nit: Added link to `CONTRIBUTING.md` from the README

[nit.git] / lib / core / math.nit

# This file is part of NIT ( http://www.nitlanguage.org ).
#
# Copyright 2004-2008 Jean Privat <jean@pryen.org>
#
# This file is free software, which comes along with NIT.  This software is
# distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
# without  even  the implied warranty of  MERCHANTABILITY or  FITNESS FOR A
# PARTICULAR PURPOSE.  You can modify it is you want,  provided this header
# is kept unaltered, and a notification of the changes is added.
# You  are  allowed  to  redistribute it and sell it, alone or is a part of
# another product.

# Mathematical operations
module math is ldflags "-lm"

import kernel
import collection

in "C header" `{
        #include <stdlib.h>
        #include <math.h>
        #include <time.h>
`}

in "C" `{
        /* Is rand shortcut? */
        static int nit_rand_seeded;
        /* Current rand seed if seeded */
        static unsigned int nit_rand_seed;

        #define NIT_RAND_MAX 0x7fffffff

        /* This algorithm is mentioned in the ISO C standard, here extended
        for 32 bits.  */
        static int
        nit_rand(void) {
                unsigned int next = nit_rand_seed;
                int result;

                next *= 1103515245;
                next += 12345;
                result = (unsigned int) (next / 65536) % 2048;

                next *= 1103515245;
                next += 12345;
                result <<= 10;
                result ^= (unsigned int) (next / 65536) % 1024;

                next *= 1103515245;
                next += 12345;
                result <<= 10;
                result ^= (unsigned int) (next / 65536) % 1024;

                nit_rand_seed = next;

                return result;
        }
`}

redef class Int
        # Returns a random `Int` in `[0 .. self[`.
        fun rand: Int `{
                if (nit_rand_seeded) return (long)(((double)self)*nit_rand()/(NIT_RAND_MAX+1.0));
                return (long)(((double)self)*rand()/(RAND_MAX+1.0));
        `}

        # Returns the result of a binary AND operation on `self` and `i`
        #
        #     assert 0x10 & 0x01 == 0
        fun &(i: Int): Int is intern `{ return self & i; `}

        # Returns the result of a binary OR operation on `self` and `i`
        #
        #     assert 0x10 | 0x01 == 0x11
        fun |(i: Int): Int is intern `{ return self | i; `}

        # Returns the result of a binary XOR operation on `self` and `i`
        #
        #     assert 0x101 ^ 0x110 == 0x11
        fun ^(i: Int): Int `{ return self ^ i; `}

        # Returns the 1's complement of `self`
        #
        #     assert ~0x2F == -48
        fun ~: Int `{ return ~self; `}

        # Returns the square root of `self`
        #
        #     assert 16.sqrt == 4
        fun sqrt: Int `{ return sqrt(self); `}

        # Returns the greatest common divisor of `self` and `o`
        #
        #     assert 54.gcd(24)   == 6
        #     assert -54.gcd(-24) == 6
        #     assert 54.gcd(-24)  == -6
        #     assert -54.gcd(24)  == -6
        #     assert 12.gcd(6)    == 6
        fun gcd(o: Int): Int
        do
                if self < 0 then return -(-self).gcd(o)
                if o < 0 then return -(self.gcd(-o))
                if self == 0 or o == self then return o
                if o == 0 then return self
                if self & 1 == 0 then
                        if o & 1 == 1 then
                                return (self >> 1).gcd(o)
                        else
                                return (self >> 1).gcd(o >> 1) << 1
                        end
                end
                if o & 1 == 0 then return self.gcd(o >> 1)
                if self > o then return ((self - o) >> 1).gcd(o)
                return ((o - self) >> 1).gcd(self)
        end

        # Is `self` even ?
        #
        #     assert 12.is_even
        fun is_even: Bool do return self % 2 == 0

        # Is `self` odd ?
        #
        #     assert not 13.is_even
        fun is_odd: Bool do return not is_even

        # Is self a prime number ?
        #
        # assert 3.is_prime
        # assert not 1.is_prime
        # assert not 15.is_prime
        fun is_prime: Bool
        do
                if self == 2 then
                        return true
                else if self <= 1 or self.is_even then
                        return false
                end
                for i in [3..self.sqrt] do
                        if self % i == 0 then return false
                end
                return true
        end

        # Returns the `self` raised to the power of `e`.
        #
        #     assert 2 ** 3 == 8
        fun **(e: Int): Int
        do
                return self.to_f.pow(e.to_f).to_i
        end

        # The factorial of `self` (aka `self!`)
        #
        # Returns `1 * 2 * 3 * ... * self-1 * self`
        #
        #     assert 0.factorial == 1  # by convention for an empty product
        #     assert 1.factorial == 1
        #     assert 4.factorial == 24
        #     assert 9.factorial == 362880
        fun factorial: Int
        do
                assert self >= 0
                var res = 1
                var n = self
                while n > 0 do
                        res = res * n
                        n -= 1
                end
                return res
        end
end

redef class Byte
        # Returns the result of a binary AND operation on `self` and `i`
        #
        #     assert 0x10u8 & 0x01u8 == 0u8
        fun &(i: Byte): Byte is intern `{ return self & i; `}

        # Returns the result of a binary OR operation on `self` and `i`
        #
        #     assert 0x10u8 | 0x01u8 == 0x11u8
        fun |(i: Byte): Byte `{ return self | i; `}

        # Returns the result of a binary XOR operation on `self` and `i`
        #
        #     assert 0x101u8 ^ 0x110u8 == 0x11u8
        fun ^(i: Byte): Byte `{ return self ^ i; `}

        # Returns the 1's complement of `self`
        #
        #     assert ~0x2Fu8 == 0xD0u8
        fun ~: Byte `{ return ~self; `}
end

redef class Float

        # Returns the non-negative square root of `self`.
        #
        #     assert 9.0.sqrt == 3.0
        #     #assert 3.0.sqrt == 1.732
        #     assert 1.0.sqrt == 1.0
        #     assert 0.0.sqrt == 0.0
        fun sqrt: Float `{ return sqrt(self); `}

        # Computes the cosine of `self` (expressed in radians).
        #
        #     #assert pi.cos == -1.0
        fun cos: Float `{ return cos(self); `}

        # Computes the sine of `self` (expressed in radians).
        #
        #     #assert pi.sin == 0.0
        fun sin: Float `{ return sin(self); `}

        # Computes the cosine of x (expressed in radians).
        #
        #     #assert 0.0.tan == 0.0
        fun tan: Float `{ return tan(self); `}

        # Computes the arc cosine of `self`.
        #
        #     #assert 0.0.acos == pi / 2.0
        fun acos: Float `{ return acos(self); `}

        # Computes the arc sine of `self`.
        #
        #     #assert 1.0.asin == pi / 2.0
        fun asin: Float `{ return asin(self); `}

        # Computes the arc tangent of `self`.
        #
        #     #assert 0.0.tan == 0.0
        fun atan: Float `{ return atan(self); `}

        # Returns the absolute value of `self`.
        #
        #     assert 12.0.abs == 12.0
        #     assert (-34.56).abs == 34.56
        #     assert -34.56.abs == -34.56
        fun abs: Float `{ return fabs(self); `}

        # Returns `self` raised at `e` power.
        #
        #     #assert 2.0.pow(0.0) == 1.0
        #     #assert 2.0.pow(3.0) == 8.0
        #     #assert 0.0.pow(9.0) == 0.0
        fun pow(e: Float): Float `{ return pow(self, e); `}

        # Natural logarithm of `self`.
        #
        #     assert 0.0.log.is_inf == -1
        #     #assert 1.0.log == 0.0
        fun log: Float `{ return log(self); `}

        # Logarithm of `self` to base `base`.
        #
        #     assert 100.0.log_base(10.0) == 2.0
        #     assert 256.0.log_base(2.0) == 8.0
        fun log_base(base: Float): Float do return log/base.log

        # Returns *e* raised to `self`.
        fun exp: Float `{ return exp(self); `}

        #     assert 1.1.ceil == 2.0
        #     assert 1.9.ceil == 2.0
        #     assert 2.0.ceil == 2.0
        #     assert (-1.5).ceil == -1.0
        fun ceil: Float `{ return ceil(self); `}

        #     assert 1.1.floor == 1.0
        #     assert 1.9.floor == 1.0
        #     assert 2.0.floor == 2.0
        #     assert (-1.5).floor == -2.0
        fun floor: Float `{ return floor(self); `}

        # Rounds the value of a float to its nearest integer value
        #
        #     assert 1.67.round == 2.0
        #     assert 1.34.round == 1.0
        #     assert -1.34.round == -1.0
        #     assert -1.67.round == -2.0
        fun round: Float `{ return round(self); `}

        # Returns a random `Float` in `[0.0 .. self[`.
        fun rand: Float `{
                if (nit_rand_seeded) return ((self)*nit_rand())/(NIT_RAND_MAX+1.0);
                return ((self)*rand())/(RAND_MAX+1.0);
        `}

        # Returns the euclidean distance from `b`.
        fun hypot_with(b: Float): Float `{ return hypotf(self, b); `}

        # Returns true is self is not a number.
        #
        # As `nan != nan`, `is_nan` should be used to test if a float is the special *not a number* value.
        #
        # ~~~
        # assert nan != nan # By IEEE 754
        # assert nan.is_nan
        # assert not 10.0.is_nan
        # ~~~
        fun is_nan: Bool `{ return isnan(self); `}

        # Is the float an infinite value
        # this function returns:
        #
        #  * 1 if self is positive infinity
        #  * -1 if self is negative infinity
        #  * 0 otherwise
        #
        # ~~~
        # assert 10.0.is_inf == 0
        # assert inf.is_inf == 1
        # assert (-inf).is_inf == -1
        # ~~~
        fun is_inf: Int do
                if native_is_inf then
                        if self < 0.0 then return -1
                        return 1
                end
                return 0
        end

        private fun native_is_inf: Bool `{ return isinf(self); `}

        # Linear interpolation between `a` and `b` using `self` as weight
        #
        # ~~~
        # assert  0.0.lerp(0.0, 128.0) == 0.0
        # assert  0.5.lerp(0.0, 128.0) == 64.0
        # assert  1.0.lerp(0.0, 128.0) == 128.0
        # assert -0.5.lerp(0.0, 128.0) == -64.0
        # ~~~
        fun lerp(a, b: Float): Float do return (1.0 - self) * a + self * b

        # Quadratic Bézier interpolation between `a` and `b` with an `handle` using `self` as weight
        #
        # ~~~
        # assert  0.00.qerp(0.0, 32.0, 128.0) == 0.0
        # assert  0.25.qerp(0.0, 32.0, 128.0) == 20.0
        # assert  0.50.qerp(0.0, 32.0, 128.0) == 48.0
        # assert  0.75.qerp(0.0, 32.0, 128.0) == 84.0
        # assert  1.00.qerp(0.0, 32.0, 128.0) == 128.0
        # ~~~
        fun qerp(a, handle, b: Float): Float do
                var p = self
                var i = 1.0 - p
                var r =     i*i * a +
                        2.0*i*p * handle +
                            p*p * b
                return r
        end

        # Cubic Bézier interpolation between `a` and `b` with two handles using `self` as weight
        #
        # The Cubic Bézier interpolation is the most common one and use two control points.
        #
        # ~~~
        # assert  0.00.cerp(0.0, 32.0, 128.0, 64.0) == 0.0
        # assert  0.25.cerp(0.0, 32.0, 128.0, 64.0) == 32.5
        # assert  0.50.cerp(0.0, 32.0, 128.0, 64.0) == 68.0
        # assert  0.75.cerp(0.0, 32.0, 128.0, 64.0) == 85.5
        # assert  1.00.cerp(0.0, 32.0, 128.0, 64.0) == 64.0
        # ~~~
        fun cerp(a, a_handle, b_handle, b: Float): Float do
                var p = self
                var i = 1.0 - p
                var r =     i*i*i  * a +
                        3.0*i*i*p * a_handle +
                        3.0*i*p*p * b_handle +
                            p*p*p * b
                return r
        end
end

# Positive float infinite (IEEE 754)
#
#     assert inf > 10.0
#     assert inf.is_inf == 1
#
# `inf` follows the arithmetic of infinites
#
#     assert (inf - 1.0) == inf
#     assert (inf - inf).is_nan
#
# The negative infinite can be used as `-inf`.
#
#     assert -inf < -10.0
#     assert (-inf).is_inf == -1
fun inf: Float do return 1.0 / 0.0

# Not a Number, representation of an undefined or unrepresentable float (IEEE 754).
#
# `nan` is not comparable with itself, you should use `Float::is_nan` to test it.
#
# ~~~
# assert nan.is_nan
# assert nan != nan # By IEEE 754
# ~~~
#
# `nan` is the quiet result of some undefined operations.
#
# ~~~
# assert (1.0 + nan).is_nan
# assert (0.0 / 0.0).is_nan
# assert (inf - inf).is_nan
# assert (inf / inf).is_nan
# assert (-1.0).sqrt.is_nan
# ~~~
fun nan: Float do return 0.0 / 0.0

redef class Collection[ E ]
        # Return a random element form the collection
        # There must be at least one element in the collection
        #
        # ~~~
        # var x = [1,2,3].rand
        # assert x == 1 or x == 2 or x == 3
        # ~~~
        fun rand: E
        do
                if is_empty then abort
                var rand_index = length.rand

                for e in self do
                        if rand_index == 0 then return e
                        rand_index -= 1
                end
                abort
        end

        # Return a new array made of elements in a random order.
        #
        # ~~~
        # var a = [1,2,1].to_shuffle
        # assert a == [1,1,2] or a == [1,2,1] or a == [2,1,1]
        # ~~~
        fun to_shuffle: Array[E]
        do
                var res = self.to_a
                res.shuffle
                return res
        end

        # Return a new array made of (at most) `length` elements randomly chosen.
        #
        # ~~~
        # var a = [1,2,1].sample(2)
        # assert a == [1,1] or a == [1,2] or a == [2,1]
        # ~~~
        #
        # If there is not enough elements, then the result only contains them in a random order.
        # See `to_shuffle`.
        #
        # ENSURE `result.length == self.length.min(length)`
        #
        # Note: the default implementation uses the Reservoir Algorithm
        fun sample(length: Int): Array[E]
        do
                if length >= self.length then return to_shuffle

                var res = new Array[E].with_capacity(length)
                var it = iterator
                for i in [0..length[ do
                        res[i] = it.item
                        it.next
                end
                res.shuffle
                for i in [length+1..self.length] do
                        var j = i.rand
                        if j < length then
                                res[j] = it.item
                        end
                        it.next
                end
                return res
        end
end

redef class SequenceRead[E]
        # Optimized for large collections using `[]`
        redef fun rand
        do
                assert not is_empty
                return self[length.rand]
        end
end

redef class AbstractArray[E]
        # Reorder randomly the elements in self.
        #
        # ~~~
        # var a = new Array[Int]
        #
        # a.shuffle
        # assert a.is_empty
        #
        # a.add 1
        # a.shuffle
        # assert a == [1]
        #
        # a.add 2
        # a.shuffle
        # assert a == [1,2] or a == [2,1]
        # ~~~
        #
        # ENSURE self.shuffle.has_exactly(old(self))
        fun shuffle
        do
                for i in [0..length[ do
                        var j = i + (length-i).rand
                        var tmp = self[i]
                        self[i] = self[j]
                        self[j] = tmp
                end
        end
end

redef class Sys
        init
        do
                srand
        end
end

# Computes the arc tangent given `y` and `x`.
#
#     assert atan2(-0.0, 1.0) == -0.0
#     assert atan2(0.0, 1.0) == 0.0
fun atan2(y: Float, x: Float): Float `{ return atan2(y, x); `}

# Approximate value of **pi**.
fun pi: Float do return 3.14159265

# Initialize the pseudo-random generator with the given seed.
# The pseudo-random generator is used by the method `rand` and other to generate sequence of numbers.
# These sequences are repeatable by calling `srand_from` with a same seed value.
#
# ~~~~
# srand_from(0)
# var a = 10.rand
# var b = 100.rand
# srand_from(0)
# assert 10.rand == a
# assert 100.rand == b
# ~~~~
fun srand_from(x: Int) `{ nit_rand_seeded = 1; nit_rand_seed = (unsigned int)x; `}

# Reinitialize the pseudo-random generator used by the method `rand` and other.
# This method is automatically invoked at the begin of the program, so usually, there is no need to manually invoke it.
# The only exception is in conjunction with `srand_from` to reset the pseudo-random generator.
fun srand `{ nit_rand_seeded = 0; srand((unsigned int)time(NULL)); `}