, out sign)) {
throw PythonOps.TypeError("TypeError: a float is required");
}
return DoubleOps.CopySign(val, sign);
}
// new in CPython 3.5
public static object gcd(BigInteger x, BigInteger y) {
var res = BigInteger.GreatestCommonDivisor(x, y);
if (res.AsInt32(out var i))
return i;
return res;
}
public static object gcd(object x, object y) {
return gcd(ObjectToBigInteger(x), ObjectToBigInteger(y));
static BigInteger ObjectToBigInteger(object x) {
BigInteger a;
switch (PythonOps.Index(x)) {
case int i:
a = i;
break;
case BigInteger bi:
a = bi;
break;
default:
throw new InvalidOperationException();
}
return a;
}
}
public static readonly double nan = double.NaN; // new in CPython 3.5
public static readonly double inf = double.PositiveInfinity; // new in CPython 3.5
// new in CPython 3.5
public static bool isclose(double a, double b, double rel_tol = 1e-09, double abs_tol = 0.0) {
if (rel_tol < 0 || abs_tol < 0) throw PythonOps.ValueError("tolerances must be non-negative");
//if (double.IsNaN(a) || double.IsNaN(b)) return false;
if (a == b) return true;
if (double.IsInfinity(a) || double.IsInfinity(b)) return false;
return Math.Abs(a - b) <= Math.Max(rel_tol * Math.Max(Math.Abs(a), Math.Abs(b)), abs_tol);
}
#region Private Implementation Details
private static void SetExponentLe(byte[] v, int exp) {
exp += Bias;
ushort oldExp = LdExponentLe(v);
ushort newExp = (ushort)(oldExp & 0x800f | (exp << 4));
StExponentLe(v, newExp);
}
private static int IntExponentLe(byte[] v) {
ushort exp = LdExponentLe(v);
return ((int)((exp & 0x7FF0) >> 4) - Bias);
}
private static ushort LdExponentLe(byte[] v) {
return (ushort)(v[6] | ((ushort)v[7] << 8));
}
private static long LdMantissaLe(byte[] v) {
int i1 = (v[0] | (v[1] << 8) | (v[2] << 16) | (v[3] << 24));
int i2 = (v[4] | (v[5] << 8) | ((v[6] & 0xF) << 16));
return i1 | (i2 << 32);
}
private static void StExponentLe(byte[] v, ushort e) {
v[6] = (byte)e;
v[7] = (byte)(e >> 8);
}
private static bool IsDenormalizedLe(byte[] v) {
ushort exp = LdExponentLe(v);
long man = LdMantissaLe(v);
return ((exp & 0x7FF0) == 0 && (man != 0));
}
private static void DecomposeLe(byte[] v, out double m, out int e) {
if (IsDenormalizedLe(v)) {
m = BitConverter.ToDouble(v, 0);
m *= Math.Pow(2.0, 1022);
v = BitConverter.GetBytes(m);
e = IntExponentLe(v) - 1022;
} else {
e = IntExponentLe(v);
}
SetExponentLe(v, 0);
m = BitConverter.ToDouble(v, 0);
}
private static double Check(double v) {
return PythonOps.CheckMath(v);
}
private static double Check(double input, double output) {
return PythonOps.CheckMath(input, output);
}
private static double Check(double in0, double in1, double output) {
return PythonOps.CheckMath(in0, in1, output);
}
#endregion
}
}