math-functions 0.1.0.0 → 0.1.1.0

raw patch · 5 files changed

+182/−42 lines, 5 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• Numeric/MathFunctions/Constants.hs +85/−0
• Numeric/Polynomial/Chebyshev.hs +10/−0
• Numeric/SpecFunctions.hs +51/−41
• Numeric/SpecFunctions/Extra.hs +33/−0
• math-functions.cabal +3/−1

@@ -0,0 +1,85 @@+-- |+-- Module    : Numeric.MathFunctions.Constants+-- Copyright : (c) 2009, 2011 Bryan O'Sullivan+-- License   : BSD3+--+-- Maintainer  : bos@serpentine.com+-- Stability   : experimental+-- Portability : portable+--+-- Constant values common to much numeric code.++module Numeric.MathFunctions.Constants+    (+      m_epsilon+    , m_huge+    , m_tiny+    , m_1_sqrt_2+    , m_2_sqrt_pi+    , m_ln_sqrt_2_pi+    , m_max_exp+    , m_sqrt_2+    , m_sqrt_2_pi+    , m_pos_inf+    , m_neg_inf+    , m_NaN+    ) where++-- | A very large number.+m_huge :: Double+m_huge = 1.7976931348623157e308+{-# INLINE m_huge #-}++m_tiny :: Double+m_tiny = 2.2250738585072014e-308+{-# INLINE m_tiny #-}++-- | The largest 'Int' /x/ such that 2**(/x/-1) is approximately+-- representable as a 'Double'.+m_max_exp :: Int+m_max_exp = 1024++-- | @sqrt 2@+m_sqrt_2 :: Double+m_sqrt_2 = 1.4142135623730950488016887242096980785696718753769480731766+{-# INLINE m_sqrt_2 #-}++-- | @sqrt (2 * pi)@+m_sqrt_2_pi :: Double+m_sqrt_2_pi = 2.5066282746310005024157652848110452530069867406099383166299+{-# INLINE m_sqrt_2_pi #-}++-- | @2 / sqrt pi@+m_2_sqrt_pi :: Double+m_2_sqrt_pi = 1.1283791670955125738961589031215451716881012586579977136881+{-# INLINE m_2_sqrt_pi #-}++-- | @1 / sqrt 2@+m_1_sqrt_2 :: Double+m_1_sqrt_2 = 0.7071067811865475244008443621048490392848359376884740365883+{-# INLINE m_1_sqrt_2 #-}++-- | The smallest 'Double' ε such that 1 + ε ≠ 1.+m_epsilon :: Double+m_epsilon = encodeFloat (signif+1) expo - 1.0+    where (signif,expo) = decodeFloat (1.0::Double)++-- | @log(sqrt((2*pi))@+m_ln_sqrt_2_pi :: Double+m_ln_sqrt_2_pi = 0.9189385332046727417803297364056176398613974736377834128171+{-# INLINE m_ln_sqrt_2_pi #-}++-- | Positive infinity.+m_pos_inf :: Double+m_pos_inf = 1/0+{-# INLINE m_pos_inf #-}++-- | Negative infinity.+m_neg_inf :: Double+m_neg_inf = -1/0+{-# INLINE m_neg_inf #-}++-- | Not a number.+m_NaN :: Double+m_NaN = 0/0+{-# INLINE m_NaN #-}

@@ -1,4 +1,14 @@ {-# LANGUAGE FlexibleContexts #-}+-- |+-- Module    : Numeric.Polynomial.Chebyshev+-- Copyright : (c) 2009, 2011 Bryan O'Sullivan+-- License   : BSD3+--+-- Maintainer  : bos@serpentine.com+-- Stability   : experimental+-- Portability : portable+--+-- Chebyshev polynomials. module Numeric.Polynomial.Chebyshev (     -- * Chebyshev polinomials     -- $chebyshev

@@ -1,4 +1,14 @@ {-# LANGUAGE BangPatterns #-}+-- |+-- Module    : Numeric.SpecFunctions+-- Copyright : (c) 2009, 2011 Bryan O'Sullivan+-- License   : BSD3+--+-- Maintainer  : bos@serpentine.com+-- Stability   : experimental+-- Portability : portable+--+-- Special functions and factorials. module Numeric.SpecFunctions (     -- * Gamma function     logGamma@@ -16,6 +26,7 @@     -- * Factorial   , factorial   , logFactorial+  , stirlingError     -- * Combinatorics   , choose     -- * References@@ -28,7 +39,9 @@ import Data.Number.Erf (erfc) import qualified Data.Vector.Unboxed as U -import Numeric.Polynomial.Chebyshev  (chebyshevBroucke)+import Numeric.Polynomial.Chebyshev    (chebyshevBroucke)+import Numeric.MathFunctions.Constants (m_epsilon, m_sqrt_2_pi, m_ln_sqrt_2_pi, +                                        m_NaN, m_neg_inf, m_pos_inf, m_sqrt_2)   @@ -470,6 +483,43 @@           z = ((-(5.95238095238e-4 * y) + 7.936500793651e-4) * y -                2.7777777777778e-3) * y + 8.3333333333333e-2 +-- | Calculate the error term of the Stirling approximation.  This is+-- only defined for non-negative values.+--+-- > stirlingError @n@ = @log(n!) - log(sqrt(2*pi*n)*(n/e)^n)+stirlingError :: Double -> Double+stirlingError n+  | n <= 15.0   = case properFraction (n+n) of+                    (i,0) -> sfe `U.unsafeIndex` i+                    _     -> logGamma (n+1.0) - (n+0.5) * log n + n -+                             m_ln_sqrt_2_pi+  | n > 500     = (s0-s1/nn)/n+  | n > 80      = (s0-(s1-s2/nn)/nn)/n+  | n > 35      = (s0-(s1-(s2-s3/nn)/nn)/nn)/n+  | otherwise   = (s0-(s1-(s2-(s3-s4/nn)/nn)/nn)/nn)/n+  where+    nn = n*n+    s0 = 0.083333333333333333333        -- 1/12+    s1 = 0.00277777777777777777778      -- 1/360+    s2 = 0.00079365079365079365079365   -- 1/1260+    s3 = 0.000595238095238095238095238  -- 1/1680+    s4 = 0.0008417508417508417508417508 -- 1/1188+    sfe = U.fromList [ 0.0,+                0.1534264097200273452913848,   0.0810614667953272582196702,+                0.0548141210519176538961390,   0.0413406959554092940938221,+                0.03316287351993628748511048,  0.02767792568499833914878929,+                0.02374616365629749597132920,  0.02079067210376509311152277,+                0.01848845053267318523077934,  0.01664469118982119216319487,+                0.01513497322191737887351255,  0.01387612882307074799874573,+                0.01281046524292022692424986,  0.01189670994589177009505572,+                0.01110455975820691732662991,  0.010411265261972096497478567,+                0.009799416126158803298389475, 0.009255462182712732917728637,+                0.008768700134139385462952823, 0.008330563433362871256469318,+                0.007934114564314020547248100, 0.007573675487951840794972024,+                0.007244554301320383179543912, 0.006942840107209529865664152,+                0.006665247032707682442354394, 0.006408994188004207068439631,+                0.006171712263039457647532867, 0.005951370112758847735624416,+                0.005746216513010115682023589, 0.005554733551962801371038690 ]   ----------------------------------------------------------------@@ -507,46 +557,6 @@     max64          = fromIntegral (maxBound :: Int64)     round64 x      = round x :: Int64 --------------------------------------------------------------------- Constants--------------------------------------------------------------------- | @sqrt 2@-m_sqrt_2 :: Double-m_sqrt_2 = 1.4142135623730950488016887242096980785696718753769480731766-{-# INLINE m_sqrt_2 #-}---- | @sqrt (2 * pi)@-m_sqrt_2_pi :: Double-m_sqrt_2_pi = 2.5066282746310005024157652848110452530069867406099383166299-{-# INLINE m_sqrt_2_pi #-}----- | The smallest 'Double' &#949; such that 1 + &#949; &#8800; 1.-m_epsilon :: Double-m_epsilon = encodeFloat (signif+1) expo - 1.0-    where (signif,expo) = decodeFloat (1.0::Double)---- | @log(sqrt((2*pi))@-m_ln_sqrt_2_pi :: Double-m_ln_sqrt_2_pi = 0.9189385332046727417803297364056176398613974736377834128171-{-# INLINE m_ln_sqrt_2_pi #-}---- | Positive infinity.-m_pos_inf :: Double-m_pos_inf = 1/0-{-# INLINE m_pos_inf #-}---- | Negative infinity.-m_neg_inf :: Double-m_neg_inf = -1/0-{-# INLINE m_neg_inf #-}---- | Not a number.-m_NaN :: Double-m_NaN = 0/0-{-# INLINE m_NaN #-}   

@@ -0,0 +1,33 @@+-- |+-- Module    : Numeric.SpecFunctions.Extra+-- Copyright : (c) 2009, 2011 Bryan O'Sullivan+-- License   : BSD3+--+-- Maintainer  : bos@serpentine.com+-- Stability   : experimental+-- Portability : portable+--+-- Less common mathematical functions.+module Numeric.SpecFunctions.Extra (+  bd0+  ) where++import Numeric.MathFunctions.Constants (m_NaN)++-- | Evaluate the deviance term @x log(x/np) + np - x@.+bd0 :: Double                   -- ^ @x@+    -> Double                   -- ^ @np@+    -> Double +bd0 x np +  | isInfinite x || isInfinite np || np == 0 = m_NaN+  | abs x_np >= 0.1*(x+np)                   = x * log (x/np) - x_np+  | otherwise                                = loop 1 (ej0*vv) s0+  where +    x_np = x - np+    v    = x_np / (x+np)+    s0   = x_np * v+    ej0  = 2*x*v+    vv   = v*v+    loop j ej s = case s + ej/(2*j+1) of+                    s' | s' == s   -> s'  -- FIXME: Comparing Doubles for equality!+                       | otherwise -> loop (j+1) (ej*vv) s'

@@ -1,5 +1,5 @@ name:           math-functions-version:        0.1.0.0+version:        0.1.1.0 cabal-version:  >= 1.8 license:        BSD3 license-file:   LICENSE@@ -24,7 +24,9 @@                         erf >= 2   exposed-modules:           Numeric.SpecFunctions+    Numeric.SpecFunctions.Extra     Numeric.Polynomial.Chebyshev+    Numeric.MathFunctions.Constants  test-suite tests   type:           exitcode-stdio-1.0