(此程序的依赖项:vector --any 和 JuicyPixels >= 2 。代码可用作 Gist。)
{-# LANGUAGE Haskell2010 #-}
{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Data.Bits
import Data.Vector.Unboxed ((!))
import Data.Word
import System.Environment (getArgs)
import qualified Codec.Picture as P
import qualified Data.ByteString as B
import qualified Data.Vector.Unboxed as V
我尝试移植 Ken Perlin's improved noise
到 Haskell，但我不完全确定我的方法是正确的。主要部分
是应该很好地推广到更高和更低维度的东西，但是
这是以后的事情:
perlin3 :: (Ord a, Num a, RealFrac a, V.Unbox a) => Permutation -> (a, a, a) -> a
perlin3 p (!x', !y', !z')
= let (!xX, !x) = actuallyProperFraction x'
(!yY, !y) = actuallyProperFraction y'
(!zZ, !z) = actuallyProperFraction z'
!u = fade x
!v = fade y
!w = fade z
!h = xX
!a = next p h + yY
!b = next p (h+1) + yY
!aa = next p a + zZ
!ab = next p (a+1) + zZ
!ba = next p b + zZ
!bb = next p (b+1) + zZ
!aaa = next p aa
!aab = next p (aa+1)
!aba = next p ab
!abb = next p (ab+1)
!baa = next p ba
!bab = next p (ba+1)
!bba = next p bb
!bbb = next p (bb+1)
in
lerp w
(lerp v
(lerp u
(grad aaa (x, y, z))
(grad baa (x-1, y, z)))
(lerp u
(grad aba (x, y-1, z))
(grad bba (x-1, y-1, z))))
(lerp v
(lerp u
(grad aab (x, y, z-1))
(grad bab (x-1, y, z-1)))
(lerp u
(grad abb (x, y-1, z-1))
(grad bbb (x-1, y-1, z-1))))
这当然伴随着
perlin3 中提到的一些功能。功能，我希望它们尽可能高效:
fade :: (Ord a, Num a) => a -> a
fade !t | 0 <= t, t <= 1 = t * t * t * (t * (t * 6 - 15) + 10)
lerp :: (Ord a, Num a) => a -> a -> a -> a
lerp !t !a !b | 0 <= t, t <= 1 = a + t * (b - a)
grad :: (Bits hash, Integral hash, Num a, V.Unbox a) => hash -> (a, a, a) -> a
grad !hash (!x, !y, !z) = dot3 (vks `V.unsafeIndex` fromIntegral (hash .&. 15)) (x, y, z)
where
vks = V.fromList
[ (1,1,0), (-1,1,0), (1,-1,0), (-1,-1,0)
, (1,0,1), (-1,0,1), (1,0,-1), (-1,0,-1)
, (0,1,1), (0,-1,1), (0,1,-1), (0,-1,-1)
, (1,1,0), (-1,1,0), (0,-1,1), (0,-1,-1)
]
dot3 :: Num a => (a, a, a) -> (a, a, a) -> a
dot3 (!x0, !y0, !z0) (!x1, !y1, !z1) = x0 * x1 + y0 * y1 + z0 * z1
-- Unlike `properFraction`, `actuallyProperFraction` rounds as intended.
actuallyProperFraction :: (RealFrac a, Integral b) => a -> (b, a)
actuallyProperFraction x
= let (ipart, fpart) = properFraction x
r = if x >= 0 then (ipart, fpart)
else (ipart-1, 1+fpart)
in r
对于排列组，我只是复制了 Perlin 在他的网站上使用的一个:
newtype Permutation = Permutation (V.Vector Word8)
mkPermutation :: [Word8] -> Permutation
mkPermutation xs
| length xs >= 256
= Permutation . V.fromList $ xs
permutation :: Permutation
permutation = mkPermutation
[151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
]
next :: Permutation -> Word8 -> Word8
next (Permutation !v) !idx'
= v `V.unsafeIndex` (fromIntegral $ idx' .&. 0xFF)
而这一切都与 JuicyPixels 联系在一起:
main = do
[target] <- getArgs
let image = P.generateImage pixelRenderer 512 512
P.writePng target image
where
pixelRenderer, pixelRenderer' :: Int -> Int -> Word8
pixelRenderer !x !y
= floor $ ((perlin3 permutation ((fromIntegral x - 256) / 32,
(fromIntegral y - 256) / 32, 0 :: Double))+1)/2 * 128
-- This code is much more readable, but also much slower.
pixelRenderer' x y
= (\w -> floor $ ((w+1)/2 * 128)) -- w should be in [-1,+1]
. perlin3 permutation
. (\(x,y,z) -> ((x-256)/32, (y-256)/32, (z-256)/32))
$ (fromIntegral x, fromIntegral y, 0 :: Double)
我的问题是
perlin3对我来说似乎很慢。如果我对其进行分析，pixelRenderer也有很多时间，但我暂时忽略它。我不知道如何优化
perlin3 .我试图用爆炸模式来暗示 GHC，它削减了执行时间减半，这很好。显式特化和内联
对
ghc -O 几乎没有帮助.是 perlin3应该这么慢？更新 :这个问题的早期版本提到了我的代码中的一个错误。这个问题已经解决了;原来是我的旧版本
actuallyProperFraction是马车。它将浮点数的整数部分隐式四舍五入为Word8。 , 然后从浮点数中减去它得到小数部分。由于Word8只能取 0 之间的值和 255包括在内，这对于该范围之外的数字(包括负数)将无法正常工作。
最佳答案
此代码似乎主要受计算限制。它可以改进一点，但不会改进很多，除非有一种方法可以使用更少的数组查找和更少的算术。
有两种有用的工具可用于测量性能:分析和代码转储。我在 perlin3 中添加了 SCC 注释这样它就会出现在个人资料中。然后我用 gcc -O2 -fforce-recomp -ddump-simpl -prof -auto 编译. -ddump-simpl flag 打印简化的代码。
Profiling:在我的电脑上，运行程序需要 0.60 秒，大约 20% 的执行时间(0.12 秒)花费在 perlin3 上。根据简介。请注意，我的个人资料信息的精度约为 +/-3%。
简化器输出:简化器产生相当干净的代码。 perlin3内联到 pixelRenderer ，所以这是您要查看的输出部分。大多数代码由未装箱的数组读取和未装箱的算术组成。为了提高性能，我们希望消除一些这种算法。
一个简单的改变是取消对 SomeFraction 的运行时检查。 (它没有出现在您的问题中，而是您上传的代码的一部分)。这将程序的执行时间减少到 0.56 秒。
-- someFraction t | 0 <= t, t < 1 = SomeFraction t
someFraction t = SomeFraction t
接下来，在简化器中显示了几个数组查找，如下所示:
case GHC.Prim.indexWord8Array#
ipv3_s23a
(GHC.Prim.+#
ipv1_s21N
(GHC.Prim.word2Int#
(GHC.Prim.and#
(GHC.Prim.narrow8Word#
(GHC.Prim.plusWord# ipv5_s256 (__word 1)))
(__word 255))))
原始操作
narrow8Word#用于从 Int 强制到 Word8 .我们可以通过使用 Int 来摆脱这种强制。而不是 Word8在 next 的定义中.next :: Permutation -> Int -> Int
next (Permutation !v) !idx'
= fromIntegral $ v `V.unsafeIndex` (fromIntegral idx' .&. 0xFF)
这将程序的执行时间减少到 0.54 秒。仅考虑在
perlin3 中花费的时间，执行时间(大约)从 0.12 秒下降到 0.06 秒。尽管很难衡量剩余时间的去向，但它很可能分散在剩余的算术和数组访问中。
关于haskell - 在 Haskell 中优化 Perlin 噪声，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/15572277/