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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);