// Copyright (c) 2019-2023 Alexander Medvednikov. All rights reserved. // Use of this source code is governed by an MIT license // that can be found in the LICENSE file. [has_globals] module rand import math.bits import rand.config import rand.constants import rand.wyrand import time // PRNG is a common interface for all PRNGs that can be used seamlessly with the rand // modules's API. It defines all the methods that a PRNG (in the vlib or custom made) must // implement in order to ensure that _all_ functions can be used with the generator. pub interface PRNG { mut: seed(seed_data []u32) u8() u8 u16() u16 u32() u32 u64() u64 block_size() int free() } // bytes returns a buffer of `bytes_needed` random bytes [inline] pub fn (mut rng PRNG) bytes(bytes_needed int) ![]u8 { if bytes_needed < 0 { return error('can not read < 0 random bytes') } mut buffer := []u8{len: bytes_needed} read_internal(mut rng, mut buffer) return buffer } // read fills in `buf` with a maximum of `buf.len` random bytes pub fn (mut rng PRNG) read(mut buf []u8) { read_internal(mut rng, mut buf) } // u32n returns a uniformly distributed pseudorandom 32-bit signed positive `u32` in range `[0, max)`. [inline] pub fn (mut rng PRNG) u32n(max u32) !u32 { if max == 0 { return error('max must be positive integer') } // Owing to the pigeon-hole principle, we can't simply do // val := rng.u32() % max. // It'll wreck the properties of the distribution unless // max evenly divides 2^32. So we divide evenly to // the closest power of two. Then we loop until we find // an int in the required range bit_len := bits.len_32(max) if _unlikely_(bit_len == 32) { for { value := rng.u32() if value < max { return value } } } else { mask := if _unlikely_(bit_len == 31) { u32(0x7FFFFFFF) } else { (u32(1) << (bit_len + 1)) - 1 } for { value := rng.u32() & mask if value < max { return value } } } return u32(0) } // u64n returns a uniformly distributed pseudorandom 64-bit signed positive `u64` in range `[0, max)`. [inline] pub fn (mut rng PRNG) u64n(max u64) !u64 { if max == 0 { return error('max must be positive integer') } bit_len := bits.len_64(max) if _unlikely_(bit_len == 64) { for { value := rng.u64() if value < max { return value } } } else { mask := if _unlikely_(bit_len == 63) { u64(0x7FFFFFFFFFFFFFFF) } else { (u64(1) << (bit_len + 1)) - 1 } for { value := rng.u64() & mask if value < max { return value } } } return u64(0) } // u32_in_range returns a uniformly distributed pseudorandom 32-bit unsigned `u32` in range `[min, max)`. [inline] pub fn (mut rng PRNG) u32_in_range(min u32, max u32) !u32 { if max <= min { return error('max must be greater than min') } return min + rng.u32n(max - min)! } // u64_in_range returns a uniformly distributed pseudorandom 64-bit unsigned `u64` in range `[min, max)`. [inline] pub fn (mut rng PRNG) u64_in_range(min u64, max u64) !u64 { if max <= min { return error('max must be greater than min') } return min + rng.u64n(max - min)! } // i8 returns a (possibly negative) pseudorandom 8-bit `i8`. [inline] pub fn (mut rng PRNG) i8() i8 { return i8(rng.u8()) } // i16 returns a (possibly negative) pseudorandom 16-bit `i16`. [inline] pub fn (mut rng PRNG) i16() i16 { return i16(rng.u16()) } // int returns a (possibly negative) pseudorandom 32-bit `int`. [inline] pub fn (mut rng PRNG) int() int { return int(rng.u32()) } // i64 returns a (possibly negative) pseudorandom 64-bit `i64`. [inline] pub fn (mut rng PRNG) i64() i64 { return i64(rng.u64()) } // int31 returns a positive pseudorandom 31-bit `int`. [inline] pub fn (mut rng PRNG) int31() int { return int(rng.u32() & constants.u31_mask) // Set the 32nd bit to 0. } // int63 returns a positive pseudorandom 63-bit `i64`. [inline] pub fn (mut rng PRNG) int63() i64 { return i64(rng.u64() & constants.u63_mask) // Set the 64th bit to 0. } // intn returns a pseudorandom `int` in range `[0, max)`. [inline] pub fn (mut rng PRNG) intn(max int) !int { if max <= 0 { return error('max has to be positive.') } return int(rng.u32n(u32(max))!) } // i64n returns a pseudorandom int that lies in `[0, max)`. [inline] pub fn (mut rng PRNG) i64n(max i64) !i64 { if max <= 0 { return error('max has to be positive.') } return i64(rng.u64n(u64(max))!) } // int_in_range returns a pseudorandom `int` in range `[min, max)`. [inline] pub fn (mut rng PRNG) int_in_range(min int, max int) !int { if max <= min { return error('max must be greater than min') } // This supports negative ranges like [-10, -5) because the difference is positive return min + rng.intn(max - min)! } // i64_in_range returns a pseudorandom `i64` in range `[min, max)`. [inline] pub fn (mut rng PRNG) i64_in_range(min i64, max i64) !i64 { if max <= min { return error('max must be greater than min') } return min + rng.i64n(max - min)! } // f32 returns a pseudorandom `f32` value in range `[0, 1)` // using rng.u32() multiplied by an f64 constant. [inline] pub fn (mut rng PRNG) f32() f32 { return f32((rng.u32() >> 9) * constants.reciprocal_2_23rd) } // f32cp returns a pseudorandom `f32` value in range `[0, 1)` // with full precision (mantissa random between 0 and 1 // and the exponent varies as well.) // See https://allendowney.com/research/rand/ for background on the method. [inline] pub fn (mut rng PRNG) f32cp() f32 { mut x := rng.u32() mut exp := u32(126) mut mask := u32(1) << 31 // check if prng returns 0; rare but keep looking for precision if _unlikely_(x == 0) { x = rng.u32() exp -= 31 } // count leading one bits and scale exponent accordingly for { if x & mask != 0 { mask >>= 1 exp -= 1 } else { break } } // if we used any high-order mantissa bits; replace x if exp < (126 - 8) { x = rng.u32() } // Assumes little-endian IEEE floating point. x = (exp << 23) | (x >> 8) & constants.ieee754_mantissa_f32_mask return bits.f32_from_bits(x) } // f64 returns a pseudorandom `f64` value in range `[0, 1)` // using rng.u64() multiplied by a constant. [inline] pub fn (mut rng PRNG) f64() f64 { return f64((rng.u64() >> 12) * constants.reciprocal_2_52nd) } // f64cp returns a pseudorandom `f64` value in range `[0, 1)` // with full precision (mantissa random between 0 and 1 // and the exponent varies as well.) // See https://allendowney.com/research/rand/ for background on the method. [inline] pub fn (mut rng PRNG) f64cp() f64 { mut x := rng.u64() mut exp := u64(1022) mut mask := u64(1) << 63 mut bitcount := u32(0) // check if prng returns 0; unlikely. if _unlikely_(x == 0) { x = rng.u64() exp -= 31 } // count leading one bits and scale exponent accordingly for { if x & mask != 0 { mask >>= 1 bitcount += 1 } else { break } } exp -= bitcount if bitcount > 11 { x = rng.u64() } x = (exp << 52) | (x & constants.ieee754_mantissa_f64_mask) return bits.f64_from_bits(x) } // f32n returns a pseudorandom `f32` value in range `[0, max]`. [inline] pub fn (mut rng PRNG) f32n(max f32) !f32 { if max < 0 { return error('max has to be non-negative.') } return rng.f32() * max } // f64n returns a pseudorandom `f64` value in range `[0, max]`. [inline] pub fn (mut rng PRNG) f64n(max f64) !f64 { if max < 0 { return error('max has to be non-negative.') } return rng.f64() * max } // f32_in_range returns a pseudorandom `f32` in range `[min, max]`. [inline] pub fn (mut rng PRNG) f32_in_range(min f32, max f32) !f32 { if max < min { return error('max must be greater than or equal to min') } return min + rng.f32n(max - min)! } // i64_in_range returns a pseudorandom `i64` in range `[min, max]`. [inline] pub fn (mut rng PRNG) f64_in_range(min f64, max f64) !f64 { if max < min { return error('max must be greater than or equal to min') } return min + rng.f64n(max - min)! } // ulid generates an Unique Lexicographically sortable IDentifier. // See https://github.com/ulid/spec . // Note: ULIDs can leak timing information, if you make them public, because // you can infer the rate at which some resource is being created, like // users or business transactions. // (https://news.ycombinator.com/item?id=14526173) pub fn (mut rng PRNG) ulid() string { return internal_ulid_at_millisecond(mut rng, u64(time.utc().unix_time_milli())) } // ulid_at_millisecond does the same as `ulid` but takes a custom Unix millisecond timestamp via `unix_time_milli`. pub fn (mut rng PRNG) ulid_at_millisecond(unix_time_milli u64) string { return internal_ulid_at_millisecond(mut rng, unix_time_milli) } // string_from_set returns a string of length `len` containing random characters sampled from the given `charset` pub fn (mut rng PRNG) string_from_set(charset string, len int) string { return internal_string_from_set(mut rng, charset, len) } // string returns a string of length `len` containing random characters in range `[a-zA-Z]`. pub fn (mut rng PRNG) string(len int) string { return internal_string_from_set(mut rng, rand.english_letters, len) } // hex returns a hexadecimal number of length `len` containing random characters in range `[a-f0-9]`. pub fn (mut rng PRNG) hex(len int) string { return internal_string_from_set(mut rng, rand.hex_chars, len) } // ascii returns a random string of the printable ASCII characters with length `len`. pub fn (mut rng PRNG) ascii(len int) string { return internal_string_from_set(mut rng, rand.ascii_chars, len) } // bernoulli returns true with a probability p. Note that 0 <= p <= 1. pub fn (mut rng PRNG) bernoulli(p f64) !bool { if p < 0 || p > 1 { return error('${p} is not a valid probability value.') } return rng.f64() <= p } // normal returns a normally distributed pseudorandom f64 with mean `mu` and standard // deviation `sigma`. By default, `mu` is 0.0 and `sigma` is 1.0. // NOTE: Use normal_pair() instead if you're generating a lot of normal variates. pub fn (mut rng PRNG) normal(conf config.NormalConfigStruct) !f64 { x, _ := rng.normal_pair(conf)! return x } // normal_pair returns a pair of normally distributed pseudorandom f64 with mean `mu` and standard // deviation `sigma`. By default, `mu` is 0.0 and `sigma` is 1.0. pub fn (mut rng PRNG) normal_pair(conf config.NormalConfigStruct) !(f64, f64) { if conf.sigma <= 0 { return error('Standard deviation must be positive') } // This is an implementation of the Marsaglia polar method // See: https://doi.org/10.1137%2F1006063 // Also: https://en.wikipedia.org/wiki/Marsaglia_polar_method for { u := rng.f64_in_range(-1, 1) or { 0.0 } v := rng.f64_in_range(-1, 1) or { 0.0 } s := u * u + v * v if s >= 1 || s == 0 { continue } t := msqrt(-2 * mlog(s) / s) x := conf.mu + conf.sigma * t * u y := conf.mu + conf.sigma * t * v return x, y } return error('Implementation error. Please file an issue.') } // binomial returns the number of successful trials out of n when the // probability of success for each trial is p. pub fn (mut rng PRNG) binomial(n int, p f64) !int { if p < 0 || p > 1 { return error('${p} is not a valid probability value.') } mut count := 0 for _ in 0 .. n { if rng.bernoulli(p)! { count++ } } return count } // exponential returns an exponentially distributed random number with the rate paremeter // lambda. It is expected that lambda is positive. pub fn (mut rng PRNG) exponential(lambda f64) f64 { if lambda <= 0 { panic('The rate (lambda) must be positive.') } // Use the inverse transform sampling method return -mlog(rng.f64()) / lambda } // shuffle randomly permutates the elements in `a`. The range for shuffling is // optional and the entire array is shuffled by default. Leave the end as 0 to // shuffle all elements until the end. [direct_array_access] pub fn (mut rng PRNG) shuffle[T](mut a []T, config_ config.ShuffleConfigStruct) ! { config_.validate_for(a)! new_end := if config_.end == 0 { a.len } else { config_.end } // We implement the Fisher-Yates shuffle: // https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm for i in config_.start .. new_end - 2 { x := rng.int_in_range(i, new_end) or { i } // swap a_i := a[i] a[i] = a[x] a[x] = a_i } } // shuffle_clone returns a random permutation of the elements in `a`. // The permutation is done on a fresh clone of `a`, so `a` remains unchanged. pub fn (mut rng PRNG) shuffle_clone[T](a []T, config_ config.ShuffleConfigStruct) ![]T { mut res := a.clone() rng.shuffle[T](mut res, config_)! return res } // choose samples k elements from the array without replacement. // This means the indices cannot repeat and it restricts the sample size to be less than or equal to the size of the given array. // Note that if the array has repeating elements, then the sample may have repeats as well. pub fn (mut rng PRNG) choose[T](array []T, k int) ![]T { n := array.len if k > n { return error('Cannot choose ${k} elements without replacement from a ${n}-element array.') } mut results := []T{len: k} mut indices := []int{len: n, init: index} rng.shuffle[int](mut indices)! for i in 0 .. k { results[i] = array[indices[i]] } return results } // element returns a random element from the given array. // Note that all the positions in the array have an equal chance of being selected. This means that if the array has repeating elements, then the probability of selecting a particular element is not uniform. pub fn (mut rng PRNG) element[T](array []T) !T { if array.len == 0 { return error('Cannot choose an element from an empty array.') } return array[rng.intn(array.len)!] } // sample samples k elements from the array with replacement. // This means the elements can repeat and the size of the sample may exceed the size of the array. pub fn (mut rng PRNG) sample[T](array []T, k int) []T { mut results := []T{len: k} for i in 0 .. k { results[i] = array[rng.intn(array.len) or { 0 }] } return results } __global default_rng &PRNG // new_default returns a new instance of the default RNG. If the seed is not provided, the current time will be used to seed the instance. [manualfree] pub fn new_default(config_ config.PRNGConfigStruct) &PRNG { mut rng := &wyrand.WyRandRNG{} rng.seed(config_.seed_) unsafe { config_.seed_.free() } return &PRNG(rng) } // get_current_rng returns the PRNG instance currently in use. If it is not changed, it will be an instance of wyrand.WyRandRNG. pub fn get_current_rng() &PRNG { return default_rng } // set_rng changes the default RNG from wyrand.WyRandRNG (or whatever the last RNG was) to the one // provided by the user. Note that this new RNG must be seeded manually with a constant seed or the // `seed.time_seed_array()` method. Also, it is recommended to store the old RNG in a variable and // should be restored if work with the custom RNG is complete. It is not necessary to restore if the // program terminates soon afterwards. pub fn set_rng(rng &PRNG) { default_rng = unsafe { rng } } // seed sets the given array of `u32` values as the seed for the `default_rng`. The default_rng is // an instance of WyRandRNG which takes 2 u32 values. When using a custom RNG, make sure to use // the correct number of u32s. pub fn seed(seed []u32) { default_rng.seed(seed) } // u8 returns a uniformly distributed pseudorandom 8-bit unsigned positive `u8`. pub fn u8() u8 { return default_rng.u8() } // u16 returns a uniformly distributed pseudorandom 16-bit unsigned positive `u16`. pub fn u16() u16 { return default_rng.u16() } // u32 returns a uniformly distributed `u32` in range `[0, 2³²)`. pub fn u32() u32 { return default_rng.u32() } // u64 returns a uniformly distributed `u64` in range `[0, 2⁶⁴)`. pub fn u64() u64 { return default_rng.u64() } // u32n returns a uniformly distributed pseudorandom 32-bit signed positive `u32` in range `[0, max)`. pub fn u32n(max u32) !u32 { return default_rng.u32n(max) } // u64n returns a uniformly distributed pseudorandom 64-bit signed positive `u64` in range `[0, max)`. pub fn u64n(max u64) !u64 { return default_rng.u64n(max) } // u32_in_range returns a uniformly distributed pseudorandom 32-bit unsigned `u32` in range `[min, max)`. pub fn u32_in_range(min u32, max u32) !u32 { return default_rng.u32_in_range(min, max) } // u64_in_range returns a uniformly distributed pseudorandom 64-bit unsigned `u64` in range `[min, max)`. pub fn u64_in_range(min u64, max u64) !u64 { return default_rng.u64_in_range(min, max) } // i16 returns a uniformly distributed pseudorandom 16-bit signed (possibly negative) `i16`. pub fn i16() i16 { return default_rng.i16() } // int returns a uniformly distributed pseudorandom 32-bit signed (possibly negative) `int`. pub fn int() int { return default_rng.int() } // intn returns a uniformly distributed pseudorandom 32-bit signed positive `int` in range `[0, max)`. pub fn intn(max int) !int { return default_rng.intn(max) } // int_in_range returns a uniformly distributed pseudorandom 32-bit signed int in range `[min, max)`. // Both `min` and `max` can be negative, but we must have `min < max`. pub fn int_in_range(min int, max int) !int { return default_rng.int_in_range(min, max) } // int31 returns a uniformly distributed pseudorandom 31-bit signed positive `int`. pub fn int31() int { return default_rng.int31() } // i64 returns a uniformly distributed pseudorandom 64-bit signed (possibly negative) `i64`. pub fn i64() i64 { return default_rng.i64() } // i64n returns a uniformly distributed pseudorandom 64-bit signed positive `i64` in range `[0, max)`. pub fn i64n(max i64) !i64 { return default_rng.i64n(max) } // i64_in_range returns a uniformly distributed pseudorandom 64-bit signed `i64` in range `[min, max)`. pub fn i64_in_range(min i64, max i64) !i64 { return default_rng.i64_in_range(min, max) } // int63 returns a uniformly distributed pseudorandom 63-bit signed positive `i64`. pub fn int63() i64 { return default_rng.int63() } // f32 returns a uniformly distributed 32-bit floating point in range `[0, 1)`. pub fn f32() f32 { return default_rng.f32() } // f32cp returns a uniformly distributed 32-bit floating point in range `[0, 1)` // with full precision mantissa. pub fn f32cp() f32 { return default_rng.f32cp() } // f64 returns a uniformly distributed 64-bit floating point in range `[0, 1)`. pub fn f64() f64 { return default_rng.f64() } // f64 returns a uniformly distributed 64-bit floating point in range `[0, 1)` // with full precision mantissa. pub fn f64cp() f64 { return default_rng.f64cp() } // f32n returns a uniformly distributed 32-bit floating point in range `[0, max)`. pub fn f32n(max f32) !f32 { return default_rng.f32n(max) } // f64n returns a uniformly distributed 64-bit floating point in range `[0, max)`. pub fn f64n(max f64) !f64 { return default_rng.f64n(max) } // f32_in_range returns a uniformly distributed 32-bit floating point in range `[min, max)`. pub fn f32_in_range(min f32, max f32) !f32 { return default_rng.f32_in_range(min, max) } // f64_in_range returns a uniformly distributed 64-bit floating point in range `[min, max)`. pub fn f64_in_range(min f64, max f64) !f64 { return default_rng.f64_in_range(min, max) } // bytes returns a buffer of `bytes_needed` random bytes pub fn bytes(bytes_needed int) ![]u8 { return default_rng.bytes(bytes_needed) } // read fills in `buf` a maximum of `buf.len` random bytes pub fn read(mut buf []u8) { read_internal(mut default_rng, mut buf) } const ( english_letters = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ' hex_chars = 'abcdef0123456789' ascii_chars = '!"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ\\^_`abcdefghijklmnopqrstuvwxyz{|}~' ) // ulid generates an Unique Lexicographically sortable IDentifier. // See https://github.com/ulid/spec . // Note: ULIDs can leak timing information, if you make them public, because // you can infer the rate at which some resource is being created, like // users or business transactions. // (https://news.ycombinator.com/item?id=14526173) pub fn ulid() string { return default_rng.ulid() } // ulid_at_millisecond does the same as `ulid` but takes a custom Unix millisecond timestamp via `unix_time_milli`. pub fn ulid_at_millisecond(unix_time_milli u64) string { return default_rng.ulid_at_millisecond(unix_time_milli) } // string_from_set returns a string of length `len` containing random characters sampled from the given `charset` pub fn string_from_set(charset string, len int) string { return default_rng.string_from_set(charset, len) } // string returns a string of length `len` containing random characters in range `[a-zA-Z]`. pub fn string(len int) string { return string_from_set(rand.english_letters, len) } // hex returns a hexadecimal number of length `len` containing random characters in range `[a-f0-9]`. pub fn hex(len int) string { return string_from_set(rand.hex_chars, len) } // ascii returns a random string of the printable ASCII characters with length `len`. pub fn ascii(len int) string { return string_from_set(rand.ascii_chars, len) } // shuffle randomly permutates the elements in `a`. The range for shuffling is // optional and the entire array is shuffled by default. Leave the end as 0 to // shuffle all elements until the end. pub fn shuffle[T](mut a []T, config_ config.ShuffleConfigStruct) ! { default_rng.shuffle[T](mut a, config_)! } // shuffle_clone returns a random permutation of the elements in `a`. // The permutation is done on a fresh clone of `a`, so `a` remains unchanged. pub fn shuffle_clone[T](a []T, config_ config.ShuffleConfigStruct) ![]T { return default_rng.shuffle_clone[T](a, config_) } // choose samples k elements from the array without replacement. // This means the indices cannot repeat and it restricts the sample size to be less than or equal to the size of the given array. // Note that if the array has repeating elements, then the sample may have repeats as well. pub fn choose[T](array []T, k int) ![]T { return default_rng.choose[T](array, k) } // element returns a random element from the given array. // Note that all the positions in the array have an equal chance of being selected. This means that if the array has repeating elements, then the probability of selecting a particular element is not uniform. pub fn element[T](array []T) !T { return default_rng.element[T](array) } // sample samples k elements from the array with replacement. // This means the elements can repeat and the size of the sample may exceed the size of the array. pub fn sample[T](array []T, k int) []T { return default_rng.sample[T](array, k) } // bernoulli returns true with a probability p. Note that 0 <= p <= 1. pub fn bernoulli(p f64) !bool { return default_rng.bernoulli(p) } // normal returns a normally distributed pseudorandom f64 with mean `mu` and standard // deviation `sigma`. By default, `mu` is 0.0 and `sigma` is 1.0. // NOTE: Use normal_pair() instead if you're generating a lot of normal variates. pub fn normal(config_ config.NormalConfigStruct) !f64 { return default_rng.normal(config_) } // normal_pair returns a pair of normally distributed pseudorandom f64 with mean `mu` and standard // deviation `sigma`. By default, `mu` is 0.0 and `sigma` is 1.0. pub fn normal_pair(config_ config.NormalConfigStruct) !(f64, f64) { return default_rng.normal_pair(config_) } // binomial returns the number of successful trials out of n when the // probability of success for each trial is p. pub fn binomial(n int, p f64) !int { return default_rng.binomial(n, p) } // exponential returns an exponentially distributed random number with the rate paremeter // lambda. It is expected that lambda is positive. pub fn exponential(lambda f64) f64 { return default_rng.exponential(lambda) }