content: -- |
  -- 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
      (
      -- * IEE754 constants
        m_epsilon
      , m_huge
      , m_tiny
      , m_max_exp
      , m_pos_inf
      , m_neg_inf
      , m_NaN
      , m_max_log
      , m_min_log
      -- * Mathematical constants
      , m_1_sqrt_2
      , m_2_sqrt_pi
      , m_ln_sqrt_2_pi
      , m_sqrt_2
      , m_sqrt_2_pi
      , m_eulerMascheroni
      ) where
  
  ----------------------------------------------------------------
  -- IEE754 constants
  ----------------------------------------------------------------
  
  -- | Largest representable finite value.
  m_huge :: Double
  m_huge = 1.7976931348623157e308
  {-# INLINE m_huge #-}
  
  -- | The smallest representable positive normalized value.
  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
  
  -- | 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 #-}
  
  -- | Maximum possible finite value of @log x@
  m_max_log :: Double
  m_max_log = 709.782712893384
  {-# INLINE m_max_log #-}
  
  -- | Logarithm of smallest normalized double ('m_tiny')
  m_min_log :: Double
  m_min_log = -708.3964185322641
  {-# INLINE m_min_log #-}
  
  
  ----------------------------------------------------------------
  -- Mathematical 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 #-}
  
  -- | @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' &#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 #-}
  
  -- | Euler–Mascheroni constant (γ = 0.57721...)
  m_eulerMascheroni :: Double
  m_eulerMascheroni = 0.5772156649015328606065121
  {-# INLINE m_eulerMascheroni #-}
  