| // 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); |