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// Copyright (c) 2012, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.
/**
* Mathematical constants and functions, plus a random number generator.
*/
library dart.math;
part "random.dart";
/**
* Base of the natural logarithms.
*
* Typically written as "e".
*/
const double E = 2.718281828459045;
/**
* Natural logarithm of 10.
*/
const double LN10 = 2.302585092994046;
/**
* Natural logarithm of 2.
*/
const double LN2 = 0.6931471805599453;
/**
* Base-2 logarithm of [E].
*/
const double LOG2E = 1.4426950408889634;
/**
* Base-10 logarithm of [E].
*/
const double LOG10E = 0.4342944819032518;
/**
* The PI constant.
*/
const double PI = 3.1415926535897932;
/**
* Square root of 1/2.
*/
const double SQRT1_2 = 0.7071067811865476;
/**
* Square root of 2.
*/
const double SQRT2 = 1.4142135623730951;
/**
* Returns the lesser of two numbers.
*
* Returns NaN if either argument is NaN.
* The lesser of [:-0.0:] and [:0.0:] is [:-0.0:].
* If the arguments are otherwise equal (including int and doubles with the
* same mathematical value) then it is unspecified which of the two arguments
* is returned.
*/
num min(num a, num b) {
// These partially redundant type checks improve code quality for dart2js.
// Most of the improvement is at call sites from the inferred non-null num
// return type.
if (a is! num) throw new ArgumentError(a);
if (b is! num) throw new ArgumentError(b);
if (a > b) return b;
if (a < b) return a;
if (b is double) {
// Special case for NaN and -0.0. If one argument is NaN return NaN.
// [min] must also distinguish between -0.0 and 0.0.
if (a is double) {
if (a == 0.0) {
// a is either 0.0 or -0.0. b is either 0.0, -0.0 or NaN.
// The following returns -0.0 if either a or b is -0.0, and it
// returns NaN if b is NaN.
return (a + b) * a * b;
}
}
// Check for NaN and b == -0.0.
if (a == 0 && b.isNegative || b.isNaN) return b;
return a;
}
return a;
}
/**
* Returns the larger of two numbers.
*
* Returns NaN if either argument is NaN.
* The larger of [:-0.0:] and [:0.0:] is [:0.0:]. If the arguments are
* otherwise equal (including int and doubles with the same mathematical value)
* then it is unspecified which of the two arguments is returned.
*/
num max(num a, num b) {
// These partially redundant type checks improve code quality for dart2js.
// Most of the improvement is at call sites from the inferred non-null num
// return type.
if (a is! num) throw new ArgumentError(a);
if (b is! num) throw new ArgumentError(b);
if (a > b) return a;
if (a < b) return b;
if (b is double) {
// Special case for NaN and -0.0. If one argument is NaN return NaN.
// [max] must also distinguish between -0.0 and 0.0.
if (a is double) {
if (a == 0.0) {
// a is either 0.0 or -0.0. b is either 0.0, -0.0, or NaN.
// The following returns 0.0 if either a or b is 0.0, and it
// returns NaN if b is NaN.
return a + b;
}
}
// Check for NaN.
if (b.isNaN) return b;
return a;
}
// max(-0.0, 0) must return 0.
if (b == 0 && a.isNegative) return b;
return a;
}
/**
* A variant of [atan].
*
* Converts both arguments to doubles.
*
* Returns the angle between the positive x-axis and the vector ([b],[a]).
* The result, in radians, is in the range -PI..PI.
*
* If [b] is positive, this is the same as [:atan(b/a):].
*
* The result is negative when [a] is negative (including when [a] is the
* double -0.0).
*
* If [a] is equal to zero, the vector ([b],[a]) is considered parallel to
* the x-axis, even if [b] is also equal to zero. The sign of [b] determines
* the direction of the vector along the x-axis.
*
* Returns NaN if either argument is NaN.
*/
external double atan2(num a, num b);
/**
* Returns [x] to the power of [exponent].
*
* If [x] is an [int] and [exponent] is a non-negative [int], the result is
* an [int], otherwise both arguments are converted to doubles first, and the
* result is a [double].
*
* For integers, the power is always equal to the mathematical result of `x` to
* the power `exponent`, only limited by the available memory.
*
* For doubles, `pow(x, y)` handles edge cases as follows:
*
* - if `y` is zero (0.0 or -0.0), the result is always 1.0.
* - if `x` is 1.0, the result is always 1.0.
* - otherwise, if either `x` or `y` is NaN then the result is NaN.
* - if `x` is negative (but not -0.0) and `y` is a finite non-integer, the
* result is NaN.
* - if `x` is Infinity and `y` is negative, the result is 0.0.
* - if `x` is Infinity and `y` is positive, the result is Infinity.
* - if `x` is 0.0 and `y` is negative, the result is Infinity.
* - if `x` is 0.0 and `y` is positive, the result is 0.0.
* - if `x` is -Infinity or -0.0 and `y` is an odd integer, then the result is
* `-pow(-x ,y)`.
* - if `x` is -Infinity or -0.0 and `y` is not an odd integer, then the result
* is the same as `pow(-x , y)`.
* - if `y` is Infinity and the absolute value of `x` is less than 1, the
* result is 0.0.
* - if `y` is Infinity and `x` is -1, the result is 1.0.
* - if `y` is Infinity and the absolute value of `x` is greater than 1,
* the result is Infinity.
* - if `y` is -Infinity, the result is `1/pow(x, Infinity)`.
*
* This corresponds to the `pow` function defined in the IEEE Standard 754-2008.
*
* Notice that an [int] result cannot overflow, but a [double] result might
* be [double.INFINITY].
*/
external num pow(num x, num exponent);
/**
* Converts [x] to a double and returns the sine of the value.
*
* If [x] is not a finite number, the result is NaN.
*/
external double sin(num x);
/**
* Converts [x] to a double and returns the cosine of the value.
*
* If [x] is not a finite number, the result is NaN.
*/
external double cos(num x);
/**
* Converts [x] to a double and returns the tangent of the value.
*
* The tangent function is equivalent to [:sin(x)/cos(x):] and may be
* infinite (positive or negative) when [:cos(x):] is equal to zero.
* If [x] is not a finite number, the result is NaN.
*/
external double tan(num x);
/**
* Converts [x] to a double and returns the arc cosine of the value.
*
* Returns a value in the range -PI..PI, or NaN if [x] is outside
* the range -1..1.
*/
external double acos(num x);
/**
* Converts [x] to a double and returns the arc sine of the value.
* Returns a value in the range -PI..PI, or NaN if [x] is outside
* the range -1..1.
*/
external double asin(num x);
/**
* Converts [x] to a dobule and returns the arc tangent of the vlaue.
* Returns a value in the range -PI/2..PI/2, or NaN if [x] is NaN.
*/
external double atan(num x);
/**
* Converts [x] to a double and returns the positive square root of the value.
*
* Returns -0.0 if [x] is -0.0, and NaN if [x] is otherwise negative or NaN.
*/
external double sqrt(num x);
/**
* Converts [x] to a double and returns the natural exponent, [E],
* to the power [x].
* Returns NaN if [x] is NaN.
*/
external double exp(num x);
/**
* Converts [x] to a double and returns the natural logarithm of the value.
* Returns negative infinity if [x] is equal to zero.
* Returns NaN if [x] is NaN or less than zero.
*/
external double log(num x);