| // 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. |
| * |
| * To use this library in your code: |
| * |
| * import 'dart:math'; |
| * |
| * {@category Core} |
| */ |
| library dart.math; |
| |
| part "jenkins_smi_hash.dart"; |
| part "point.dart"; |
| part "random.dart"; |
| part "rectangle.dart"; |
| |
| /** |
| * Base of the natural logarithms. |
| * |
| * Typically written as "e". |
| */ |
| const double e = 2.718281828459045; |
| |
| /** |
| * Natural logarithm of 10. |
| * |
| * The natural logarithm of 10 is the number such that `pow(E, LN10) == 10`. |
| * This value is not exact, but it is the closest representable double to the |
| * exact mathematical value. |
| */ |
| const double ln10 = 2.302585092994046; |
| |
| /** |
| * Natural logarithm of 2. |
| * |
| * The natural logarithm of 2 is the number such that `pow(E, LN2) == 2`. |
| * This value is not exact, but it is the closest representable double to the |
| * exact mathematical value. |
| */ |
| 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; |
| |
| @Deprecated("Use e instead") |
| const double E = e; |
| @Deprecated("Use ln10 instead") |
| const double LN10 = ln10; |
| @Deprecated("Use ln2 instead") |
| const double LN2 = ln2; |
| @Deprecated("Use log2e instead") |
| const double LOG2E = log2e; |
| @Deprecated("Use log10e instead") |
| const double LOG10E = log10e; |
| @Deprecated("Use pi instead") |
| const double PI = pi; |
| @Deprecated("Use sqrt1_2 instead") |
| const double SQRT1_2 = sqrt1_2; |
| @Deprecated("Use sqrt2 instead") |
| const double SQRT2 = sqrt2; |
| |
| /** |
| * 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. |
| */ |
| external T min<T extends num>(T a, T b); |
| |
| /** |
| * 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. |
| */ |
| external T max<T extends num>(T a, T b); |
| |
| /** |
| * A variant of [atan]. |
| * |
| * Converts both arguments to [double]s. |
| * |
| * Returns the angle in radians between the positive x-axis |
| * and the vector ([b],[a]). |
| * The result 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 [radians] to a [double] and returns the sine of the value. |
| * |
| * If [radians] is not a finite number, the result is NaN. |
| */ |
| external double sin(num radians); |
| |
| /** |
| * Converts [radians] to a [double] and returns the cosine of the value. |
| * |
| * If [radians] is not a finite number, the result is NaN. |
| */ |
| external double cos(num radians); |
| |
| /** |
| * Converts [radians] to a [double] and returns the tangent of the value. |
| * |
| * The tangent function is equivalent to `sin(radians)/cos(radians)` and may be |
| * infinite (positive or negative) when `cos(radians)` is equal to zero. |
| * If [radians] is not a finite number, the result is NaN. |
| */ |
| external double tan(num radians); |
| |
| /** |
| * Converts [x] to a [double] and returns its arc cosine in radians. |
| * |
| * Returns a value in the range 0..PI, or NaN if [x] is outside |
| * the range -1..1. |
| */ |
| external double acos(num x); |
| |
| /** |
| * Converts [x] to a [double] and returns its arc sine in radians. |
| * |
| * Returns a value in the range -PI/2..PI/2, or NaN if [x] is outside |
| * the range -1..1. |
| */ |
| external double asin(num x); |
| |
| /** |
| * Converts [x] to a [double] and returns its arc tangent in radians. |
| * |
| * 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); |