From ad91a75ed0dbc8b1353aeb56faa9a5127d0c4fd9 Mon Sep 17 00:00:00 2001 From: jordan4ibanez Date: Sat, 7 Sep 2024 07:58:42 -0400 Subject: [PATCH] Add Fortran (#144) * C to Fortran translation * Swap the enums for raw parameters * Add a simple example. --- Fortran/README.md | 28 + Fortran/fast_noise_lite.f90 | 2642 +++++++++++++++++++++++++++++++++++ README.md | 1 + 3 files changed, 2671 insertions(+) create mode 100644 Fortran/README.md create mode 100644 Fortran/fast_noise_lite.f90 diff --git a/Fortran/README.md b/Fortran/README.md new file mode 100644 index 0000000..cfbc2e6 --- /dev/null +++ b/Fortran/README.md @@ -0,0 +1,28 @@ +## Getting Started + +Here's an example for creating a 128x128 array of OpenSimplex2S noise + +```Fortran +program test_fast_noise + use :: fast_noise_lite + use, intrinsic :: iso_c_binding + implicit none + + type(fnl_state) :: noise_state + real(c_float), dimension(128,128) :: noise_data + integer(c_int) :: x, y + + ! Create the state. + noise_state = fnl_state() + noise_state%noise_type = FNL_NOISE_OPENSIMPLEX2S + + ! Collect the noise data. + do y = 1,128 + do x = 1,128 + noise_data(x,y) = fnl_get_noise_2d(noise_state, real(x, c_float), real(y, c_float)) + end do + end do + + ! Do something with this data... +end program test_fast_noise +``` \ No newline at end of file diff --git a/Fortran/fast_noise_lite.f90 b/Fortran/fast_noise_lite.f90 new file mode 100644 index 0000000..31242a5 --- /dev/null +++ b/Fortran/fast_noise_lite.f90 @@ -0,0 +1,2642 @@ +module fast_noise_lite + use :: iso_c_binding + implicit none + + + private + + + ! MIT License + ! + ! Copyright(c) 2023 Jordan Peck (jordan.me2@gmail.com) + ! Copyright(c) 2023 Contributors + ! Translated by jordan4ibanez: 2024 + ! + ! Permission is hereby granted, free of charge, to any person obtaining a copy + ! of this software and associated documentation files(the "Software"), to deal + ! in the Software without restriction, including without limitation the rights + ! to use, copy, modify, merge, publish, distribute, sublicense, and / or sell + ! copies of the Software, and to permit persons to whom the Software is + ! furnished to do so, subject to the following conditions : + ! + ! The above copyright notice and this permission notice shall be included in all + ! copies or substantial portions of the Software. + ! + ! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + ! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + ! FITNESS FOR A PARTICULAR PURPOSE AND _NONINFRINGEMENT.IN NO EVENT SHALL THE + ! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + ! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + ! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + ! SOFTWARE. + ! + ! .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll + ! ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo + ! ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd + ! ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx + ! .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx + ! . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd + ! .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo + ! .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo + ! ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo + ! ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo + ! c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo + ! ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo + ! dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl + ! xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c + ! dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c + ! ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc + ! c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll + ! ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo + ! .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd + ! . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk + ! ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000 + ! ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX + ! + ! VERSION: 1.1.1 + ! https://github.com/Auburn/FastNoiseLite + + + ! Allow switching from f64 to f32 by changing kind with comment swap. + ! real(c_double), parameter :: data_sample = 0.0d0 + real(c_float), parameter :: data_sample = 0.0 + + integer, parameter :: fnl_float = kind(c_double) + + real(fnl_float) :: f__ + real(c_float), public, parameter :: FLT_MAX = huge(f__) + + ! Enums + + integer(c_int), parameter :: fnl_noise_type = 0 + integer(c_int), parameter, public :: FNL_NOISE_OPENSIMPLEX2 = 1 + integer(c_int), parameter, public :: FNL_NOISE_OPENSIMPLEX2S = 2 + integer(c_int), parameter, public :: FNL_NOISE_CELLULAR = 3 + integer(c_int), parameter, public :: FNL_NOISE_PERLIN = 4 + integer(c_int), parameter, public :: FNL_NOISE_VALUE_CUBIC = 5 + integer(c_int), parameter, public :: FNL_NOISE_VALUE = 6 + + + integer(c_int), parameter :: fnl_rotation_type_3d = 7 + integer(c_int), parameter, public :: FNL_ROTATION_NONE = 8 + integer(c_int), parameter, public :: FNL_ROTATION_IMPROVE_XY_PLANES = 9 + integer(c_int), parameter, public :: FNL_ROTATION_IMPROVE_XZ_PLANES = 10 + + + integer(c_int), parameter :: fnl_fractal_type = 11 + integer(c_int), parameter, public :: FNL_FRACTAL_NONE = 12 + integer(c_int), parameter, public :: FNL_FRACTAL_FBM = 13 + integer(c_int), parameter, public :: FNL_FRACTAL_RIDGED = 14 + integer(c_int), parameter, public :: FNL_FRACTAL_PINGPONG = 15 + integer(c_int), parameter, public :: FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE = 16 + integer(c_int), parameter, public :: FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT = 17 + + + integer(c_int), parameter :: fnl_cellular_distance_func = 18 + integer(c_int), parameter, public :: FNL_CELLULAR_DISTANCE_EUCLIDEAN = 19 + integer(c_int), parameter, public :: FNL_CELLULAR_DISTANCE_EUCLIDEANSQ = 20 + integer(c_int), parameter, public :: FNL_CELLULAR_DISTANCE_MANHATTAN = 21 + integer(c_int), parameter, public :: FNL_CELLULAR_DISTANCE_HYBRID = 22 + + + integer(c_int), parameter :: fnl_cellular_return_type = 23 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_CELLVALUE = 24 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE = 25 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE2 = 26 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD = 27 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB = 28 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL = 29 + integer(c_int), parameter, public :: FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV = 30 + + + integer(c_int), parameter :: fnl_domain_warp_type = 31 + integer(c_int), parameter, public :: FNL_DOMAIN_WARP_OPENSIMPLEX2 = 32 + integer(c_int), parameter, public :: FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED = 33 + integer(c_int), parameter, public :: FNL_DOMAIN_WARP_BASICGRID = 34 + + + !* + !* Structure containing entire noise system state. + !* @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set. + !* + type, public :: fnl_state + + ! + ! Seed used for all noise types. + ! @remark Default: 1337 + ! + integer(c_int) :: seed = 1337 + + ! + ! The frequency for all noise types. + ! @remark Default: 0.01 + ! + real(c_float) :: frequency = 0.01 + + ! + ! The noise algorithm to be used by GetNoise(...). + ! @remark Default: FNL_NOISE_OPENSIMPLEX2 + ! + integer(kind(fnl_noise_type)) :: noise_type = FNL_NOISE_OPENSIMPLEX2 + + ! + ! Sets noise rotation type for 3D. + ! @remark Default: FNL_ROTATION_NONE + ! + integer(kind(fnl_rotation_type_3d)) :: rotation_type_3d = FNL_NOISE_OPENSIMPLEX2 + + ! + ! The method used for combining octaves for all fractal noise types. + ! @remark Default: FNL_FRACTAL_NONE + ! @remark FNL_FRACTAL_DOMAIN_WARP_... only effects fnlDomainWarp... + ! + integer(kind(fnl_fractal_type)) :: fractal_type = FNL_FRACTAL_NONE + + ! + ! The octave count for all fractal noise types. + ! @remark Default: 3 + ! + integer(c_int) :: octaves = 3 + + ! + ! The octave lacunarity for all fractal noise types. + ! @remark Default: 2.0 + ! + real(c_float) :: lacunarity = 2.0 + + ! + ! The octave gain for all fractal noise types. + ! @remark Default: 0.5 + ! + real(c_float) :: gain = 0.5 + + ! + ! The octave weighting for all none Domaain Warp fractal types. + ! @remark Default: 0.0 + ! @remark + ! + real(c_float) :: weighted_strength = 0.0 + + ! + ! The strength of the fractal ping pong effect. + ! @remark Default: 2.0 + ! + real(c_float) :: ping_pong_strength = 2.0 + + ! + ! The distance function used in cellular noise calculations. + ! @remark Default: FNL_CELLULAR_DISTANCE_EUCLIDEANSQ + ! + integer(kind(fnl_cellular_distance_func)) :: cellular_distance_func = FNL_CELLULAR_DISTANCE_EUCLIDEANSQ + + ! + ! The cellular return type from cellular noise calculations. + ! @remark Default: FNL_CELLULAR_RETURN_TYPE_DISTANCE + ! + integer(kind(fnl_cellular_return_type)) :: cellular_return_type = FNL_CELLULAR_RETURN_TYPE_DISTANCE + + ! + ! The maximum distance a cellular point can move from it's grid position. + ! @remark Default: 1.0 + ! @note Setting this higher than 1 will cause artifacts. + ! + real(c_float) :: cellular_jitter_mod = 1.0 + + ! + ! The warp algorithm when using fnlDomainWarp... + ! @remark Default: OpenSimplex2 + ! + integer(kind(fnl_domain_warp_type)) :: domain_warp_type = FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED + + ! + ! The maximum warp distance from original position when using fnlDomainWarp... + ! @remark Default: 1.0 + ! + real(c_float) :: domain_warp_amp = 1.0 + end type fnl_state + + + interface fnl_state + module procedure :: constructor_fnl_state + end interface fnl_state + + + ! Expose public api. + + + public :: fnl_get_noise_2d + public :: fnl_get_noise_3d + public :: fnl_domain_warp_2d + public :: fnl_domain_warp_3d + + + ! ===================================== + ! Below this line is the implementation + ! ===================================== + + + ! Constants + + + real(c_float), dimension(256), parameter :: GRADIENTS_2D = (/ & + 0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721, & + 0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509, & + 0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381, & + -0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721, & + -0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509, & + -0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381, & + 0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721, & + 0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509, & + 0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381, & + -0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721, & + -0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509, & + -0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381, & + 0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721, & + 0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509, & + 0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381, & + -0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721, & + -0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509, & + -0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381, & + 0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721, & + 0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509, & + 0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381, & + -0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721, & + -0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509, & + -0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381, & + 0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721, & + 0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509, & + 0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381, & + -0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721, & + -0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509, & + -0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381, & + 0.38268343236509, 0.923879532511287, 0.923879532511287, 0.38268343236509, 0.923879532511287, -0.38268343236509, 0.38268343236509, -0.923879532511287, & + -0.38268343236509, -0.923879532511287, -0.923879532511287, -0.38268343236509, -0.923879532511287, 0.38268343236509, -0.38268343236509, 0.923879532511287 & + /) + + + real(c_float), dimension(512), parameter :: RAND_VECS_2D = (/ & + -0.2700222198, -0.9628540911, 0.3863092627, -0.9223693152, 0.04444859006, -0.999011673, -0.5992523158, -0.8005602176, -0.7819280288, 0.6233687174, 0.9464672271, 0.3227999196, -0.6514146797, -0.7587218957, 0.9378472289, 0.347048376, & + -0.8497875957, -0.5271252623, -0.879042592, 0.4767432447, -0.892300288, -0.4514423508, -0.379844434, -0.9250503802, -0.9951650832, 0.0982163789, 0.7724397808, -0.6350880136, 0.7573283322, -0.6530343002, -0.9928004525, -0.119780055, & + -0.0532665713, 0.9985803285, 0.9754253726, -0.2203300762, -0.7665018163, 0.6422421394, 0.991636706, 0.1290606184, -0.994696838, 0.1028503788, -0.5379205513, -0.84299554, 0.5022815471, -0.8647041387, 0.4559821461, -0.8899889226, & + -0.8659131224, -0.5001944266, 0.0879458407, -0.9961252577, -0.5051684983, 0.8630207346, 0.7753185226, -0.6315704146, -0.6921944612, 0.7217110418, -0.5191659449, -0.8546734591, 0.8978622882, -0.4402764035, -0.1706774107, 0.9853269617, & + -0.9353430106, -0.3537420705, -0.9992404798, 0.03896746794, -0.2882064021, -0.9575683108, -0.9663811329, 0.2571137995, -0.8759714238, -0.4823630009, -0.8303123018, -0.5572983775, 0.05110133755, -0.9986934731, -0.8558373281, -0.5172450752, & + 0.09887025282, 0.9951003332, 0.9189016087, 0.3944867976, -0.2439375892, -0.9697909324, -0.8121409387, -0.5834613061, -0.9910431363, 0.1335421355, 0.8492423985, -0.5280031709, -0.9717838994, -0.2358729591, 0.9949457207, 0.1004142068, & + 0.6241065508, -0.7813392434, 0.662910307, 0.7486988212, -0.7197418176, 0.6942418282, -0.8143370775, -0.5803922158, 0.104521054, -0.9945226741, -0.1065926113, -0.9943027784, 0.445799684, -0.8951327509, 0.105547406, 0.9944142724, & + -0.992790267, 0.1198644477, -0.8334366408, 0.552615025, 0.9115561563, -0.4111755999, 0.8285544909, -0.5599084351, 0.7217097654, -0.6921957921, 0.4940492677, -0.8694339084, -0.3652321272, -0.9309164803, -0.9696606758, 0.2444548501, & + 0.08925509731, -0.996008799, 0.5354071276, -0.8445941083, -0.1053576186, 0.9944343981, -0.9890284586, 0.1477251101, 0.004856104961, 0.9999882091, 0.9885598478, 0.1508291331, 0.9286129562, -0.3710498316, -0.5832393863, -0.8123003252, & + 0.3015207509, 0.9534596146, -0.9575110528, 0.2883965738, 0.9715802154, -0.2367105511, 0.229981792, 0.9731949318, 0.955763816, -0.2941352207, 0.740956116, 0.6715534485, -0.9971513787, -0.07542630764, 0.6905710663, -0.7232645452, & + -0.290713703, -0.9568100872, 0.5912777791, -0.8064679708, -0.9454592212, -0.325740481, 0.6664455681, 0.74555369, 0.6236134912, 0.7817328275, 0.9126993851, -0.4086316587, -0.8191762011, 0.5735419353, -0.8812745759, -0.4726046147, & + 0.9953313627, 0.09651672651, 0.9855650846, -0.1692969699, -0.8495980887, 0.5274306472, 0.6174853946, -0.7865823463, 0.8508156371, 0.52546432, 0.9985032451, -0.05469249926, 0.1971371563, -0.9803759185, 0.6607855748, -0.7505747292, & + -0.03097494063, 0.9995201614, -0.6731660801, 0.739491331, -0.7195018362, -0.6944905383, 0.9727511689, 0.2318515979, 0.9997059088, -0.0242506907, 0.4421787429, -0.8969269532, 0.9981350961, -0.061043673, -0.9173660799, -0.3980445648, & + -0.8150056635, -0.5794529907, -0.8789331304, 0.4769450202, 0.0158605829, 0.999874213, -0.8095464474, 0.5870558317, -0.9165898907, -0.3998286786, -0.8023542565, 0.5968480938, -0.5176737917, 0.8555780767, -0.8154407307, -0.5788405779, & + 0.4022010347, -0.9155513791, -0.9052556868, -0.4248672045, 0.7317445619, 0.6815789728, -0.5647632201, -0.8252529947, -0.8403276335, -0.5420788397, -0.9314281527, 0.363925262, 0.5238198472, 0.8518290719, 0.7432803869, -0.6689800195, & + -0.985371561, -0.1704197369, 0.4601468731, 0.88784281, 0.825855404, 0.5638819483, 0.6182366099, 0.7859920446, 0.8331502863, -0.553046653, 0.1500307506, 0.9886813308, -0.662330369, -0.7492119075, -0.668598664, 0.743623444, & + 0.7025606278, 0.7116238924, -0.5419389763, -0.8404178401, -0.3388616456, 0.9408362159, 0.8331530315, 0.5530425174, -0.2989720662, -0.9542618632, 0.2638522993, 0.9645630949, 0.124108739, -0.9922686234, -0.7282649308, -0.6852956957, & + 0.6962500149, 0.7177993569, -0.9183535368, 0.3957610156, -0.6326102274, -0.7744703352, -0.9331891859, -0.359385508, -0.1153779357, -0.9933216659, 0.9514974788, -0.3076565421, -0.08987977445, -0.9959526224, 0.6678496916, 0.7442961705, & + 0.7952400393, -0.6062947138, -0.6462007402, -0.7631674805, -0.2733598753, 0.9619118351, 0.9669590226, -0.254931851, -0.9792894595, 0.2024651934, -0.5369502995, -0.8436138784, -0.270036471, -0.9628500944, -0.6400277131, 0.7683518247, & + -0.7854537493, -0.6189203566, 0.06005905383, -0.9981948257, -0.02455770378, 0.9996984141, -0.65983623, 0.751409442, -0.6253894466, -0.7803127835, -0.6210408851, -0.7837781695, 0.8348888491, 0.5504185768, -0.1592275245, 0.9872419133, & + 0.8367622488, 0.5475663786, -0.8675753916, -0.4973056806, -0.2022662628, -0.9793305667, 0.9399189937, 0.3413975472, 0.9877404807, -0.1561049093, -0.9034455656, 0.4287028224, 0.1269804218, -0.9919052235, -0.3819600854, 0.924178821, & + 0.9754625894, 0.2201652486, -0.3204015856, -0.9472818081, -0.9874760884, 0.1577687387, 0.02535348474, -0.9996785487, 0.4835130794, -0.8753371362, -0.2850799925, -0.9585037287, -0.06805516006, -0.99768156, -0.7885244045, -0.6150034663, & + 0.3185392127, -0.9479096845, 0.8880043089, 0.4598351306, 0.6476921488, -0.7619021462, 0.9820241299, 0.1887554194, 0.9357275128, -0.3527237187, -0.8894895414, 0.4569555293, 0.7922791302, 0.6101588153, 0.7483818261, 0.6632681526, & + -0.7288929755, -0.6846276581, 0.8729032783, -0.4878932944, 0.8288345784, 0.5594937369, 0.08074567077, 0.9967347374, 0.9799148216, -0.1994165048, -0.580730673, -0.8140957471, -0.4700049791, -0.8826637636, 0.2409492979, 0.9705377045, & + 0.9437816757, -0.3305694308, -0.8927998638, -0.4504535528, -0.8069622304, 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0.5828709909, 0.3196460933, -0.9475370046, 0.9570913859, 0.2897862643, -0.6876655497, -0.7260276109, & + -0.9988770922, -0.047376731, -0.1250179027, 0.992154486, -0.8280133617, 0.560708367, 0.9324863769, -0.3612051451, 0.6394653183, 0.7688199442, -0.01623847064, -0.9998681473, -0.9955014666, -0.09474613458, -0.81453315, 0.580117012, & + 0.4037327978, -0.9148769469, 0.9944263371, 0.1054336766, -0.1624711654, 0.9867132919, -0.9949487814, -0.100383875, -0.6995302564, 0.7146029809, 0.5263414922, -0.85027327, -0.5395221479, 0.841971408, 0.6579370318, 0.7530729462, & + 0.01426758847, -0.9998982128, -0.6734383991, 0.7392433447, 0.639412098, -0.7688642071, 0.9211571421, 0.3891908523, -0.146637214, -0.9891903394, -0.782318098, 0.6228791163, -0.5039610839, -0.8637263605, -0.7743120191, -0.6328039957 & + /) + + real(c_float), dimension(256), parameter :: GRADIENTS_3D = (/ & + 0.0, 1.0, 1.0, 0.0, 0.0,-1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0,-1.0,-1.0, 0.0, & + 1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, -1.0, 0.0,-1.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0, -1.0,-1.0, 0.0, 0.0, & + 0.0, 1.0, 1.0, 0.0, 0.0,-1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0,-1.0,-1.0, 0.0, & + 1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, -1.0, 0.0,-1.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0, -1.0,-1.0, 0.0, 0.0, & + 0.0, 1.0, 1.0, 0.0, 0.0,-1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0,-1.0,-1.0, 0.0, & + 1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, -1.0, 0.0,-1.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0, -1.0,-1.0, 0.0, 0.0, & + 0.0, 1.0, 1.0, 0.0, 0.0,-1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0,-1.0,-1.0, 0.0, & + 1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, -1.0, 0.0,-1.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0, -1.0,-1.0, 0.0, 0.0, & + 0.0, 1.0, 1.0, 0.0, 0.0,-1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0,-1.0,-1.0, 0.0, & + 1.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 0.0,-1.0, 0.0, -1.0, 0.0,-1.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, -1.0, 1.0, 0.0, 0.0, 1.0,-1.0, 0.0, 0.0, -1.0,-1.0, 0.0, 0.0, & + 1.0, 1.0, 0.0, 0.0, 0.0,-1.0, 1.0, 0.0, -1.0, 1.0, 0.0, 0.0, 0.0,-1.0,-1.0, 0.0 & + /) + + + real(c_float), dimension(1024), parameter :: RAND_VECS_3D = (/ & + -0.7292736885, -0.6618439697, 0.1735581948, 0.0, 0.790292081, -0.5480887466, -0.2739291014, 0.0, 0.7217578935, 0.6226212466, -0.3023380997, 0.0, 0.565683137, -0.8208298145, -0.0790000257, 0.0, 0.760049034, -0.5555979497, -0.3370999617, 0.0, 0.3713945616, 0.5011264475, 0.7816254623, 0.0, -0.1277062463, -0.4254438999, -0.8959289049, 0.0, -0.2881560924, -0.5815838982, 0.7607405838, 0.0, & + 0.5849561111, -0.662820239, -0.4674352136, 0.0, 0.3307171178, 0.0391653737, 0.94291689, 0.0, 0.8712121778, -0.4113374369, -0.2679381538, 0.0, 0.580981015, 0.7021915846, 0.4115677815, 0.0, 0.503756873, 0.6330056931, -0.5878203852, 0.0, 0.4493712205, 0.601390195, 0.6606022552, 0.0, -0.6878403724, 0.09018890807, -0.7202371714, 0.0, -0.5958956522, -0.6469350577, 0.475797649, 0.0, & + -0.5127052122, 0.1946921978, -0.8361987284, 0.0, -0.9911507142, -0.05410276466, -0.1212153153, 0.0, -0.2149721042, 0.9720882117, -0.09397607749, 0.0, -0.7518650936, -0.5428057603, 0.3742469607, 0.0, 0.5237068895, 0.8516377189, -0.02107817834, 0.0, 0.6333504779, 0.1926167129, -0.7495104896, 0.0, -0.06788241606, 0.3998305789, 0.9140719259, 0.0, -0.5538628599, -0.4729896695, -0.6852128902, 0.0, & + -0.7261455366, -0.5911990757, 0.3509933228, 0.0, -0.9229274737, -0.1782808786, 0.3412049336, 0.0, -0.6968815002, 0.6511274338, 0.3006480328, 0.0, 0.9608044783, -0.2098363234, -0.1811724921, 0.0, 0.06817146062, -0.9743405129, 0.2145069156, 0.0, -0.3577285196, -0.6697087264, -0.6507845481, 0.0, -0.1868621131, 0.7648617052, -0.6164974636, 0.0, -0.6541697588, 0.3967914832, 0.6439087246, 0.0, & + 0.6993340405, -0.6164538506, 0.3618239211, 0.0, -0.1546665739, 0.6291283928, 0.7617583057, 0.0, -0.6841612949, -0.2580482182, -0.6821542638, 0.0, 0.5383980957, 0.4258654885, 0.7271630328, 0.0, -0.5026987823, -0.7939832935, -0.3418836993, 0.0, 0.3202971715, 0.2834415347, 0.9039195862, 0.0, 0.8683227101, -0.0003762656404, -0.4959995258, 0.0, 0.791120031, -0.08511045745, 0.6057105799, 0.0, & + -0.04011016052, -0.4397248749, 0.8972364289, 0.0, 0.9145119872, 0.3579346169, -0.1885487608, 0.0, -0.9612039066, -0.2756484276, 0.01024666929, 0.0, 0.6510361721, -0.2877799159, -0.7023778346, 0.0, -0.2041786351, 0.7365237271, 0.644859585, 0.0, -0.7718263711, 0.3790626912, 0.5104855816, 0.0, -0.3060082741, -0.7692987727, 0.5608371729, 0.0, 0.454007341, -0.5024843065, 0.7357899537, 0.0, & + 0.4816795475, 0.6021208291, -0.6367380315, 0.0, 0.6961980369, -0.3222197429, 0.641469197, 0.0, -0.6532160499, -0.6781148932, 0.3368515753, 0.0, 0.5089301236, -0.6154662304, -0.6018234363, 0.0, -0.1635919754, -0.9133604627, -0.372840892, 0.0, 0.52408019, -0.8437664109, 0.1157505864, 0.0, 0.5902587356, 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PRIME_Y = 1136930381 + integer(c_int), parameter :: PRIME_Z = 1720413743 + + +contains + + +! Utilities + + + real(c_float) function internal_fnl_inv_sqrt(a) result(out) + implicit none + + real(c_float), intent(in), value :: a + real(c_float) :: xhalf + integer(c_int), parameter :: magic = int(z"5f3759df", c_int) + + xhalf = 0.5 * a + out = real(magic - (shiftr(int(a), 1))) + out = out * (1.5 - xhalf * a * a) + end function internal_fnl_inv_sqrt + + + real(c_float) function internal_fnl_lerp(a, b, t) result(output) + implicit none + + real(c_float), intent(in), value :: a, b, t + + output = a + t * (b - a) + end function internal_fnl_lerp + + + real(c_float) function internal_fnl_interp_hermite(t) result(output) + implicit none + + real(c_float), intent(in), value :: t + + output = t * t * (3 - 2 * t) + end function internal_fnl_interp_hermite + + + real(c_float) function internal_fnl_interp_quintic(t) result(output) + implicit none + + real(c_float), intent(in), value :: t + + output = t * t * t * (t * (t * 6 - 15) + 10) + end function internal_fnl_interp_quintic + + + real(c_float) function internal_fnl_cubic_lerp(a, b, c, d, t) result(output) + implicit none + + real(c_float), intent(in), value :: a, b, c, d, t + real(c_float) :: p + + p = (d - c) - (a - b) + output = t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b + end function internal_fnl_cubic_lerp + + + real(c_float) function internal_fnl_ping_pong(t) result(output) + implicit none + + real(c_float), intent(in), value :: t + real(c_float) :: i + + i = i - (int(t * 0.5) * 2) + + output = merge(t, 2 - t, i < 1) + end function internal_fnl_ping_pong + + + real(c_float) function internal_fnl_calculate_fractal_bounding(state) result(output) + implicit none + + type(fnl_state), intent(in) :: state + real(c_float) :: gain, amp, amp_fractal + integer(c_int) :: i + + gain = abs(state%gain) + amp = gain + amp_fractal = 1.0 + + do i = 1,state%octaves - 1 + amp_fractal = amp_fractal + amp + amp = amp * gain + end do + output = 1.0 / amp_fractal + end function internal_fnl_calculate_fractal_bounding + + +! Hashing + + + integer(c_int) function internal_fnl_hash_2d(seed, x_primed, y_primed) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed + integer(c_int), parameter :: magic = int(z"27d4eb2d") + + hash = xor(xor(seed, x_primed), y_primed) + + hash = hash * magic + end function internal_fnl_hash_2d + + + integer(c_int) function internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed, z_primed + integer(c_int), parameter :: magic = int(z"27d4eb2d") + + hash = xor(xor(xor(seed, x_primed), y_primed), z_primed) + + hash = hash * magic + end function internal_fnl_hash_3d + + + real(c_float) function internal_fnl_val_coord_2d(seed, x_primed, y_primed) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed + integer(c_int) :: int_hash + + int_hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + + int_hash = int_hash * int_hash + + int_hash = xor(int_hash, (shiftl(int_hash, 19))) + + hash = int_hash * (1 / 2147483648.0) + end function internal_fnl_val_coord_2d + + + real(c_float) function internal_fnl_val_coord_3d(seed, x_primed, y_primed, z_primed) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed, z_primed + integer(c_int) :: int_hash + + int_hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + int_hash = int_hash * int_hash + + int_hash = xor(int_hash, shiftl(int_hash, 19)) + + hash = int_hash * (1 / 2147483648.0) + end function internal_fnl_val_coord_3d + + + real(c_float) function internal_fnl_grad_coord_2d(seed, x_primed, y_primed, xd, yd) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed + real(c_float), intent(in), value :: xd, yd + integer(c_int) :: int_hash + + int_hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + + int_hash = xor(int_hash, shiftr(int_hash, 15)) + + int_hash = and(int_hash, shiftl(127, 1)) + + hash = xd * GRADIENTS_2D(int_hash + 1) + yd * GRADIENTS_2D(ior(int_hash, 1) + 1) + end function internal_fnl_grad_coord_2d + + + real(c_float) function internal_fnl_grad_coord_3d(seed, x_primed, y_primed, z_primed, xd, yd, zd) result(hash) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed, z_primed + real(c_float), intent(in), value :: xd, yd, zd + integer(c_int) :: int_hash + + + int_hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + + int_hash = xor(int_hash, shiftr(int_hash, 15)) + + int_hash = and(int_hash, shiftl(63, 2)) + + hash = xd * GRADIENTS_3D(int_hash + 1) + yd * GRADIENTS_3D(ior(int_hash, 1) + 1) + zd * GRADIENTS_3D(ior(int_hash, 2) + 1) + end function internal_fnl_grad_coord_3d + + + subroutine internal_fnl_grad_coord_out_2d(seed, x_primed, y_primed, xo, yo) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed + real(c_float), intent(inout) :: xo, yo + integer(c_int) :: int_hash + + + int_hash = and(internal_fnl_hash_2d(seed, x_primed, y_primed), shiftl(255, 1)) + + xo = RAND_VECS_2D(int_hash + 1) + yo = RAND_VECS_2D(ior(int_hash, 1) + 1) + end subroutine internal_fnl_grad_coord_out_2d + + + subroutine internal_fnl_grad_coord_out_3d(seed, x_primed, y_primed, z_primed, xo, yo, zo) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed, z_primed + real(c_float), intent(inout) :: xo, yo, zo + integer(c_int) :: int_hash + + int_hash = and(internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed), shiftl(255, 2)) + + xo = RAND_VECS_3D(int_hash + 1) + yo = RAND_VECS_3D(ior(int_hash, 1) + 1) + zo = RAND_VECS_3D(ior(int_hash, 2) + 1) + end subroutine internal_fnl_grad_coord_out_3d + + + subroutine internal_fnl_grad_coord_dual_2d(seed, x_primed, y_primed, xd, yd, xo, yo) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed + real(c_float), intent(in) :: xd, yd + real(c_float), intent(inout) :: xo, yo + integer(c_int) :: int_hash, index_1, index_2 + real(c_float) :: xg, yg, value, xgo, ygo + + int_hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + index_1 = and(int_hash, shiftl(127, 1)) + index_2 = and(shiftr(int_hash, 7), shiftl(255, 1)) + + xg = GRADIENTS_2D(index_1 + 1) + yg = GRADIENTS_2D(ior(index_1, 1) + 1) + value = xd * xg + yd * yg + + xgo = RAND_VECS_2D(index_2 + 1) + ygo = RAND_VECS_2D(ior(index_2, 1) + 1) + + xo = value * xgo + yo = value * ygo + end subroutine internal_fnl_grad_coord_dual_2d + + + subroutine internal_fnl_grad_coord_dual_3d(seed, x_primed, y_primed, z_primed, xd, yd, zd, xo, yo, zo) + implicit none + + integer(c_int), intent(in), value :: seed, x_primed, y_primed, z_primed + real(c_float), intent(in) :: xd, yd, zd + real(c_float), intent(inout) :: xo, yo, zo + integer(c_int) :: int_hash, index_1, index_2 + real(c_float) :: xg, yg, zg, value, xgo, ygo, zgo + + int_hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + index_1 = and(int_hash, shiftl(63, 2)) + index_2 = and(shiftr(int_hash, 6), shiftl(255, 2)) + + xg = GRADIENTS_3D(index_1 + 1) + yg = GRADIENTS_3D(ior(index_1, 1) + 1) + zg = GRADIENTS_3D(ior(index_1, 2) + 1) + value = xd * xg + yd * yg + zd * zg + + xgo = RAND_VECS_3D(index_2 + 1) + ygo = RAND_VECS_3D(ior(index_2, 1) + 1) + zgo = RAND_VECS_3D(ior(index_2, 2) + 1) + + xo = value * xgo + yo = value * ygo + zo = value * zgo + end subroutine internal_fnl_grad_coord_dual_3d + + +! Generic Noise Gen + + + real(c_float) function internal_fnl_gen_noise_single_2d(state, seed, x, y) result(output) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + + select case(state%noise_type) + case (FNL_NOISE_OPENSIMPLEX2) + output = internal_fnl_single_simplex_2d(seed, x, y) + case (FNL_NOISE_OPENSIMPLEX2S) + output = internal_fnl_single_open_simplex_2s_2d(seed, x, y) + case (FNL_NOISE_CELLULAR) + output = internal_fnl_single_cellular_2d(state, seed, x, y) + case (FNL_NOISE_PERLIN) + output = internal_fnl_single_perlin_2d(seed, x, y) + case (FNL_NOISE_VALUE_CUBIC) + output = internal_fnl_single_value_cubic_2d(seed, x, y) + case (FNL_NOISE_VALUE) + output = internal_fnl_single_value_2d(seed, x, y) + case default + output = 0.0 + end select + end function internal_fnl_gen_noise_single_2d + + + real(c_float) function internal_fnl_gen_noise_single_3d(state, seed, x, y, z) result(output) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + + + select case (state%noise_type) + case (FNL_NOISE_OPENSIMPLEX2) + output = internal_fnl_single_open_simplex_2_3d(seed, x, y, z) + case (FNL_NOISE_OPENSIMPLEX2S) + output = internal_fnl_single_open_simplex_2d_3d(seed, x, y, z) + case (FNL_NOISE_CELLULAR) + output = internal_fnl_single_cellular_3d(state, seed, x, y, z) + case (FNL_NOISE_PERLIN) + output = internal_fnl_single_perlin_3d(seed, x, y, z) + case (FNL_NOISE_VALUE_CUBIC) + output = internal_fnl_single_value_cubic_3d(seed, x, y, z) + case (FNL_NOISE_VALUE) + output = internal_fnl_single_value_3d(seed, x, y, z) + case default + output = 0.0 + end select + end function internal_fnl_gen_noise_single_3d + + +! Noise Coordinate Transforms (frequency, and possible skew or rotation) + + + subroutine internal_fnl_transform_noise_coordinate_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + real(fnl_float) :: t + real(fnl_float), parameter :: SQRT_3 = real(1.7320508075688772935274463415059, fnl_float) + real(fnl_float), parameter :: F2 = 0.5 * (SQRT_3 - 1.0) + + x = x * state%frequency + y = y * state%frequency + + select case(state%noise_type) + case (FNL_NOISE_OPENSIMPLEX2, FNL_NOISE_OPENSIMPLEX2S) + t = (x + y) * F2 + x = x + t + y = y + t + case default + end select + end subroutine internal_fnl_transform_noise_coordinate_2d + + + subroutine internal_fnl_transform_noise_coordinates_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + real(fnl_float) xy, s2, xz, r3, r + + x = x * state%frequency + y = y * state%frequency + z = z * state%frequency + + select case (state%rotation_type_3d) + case (FNL_ROTATION_IMPROVE_XY_PLANES) + xy = x + y + s2 = xy * (-real(0.211324865405187, fnl_float)) + z = z * real(0.577350269189626, fnl_float) + x = x + (s2 - z) + y = y + s2 - z + z = z + (xy * real(0.577350269189626, fnl_float)) + + case (FNL_ROTATION_IMPROVE_XZ_PLANES) + xz = x + z + s2 = xz * (-real(0.211324865405187, fnl_float)) + y = y * real(0.577350269189626, fnl_float) + x = x + (s2 - y) + z = z + (s2 - y) + y = y + (xz * real(0.577350269189626, fnl_float)) + + case default + select case (state%noise_type) + case (FNL_NOISE_OPENSIMPLEX2S, FNL_NOISE_OPENSIMPLEX2) + + r3 = real((2.0 / 3.0), fnl_float) + r = (x + y + z) * r3 ! Rotation, not skew + x = r - x + y = r - y + z = r - z + + case default + end select + end select ! state%rotation_type_3d + end subroutine internal_fnl_transform_noise_coordinates_3d + + +! Domain Warp Coordinate Transforms + + + subroutine internal_fnl_transform_domain_warp_coordinate_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + real(fnl_float) :: t + real(fnl_float), parameter :: SQRT_3 = real(1.7320508075688772935274463415059, fnl_float) + real(fnl_float), parameter :: F2 = 0.5 * (SQRT_3 - 1.0) + + select case (state%domain_warp_type) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED, FNL_DOMAIN_WARP_OPENSIMPLEX2) + t = (x + y) * F2 + x = x + t + y = y + t + case default + end select + end subroutine internal_fnl_transform_domain_warp_coordinate_2d + + + subroutine internal_fnl_transform_domain_warp_coordinate_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + real(fnl_float) :: xy, s2, xz, r3, r + + select case (state%rotation_type_3d) + case (FNL_ROTATION_IMPROVE_XY_PLANES) + xy = x + y + s2 = xy * (-real(0.211324865405187, fnl_float)) + z = z * real(0.577350269189626, fnl_float) + x = x + (s2 - z) + y = y + s2 - z + z = z + (xy * real(0.577350269189626, fnl_float)) + case (FNL_ROTATION_IMPROVE_XZ_PLANES) + xz = x + z + s2 = xz * (-real(0.211324865405187, fnl_float)) + y = y * real(0.577350269189626, fnl_float) + x = x + (s2 - y) + z = z + (s2 - y) + y = y + (xz * real(0.577350269189626, fnl_float)) + case default + select case (state%domain_warp_type) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED, FNL_DOMAIN_WARP_OPENSIMPLEX2) + r3 = real(2.0 / 3.0, fnl_float) + r = (x + y + z) * r3 ! Rotation, not skew + x = r - x + y = r - y + z = r - z + case default + end select + end select + end subroutine internal_fnl_transform_domain_warp_coordinate_3d + + +! Fractal FBm + + + real(c_float) function internal_fnl_gen_fraction_fbm_2d(state, x, y) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy + + xx = x + yy = y + seed = state%seed + sum = 0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1,state%octaves + seed = seed + 1 + noise = internal_fnl_gen_noise_single_2d(state, seed, xx, yy) + sum = sum + (noise * amp) + amp = amp * (internal_fnl_lerp(1.0, min(noise + 1.0, 2.0) * 0.5, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + amp = amp * state%gain + end do + end function internal_fnl_gen_fraction_fbm_2d + + + real(c_float) function internal_fnl_gen_fractal_fbm_3d(state, x, y, z) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy, zz + + xx = x + yy = y + zz = z + seed = state%seed + sum = 0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1, state%octaves + seed = seed + 1 + noise = internal_fnl_gen_noise_single_3d(state, seed, xx, yy, zz) + sum = sum + (noise * amp) + amp = amp * (internal_fnl_lerp(1.0, (noise + 1.0) * 0.5, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + zz = zz * state%lacunarity + amp = amp * state%gain + end do + end function internal_fnl_gen_fractal_fbm_3d + + +! Fractal Ridged + + + real(c_float) function internal_fnm_gen_fractal_ridged_2d(state, x, y) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy + + xx = x + yy = y + seed = state%seed + sum = 0.0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1, state%octaves + seed = seed + 1 + noise = abs(internal_fnl_gen_noise_single_2d(state, seed, xx, yy)) + sum = sum + ((noise * (-2.0) + 1.0) * amp) + amp = amp * (internal_fnl_lerp(1.0, 1.0 - noise, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + amp = amp * state%gain + end do + end function internal_fnm_gen_fractal_ridged_2d + + + real(c_float) function internal_fnl_gen_fractal_ridged_3d(state, x, y, z) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy, zz + + xx = x + yy = y + zz = z + seed = state%seed + sum = 0.0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1, state%octaves + seed = seed + 1 + noise = abs(internal_fnl_gen_noise_single_3d(state, seed, xx, yy, zz)) + sum = sum + ((noise * (-2.0) + 1.0) * amp) + amp = amp * (internal_fnl_lerp(1.0, 1.0 - noise, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + zz = zz * state%lacunarity + amp = amp * state%gain + end do + end function internal_fnl_gen_fractal_ridged_3d + + +! Fractal PingPong + + + real(c_float) function internal_fnl_gen_fractal_ping_pong_2d(state, x, y) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy + + xx = x + yy = y + seed = state%seed + sum = 0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1, state%octaves + + seed = seed + 1 + noise = internal_fnl_ping_pong((internal_fnl_gen_noise_single_2d(state, seed, xx, yy) + 1.0) * state%ping_pong_strength) + sum = sum + ((noise - 0.5) * 2.0 * amp) + amp = amp * (internal_fnl_lerp(1.0, noise, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + amp = amp * state%gain + end do + end function internal_fnl_gen_fractal_ping_pong_2d + + + real(c_float) function internal_fnl_gen_fractal_ping_pong_3d(state, x, y, z) result(sum) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: seed, i + real(c_float) :: amp, noise + real(fnl_float) :: xx, yy, zz + + xx = x + yy = y + zz = z + seed = state%seed + sum = 0 + amp = internal_fnl_calculate_fractal_bounding(state) + + do i = 1, state%octaves + seed = seed + 1 + noise = internal_fnl_ping_pong((internal_fnl_gen_noise_single_3d(state, seed, xx, yy, zz) + 1) * state%ping_pong_strength) + sum = sum + ((noise - 0.5) * 2.0 * amp) + amp = amp * (internal_fnl_lerp(1.0, noise, state%weighted_strength)) + + xx = xx * state%lacunarity + yy = yy * state%lacunarity + zz = zz * state%lacunarity + amp = amp * state%gain + end do + + end function internal_fnl_gen_fractal_ping_pong_3d + + +! Simplex/OpenSimplex2 Noise + + + real(c_float) function internal_fnl_single_simplex_2d(seed, x, y) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + real(c_float) :: xi, yi, t, x0, y0, n0, n1, n2, a, b, c, x2, y2, x1, y1 + integer(c_int):: i, j + real(c_float), parameter :: SQRT_3 = 1.7320508075688772935274463415059 + real(c_float), parameter :: G2 = (3.0 - SQRT_3) / 6.0 + + ! 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex. + + ! + ! --- Skew moved to TransformNoiseCoordinate method --- + ! const FNLfloat F2 = 0.5f * (SQRT_3 - 1) + ! FNLfloat s = (x + y) * F2 + ! x += s y += s + ! + + i = floor(x) + j = floor(y) + xi = real(x - i, c_float) + yi = real(y - j, c_float) + + t = (xi + yi) * G2 + x0 = real(xi - t, c_float) + y0 = real(yi - t, c_float) + + i = i * PRIME_X + j = j * PRIME_Y + + a = 0.5 - x0 * x0 - y0 * y0 + if (a <= 0) then + n0 = 0.0 + else + n0 = (a * a) * (a * a) * internal_fnl_grad_coord_2d(seed, i, j, x0, y0) + end if + + c = real(2.0 * (1.0 - 2.0 * G2) * (1.0 / G2 - 2.0), c_float) * t + (real(-2.0 * (1.0 - 2.0 * G2) * (1.0 - 2.0 * G2), c_float) + a) + if (c <= 0) then + n2 = 0.0 + else + x2 = x0 + (2.0 * real(G2, c_float) - 1.0) + y2 = y0 + (2.0 * real(G2, c_float) - 1.0) + n2 = (c * c) * (c * c) * internal_fnl_grad_coord_2d(seed, i + PRIME_X, j + PRIME_Y, x2, y2) + end if + + if (y0 > x0) then + x1 = x0 + real(G2, c_float) + y1 = y0 + (real(G2, c_float) - 1.0) + b = 0.5 - x1 * x1 - y1 * y1 + if (b <= 0) then + n1 = 0.0 + else + n1 = (b * b) * (b * b) * internal_fnl_grad_coord_2d(seed, i, j + PRIME_Y, x1, y1) + end if + else + x1 = x0 + (real(G2, c_float) - 1.0) + y1 = y0 + real(G2, c_float) + b = 0.5 - x1 * x1 - y1 * y1 + if (b <= 0) then + n1 = 0.0 + else + n1 = (b * b) * (b * b) * internal_fnl_grad_coord_2d(seed, i + PRIME_X, j, x1, y1) + end if + end if + + output = (n0 + n1 + n2) * 99.83685446303647 + end function internal_fnl_single_simplex_2d + + + real(c_float) function internal_fnl_single_open_simplex_2_3d(seed, x, y, z) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + real(c_float) :: x0, y0, z0, a, b, x1, y1, z1, ax0, az0, ay0, value + integer(c_int):: mutable_seed, i, j, k, x_n_sign, y_n_sign, z_n_sign, l, i1, j1, k1 + + ! 3D OpenSimplex2 case uses two offset rotated cube grids. + + ! + ! --- Rotation moved to TransformNoiseCoordinate method --- + ! const FNLfloat R3 = (FNLfloat)(2.0 / 3.0) + ! FNLfloat r = (x + y + z) * R3 // Rotation, not skew + ! x = r - x y = r - y z = r - z + ! + + mutable_seed = seed + + i = nint(x) + j = nint(y) + k = nint(z) + x0 = real(x - i, c_float) + y0 = real(y - j, c_float) + z0 = real(z - k, c_float) + + x_n_sign = ior(int((-1.0) - x0, c_int), 1) + y_n_sign = ior(int((-1.0) - y0, c_int), 1) + z_n_sign = ior(int((-1.0) - z0, c_int), 1) + + ax0 = x_n_sign * (-x0) + ay0 = y_n_sign * (-y0) + az0 = z_n_sign * (-z0) + + i = i * PRIME_X + j = j * PRIME_Y + k = k * PRIME_Z + + value = 0 + a = (0.6 - x0 * x0) - (y0 * y0 + z0 * z0) + + l = 0 + do + l = l + 1 + + if (a > 0) then + value = value + ((a * a) * (a * a) * internal_fnl_grad_coord_3d(mutable_seed, i, j, k, x0, y0, z0)) + end if + + b = a + 1 + i1 = i + j1 = j + k1 = k + x1 = x0 + y1 = y0 + z1 = z0 + + if (ax0 >= ay0 .and. ax0 >= az0) then + x1 = x1 + x_n_sign + b = b - (x_n_sign * 2 * x1) + i1 = i1 - (x_n_sign * PRIME_X) + else if (ay0 > ax0 .and. ay0 >= az0) then + + y1 = y1 + y_n_sign + b = b - (y_n_sign * 2 * y1) + j1 = j1 - (y_n_sign * PRIME_Y) + else + z1 = z1 + z_n_sign + b = b - (z_n_sign * 2 * z1) + k1 = k1 - (z_n_sign * PRIME_Z) + end if + + if (b > 0) then + value = value + ((b * b) * (b * b) * internal_fnl_grad_coord_3d(mutable_seed, i1, j1, k1, x1, y1, z1)) + end if + + if (l == 1) then + exit + end if + + ax0 = 0.5 - ax0 + ay0 = 0.5 - ay0 + az0 = 0.5 - az0 + + x0 = x_n_sign * ax0 + y0 = y_n_sign * ay0 + z0 = z_n_sign * az0 + + a = a + ((0.75 - ax0) - (ay0 + az0)) + + i = i + and(shiftr(x_n_sign, 1), PRIME_X) + j = j + and(shiftr(y_n_sign, 1), PRIME_Y) + k = k + and(shiftr(z_n_sign, 1), PRIME_Z) + + x_n_sign = -x_n_sign + y_n_sign = -y_n_sign + z_n_sign = -z_n_sign + + mutable_seed = not(mutable_seed) + end do + + output = value * 32.69428253173828125 + end function internal_fnl_single_open_simplex_2_3d + + +! OpenSimplex2S Noise + + + real(c_float) function internal_fnl_single_open_simplex_2s_2d(seed, x, y) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + real(c_float) :: xi, yi, t, x0, y0, x2, y2, x1, y1, value, a0, a1, xmyi, a2, x3, y3, a3 + integer(c_int):: i, j, i1, j1 + real(fnl_float), parameter :: SQRT_3 = real(1.7320508075688772935274463415059, fnl_float) + real(fnl_float), parameter :: G2 = (3.0 - SQRT_3) / 6.0 + + ! 2D OpenSimplex2S case is a modified 2D simplex noise. + + ! + ! --- Skew moved to TransformNoiseCoordinate method --- + ! const FNLfloat F2 = 0.5f * (SQRT_3 - 1) + ! FNLfloat s = (x + y) * F2 + ! x += s y += s + ! + + i = floor(x) + j = floor(y) + xi = real(x - i, c_float) + yi = real(y - j, c_float) + + i = i * PRIME_X + j = j * PRIME_Y + i1 = i + PRIME_X + j1 = j + PRIME_Y + + t = (xi + yi) * real(G2, c_float) + x0 = xi - t + y0 = yi - t + + a0 = (2.0 / 3.0) - x0 * x0 - y0 * y0 + value = (a0 * a0) * (a0 * a0) * internal_fnl_grad_coord_2d(seed, i, j, x0, y0) + + a1 = real(2 * (1.0 - 2.0 * G2) * (1.0 / G2 - 2.0), c_float) * t + (real(-2.0 * (1.0 - 2.0 * G2) * (1.0 - 2.0 * G2), c_float) + a0) + x1 = x0 - real(1.0 - 2.0 * G2, c_float) + y1 = y0 - real(1.0 - 2.0 * G2, c_float) + value = value + ((a1 * a1) * (a1 * a1) * internal_fnl_grad_coord_2d(seed, i1, j1, x1, y1)) + + ! Nested conditionals were faster than compact bit logic/arithmetic. + xmyi = xi - yi + + if (t > G2) then + if (xi + xmyi > 1) then + x2 = x0 + real(3.0 * G2 - 2.0, c_float) + y2 = y0 + real(3.0 * G2 - 1.0, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i + shiftl(PRIME_X, 1), j + PRIME_Y, x2, y2)) + end if + else + x2 = x0 + real(G2, c_float) + y2 = y0 + real(G2 - 1.0, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i, j + PRIME_Y, x2, y2)) + end if + end if + if (yi - xmyi > 1) then + x3 = x0 + real(3.0 * G2 - 1.0, c_float) + y3 = y0 + real(3.0 * G2 - 2.0, c_float) + a3 = (2.0 / 3.0) - x3 * x3 - y3 * y3 + if (a3 > 0) then + value = value + ((a3 * a3) * (a3 * a3) * internal_fnl_grad_coord_2d(seed, i + PRIME_X, j + shiftl(PRIME_Y, 1), x3, y3)) + end if + else + x3 = x0 + real(G2 - 1.0, c_float) + y3 = y0 + real(G2, c_float) + a3 = (2.0 / 3.0) - x3 * x3 - y3 * y3 + if (a3 > 0) then + value = value + ((a3 * a3) * (a3 * a3) * internal_fnl_grad_coord_2d(seed, i + PRIME_X, j, x3, y3)) + end if + end if + else + if (xi + xmyi < 0) then + x2 = x0 + real(1.0 - G2, c_float) + y2 = y0 - real(G2, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i - PRIME_X, j, x2, y2)) + end if + else + x2 = x0 + real(G2 - 1.0, c_float) + y2 = y0 + real(G2, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i + PRIME_X, j, x2, y2)) + end if + end if + if (yi < xmyi) then + x2 = x0 - real(G2, c_float) + y2 = y0 - real(G2 - 1.0, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i, j - PRIME_Y, x2, y2)) + end if + else + x2 = x0 + real(G2, c_float) + y2 = y0 + real(G2 - 1, c_float) + a2 = (2.0 / 3.0) - x2 * x2 - y2 * y2 + if (a2 > 0) then + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_2d(seed, i, j + PRIME_Y, x2, y2)) + end if + end if + end if + + output = value * 18.24196194486065 + end function internal_fnl_single_open_simplex_2s_2d + + real(c_float) function internal_fnl_single_open_simplex_2d_3d(seed, x, y, z) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + real(c_float) :: xi, yi, zi, x0, y0, z0,x2, y2, z2, x1, y1, z1, value, a0, a1, a2, x3, y3, z3, a3, & + x_a_flip_mask_0, y_a_flip_mask_0, z_a_flip_mask_0, x_a_flip_mask_1, y_a_flip_mask_1, z_a_flip_mask_1, & + a4, x4, y4, z4, a6, x6, y6, z6, x7, y7, z7, a7, a8, x8, y8, z8, aA, & + xA, yA, zA, xB, yB, zB, xC, yC, zC, aB, aC, a5, x5, y5, z5, a9, x9, y9, z9, aD, xD, yD, zD + integer(c_int):: i, j, k, seed_2, x_n_mask, y_n_mask, z_n_mask + logical(c_bool) :: skip5, skip9, skipD + + ! 3D OpenSimplex2S case uses two offset rotated cube grids. + + ! + ! --- Rotation moved to TransformNoiseCoordinate method --- + ! const FNLfloat R3 = (FNLfloat)(2.0 / 3.0) + ! FNLfloat r = (x + y + z) * R3 // Rotation, not skew + ! x = r - x y = r - y z = r - z + ! + + i = floor(x) + j = floor(y) + k = floor(z) + xi = real(x - i, c_float) + yi = real(y - j, c_float) + zi = real(z - k, c_float) + + i = i * PRIME_X + j = j * PRIME_Y + k = k * PRIME_Z + seed_2 = seed + 1293373 + + x_n_mask = int(-0.5 - xi, c_int) + y_n_mask = int(-0.5 - yi, c_int) + z_n_mask = int(-0.5 - zi, c_int) + + x0 = xi + x_n_mask + y0 = yi + y_n_mask + z0 = zi + z_n_mask + a0 = 0.75 - x0 * x0 - y0 * y0 - z0 * z0 + value = (a0 * a0) * (a0 * a0) * internal_fnl_grad_coord_3d(seed, & + i + and(x_n_mask, PRIME_X), j + and(y_n_mask, PRIME_Y), k + and(z_n_mask, PRIME_Z), x0, y0, z0) + + x1 = xi - 0.5 + y1 = yi - 0.5 + z1 = zi - 0.5 + a1 = 0.75 - x1 * x1 - y1 * y1 - z1 * z1 + value = value + ((a1 * a1) * (a1 * a1) * internal_fnl_grad_coord_3d(seed_2, & + i + PRIME_X, j + PRIME_Y, k + PRIME_Z, x1, y1, z1)) + + x_a_flip_mask_0 = shiftl(ior(x_n_mask, 1), 1) * x1 + y_a_flip_mask_0 = shiftl(ior(y_n_mask, 1), 1) * y1 + z_a_flip_mask_0 = shiftl(ior(z_n_mask, 1), 1) * z1 + x_a_flip_mask_1 = ((-2) - shiftl(x_n_mask, 2)) * x1 - 1.0 + y_a_flip_mask_1 = ((-2) - shiftl(y_n_mask, 2)) * y1 - 1.0 + z_a_flip_mask_1 = ((-2) - shiftl(z_n_mask, 2)) * z1 - 1.0 + + skip5 = .false. + a2 = x_a_flip_mask_0 + a0 + if (a2 > 0) then + x2 = x0 - ior(x_n_mask, 1) + y2 = y0 + z2 = z0 + value = value + ((a2 * a2) * (a2 * a2) * internal_fnl_grad_coord_3d(seed, & + i + and(not(x_n_mask), PRIME_X), j + and(y_n_mask, PRIME_Y), k + and(z_n_mask, PRIME_Z), x2, y2, z2)) + else + a3 = y_a_flip_mask_0 + z_a_flip_mask_0 + a0 + if (a3 > 0) then + x3 = x0 + y3 = y0 - ior(y_n_mask, 1) + z3 = z0 - ior(z_n_mask, 1) + value = value + ((a3 * a3) * (a3 * a3) * internal_fnl_grad_coord_3d(seed, & + i + and(x_n_mask, PRIME_X), j + and(not(y_n_mask), PRIME_Y), k + and(not(z_n_mask), PRIME_Z), x3, y3, z3)) + end if + a4 = x_a_flip_mask_1 + a1 + if (a4 > 0) then + x4 = ior(x_n_mask, 1) + x1 + y4 = y1 + z4 = z1 + value = value + ((a4 * a4) * (a4 * a4) * internal_fnl_grad_coord_3d(seed_2, & + i + and(x_n_mask, (PRIME_X * 2)), j + PRIME_Y, k + PRIME_Z, x4, y4, z4)) + skip5 = .true. + end if + end if + + skip9 = .false. + a6 = y_a_flip_mask_0 + a0 + if (a6 > 0) then + x6 = x0 + y6 = y0 - ior(y_n_mask, 1) + z6 = z0 + value = value + ((a6 * a6) * (a6 * a6) * internal_fnl_grad_coord_3d(seed, & + i + and(x_n_mask, PRIME_X), j + and(not(y_n_mask), PRIME_Y), k + and(z_n_mask, PRIME_Z), x6, y6, z6)) + else + a7 = x_a_flip_mask_0 + z_a_flip_mask_0 + a0 + if (a7 > 0) then + x7 = x0 - ior(x_n_mask, 1) + y7 = y0 + z7 = z0 - ior(z_n_mask, 1) + value = value + ((a7 * a7) * (a7 * a7) * internal_fnl_grad_coord_3d(seed, & + i + and(not(x_n_mask), PRIME_X), j + and(y_n_mask, PRIME_Y), k + and(not(z_n_mask), PRIME_Z), x7, y7, z7)) + end if + a8 = y_a_flip_mask_1 + a1 + if (a8 > 0) then + x8 = x1 + y8 = ior(y_n_mask, 1) + y1 + z8 = z1 + value = value + ((a8 * a8) * (a8 * a8) * internal_fnl_grad_coord_3d(seed_2, & + i + PRIME_X, j + and(y_n_mask, shiftl(PRIME_Y, 1)), k + PRIME_Z, x8, y8, z8)) + skip9 = .true. + end if + end if + + skipD = .false. + aA = z_a_flip_mask_0 + a0 + if (aA > 0) then + xA = x0 + yA = y0 + zA = z0 - ior(z_n_mask, 1) + value = value + ((aA * aA) * (aA * aA) * internal_fnl_grad_coord_3d(seed, & + i + and(x_n_mask, PRIME_X), j + and(y_n_mask, PRIME_Y), k + and(not(z_n_mask), PRIME_Z), xA, yA, zA)) + else + aB = x_a_flip_mask_0 + y_a_flip_mask_0 + a0 + if (aB > 0) then + xB = x0 - ior(x_n_mask, 1) + yB = y0 - ior(y_n_mask, 1) + zB = z0 + value = value + ((aB * aB) * (aB * aB) * internal_fnl_grad_coord_3d(seed, & + i + and(not(x_n_mask), PRIME_X), j + and(not(y_n_mask), PRIME_Y), k + and(z_n_mask, PRIME_Z), xB, yB, zB)) + end if + aC = z_a_flip_mask_1 + a1 + if (aC > 0) then + xC = x1 + yC = y1 + zC = ior(z_n_mask, 1) + z1 + value = value + ((aC * aC) * (aC * aC) * internal_fnl_grad_coord_3d(seed_2, & + i + PRIME_X, j + PRIME_Y, k + and(z_n_mask, shiftl(PRIME_Z, 1)), xC, yC, zC)) + skipD = .true. + end if + end if + + if (.not. skip5) then + a5 = y_a_flip_mask_1 + z_a_flip_mask_1 + a1 + if (a5 > 0) then + x5 = x1 + y5 = ior(y_n_mask, 1) + y1 + z5 = ior(z_n_mask, 1) + z1 + value = value + ((a5 * a5) * (a5 * a5) * internal_fnl_grad_coord_3d(seed_2, & + i + PRIME_X, j + and(y_n_mask, shiftl(PRIME_Y, 1)), k + and(z_n_mask, shiftl(PRIME_Z, 1)), x5, y5, z5)) + end if + end if + + if (.not. skip9) then + a9 = x_a_flip_mask_1 + z_a_flip_mask_1 + a1 + if (a9 > 0) then + x9 = ior(x_n_mask, 1) + x1 + y9 = y1 + z9 = ior(z_n_mask, 1) + z1 + value = value + ((a9 * a9) * (a9 * a9) * internal_fnl_grad_coord_3d(seed_2, & + i + and(x_n_mask, (PRIME_X * 2)), j + PRIME_Y, k + and(z_n_mask, shiftl(PRIME_Z, 1)), x9, y9, z9)) + end if + end if + + if (.not. skipD) then + aD = x_a_flip_mask_1 + y_a_flip_mask_1 + a1 + if (aD > 0) then + xD = ior(x_n_mask, 1) + x1 + yD = ior(y_n_mask, 1) + y1 + zD = z1 + value = value + ((aD * aD) * (aD * aD) * internal_fnl_grad_coord_3d(seed_2, & + i + and(x_n_mask, shiftl(PRIME_X, 1)), j + and(y_n_mask, shiftl(PRIME_Y, 1)), k + PRIME_Z, xD, yD, zD)) + end if + end if + + output = value * 9.046026385208288 + end function internal_fnl_single_open_simplex_2d_3d + + +! Cellular Noise + + + real(c_float) function internal_fnl_single_cellular_2d(state, seed, x, y) result(output) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: xr, yr, x_primed, y_primed, y_primedBase, xi, yi, hash, idx + real(c_float) :: distance_0, distance_1, cellular_jitter, vec_x, vec_y, new_distance, closest_hash + + xr = nint(x) + yr = nint(y) + + distance_0 = FLT_MAX + distance_1 = FLT_MAX + closest_hash = 0 + + cellular_jitter = 0.43701595 * state%cellular_jitter_mod + + x_primed = (xr - 1) * PRIME_X + y_primedBase = (yr - 1) * PRIME_Y + + select case (state%cellular_distance_func) + case (FNL_CELLULAR_DISTANCE_MANHATTAN) + do xi = xr - 1, xr + 1 + y_primed = y_primedBase + do yi = yr - 1, yr + 1 + hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + idx = and(hash, shiftl(255, 1)) + vec_x = real(xi - x, c_float) + RAND_VECS_2D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_2D(iand(idx, 1) + 1) * cellular_jitter + new_distance = abs(vec_x) + abs(vec_y) + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + case (FNL_CELLULAR_DISTANCE_HYBRID) + do xi = xr - 1, xr + 1 + y_primed = y_primedBase + do yi = yr - 1, yr + 1 + hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + idx = and(hash, shiftl(255, 1)) + vec_x = real(xi - x, c_float) + RAND_VECS_2D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_2D(ior(idx, 1)) * cellular_jitter + new_distance = (abs(vec_x) + abs(vec_y)) + (vec_x * vec_x + vec_y * vec_y) + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + case default + do xi = xr - 1, xr + 1 + y_primed = y_primedBase + do yi = yr - 1, yr + 1 + hash = internal_fnl_hash_2d(seed, x_primed, y_primed) + idx = and(hash, shiftl(255, 1)) + vec_x = real(xi - x, c_float) + RAND_VECS_2D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_2D(ior(idx, 1) + 1) * cellular_jitter + new_distance = vec_x * vec_x + vec_y * vec_y + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + end select + + if (state%cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN .and. state%cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE) then + distance_0 = sqrt(distance_0) + if (state%cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE2) then + distance_1 = sqrt(distance_1) + end if + end if + + select case (state%cellular_return_type) + case (FNL_CELLULAR_RETURN_TYPE_CELLVALUE) + output = closest_hash * (1.0 / 2147483648.0) + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE) + output = distance_0 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2) + output = distance_1 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD) + output = (distance_1 + distance_0) * 0.5 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB) + output = distance_1 - distance_0 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL) + output = distance_1 * distance_0 * 0.5 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV) + output = distance_0 / distance_1 - 1.0 + case default + output = 0.0 + end select + end function internal_fnl_single_cellular_2d + + + real(c_float) function internal_fnl_single_cellular_3d(state, seed, x, y, z) result(output) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: xr, yr, zr, x_primed, y_primed, z_primed, y_primed_base, z_primed_base, xi, yi, zi, hash, idx + real(c_float) :: distance_0, distance_1, cellular_jitter, vec_x, vec_y, vec_z, new_distance, closest_hash + + xr = nint(x) + yr = nint(y) + zr = nint(z) + + distance_0 = FLT_MAX + distance_1 = FLT_MAX + closest_hash = 0 + + cellular_jitter = 0.39614353 * state%cellular_jitter_mod + + x_primed = (xr - 1) * PRIME_X + y_primed_base = (yr - 1) * PRIME_Y + z_primed_base = (zr - 1) * PRIME_Z + + select case (state%cellular_distance_func) + case (FNL_CELLULAR_DISTANCE_MANHATTAN) + do xi = xr - 1, xr + 1 + y_primed = y_primed_base + do yi = yr - 1, yr + 1 + z_primed = z_primed_base + do zi = zr - 1, zr + 1 + hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + idx = and(hash, shiftl(255, 2)) + vec_x = real(xi - x, c_float) + RAND_VECS_3D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_3D(ior(idx, 1) + 1) * cellular_jitter + vec_z = real(zi - z, c_float) + RAND_VECS_3D(ior(idx, 2) + 1) * cellular_jitter + new_distance = abs(vec_x) + abs(vec_y) + abs(vec_z) + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + z_primed = z_primed + PRIME_Z + end do + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + case (FNL_CELLULAR_DISTANCE_HYBRID) + do xi = xr - 1, xr + 1 + y_primed = y_primed_base + do yi = yr - 1, yr + 1 + z_primed = z_primed_base + do zi = zr - 1, zr + 1 + hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + idx = and(hash, shiftl(255, 2)) + vec_x = real(xi - x, c_float) + RAND_VECS_3D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_3D(ior(idx, 1) + 1) * cellular_jitter + vec_z = real(zi - z, c_float) + RAND_VECS_3D(ior(idx, 2) + 1) * cellular_jitter + new_distance = (abs(vec_x) + abs(vec_y) + abs(vec_z)) + (vec_x * vec_x + vec_y * vec_y + vec_z * vec_z) + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + z_primed = z_primed + PRIME_Z + end do + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + case default + do xi = xr - 1, xr + 1 + y_primed = y_primed_base + do yi = yr - 1, yr + 1 + z_primed = z_primed_base + do zi = zr - 1, zr + 1 + hash = internal_fnl_hash_3d(seed, x_primed, y_primed, z_primed) + idx = and(hash, shiftl(255, 2)) + vec_x = real(xi - x, c_float) + RAND_VECS_3D(idx + 1) * cellular_jitter + vec_y = real(yi - y, c_float) + RAND_VECS_3D(ior(idx, 1) + 1) * cellular_jitter + vec_z = real(zi - z, c_float) + RAND_VECS_3D(ior(idx, 2) + 1) * cellular_jitter + new_distance = vec_x * vec_x + vec_y * vec_y + vec_z * vec_z + distance_1 = max(min(distance_1, new_distance), distance_0) + if (new_distance < distance_0) then + distance_0 = new_distance + closest_hash = hash + end if + z_primed = z_primed + PRIME_Z + end do + y_primed = y_primed + PRIME_Y + end do + x_primed = x_primed + PRIME_X + end do + end select + + if (state%cellular_distance_func == FNL_CELLULAR_DISTANCE_EUCLIDEAN .and. state%cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE) then + distance_0 = sqrt(distance_0) + if (state%cellular_return_type >= FNL_CELLULAR_RETURN_TYPE_DISTANCE2) then + distance_1 = sqrt(distance_1) + end if + end if + + select case (state%cellular_return_type) + case (FNL_CELLULAR_RETURN_TYPE_CELLVALUE) + output = closest_hash * (1 / 2147483648.0) + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE) + output = distance_0 - 1 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2) + output = distance_1 - 1 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD) + output = (distance_1 + distance_0) * 0.5 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB) + output = distance_1 - distance_0 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL) + output = distance_1 * distance_0 * 0.5 - 1.0 + case (FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV) + output = distance_0 / distance_1 - 1.0 + case default + output = 0.0 + end select + end function internal_fnl_single_cellular_3d + + +! Perlin Noise + + + real(c_float) function internal_fnl_single_perlin_2d(seed, x, y) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: x0, y0, x1, y1 + real(c_float) :: xd0, yd0, xd1, yd1, xs, ys, xf0, xf1 + + x0 = floor(x) + y0 = floor(y) + + xd0 = real(x - x0, c_float) + yd0 = real(y - y0, c_float) + xd1 = xd0 - 1 + yd1 = yd0 - 1 + + xs = internal_fnl_interp_quintic(xd0) + ys = internal_fnl_interp_quintic(yd0) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + + xf0 = internal_fnl_lerp(internal_fnl_grad_coord_2d(seed, x0, y0, xd0, yd0), internal_fnl_grad_coord_2d(seed, x1, y0, xd1, yd0), xs) + xf1 = internal_fnl_lerp(internal_fnl_grad_coord_2d(seed, x0, y1, xd0, yd1), internal_fnl_grad_coord_2d(seed, x1, y1, xd1, yd1), xs) + + output = internal_fnl_lerp(xf0, xf1, ys) * 1.4247691104677813 + end function internal_fnl_single_perlin_2d + + + real(c_float) function internal_fnl_single_perlin_3d(seed, x, y, z) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: x0, y0, z0, x1, y1, z1 + real(c_float) :: xd0, yd0, zd0, xd1, yd1, zd1, xs, ys, zs, xf00, xf10, xf01, xf11, yf0, yf1 + x0 = floor(x) + y0 = floor(y) + z0 = floor(z) + + xd0 = real(x - x0, c_float) + yd0 = real(y - y0, c_float) + zd0 = real(z - z0, c_float) + xd1 = xd0 - 1 + yd1 = yd0 - 1 + zd1 = zd0 - 1 + + xs = internal_fnl_interp_quintic(xd0) + ys = internal_fnl_interp_quintic(yd0) + zs = internal_fnl_interp_quintic(zd0) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + z0 = z0 * PRIME_Z + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + z1 = z0 + PRIME_Z + + xf00 = internal_fnl_lerp(internal_fnl_grad_coord_3d(seed, x0, y0, z0, xd0, yd0, zd0), internal_fnl_grad_coord_3d(seed, x1, y0, z0, xd1, yd0, zd0), xs) + xf10 = internal_fnl_lerp(internal_fnl_grad_coord_3d(seed, x0, y1, z0, xd0, yd1, zd0), internal_fnl_grad_coord_3d(seed, x1, y1, z0, xd1, yd1, zd0), xs) + xf01 = internal_fnl_lerp(internal_fnl_grad_coord_3d(seed, x0, y0, z1, xd0, yd0, zd1), internal_fnl_grad_coord_3d(seed, x1, y0, z1, xd1, yd0, zd1), xs) + xf11 = internal_fnl_lerp(internal_fnl_grad_coord_3d(seed, x0, y1, z1, xd0, yd1, zd1), internal_fnl_grad_coord_3d(seed, x1, y1, z1, xd1, yd1, zd1), xs) + + yf0 = internal_fnl_lerp(xf00, xf10, ys) + yf1 = internal_fnl_lerp(xf01, xf11, ys) + + output = internal_fnl_lerp(yf0, yf1, zs) * 0.964921414852142333984375 + end function internal_fnl_single_perlin_3d + + +! Value Cubic + + + real(c_float) function internal_fnl_single_value_cubic_2d(seed, x, y) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: x1, y1, x0, y0, x2, y2, x3, y3 + real(c_float) :: xs, ys + + x1 = floor(x) + y1 = floor(y) + + xs = x - real(x1, c_float) + ys = y - real(y1, c_float) + + x1 = x1 * PRIME_X + y1 = y1 * PRIME_Y + + x0 = x1 - PRIME_X + y0 = y1 - PRIME_Y + x2 = x1 + PRIME_X + y2 = y1 + PRIME_Y + x3 = x1 + int(shiftl(PRIME_X, 1), c_int) + y3 = y1 + int(shiftl(PRIME_Y, 1), c_int) + + output = internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp(internal_fnl_val_coord_2d(seed, x0, y0), internal_fnl_val_coord_2d(seed, x1, y0), internal_fnl_val_coord_2d(seed, x2, y0), internal_fnl_val_coord_2d(seed, x3, y0), & + xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_2d(seed, x0, y1), internal_fnl_val_coord_2d(seed, x1, y1), internal_fnl_val_coord_2d(seed, x2, y1), internal_fnl_val_coord_2d(seed, x3, y1), & + xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_2d(seed, x0, y2), internal_fnl_val_coord_2d(seed, x1, y2), internal_fnl_val_coord_2d(seed, x2, y2), internal_fnl_val_coord_2d(seed, x3, y2), & + xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_2d(seed, x0, y3), internal_fnl_val_coord_2d(seed, x1, y3), internal_fnl_val_coord_2d(seed, x2, y3), internal_fnl_val_coord_2d(seed, x3, y3), & + xs), & + ys) * (1.0 / (1.5 * 1.5)) + end function internal_fnl_single_value_cubic_2d + + + real(c_float) function internal_fnl_single_value_cubic_3d(seed, x, y, z) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: x1, y1, z1, x0, y0, z0, x2, y2, z2, x3, y3, z3 + real(c_float) :: xs, ys, zs + + x1 = floor(x) + y1 = floor(y) + z1 = floor(z) + + xs = x - real(x1, c_float) + ys = y - real(y1, c_float) + zs = z - real(z1, c_float) + + x1 = x1 * PRIME_X + y1 = y1 * PRIME_Y + z1 = z1 * PRIME_Z + + x0 = x1 - PRIME_X + y0 = y1 - PRIME_Y + z0 = z1 - PRIME_Z + x2 = x1 + PRIME_X + y2 = y1 + PRIME_Y + z2 = z1 + PRIME_Z + x3 = x1 + int(shiftl(PRIME_X, 1), c_int) + y3 = y1 + int(shiftl(PRIME_Y, 1), c_int) + z3 = z1 + int(shiftl(PRIME_Z, 1), c_int) + + output = internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z0), internal_fnl_val_coord_3d(seed, x1, y0, z0), internal_fnl_val_coord_3d(seed, x2, y0, z0), internal_fnl_val_coord_3d(seed, x3, y0, z0), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z0), internal_fnl_val_coord_3d(seed, x1, y1, z0), internal_fnl_val_coord_3d(seed, x2, y1, z0), internal_fnl_val_coord_3d(seed, x3, y1, z0), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y2, z0), internal_fnl_val_coord_3d(seed, x1, y2, z0), internal_fnl_val_coord_3d(seed, x2, y2, z0), internal_fnl_val_coord_3d(seed, x3, y2, z0), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y3, z0), internal_fnl_val_coord_3d(seed, x1, y3, z0), internal_fnl_val_coord_3d(seed, x2, y3, z0), internal_fnl_val_coord_3d(seed, x3, y3, z0), xs), & + ys), & + internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z1), internal_fnl_val_coord_3d(seed, x1, y0, z1), internal_fnl_val_coord_3d(seed, x2, y0, z1), internal_fnl_val_coord_3d(seed, x3, y0, z1), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z1), internal_fnl_val_coord_3d(seed, x1, y1, z1), internal_fnl_val_coord_3d(seed, x2, y1, z1), internal_fnl_val_coord_3d(seed, x3, y1, z1), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y2, z1), internal_fnl_val_coord_3d(seed, x1, y2, z1), internal_fnl_val_coord_3d(seed, x2, y2, z1), internal_fnl_val_coord_3d(seed, x3, y2, z1), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y3, z1), internal_fnl_val_coord_3d(seed, x1, y3, z1), internal_fnl_val_coord_3d(seed, x2, y3, z1), internal_fnl_val_coord_3d(seed, x3, y3, z1), xs), & + ys), & + internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z2), internal_fnl_val_coord_3d(seed, x1, y0, z2), internal_fnl_val_coord_3d(seed, x2, y0, z2), internal_fnl_val_coord_3d(seed, x3, y0, z2), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z2), internal_fnl_val_coord_3d(seed, x1, y1, z2), internal_fnl_val_coord_3d(seed, x2, y1, z2), internal_fnl_val_coord_3d(seed, x3, y1, z2), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y2, z2), internal_fnl_val_coord_3d(seed, x1, y2, z2), internal_fnl_val_coord_3d(seed, x2, y2, z2), internal_fnl_val_coord_3d(seed, x3, y2, z2), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y3, z2), internal_fnl_val_coord_3d(seed, x1, y3, z2), internal_fnl_val_coord_3d(seed, x2, y3, z2), internal_fnl_val_coord_3d(seed, x3, y3, z2), xs), & + ys), & + internal_fnl_cubic_lerp( & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z3), internal_fnl_val_coord_3d(seed, x1, y0, z3), internal_fnl_val_coord_3d(seed, x2, y0, z3), internal_fnl_val_coord_3d(seed, x3, y0, z3), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z3), internal_fnl_val_coord_3d(seed, x1, y1, z3), internal_fnl_val_coord_3d(seed, x2, y1, z3), internal_fnl_val_coord_3d(seed, x3, y1, z3), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y2, z3), internal_fnl_val_coord_3d(seed, x1, y2, z3), internal_fnl_val_coord_3d(seed, x2, y2, z3), internal_fnl_val_coord_3d(seed, x3, y2, z3), xs), & + internal_fnl_cubic_lerp(internal_fnl_val_coord_3d(seed, x0, y3, z3), internal_fnl_val_coord_3d(seed, x1, y3, z3), internal_fnl_val_coord_3d(seed, x2, y3, z3), internal_fnl_val_coord_3d(seed, x3, y3, z3), xs), & + ys), & + zs) * (1.0 / 1.5 * 1.5 * 1.5) + end function internal_fnl_single_value_cubic_3d + + +! Value noise + + + real(c_float) function internal_fnl_single_value_2d(seed, x, y) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y + integer(c_int) :: x0, y0, x1, y1 + real(c_float) :: xs, ys, xf0, xf1 + + x0 = floor(x) + y0 = floor(y) + + xs = internal_fnl_interp_hermite(real(x - x0, c_float)) + ys = internal_fnl_interp_hermite(real(y - y0, c_float)) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + + xf0 = internal_fnl_lerp(internal_fnl_val_coord_2d(seed, x0, y0), internal_fnl_val_coord_2d(seed, x1, y0), xs) + xf1 = internal_fnl_lerp(internal_fnl_val_coord_2d(seed, x0, y1), internal_fnl_val_coord_2d(seed, x1, y1), xs) + + output = internal_fnl_lerp(xf0, xf1, ys) + end function internal_fnl_single_value_2d + + + real(c_float) function internal_fnl_single_value_3d(seed, x, y, z) result(output) + implicit none + + integer(c_int), intent(in), value :: seed + real(fnl_float), intent(in), value :: x, y, z + integer(c_int) :: x0, y0, z0, x1, y1, z1 + real(c_float) :: xs, ys, zs, xf00, xf10, xf01, xf11, yf0, yf1 + + x0 = floor(x) + y0 = floor(y) + z0 = floor(z) + + xs = internal_fnl_interp_hermite(real(x - x0, c_float)) + ys = internal_fnl_interp_hermite(real(y - y0, c_float)) + zs = internal_fnl_interp_hermite(real(z - z0, c_float)) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + z0 = z0 *PRIME_Z + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + z1 = z0 + PRIME_Z + + xf00 = internal_fnl_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z0), internal_fnl_val_coord_3d(seed, x1, y0, z0), xs) + xf10 = internal_fnl_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z0), internal_fnl_val_coord_3d(seed, x1, y1, z0), xs) + xf01 = internal_fnl_lerp(internal_fnl_val_coord_3d(seed, x0, y0, z1), internal_fnl_val_coord_3d(seed, x1, y0, z1), xs) + xf11 = internal_fnl_lerp(internal_fnl_val_coord_3d(seed, x0, y1, z1), internal_fnl_val_coord_3d(seed, x1, y1, z1), xs) + + yf0 = internal_fnl_lerp(xf00, xf10, ys) + yf1 = internal_fnl_lerp(xf01, xf11, ys) + + output = internal_fnl_lerp(yf0, yf1, zs) + end function internal_fnl_single_value_3d + + +! Domain Warp + + + subroutine internal_fnl_do_single_domain_warp_2d(state, seed, amp, freq, x, y, xp, yp) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(c_float), intent(in), value :: amp, freq + real(fnl_float), intent(in), value :: x, y + real(fnl_float), intent(inout) :: xp, yp + + select case (state%domain_warp_type) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2) + call internal_fnl_single_domain_warp_simplex_gradient(seed, amp * 38.283687591552734375, freq, x, y, xp, yp, .false.) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED) + call internal_fnl_single_domain_warp_simplex_gradient(seed, amp * 16.0, freq, x, y, xp, yp, .true.) + case (FNL_DOMAIN_WARP_BASICGRID) + call internal_fnl_single_domain_warp_basic_grid_2d(seed, amp, freq, x, y, xp, yp) + end select + end subroutine internal_fnl_do_single_domain_warp_2d + + + subroutine internal_fnl_do_single_domain_warp_3d(state, seed, amp, freq, x, y, z, xp, yp, zp) + implicit none + + type(fnl_state), intent(in) :: state + integer(c_int), intent(in), value :: seed + real(c_float), intent(in), value :: amp, freq + real(fnl_float), intent(in), value :: x, y, z + real(fnl_float), intent(inout) :: xp, yp, zp + + select case (state%domain_warp_type) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2) + call internal_fnl_single_domain_warp_open_simplex2_gradient(seed, amp * 32.69428253173828125, freq, x, y, z, xp, yp, zp, .false.) + case (FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED) + call internal_fnl_single_domain_warp_open_simplex2_gradient(seed, amp * 7.71604938271605, freq, x, y, z, xp, yp, zp, .true.) + case (FNL_DOMAIN_WARP_BASICGRID) + call internal_fnl_single_domain_warp_basic_grid_3d(seed, amp, freq, x, y, z, xp, yp, zp) + end select + end subroutine internal_fnl_do_single_domain_warp_3d + + +! Domain Warp Single Wrapper + + + subroutine internal_fnl_domain_warp_single_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + integer(c_int) :: seed + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + xs = x + ys = y + call internal_fnl_transform_domain_warp_coordinate_2d(state, xs, ys) + + call internal_fnl_do_single_domain_warp_2d(state, seed, amp, freq, xs, ys, x, y) + end subroutine internal_fnl_domain_warp_single_2d + + + subroutine internal_fnl_domain_warp_single_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + integer(c_int) :: seed + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys, zs + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + xs = x + ys = y + zs = z + call internal_fnl_transform_domain_warp_coordinate_3d(state, xs, ys, zs) + + call internal_fnl_do_single_domain_warp_3d(state, seed, amp, freq, xs, ys, zs, x, y, z) + end subroutine internal_fnl_domain_warp_single_3d + + +! Domain Warp Fractal Progressive + + + subroutine internal_fnl_domain_warp_fractal_progressive_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + integer(c_int) :: seed, i + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + do i = 1, state%octaves + + xs = x + ys = y + call internal_fnl_transform_domain_warp_coordinate_2d(state, xs, ys) + + call internal_fnl_do_single_domain_warp_2d(state, seed, amp, freq, xs, ys, x, y) + + seed = seed + 1 + + amp = amp * state%gain + freq = freq * state%lacunarity + end do + end subroutine internal_fnl_domain_warp_fractal_progressive_2d + + + subroutine internal_fnl_domain_warp_fractal_progressive_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + integer(c_int) :: seed, i + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys, zs + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + do i = 1, state%octaves + + xs = x + ys = y + zs = z + call internal_fnl_transform_domain_warp_coordinate_3d(state, xs, ys, zs) + + call internal_fnl_do_single_domain_warp_3d(state, seed, amp, freq, xs, ys, zs, x, y, z) + + seed = seed + 1 + amp = amp * state%gain + freq = freq * state%lacunarity + end do + end subroutine internal_fnl_domain_warp_fractal_progressive_3d + + +! Domain Warp Fractal Independent + + + subroutine internal_dnl_domain_warp_fractal_independent_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + integer(c_int) :: seed, i + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys + + xs = x + ys = y + call internal_fnl_transform_domain_warp_coordinate_2d(state, xs, ys) + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + do i = 1, state%octaves + + call internal_fnl_do_single_domain_warp_2d(state, seed, amp, freq, xs, ys, x, y) + + seed = seed + 1 + + amp = amp * state%gain + freq = freq * state%lacunarity + end do + end subroutine internal_dnl_domain_warp_fractal_independent_2d + + + subroutine internal_dnl_domain_warp_fractal_independent_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + integer(c_int) :: seed, i + real(c_float) :: amp, freq + real(fnl_float) :: xs, ys, zs + + xs = x + ys = y + zs = z + call internal_fnl_transform_domain_warp_coordinate_3d(state, xs, ys, zs) + + seed = state%seed + amp = state%domain_warp_amp * internal_fnl_calculate_fractal_bounding(state) + freq = state%frequency + + do i = 1,state%octaves + call internal_fnl_do_single_domain_warp_3d(state, seed, amp, freq, xs, ys, zs, x, y, z) + + seed = seed + 1 + + amp = amp * state%gain + freq = freq * state%lacunarity + end do + end subroutine internal_dnl_domain_warp_fractal_independent_3d + + +! Domain Warp Basic Grid + + + subroutine internal_fnl_single_domain_warp_basic_grid_2d(seed, warp_amp, frequency, x, y, xp, yp) + implicit none + + integer(c_int), intent(in), value :: seed + real(c_float), intent(in), value :: warp_amp, frequency + real(fnl_float), intent(in), value :: x, y + real(fnl_float), intent(inout) :: xp, yp + real(fnl_float) :: xf, yf, xs, ys, lx0x, ly0x, lx1x, ly1x + integer(c_int) :: x0, y0, x1, y1, idx0, idx1 + + xf = x * frequency + yf = y * frequency + + x0 = floor(xf) + y0 = floor(yf) + + xs = internal_fnl_interp_hermite(real(xf - x0, c_float)) + ys = internal_fnl_interp_hermite(real(yf - y0, c_float)) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + + idx0 = and(internal_fnl_hash_2d(seed, x0, y0), shiftl(255, 1)) + idx1 = and(internal_fnl_hash_2d(seed, x1, y0), shiftl(255, 1)) + + lx0x = internal_fnl_lerp(RAND_VECS_2D(idx0 + 1), RAND_VECS_2D(idx1 + 1), xs) + ly0x = internal_fnl_lerp(RAND_VECS_2D(ior(idx0, 1) + 1), RAND_VECS_2D(ior(idx1, 1) + 1), xs) + + idx0 = and(internal_fnl_hash_2d(seed, x0, y1), shiftl(255, 1)) + idx1 = and(internal_fnl_hash_2d(seed, x1, y1), shiftl(255, 1)) + + lx1x = internal_fnl_lerp(RAND_VECS_2D(idx0 + 1), RAND_VECS_2D(idx1 + 1), xs) + ly1x = internal_fnl_lerp(RAND_VECS_2D(ior(idx0, 1) + 1), RAND_VECS_2D(ior(idx1, 1) + 1), xs) + + xp = xp + (internal_fnl_lerp(lx0x, lx1x, ys) * warp_amp) + yp = yp + (internal_fnl_lerp(ly0x, ly1x, ys) * warp_amp) + end subroutine internal_fnl_single_domain_warp_basic_grid_2d + + + subroutine internal_fnl_single_domain_warp_basic_grid_3d(seed, warp_amp, frequency, x, y, z, xp, yp, zp) + implicit none + + integer(c_int), intent(in), value :: seed + real(c_float), intent(in), value :: warp_amp, frequency + real(fnl_float), intent(in), value :: x, y, z + real(fnl_float), intent(inout) :: xp, yp, zp + real(fnl_float) :: xf, yf, zf, xs, ys, zs, lx0x, ly0x, lz0x, lx1x, ly1x, lz1x, lx0y, ly0y, lz0y + integer(c_int) :: x0, y0, z0, x1, y1, z1, idx0, idx1 + + xf = x * frequency + yf = y * frequency + zf = z * frequency + + x0 = floor(xf) + y0 = floor(yf) + z0 = floor(zf) + + xs = internal_fnl_interp_hermite(real(xf - x0, c_float)) + ys = internal_fnl_interp_hermite(real(yf - y0, c_float)) + zs = internal_fnl_interp_hermite(real(zf - z0, c_float)) + + x0 = x0 * PRIME_X + y0 = y0 * PRIME_Y + z0 = z0 * PRIME_Z + x1 = x0 + PRIME_X + y1 = y0 + PRIME_Y + z1 = z0 + PRIME_Z + + idx0 = and(internal_fnl_hash_3d(seed, x0, y0, z0), shiftl(255, 2)) + idx1 = and(internal_fnl_hash_3d(seed, x1, y0, z0), shiftl(255, 2)) + + lx0x = internal_fnl_lerp(RAND_VECS_3D(idx0 + 1), RAND_VECS_3D(idx1 + 1), xs) + ly0x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 1) + 1), RAND_VECS_3D(ior(idx1, 1) + 1), xs) + lz0x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 2) + 1), RAND_VECS_3D(ior(idx1, 2) + 1), xs) + + idx0 = and(internal_fnl_hash_3d(seed, x0, y1, z0), shiftl(255, 2)) + idx1 = and(internal_fnl_hash_3d(seed, x1, y1, z0), shiftl(255, 2)) + + lx1x = internal_fnl_lerp(RAND_VECS_3D(idx0 + 1), RAND_VECS_3D(idx1 + 1), xs) + ly1x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 1) + 1), RAND_VECS_3D(ior(idx1, 1) + 1), xs) + lz1x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 2) + 1), RAND_VECS_3D(ior(idx1, 2) + 1), xs) + + lx0y = internal_fnl_lerp(lx0x, lx1x, ys) + ly0y = internal_fnl_lerp(ly0x, ly1x, ys) + lz0y = internal_fnl_lerp(lz0x, lz1x, ys) + + idx0 = and(internal_fnl_hash_3d(seed, x0, y0, z1), shiftl(255, 2)) + idx1 = and(internal_fnl_hash_3d(seed, x1, y0, z1), shiftl(255, 2)) + + lx0x = internal_fnl_lerp(RAND_VECS_3D(idx0 + 1), RAND_VECS_3D(idx1 + 1), xs) + ly0x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 1) + 1), RAND_VECS_3D(ior(idx1, 1) + 1), xs) + lz0x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 2) + 1), RAND_VECS_3D(ior(idx1, 2) + 1), xs) + + idx0 = and(internal_fnl_hash_3d(seed, x0, y1, z1), shiftl(255, 2)) + idx1 = and(internal_fnl_hash_3d(seed, x1, y1, z1), shiftl(255, 2)) + + lx1x = internal_fnl_lerp(RAND_VECS_3D(idx0 + 1), RAND_VECS_3D(idx1 + 1), xs) + ly1x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 1) + 1), RAND_VECS_3D(ior(idx1, 1) + 1), xs) + lz1x = internal_fnl_lerp(RAND_VECS_3D(ior(idx0, 2) + 1), RAND_VECS_3D(ior(idx1, 2) + 1), xs) + + xp = xp + (internal_fnl_lerp(lx0y, internal_fnl_lerp(lx0x, lx1x, ys), zs) * warp_amp) + yp = yp + (internal_fnl_lerp(ly0y, internal_fnl_lerp(ly0x, ly1x, ys), zs) * warp_amp) + zp = zp + (internal_fnl_lerp(lz0y, internal_fnl_lerp(lz0x, lz1x, ys), zs) * warp_amp) + end subroutine internal_fnl_single_domain_warp_basic_grid_3d + + +! Domain Warp Simplex/OpenSimplex2 + + + subroutine internal_fnl_single_domain_warp_simplex_gradient(seed, warp_amp, frequency, xx, yy, xr, yr, outGradOnly) + implicit none + + integer(c_int), intent(in), value :: seed + real(c_float), intent(in), value :: warp_amp, frequency + real(fnl_float), intent(in), value :: xx, yy + real(fnl_float), intent(inout) :: xr, yr + logical, intent(in), value :: outGradOnly + real(c_float) :: x, y, xi, yi, t, x0, y0, vx, vy, a, aaaa, xo, yo, b, c, bbbb, cccc, x1, y1, x2, y2 + integer(c_int) :: i, j + real(fnl_float), parameter :: SQRT_3 = 1.7320508075688772935274463415059 + real(fnl_float), parameter :: G2 = (3.0 - SQRT_3) / 6.0 + + ! Use xx and so forth as mutable subroutine variables. + x = xx * frequency + y = yy * frequency + + ! + ! --- Skew moved to TransformNoiseCoordinate method --- + ! const FNLfloat F2 = 0.5f * (SQRT_3 - 1) + ! FNLfloat s = (x + y) * F2 + ! x += s y += s + ! + + i = floor(x) + j = floor(y) + xi = real(x - i, c_float) + yi = real(y - j, c_float) + + t = (xi + yi) * G2 + x0 = real(xi - t, c_float) + y0 = real(yi - t, c_float) + + i = i * PRIME_X + j = j * PRIME_Y + + vx = 0.0 + vy = 0.0 + + a = 0.5 - x0 * x0 - y0 * y0 + + if (a > 0) then + aaaa = (a * a) * (a * a) + + if (outGradOnly) then + call internal_fnl_grad_coord_out_2d(seed, i, j, xo, yo) + else + call internal_fnl_grad_coord_dual_2d(seed, i, j, x0, y0, xo, yo) + end if + vx = vx + (aaaa * xo) + vy = vy + (aaaa * yo) + end if + + c = real(2 * (1 - 2 * G2) * (1 / G2 - 2), c_float) * t + (real(-2 * (1 - 2 * G2) * (1 - 2 * G2), c_float) + a) + if (c > 0) then + x2 = x0 + (2 * real(G2, c_float) - 1) + y2 = y0 + (2 * real(G2, c_float) - 1) + cccc = (c * c) * (c * c) + if (outGradOnly) then + call internal_fnl_grad_coord_out_2d(seed, i + PRIME_X, j + PRIME_Y, xo, yo) + else + call internal_fnl_grad_coord_dual_2d(seed, i + PRIME_X, j + PRIME_Y, x2, y2, xo, yo) + end if + vx = vx + (cccc * xo) + vy = vy + (cccc * yo) + end if + + if (y0 > x0) then + x1 = x0 + real(G2, c_float) + y1 = y0 + (real(G2, c_float) - 1) + b = 0.5 - x1 * x1 - y1 * y1 + if (b > 0) then + bbbb = (b * b) * (b * b) + + if (outGradOnly) then + call internal_fnl_grad_coord_out_2d(seed, i, j + PRIME_Y, xo, yo) + else + call internal_fnl_grad_coord_dual_2d(seed, i, j + PRIME_Y, x1, y1, xo, yo) + end if + vx = vx + (bbbb * xo) + vy = vy + (bbbb * yo) + end if + else + x1 = x0 + (real(G2, c_float) - 1) + y1 = y0 + real(G2, c_float) + b = 0.5 - x1 * x1 - y1 * y1 + if (b > 0) then + bbbb = (b * b) * (b * b) + if (outGradOnly) then + call internal_fnl_grad_coord_out_2d(seed, i + PRIME_X, j, xo, yo) + else + call internal_fnl_grad_coord_dual_2d(seed, i + PRIME_X, j, x1, y1, xo, yo) + end if + vx = vx + (bbbb * xo) + vy = vy + (bbbb * yo) + end if + end if + + xr = xr + (vx * warp_amp) + yr = yr + (vy * warp_amp) + end subroutine internal_fnl_single_domain_warp_simplex_gradient + + + subroutine internal_fnl_single_domain_warp_open_simplex2_gradient(val_seed, warp_amp, frequency, xx, yy, zz, xr, yr, zr, outGradOnly) + integer(c_int), intent(in), value :: val_seed + real(c_float), intent(in), value :: warp_amp, frequency + real(fnl_float), intent(in), value :: xx, yy, zz + real(fnl_float), intent(inout) :: xr, yr, zr + logical, intent(in), value :: outGradOnly + real(c_float) :: x, y, z, x0, y0, z0, vx, vy, vz, a, aaaa, xo, yo, zo, b, bbbb, x1, y1, z1, ax0, ay0, az0 + integer(c_int) :: seed, i, j, k, x_n_sign, y_n_sign, z_n_sign, l, i1, j1, k1 + + ! Use xx and so forth as mutable subroutine variables. + x = xx * frequency + x = yy * frequency + z = zz * frequency + seed = val_seed + + ! + ! --- Rotation moved to TransformDomainWarpCoordinate method --- + ! const FNLfloat R3 = (FNLfloat)(2.0 / 3.0) + ! FNLfloat r = (x + y + z) * R3 // Rotation, not skew + ! x = r - x y = r - y z = r - z + ! + + i = nint(x) + j = nint(y) + k = nint(z) + x0 = real(x, c_float) - i + y0 = real(y, c_float) - j + z0 = real(z, c_float) - k + + x_n_sign = ior(int(-x0 - 1.0, c_int), 1) + y_n_sign = ior(int(-y0 - 1.0, c_int), 1) + z_n_sign = ior(int(-z0 - 1.0, c_int), 1) + + ax0 = x_n_sign * (-x0) + ay0 = y_n_sign * (-y0) + az0 = z_n_sign * (-z0) + + i = i * PRIME_X + j = j * PRIME_Y + k = k * PRIME_Z + + vx = 0.0 + vy = 0.0 + vz = 0.0 + + a = (0.6 - x0 * x0) - (y0 * y0 + z0 * z0) + + do l = 1,2 + if (a > 0) then + aaaa = (a * a) * (a * a) + if (outGradOnly) then + call internal_fnl_grad_coord_out_3d(seed, i, j, k, xo, yo, zo) + else + call internal_fnl_grad_coord_dual_3d(seed, i, j, k, x0, y0, z0, xo, yo, zo) + end if + vx = vx + (aaaa * xo) + vy = vy + (aaaa * yo) + vz = vz + (aaaa * zo) + end if + + b = a + 1 + i1 = i + j1 = j + k1 = k + x1 = x0 + y1 = y0 + z1 = z0 + if (ax0 >= ay0 .and. ax0 >= az0) then + x1 = x1 + x_n_sign + b = b - (x_n_sign * 2 * x1) + i1 = i1 - (x_n_sign * PRIME_X) + else if (ay0 > ax0 .and. ay0 >= az0) then + y1 = y1 + y_n_sign + b = b - (y_n_sign * 2 * y1) + j1 = j1 - (y_n_sign * PRIME_Y) + else + z1 = z1 + z_n_sign + b = b - (z_n_sign * 2 * z1) + k1 = k1 - (z_n_sign * PRIME_Z) + end if + if (b > 0) then + bbbb = (b * b) * (b * b) + if (outGradOnly) then + call internal_fnl_grad_coord_out_3d(seed, i1, j1, k1, xo, yo, zo) + else + call internal_fnl_grad_coord_dual_3d(seed, i1, j1, k1, x1, y1, z1, xo, yo, zo) + end if + vx = vx + (bbbb * xo) + vy = vy + (bbbb * yo) + vz = vz + (bbbb * zo) + end if + + if (l == 2) then + exit + end if + + ax0 = 0.5 - ax0 + ay0 = 0.5 - ay0 + az0 = 0.5 - az0 + + x0 = x_n_sign * ax0 + y0 = y_n_sign * ay0 + z0 = z_n_sign * az0 + + a = a + ((0.75 - ax0) - (ay0 + az0)) + + i = i + and(shiftr(x_n_sign, 1), PRIME_X) + j = j + and(shiftr(y_n_sign, 1), PRIME_Y) + k = k + and(shiftr(z_n_sign, 1), PRIME_Z) + + x_n_sign = -x_n_sign + y_n_sign = -y_n_sign + z_n_sign = -z_n_sign + + seed = seed + 1293373 + end do + + xr = xr + (vx * warp_amp) + yr = yr + (vy * warp_amp) + zr = zr + (vz * warp_amp) + end subroutine internal_fnl_single_domain_warp_open_simplex2_gradient + + +! ==================== +! Public API +! ==================== + + + !* + !* Creates a noise state with default values. + !* @param seed Optionally set the state seed. + !* + type(fnl_state) function constructor_fnl_state() result(state_new) + implicit none + + state_new%seed = 1337 + state_new%frequency = 0.01 + state_new%noise_type = FNL_NOISE_OPENSIMPLEX2 + state_new%rotation_type_3d = FNL_ROTATION_NONE + state_new%fractal_type = FNL_FRACTAL_NONE + state_new%octaves = 3 + state_new%lacunarity = 2.0 + state_new%gain = 0.5 + state_new%weighted_strength = 0.0 + state_new%ping_pong_strength = 2.0 + state_new%cellular_distance_func = FNL_CELLULAR_DISTANCE_EUCLIDEANSQ + state_new%cellular_return_type = FNL_CELLULAR_RETURN_TYPE_DISTANCE + state_new%cellular_jitter_mod = 1.0 + state_new%domain_warp_amp = 30.0 + state_new%domain_warp_type = FNL_DOMAIN_WARP_OPENSIMPLEX2 + end function constructor_fnl_state + + + !* + !* 2D noise at given position using the state settings + !* @returns Noise output bounded between -1 and 1. + !* + real(c_float) function fnl_get_noise_2d(state, x, y) result(output) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y + real(fnl_float) :: xx, yy + + ! Use xx and so forth as mutable subroutine variables. + xx = x + yy = y + + call internal_fnl_transform_noise_coordinate_2d(state, xx, yy) + + select case (state%fractal_type) + case (FNL_FRACTAL_FBM) + output = internal_fnl_gen_fraction_fbm_2d(state, xx, yy) + case (FNL_FRACTAL_RIDGED) + output = internal_fnm_gen_fractal_ridged_2d(state, xx, yy) + case (FNL_FRACTAL_PINGPONG) + output = internal_fnl_gen_fractal_ping_pong_2d(state, xx, yy) + case default + output = internal_fnl_gen_noise_single_2d(state, state%seed, xx, yy) + end select + end function fnl_get_noise_2d + + + !* + !* 3D noise at given position using the state settings + !* @returns Noise output bounded between -1 and 1. + !* + real(c_float) function fnl_get_noise_3d(state, x, y, z) result(output) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(in), value :: x, y, z + real(fnl_float) :: xx, yy, zz + + ! Use xx and so forth as mutable subroutine variables. + xx = x + yy = y + zz = z + + call internal_fnl_transform_noise_coordinates_3d(state, xx, yy, zz) + + ! Select a noise type + select case (state%fractal_type) + case (FNL_FRACTAL_FBM) + output = internal_fnl_gen_fractal_fbm_3d(state, xx, yy, zz) + case (FNL_FRACTAL_RIDGED) + output = internal_fnl_gen_fractal_ridged_3d(state, xx, yy, zz) + case (FNL_FRACTAL_PINGPONG) + output = internal_fnl_gen_fractal_ping_pong_3d(state, xx, yy, zz) + case default + output = internal_fnl_gen_noise_single_3d(state, state%seed, xx, yy, zz) + end select + end function fnl_get_noise_3d + + + !* + !* 2D warps the input position using current domain warp settings. + !* + !* Example usage with fnl_get_noise_2d: + !* ``` + !* fnlDomainWarp2D(&state, &x, &y) + !* noise = fnl_get_noise_2d(&state, x, y) + !* ``` + !* + subroutine fnl_domain_warp_2d(state, x, y) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y + + select case (state%fractal_type) + case (FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE) + call internal_fnl_domain_warp_fractal_progressive_2d(state, x, y) + case (FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT) + call internal_dnl_domain_warp_fractal_independent_2d(state, x, y) + case default + call internal_fnl_domain_warp_single_2d(state, x, y) + end select + end subroutine fnl_domain_warp_2d + + + !* + !* 3D warps the input position using current domain warp settings. + !* + !* Example usage with fnlGetNoise3D: + !* ``` + !* fnlDomainWarp3D(&state, &x, &y, &z) + !* noise = fnlGetNoise3D(&state, x, y, z) + !* ``` + !* + subroutine fnl_domain_warp_3d(state, x, y, z) + implicit none + + type(fnl_state), intent(in) :: state + real(fnl_float), intent(inout) :: x, y, z + + select case (state%fractal_type) + case (FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE) + call internal_fnl_domain_warp_fractal_progressive_3d(state, x, y, z) + case (FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT) + call internal_dnl_domain_warp_fractal_independent_3d(state, x, y, z) + case default + call internal_fnl_domain_warp_single_3d(state, x, y, z) + end select + end subroutine fnl_domain_warp_3d + + +end module fast_noise_lite diff --git a/README.md b/README.md index e8229c0..9c14522 100644 --- a/README.md +++ b/README.md @@ -87,6 +87,7 @@ Million points of noise generated per second (higher = better) - [@dotlogix](https://github.com/dotlogix) for creating the GLSL port. - [@ForeverZer0](https://github.com/ForeverZer0) for creating the Go port. - [@Keavon](https://github.com/Keavon) for creating the Rust port. +- [@jordan4ibanez](https://github.com/jordan4ibanez) for creating the Fortran port. # Examples