├── .gitignore ├── README.md ├── Makefile ├── example.f90 ├── LICENSE_XOROSHIRO128PLUS ├── parallel_test.f90 ├── performance_test.f90 ├── m_random.f90 └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | /example 2 | /performance_test 3 | /m_random.mod 4 | /m_random.o 5 | /parallel_test 6 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # rng_fortran 2 | 3 | A module for generating (pseudo) random numbers. Internally, the 4 | xoroshiro128plus generator is used. The following types of random numbers are 5 | currently supported: 6 | 7 | * 8 byte random integers 8 | * 4 byte random integers 9 | * (0,1] uniform random numbers 10 | * Normal random numbers (in pairs of two) 11 | * Poisson-distributed random numbers 12 | * Random points on a circle 13 | * Random points on a sphere 14 | 15 | A usage example is given in `example.f90`. 16 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | FC := gfortran 2 | FFLAGS := -O3 -flto -g -std=f2008 -Wall -Wextra -fopenmp 3 | OBJS := m_random.o 4 | TESTS := example performance_test parallel_test 5 | 6 | .PHONY: all clean 7 | 8 | all: $(TESTS) 9 | 10 | clean: 11 | $(RM) $(TESTS) $(OBJS) $(OBJS:.o=.mod) 12 | 13 | # Dependency information 14 | $(TESTS): $(OBJS) 15 | 16 | # How to get .o object files from .f90 source files 17 | %.o: %.f90 18 | $(FC) -c -o $@ $< $(FFLAGS) 19 | 20 | # How to get executables from .o object files 21 | %: %.o 22 | $(FC) -o $@ $^ $(FFLAGS) 23 | -------------------------------------------------------------------------------- /example.f90: -------------------------------------------------------------------------------- 1 | program example 2 | use m_random 3 | 4 | ! Define double precision real type 5 | integer, parameter :: dp = kind(0.0d0) 6 | 7 | ! Create a random number generator 8 | type(RNG_t) :: rng 9 | 10 | ! Set the initial seed for the generator 11 | call rng%set_random_seed() 12 | 13 | ! Print some random numbers 14 | print *, "Uniform random number: ", rng%unif_01() 15 | print *, "8-byte random integer: ", rng%int_64() 16 | print *, "4-byte random integer: ", rng%int_32() 17 | print *, "Two normal numbers: ", rng%two_normals() 18 | print *, "Poisson(10.0) deviate: ", rng%poisson(10.0_dp) 19 | print *, "Point on unit circle: ", rng%circle(1.0_dp) 20 | print *, "Point on unit sphere: ", rng%sphere(1.0_dp) 21 | end program example 22 | -------------------------------------------------------------------------------- /LICENSE_XOROSHIRO128PLUS: -------------------------------------------------------------------------------- 1 | ** License for the xoroshiro128plus random number generator ** 2 | 3 | Written in 2016 by David Blackman and Sebastiano Vigna (vigna@acm.org) 4 | Translated to Fortran 2008 by Jannis Teunissen 5 | 6 | To the extent possible under law, the author has dedicated all copyright 7 | and related and neighboring rights to this software to the public domain 8 | worldwide. This software is distributed without any warranty. 9 | 10 | See . 11 | 12 | This is the successor to xorshift128+. It is the fastest full-period 13 | generator passing BigCrush without systematic failures, but due to the 14 | relatively short period it is acceptable only for applications with a 15 | mild amount of parallelism; otherwise, use a xorshift1024* generator. 16 | 17 | Beside passing BigCrush, this generator passes the PractRand test suite 18 | up to (and included) 16TB, with the exception of binary rank tests, 19 | which fail due to the lowest bit being an LFSR; all other bits pass all 20 | tests. We suggest to use a sign test to extract a random Boolean value. 21 | 22 | Note that the generator uses a simulated rotate operation, which most C 23 | compilers will turn into a single instruction. In Java, you can use 24 | Long.rotateLeft(). In languages that do not make low-level rotation 25 | instructions accessible xorshift128+ could be faster. 26 | 27 | The state must be seeded so that it is not everywhere zero. If you have 28 | a 64-bit seed, we suggest to seed a splitmix64 generator and use its 29 | output to fill s. -------------------------------------------------------------------------------- /parallel_test.f90: -------------------------------------------------------------------------------- 1 | program test_parallel 2 | use m_random 3 | use omp_lib 4 | 5 | implicit none 6 | integer, parameter :: dp = kind(0.0d0) 7 | integer, parameter :: i8 = selected_int_kind(18) 8 | integer, parameter :: n_samples = 100*1000*1000 9 | integer :: n, tid 10 | integer :: time_start, time_end, count_rate 11 | real(dp) :: mean, variance 12 | real(dp), allocatable :: rand_results(:) 13 | type(RNG_t) :: rng 14 | type(PRNG_t) :: prng 15 | 16 | print *, "Testing parallel random number generation" 17 | print *, "Number of threads", omp_get_max_threads() 18 | 19 | allocate(rand_results(n_samples)) 20 | 21 | call rng%set_seed([89732_i8, 1892342989_i8]) 22 | call prng%init_parallel(omp_get_max_threads(), rng) 23 | call system_clock(time_start, count_rate) 24 | 25 | !$omp parallel private(n, tid, rng) 26 | tid = omp_get_thread_num() + 1 27 | !$omp do 28 | do n = 1, n_samples 29 | rand_results(n) = prng%rngs(tid)%unif_01() 30 | end do 31 | !$omp end do 32 | !$omp end parallel 33 | 34 | ! Update the rng seed afterwards, using the 'evolved' prng state 35 | call prng%update_seed(rng) 36 | 37 | call system_clock(time_end) 38 | 39 | mean = sum(rand_results) / n_samples 40 | variance = sum((rand_results - mean)**2) / n_samples 41 | 42 | print *, "" 43 | print *, "For uniform random numbers (unif_01), the result is:" 44 | print *, "nanoseconds per number (upper bound)", & 45 | (1.0e9_dp/count_rate) * (time_end - time_start) / n_samples 46 | print *, "mean/", mean/0.5_dp 47 | print *, "std dev/", sqrt(variance)*sqrt(12.0_dp) 48 | 49 | end program test_parallel 50 | -------------------------------------------------------------------------------- /performance_test.f90: -------------------------------------------------------------------------------- 1 | program test_m_random 2 | use iso_fortran_env, only: int64, real64 3 | use m_random 4 | 5 | implicit none 6 | integer, parameter :: dp = real64 7 | integer, parameter :: n_samples = 10*1000*1000 8 | integer :: nn, rng_seed 9 | real(dp) :: mean, variance, p 10 | real(dp), parameter :: poisson_lambda = 15.0_dp 11 | real(dp) :: time_start, time_end 12 | real(dp), allocatable :: rand_results(:) 13 | integer(int64), allocatable :: int64_results(:) 14 | type(RNG_t) :: rng 15 | 16 | allocate(rand_results(n_samples)) 17 | allocate(int64_results(n_samples)) 18 | 19 | print *, "Testing implementation of m_random.f90" 20 | print *, "This is just checking whether everything works, and by no means" 21 | print *, "a test of the 'randomness' of the pseudo random number generator." 22 | print *, "For these tests, ", n_samples, " values are used" 23 | 24 | call system_clock(count=rng_seed) 25 | 26 | call cpu_time(time_start) 27 | call random_number(rand_results) 28 | call cpu_time(time_end) 29 | mean = sum(rand_results) / n_samples 30 | variance = sum((rand_results - mean)**2) / n_samples 31 | 32 | print *, "" 33 | print *, "For uniform random numbers (built-in), the result is:" 34 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 35 | print *, "mean/", mean/0.5_dp 36 | print *, "std dev/", sqrt(variance)*sqrt(12.0_dp) 37 | 38 | call rng%set_random_seed() 39 | 40 | call cpu_time(time_start) 41 | do nn = 1, n_samples 42 | rand_results(nn) = rng%unif_01() 43 | end do 44 | call cpu_time(time_end) 45 | mean = sum(rand_results) / n_samples 46 | variance = sum((rand_results - mean)**2) / n_samples 47 | 48 | print *, "" 49 | print *, "For uniform random numbers (unif_01), the result is:" 50 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 51 | print *, "mean/", mean/0.5_dp 52 | print *, "std dev/", sqrt(variance)*sqrt(12.0_dp) 53 | 54 | call cpu_time(time_start) 55 | do nn = 1, n_samples 56 | rand_results(nn) = rng%normal() 57 | end do 58 | call cpu_time(time_end) 59 | rand_results = rand_results + 1 60 | mean = sum(rand_results) / n_samples 61 | variance = sum((rand_results - mean)**2) / n_samples 62 | 63 | print *, "" 64 | print *, "For normal/Gaussian random numbers, the result is:" 65 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 66 | print *, "mean/", mean/1.0_dp ! Above we add one to RNG_normal() 67 | print *, "std dev/", sqrt(variance) 68 | 69 | call cpu_time(time_start) 70 | do nn = 1, n_samples 71 | rand_results(nn) = rng%poisson(poisson_lambda) 72 | end do 73 | call cpu_time(time_end) 74 | mean = sum(rand_results) / n_samples 75 | variance = sum((rand_results - mean)**2) / n_samples 76 | 77 | print *, "" 78 | print *, "For Poisson random numbers, the result is:" 79 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 80 | print *, "mean/", mean/poisson_lambda ! Above we add one to RNG_normal() 81 | print *, "std dev/", sqrt(variance/poisson_lambda) 82 | 83 | call cpu_time(time_start) 84 | do nn = 1, n_samples 85 | rand_results(nn) = rng%exponential(1.0_dp) 86 | end do 87 | call cpu_time(time_end) 88 | mean = sum(rand_results) / n_samples 89 | variance = sum((rand_results - mean)**2) / n_samples 90 | 91 | print *, "" 92 | print *, "For exponential random numbers, the result is:" 93 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 94 | print *, "mean/", mean 95 | print *, "std dev/", sqrt(variance) 96 | 97 | p = 1e-10_dp 98 | call cpu_time(time_start) 99 | do nn = 1, n_samples 100 | int64_results(nn) = rng%geometric(p) 101 | end do 102 | call cpu_time(time_end) 103 | mean = sum(real(int64_results, dp)) / n_samples 104 | variance = sum((int64_results - mean)**2) / n_samples 105 | 106 | if (minval(int64_results) < 1) & 107 | error stop "Got negative sample from geometric distribution" 108 | 109 | print *, "" 110 | print *, "For geometric random numbers, the result is:" 111 | print *, "nanoseconds per number (upper bound)", 1.0e9_dp * (time_end - time_start) / n_samples 112 | print *, "mean/", mean * p 113 | print *, "std dev/", sqrt(variance) / sqrt((1-p) / p**2) 114 | 115 | end program test_m_random 116 | -------------------------------------------------------------------------------- /m_random.f90: -------------------------------------------------------------------------------- 1 | !> Module for pseudo random number generation. The internal pseudo random 2 | !> generator is the xoroshiro128plus method. 3 | module m_random 4 | use iso_fortran_env, only: int32, int64, real64 5 | 6 | implicit none 7 | private 8 | 9 | ! A 64 bit floating point type 10 | integer, parameter :: dp = real64 11 | 12 | !> Random number generator type, which contains the state 13 | type rng_t 14 | !> The rng state (always use your own seed) 15 | integer(int64), private :: s(2) = [123456789_int64, 987654321_int64] 16 | integer(int64), private :: separator(32) ! Separate cache lines (parallel use) 17 | real(dp), private :: stored_normal 18 | logical, private :: have_stored_normal = .false. 19 | logical, private :: initialized = .false. 20 | contains 21 | procedure, non_overridable :: set_seed ! Seed the generator 22 | procedure, non_overridable :: set_random_seed ! Use a random seed 23 | procedure, non_overridable :: jump ! Jump function (see below) 24 | procedure, non_overridable :: int_32 ! 4-byte random integer 25 | procedure, non_overridable :: int_64 ! 8-byte random integer 26 | procedure, non_overridable :: unif_01 ! Uniform (0,1] real 27 | procedure, non_overridable :: normal ! One normal(0,1) sample 28 | procedure, non_overridable :: two_normals ! Two normal(0,1) samples 29 | procedure, non_overridable :: poisson ! Sample from Poisson-dist. 30 | procedure, non_overridable :: poisson_knuth ! Sample from Poisson-dist. 31 | procedure, non_overridable :: poisson_reject ! Sample from Poisson-dist. 32 | procedure, non_overridable :: exponential_standard ! Sample from standard exponential dist. 33 | procedure, non_overridable :: exponential ! Sample from exponential dist. 34 | procedure, non_overridable :: geometric ! Sample from geometric distribution 35 | procedure, non_overridable :: circle ! Sample on a circle 36 | procedure, non_overridable :: sphere ! Sample on a sphere 37 | procedure, non_overridable :: next ! Internal method 38 | procedure, non_overridable, nopass :: log1p ! Internal method 39 | end type rng_t 40 | 41 | !> Parallel random number generator type 42 | type prng_t 43 | type(rng_t), allocatable :: rngs(:) 44 | contains 45 | procedure, non_overridable :: init_parallel 46 | procedure, non_overridable :: update_seed 47 | end type prng_t 48 | 49 | public :: rng_t 50 | public :: prng_t 51 | 52 | contains 53 | 54 | !> Initialize a collection of rng's for parallel use 55 | subroutine init_parallel(self, n_proc, rng) 56 | class(prng_t), intent(inout) :: self 57 | type(rng_t), intent(inout) :: rng 58 | integer, intent(in) :: n_proc 59 | integer :: n 60 | 61 | if (n_proc < 1) error stop "init_parallel: n_proc < 1" 62 | 63 | allocate(self%rngs(n_proc)) 64 | self%rngs(1) = rng 65 | call self%rngs(1)%jump() 66 | 67 | do n = 2, n_proc 68 | self%rngs(n) = self%rngs(n-1) 69 | call self%rngs(n)%jump() 70 | end do 71 | end subroutine init_parallel 72 | 73 | !> Parallel RNG instances are often used temporarily. This routine can 74 | !> afterwards be used to update the seed of the user's sequential RNG. 75 | subroutine update_seed(self, rng) 76 | class(prng_t), intent(inout) :: self 77 | type(rng_t), intent(inout) :: rng 78 | integer :: n 79 | 80 | do n = 1, size(self%rngs) 81 | ! Perform exclusive-or with each parallel rng 82 | rng%s(1) = ieor(rng%s(1), self%rngs(n)%s(1)) 83 | rng%s(2) = ieor(rng%s(2), self%rngs(n)%s(2)) 84 | end do 85 | end subroutine update_seed 86 | 87 | !> Set a seed for the rng 88 | subroutine set_seed(self, the_seed) 89 | class(rng_t), intent(inout) :: self 90 | integer(int64), intent(in) :: the_seed(2) 91 | 92 | self%s = the_seed 93 | 94 | ! Simulate calls to next() to improve randomness of first number 95 | call self%jump() 96 | end subroutine set_seed 97 | 98 | subroutine set_random_seed(self) 99 | class(rng_t), intent(inout) :: self 100 | integer :: i 101 | real(dp) :: rr 102 | integer(int64) :: time 103 | 104 | ! Get a random seed from the system (this does not always work) 105 | call random_seed() 106 | 107 | ! Get some count of the time 108 | call system_clock(time) 109 | 110 | do i = 1, 2 111 | call random_number(rr) 112 | self%s(i) = ieor(transfer(rr, 1_int64), transfer(time, 1_int64)) 113 | end do 114 | 115 | ! Simulate calls to next() to improve randomness of first number 116 | call self%jump() 117 | end subroutine set_random_seed 118 | 119 | ! This is the jump function for the generator. It is equivalent 120 | ! to 2^64 calls to next(); it can be used to generate 2^64 121 | ! non-overlapping subsequences for parallel computations. 122 | subroutine jump(self) 123 | class(rng_t), intent(inout) :: self 124 | integer :: i, b 125 | integer(int64) :: t(2), dummy 126 | 127 | ! The signed equivalent of the unsigned constants 128 | integer(int64), parameter :: jmp_c(2) = & 129 | (/-4707382666127344949_int64, -2852180941702784734_int64/) 130 | 131 | t = 0 132 | do i = 1, 2 133 | do b = 0, 63 134 | if (iand(jmp_c(i), shiftl(1_int64, b)) /= 0) then 135 | t = ieor(t, self%s) 136 | end if 137 | dummy = self%next() 138 | end do 139 | end do 140 | 141 | self%s = t 142 | end subroutine jump 143 | 144 | !> Return 4-byte integer 145 | integer(int32) function int_32(self) 146 | class(rng_t), intent(inout) :: self 147 | int_32 = int(self%next(), int32) 148 | end function int_32 149 | 150 | !> Return 8-byte integer 151 | integer(int64) function int_64(self) 152 | class(rng_t), intent(inout) :: self 153 | int_64 = self%next() 154 | end function int_64 155 | 156 | !> Get a uniform [0,1) random real (double precision) 157 | real(dp) function unif_01(self) 158 | class(rng_t), intent(inout) :: self 159 | integer(int64) :: x 160 | real(dp) :: tmp 161 | 162 | x = self%next() 163 | x = ior(shiftl(1023_int64, 52), shiftr(x, 12)) 164 | unif_01 = transfer(x, tmp) - 1.0_dp 165 | end function unif_01 166 | 167 | !> Return normal random variate with mean 0 and variance 1 168 | real(dp) function normal(self) 169 | class(rng_t), intent(inout) :: self 170 | real(dp) :: two_normals(2) 171 | 172 | if (self%have_stored_normal) then 173 | normal = self%stored_normal 174 | self%have_stored_normal = .false. 175 | else 176 | two_normals = self%two_normals() 177 | normal = two_normals(1) 178 | self%stored_normal = two_normals(2) 179 | self%have_stored_normal = .true. 180 | end if 181 | end function normal 182 | 183 | !> Return two normal random variates with mean 0 and variance 1. 184 | !> http://en.wikipedia.org/wiki/Marsaglia_polar_method 185 | function two_normals(self) result(rands) 186 | class(rng_t), intent(inout) :: self 187 | real(dp) :: rands(2), sum_sq 188 | 189 | do 190 | rands(1) = 2 * self%unif_01() - 1 191 | rands(2) = 2 * self%unif_01() - 1 192 | sum_sq = sum(rands**2) 193 | if (sum_sq < 1.0_dp .and. sum_sq > 0.0_dp) exit 194 | end do 195 | rands = rands * sqrt(-2 * log(sum_sq) / sum_sq) 196 | end function two_normals 197 | 198 | !> Compute log(1+x) with good accuracy, see "What Every Computer Scientist 199 | !> Should Know About Floating-Point Arithmetic" 200 | real(dp) function log1p(x) 201 | real(dp), intent(in) :: x 202 | 203 | if (1.0_dp + abs(x) > 1.0_dp) then 204 | log1p = log(1.0_dp + x) * x / ((1.0_dp + x) - 1.0_dp) 205 | else 206 | log1p = x 207 | endif 208 | end function log1p 209 | 210 | !> Return exponential random variate with a rate of one 211 | real(dp) function exponential_standard(self) 212 | class(rng_t), intent(inout) :: self 213 | real(dp) :: unif_01 214 | 215 | ! It is assumes 1 - unif_01 is in (0, 1], so we avoid log(0.) below 216 | unif_01 = self%unif_01() 217 | 218 | if (unif_01 < 0.5_dp) then 219 | exponential_standard = -log1p(-unif_01) 220 | else 221 | exponential_standard = -log(1 - unif_01) 222 | end if 223 | end function exponential_standard 224 | 225 | !> Return exponential random variate with rate lambda 226 | real(dp) function exponential(self, lambda) 227 | class(rng_t), intent(inout) :: self 228 | real(dp), intent(in) :: lambda 229 | exponential = self%exponential_standard()/lambda 230 | end function exponential 231 | 232 | !> Sample from geometric distribution with Pr(X = k) = (1 - p)^(k-1) * p 233 | integer(int64) function geometric(self, p) 234 | class(rng_t), intent(inout) :: self 235 | real(dp), intent(in) :: p 236 | real(dp) :: tmp 237 | real(dp), parameter :: threshold = real(huge(1_int64) - 1, dp) 238 | 239 | ! Perform inversion sampling X = ceiling(log(U)/log(1-p)) 240 | tmp = -self%exponential_standard() / log1p(-p) 241 | 242 | ! Avoid overflow 243 | if (tmp < threshold) then 244 | geometric = ceiling(tmp, int64) 245 | else 246 | geometric = huge(1_int64) 247 | end if 248 | 249 | end function geometric 250 | 251 | !> Return Poisson random variate with rate lambda. Works well for lambda < 30 252 | !> or so. For lambda >> 1 it can produce wrong results due to roundoff error. 253 | function poisson_knuth(self, lambda) result(rr) 254 | class(rng_t), intent(inout) :: self 255 | real(dp), intent(in) :: lambda 256 | integer(int32) :: rr 257 | real(dp) :: expl, p 258 | 259 | expl = exp(-lambda) 260 | rr = 0 261 | p = self%unif_01() 262 | 263 | do while (p > expl) 264 | rr = rr + 1 265 | p = p * self%unif_01() 266 | end do 267 | end function poisson_knuth 268 | 269 | !> The transformed rejection method for generating Poisson random variables 270 | !> 271 | !> Translated from Numpy C code at: 272 | !> https://github.com/numpy/numpy/blob/main/numpy/random/src/distributions/distributions.c 273 | !> 274 | !> W. Hoermann 275 | !> Insurance: Mathematics and Economics 12, 39-45 (1993) 276 | function poisson_reject(self, lambda) result(k) 277 | class(rng_t), intent(inout) :: self 278 | real(dp), intent(in) :: lambda 279 | integer(int32) :: k 280 | real(dp) :: U, V, sqrt_lambda, log_lambda 281 | real(dp) :: a, b, invalpha, vr, us 282 | 283 | sqrt_lambda = sqrt(lambda) 284 | log_lambda = log(lambda) 285 | 286 | b = 0.931_dp + 2.53_dp * sqrt_lambda 287 | a = -0.059_dp + 0.02483_dp * b 288 | invalpha = 1.1239_dp + 1.1328_dp / (b - 3.4_dp) 289 | vr = 0.9277_dp - 3.6224_dp / (b - 2) 290 | 291 | do 292 | U = self%unif_01() - 0.5_dp 293 | V = 1.0_dp - self%unif_01() ! Avoid 0 294 | us = 0.5_dp - abs(U); 295 | 296 | k = floor((2 * a / us + b) * U + lambda + 0.43_dp); 297 | 298 | if (us >= 0.07_dp .and. V <= vr) return 299 | if (k < 0 .or. us < 0.013_dp .and. V > us) cycle 300 | 301 | if ((log(V) + log(invalpha) - log(a / (us * us) + b)) <= & 302 | (-lambda + k * log_lambda - log_gamma(k + 1.0_dp))) return 303 | end do 304 | end function poisson_reject 305 | 306 | !> Return Poisson random variate with rate lambda 307 | function poisson(self, lambda) result(rr) 308 | class(rng_t), intent(inout) :: self 309 | real(dp), intent(in) :: lambda 310 | integer(int32) :: rr 311 | 312 | if (lambda < 10) then 313 | ! Algorithm for small value of lambda 314 | rr = self%poisson_knuth(lambda) 315 | else 316 | ! Rejection sampling 317 | rr = self%poisson_reject(lambda) 318 | end if 319 | end function poisson 320 | 321 | !> Sample point on a circle with given radius 322 | function circle(self, radius) result(xy) 323 | class(rng_t), intent(inout) :: self 324 | real(dp), intent(in) :: radius 325 | real(dp) :: rands(2), xy(2) 326 | real(dp) :: sum_sq 327 | 328 | ! Method for uniform sampling on circle 329 | do 330 | rands(1) = 2 * self%unif_01() - 1 331 | rands(2) = 2 * self%unif_01() - 1 332 | sum_sq = sum(rands**2) 333 | if (sum_sq <= 1) exit 334 | end do 335 | 336 | xy(1) = (rands(1)**2 - rands(2)**2) / sum_sq 337 | xy(2) = 2 * rands(1) * rands(2) / sum_sq 338 | xy = xy * radius 339 | end function circle 340 | 341 | !> Sample point on a sphere with given radius 342 | function sphere(self, radius) result(xyz) 343 | class(rng_t), intent(inout) :: self 344 | real(dp), intent(in) :: radius 345 | real(dp) :: rands(2), xyz(3) 346 | real(dp) :: sum_sq, tmp_sqrt 347 | 348 | ! Marsaglia method for uniform sampling on sphere 349 | do 350 | rands(1) = 2 * self%unif_01() - 1 351 | rands(2) = 2 * self%unif_01() - 1 352 | sum_sq = sum(rands**2) 353 | if (sum_sq <= 1) exit 354 | end do 355 | 356 | tmp_sqrt = sqrt(1 - sum_sq) 357 | xyz(1:2) = 2 * rands(1:2) * tmp_sqrt 358 | xyz(3) = 1 - 2 * sum_sq 359 | xyz = xyz * radius 360 | end function sphere 361 | 362 | !> Interal routine: get the next value (returned as 64 bit signed integer) 363 | function next(self) result(res) 364 | class(rng_t), intent(inout) :: self 365 | integer(int64) :: res 366 | integer(int64) :: t(2) 367 | 368 | t = self%s 369 | res = t(1) + t(2) 370 | t(2) = ieor(t(1), t(2)) 371 | self%s(1) = ieor(ieor(rotl(t(1), 55), t(2)), shiftl(t(2), 14)) 372 | self%s(2) = rotl(t(2), 36) 373 | end function next 374 | 375 | !> Helper function for next() 376 | pure function rotl(x, k) result(res) 377 | integer(int64), intent(in) :: x 378 | integer, intent(in) :: k 379 | integer(int64) :: res 380 | 381 | res = ior(shiftl(x, k), shiftr(x, 64 - k)) 382 | end function rotl 383 | 384 | end module m_random 385 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------