diff --git a/CHANGELOG.md b/CHANGELOG.md --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,6 +1,12 @@ Changes ======= +Version 0.1.5.0 +---------------- + +Convenient combinators for linear forms and constraints. +New experimental functions in Math.ExpPairs.Kratzel: tauabcd and tauA for general multidimensional divisor problems. + Version 0.1.4.0 ---------------- diff --git a/Math/ExpPairs.hs b/Math/ExpPairs.hs --- a/Math/ExpPairs.hs +++ b/Math/ExpPairs.hs @@ -14,7 +14,9 @@ A set of useful applications can be found in "Math.ExpPairs.Ivic", "Math.ExpPairs.Kratzel" and "Math.ExpPairs.MenzerNowak". -} -{-# LANGUAGE CPP #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE PatternSynonyms #-} +{-# LANGUAGE TemplateHaskell #-} module Math.ExpPairs ( optimize @@ -24,14 +26,19 @@ , optimalPath , simulateOptimize , simulateOptimize' - , LinearForm (..) + , LinearForm , RationalForm (..) - , IneqType (..) - , Constraint (..) + , IneqType + , Constraint , InitPair , Path , RatioInf (..) , RationalInf + , pattern K + , pattern L + , pattern M + , (>.), (>=.), (<.), (<=.) + , scaleLF ) where import Control.Arrow hiding ((<+>)) @@ -39,18 +46,47 @@ import Data.Ord (comparing) import Data.List (minimumBy) import Data.Monoid +import Data.Ratio import Text.PrettyPrint.Leijen hiding ((<$>), (<>)) import qualified Text.PrettyPrint.Leijen as PP import Text.Printf +import Data.Function.Memoize (deriveMemoizable) import Math.ExpPairs.LinearForm import Math.ExpPairs.Process import Math.ExpPairs.Pair import Math.ExpPairs.RatioInf +-- | For a given @c@ returns linear form @c * k@ +pattern K n = LinearForm n 0 0 +-- | For a given @c@ returns linear form @c * l@ +pattern L n = LinearForm 0 n 0 +-- | For a given @c@ returns linear form @c * m@ +pattern M n = LinearForm 0 0 n + +-- | Build a constraint, which states that the value of the first linear form is greater than the value of the second one. +(>.) :: Num t => LinearForm t -> LinearForm t -> Constraint t +lf1 >. lf2 = Constraint (lf1 - lf2) Strict +infix 5 >. + +-- | Build a constraint, which states that the value of the first linear form is greater or equal to the value of the second one. +(>=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t +lf1 >=. lf2 = Constraint (lf1 - lf2) NonStrict +infix 5 >=. + +-- | Build a constraint, which states that the value of the first linear form is less than the value of the second one. +(<.) :: Num t => LinearForm t -> LinearForm t -> Constraint t +lf1 <. lf2 = Constraint (lf2 - lf1) Strict +infix 5 <. + +-- | Build a constraint, which states that the value of the first linear form is less or equal to the value of the second one. +(<=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t +lf1 <=. lf2 = Constraint (lf2 - lf1) NonStrict +infix 5 <=. + evalFunctional :: [InitPair] -> [InitPair] -> [RationalForm Rational] -> [Constraint Rational] -> Path -> (RationalInf, InitPair) evalFunctional corners interiors rfs cons path = case rs of - [] -> (InfPlus, undefined) + [] -> (InfPlus, error "evalFunctional: cannot find any exponential pair, which satisfies constraints") _ -> minimumBy (comparing fst) rs where applyPath = map (evalPath path . initPairToProjValue &&& id) @@ -58,9 +94,10 @@ interiors' = applyPath interiors predicate (p, _) = all (checkConstraint p) cons - qs = if all predicate corners' - then corners' - else filter predicate interiors' + qs + | all predicate corners' = corners' + | any predicate corners' = filter predicate interiors' + | otherwise = [] rs = map (first $ \p -> maximum (map (evalRF p) rfs)) qs @@ -80,11 +117,18 @@ } deriving (Show) +deriveMemoizable ''OptimizeResult + instance Pretty OptimizeResult where - pretty (OptimizeResult r' ip p) = pretty' r' PP.<$> pretty ip pretty p where - pretty' r@(Finite rr) = text (printf "%.6f" (fromRational rr :: Double)) <+> equals <+> pretty r - pretty' r = pretty r + pretty (OptimizeResult r' ip p) = pretty1 r' PP.<$> + (parens (pretty (k%m) PP.<> comma PP.<> pretty (l%m)) <+> equals <+> pretty p pretty ip) + where + pretty1 r@(Finite rr) = text (printf "%.6f" (fromRational rr :: Double)) <+> equals <+> pretty r + pretty1 r = pretty r + (k, l, m) = evalPath p $ initPairToProjValue ip + + instance Eq OptimizeResult where (==) = (==) `on` optimalValue @@ -127,5 +171,5 @@ pathba = path <> baPath branchB@(OptimizeResult r2' _ _) = optimize' rfs cons (OptimizeResult r1 ip1 pathba) - consBuilder rr (RationalForm num den) = Constraint (substituteLF (num, den, 1) (LinearForm (-1) (toRational rr) 0)) Strict + consBuilder rr (num :/: den) = (substituteLF (num, den, 1) (L (toRational rr) - K 1)) >. 0 diff --git a/Math/ExpPairs/Ivic.hs b/Math/ExpPairs/Ivic.hs --- a/Math/ExpPairs/Ivic.hs +++ b/Math/ExpPairs/Ivic.hs @@ -21,6 +21,7 @@ , findMinAbscissa , mBigOnHalf , reverseMBigOnHalf + , kolpakova2011 ) where import Data.Ratio @@ -35,8 +36,8 @@ zetaOnS s | s >= 1 = simulateOptimize 0 | s >= 1%2 = optimize - [RationalForm (LinearForm 1 1 (-s)) 2] - [Constraint (LinearForm (-1) 1 (-s)) NonStrict] + [K 1 + L 1 - M s :/: 2] + [L 1 >=. K 1 + M s] | otherwise = optRes {optimalValue = r} where optRes = zetaOnS (1-s) r = Finite (1%2 - s) + optimalValue optRes @@ -48,10 +49,10 @@ reverseZetaOnS :: Rational -> OptimizeResult reverseZetaOnS mu | mu >= 1%2 = simulateOptimize 0 - | mu > zetaOnHalf = optimize [RationalForm (LinearForm 1 (-1) 1) 1] [Constraint (LinearForm 0 (-2) (1+2*mu)) NonStrict] + | mu > zetaOnHalf = optimize [K 1 - L 1 + M 1 :/: 1] [M (1 + 2 * mu) >=. L 2] | mu == zetaOnHalf = simulateOptimize (1 % 2) | otherwise = optRes {optimalValue = negate $ optimalValue optRes} where - optRes = optimize [RationalForm (LinearForm 1 (-1) 0) 1] [Constraint (LinearForm 1 0 (-mu)) NonStrict, Constraint (LinearForm (-1) 1 (-1%2)) NonStrict] + optRes = optimize [K 1 - L 1 :/: 1] [K 1 >=. M mu, L 2 >=. K 2 + 1] lemma82_f :: Rational -> Rational lemma82_f s @@ -77,42 +78,58 @@ beta1 = -12/(1+2*s) x1 = optRes {optimalValue = Finite $ (1-alpha1)/muS - beta1} - --alpha2 = 4*(1-s)*(k+l)/((2*m+4*l)*s-m+2*k-2*l) - --beta2 = -4*(m+2*k+2*l)/((2*m+4*l)*s-m+2*k-2*l) - --ratio = (1-alpha2)/muS - beta2 - --numer = numerator ratio - --denom = denominator ratio - numer = LinearForm - (-4*s + (-8*muS + 2)) - (-8*s + (-8*muS + 6)) - (-2*s + (-4*muS + 1)) - denom = LinearForm - (2*muS) - (4*muS*s - 2*muS) - (2*muS*s - muS) + -- alpha2 = 4*(1-s)*(k+l)/((2*m+4*l)*s-m+2*k-2*l) + -- beta2 = -4*(m+2*k+2*l)/((2*m+4*l)*s-m+2*k-2*l) + -- numer % denom = (1-alpha2)/muS - beta2 + t = scaleLF s (L 4 + 2) - 1 + K 2 - L 2 + numer = t - scaleLF (4 * (1-s)) (K 1 + L 1) + scaleLF (4 * muS) (K 2 + L 2 + 1) + denom = scaleLF muS t - cons = if s >= 2%3 then [] else [Constraint - (LinearForm (4*s-2) (8*s-6) (2*s-1)) NonStrict - ] + cons = if s >= 2%3 then [] else [scaleLF s (K 4 + L 8 + 2) >=. K 2 + L 6 + 1] - x2' = optimize [RationalForm numer denom] cons + x2' = optimize [- numer :/: denom] cons x2 = x2' {optimalValue = negate $ optimalValue x2'} +data Choice = Least | Median | Greatest + +binarySearch :: (Rational -> Bool) -> Choice -> Rational -> Rational -> Rational -> Rational +binarySearch predicate choice precision = go + where + go a b + | b - a < precision = case choice of + Least -> a + Median -> c + Greatest -> b + | predicate c = go a c + | otherwise = go c b + where + c = (numerator a + numerator b) % (denominator a + denominator b) + +mOnSTwoThird :: RationalInf +mOnSTwoThird = optimalValue $ mOnS $ 2 % 3 + -- | Try to reverse 'mOnS': for a given precision and m compute minimal possible σ. -- Implementation is usual try-and-divide search, so performance is very poor. -- Sometimes, when 'mOnS' gets especially lucky exponent pair, 'reverseMOnS' can miss --- real σ and returns bigger value. +-- real σ and returns significantly bigger value. +-- +-- For integer m>=4 this function corresponds to the multidimensional Dirichlet problem +-- and returns σ from error term O(x^{σ+ε}). See Ch. 13 in Ivić2003. reverseMOnS :: Rational -> RationalInf -> Rational -reverseMOnS prec m = reverseMOnS' from to where - from = 1 % 2 - to = 1 - reverseMOnS' a b - | b - a < prec = c - | optimalValue (mOnS c) > m = reverseMOnS' a c - | otherwise = reverseMOnS' c b - where - c = (numerator a + numerator b) % (denominator a + denominator b) +reverseMOnS _ InfPlus = 1 +reverseMOnS _ (Finite m) + | m <= 4 = 1 % 2 + | m <= 8 = 3 % 4 - recip m +reverseMOnS prec m + | m < mOnSTwoThird = go (5 % 8) (2 % 3) + | otherwise = go (2 % 3) 1 + where + go = binarySearch (\c -> optimalValue (mOnS c) > m) Greatest prec +-- | An estimate of the symmetric multidimensional divisor function from Kolpakova, 2011. +kolpakova2011 :: Integer -> Double +kolpakova2011 k = 1 - 1/3 * 2**(2/3) * (4.45 * fromInteger k)**(-2/3) + -- | Check whether ∫_1^T Π_i |ζ(n_i*σ+it)|^m_i dt ≪ T^(1+ε) for a given list of pairs [(n_1, m_1), ...] and fixed σ. checkAbscissa :: [(Rational, Rational)] -> Rational -> Bool checkAbscissa xs s = sum rs < Finite 1 where @@ -122,15 +139,7 @@ -- | Find for a given precision and list of pairs [(n_1, m_1), ...] the minimal σ -- such that ∫_1^T Π_i|ζ(n_i*σ+it)|^m_i dt ≪ T^(1+ε). findMinAbscissa :: Rational -> [(Rational, Rational)] -> Rational -findMinAbscissa prec xs = searchMinAbscissa' from to where - from = 1 % 2 / minimum (map fst xs) - to = 1 % 1 - searchMinAbscissa' a b - | b - a < prec = b - | checkAbscissa xs c = searchMinAbscissa' a c - | otherwise = searchMinAbscissa' c b - where - c = (numerator a + numerator b) % (denominator a + denominator b) +findMinAbscissa prec xs = binarySearch (checkAbscissa xs) Greatest prec (1 % 2 / minimum (map fst xs)) 1 -- | Compute minimal M(A) such that ∫_1^T |ζ(1/2+it)|^A dt ≪ T^(M(A)+ε). -- See Ch. 8 in Ivić2003. Further justification will be published elsewhere. @@ -138,16 +147,16 @@ mBigOnHalf a | a < 4 = simulateOptimize 1 | a < 12 = simulateOptimize $ 1+(a-4)/8 - | a > 41614060315296730740083860226662 % 2636743270445733804969041895717 = simulateOptimize $ 1 + 32*(a-6)/205 + | a > 41614060315296730740083860226662 % 2636743270445733804969041895717 = simulateOptimize $ 1 + (a - 6) * zetaOnHalf | otherwise = if Finite x >= optimalValue optRes then simulateOptimize x else optRes where - optRes = optimize [RationalForm (LinearForm 1 1 0) (LinearForm 1 0 0)] - [Constraint (LinearForm (4-a) 4 2) NonStrict] + optRes = optimize [K 1 + L 1 :/: K 1] + [K (4 - a) + L 4 + 2 >=. 0] x = 1 + 32*(a-6)/205 -- Constant 41614060315296730740083860226662 % 2636743270445733804969041895717 -- is produced by --- optimize [RationalForm (LinearForm 4 4 2) (LinearForm 1 0 0)] [Constraint (LinearForm (-64) (-77) 64) Strict] +-- optimize [K 4 + L 4 + 2 :/: K 1] [64 >. K 64 + L 77] -- | Try to reverse 'mBigOnHalf': for a given M(A) find maximal possible A. -- Sometimes, when 'mBigOnHalf' gets especially lucky exponent pair, 'reverseMBigOnHalf' can miss @@ -158,7 +167,5 @@ | otherwise = if Finite a <= optimalValue optRes then simulateOptimize a else optRes where - a = (m-1)*205/32 + 6 - optRes = optimize [RationalForm (LinearForm 4 4 2) (LinearForm 1 0 0)] [Constraint (LinearForm (1-m) 1 0) NonStrict] - - + a = (m - 1) / zetaOnHalf + 6 + optRes = optimize [K 4 + L 4 + 2 :/: K 1] [K (1 - m) + L 1 >=. 0] diff --git a/Math/ExpPairs/Kratzel.hs b/Math/ExpPairs/Kratzel.hs --- a/Math/ExpPairs/Kratzel.hs +++ b/Math/ExpPairs/Kratzel.hs @@ -24,20 +24,32 @@ He also provided a set of theorems to estimate Θ(a, b) and Θ(a, b, c). -} + +{-# LANGUAGE TemplateHaskell #-} + module Math.ExpPairs.Kratzel ( TauabTheorem (..) , tauab , TauabcTheorem (..) , tauabc + , TauabcdTheorem (..) + , tauabcd + , Theorem (..) + , TauAResult (..) + , tauA ) where -import Control.Arrow -import Data.Ratio ((%)) +import Control.Arrow hiding ((<+>)) +import Data.Function +import Data.Maybe +import Data.Ratio import Data.Ord (comparing) -import Data.List (minimumBy) +import Data.List (minimumBy, sort) import Text.PrettyPrint.Leijen +import Data.Function.Memoize (memoize, deriveMemoizable) import Math.ExpPairs +import Math.ExpPairs.Ivic -- |Special type to specify the theorem of Krätzel1988, -- which provided the best estimate of Θ(a, b) @@ -58,32 +70,36 @@ divideResult :: Real a => a -> (b, OptimizeResult) -> (b, OptimizeResult) divideResult d = second (\o -> o {optimalValue = optimalValue o / Finite (toRational d)}) +tauab' :: Rational -> Rational -> (TauabTheorem, OptimizeResult) +tauab' a b = minimumBy (comparing snd) [kr511a, kr511b, kr512a, kr512b] + where + kr511a = (Kr511a, optimize + [K 2 + L 2 - 1 :/: M (a+b)] + [L (2 * a) >=. K (2 * b) + M a]) + kr511b = (Kr511b, optimize + [K 1 :/: K b - L a + M a] + [K (2 * b) + M a >. L (2 * a)]) + kr512a = (Kr512a, simulateOptimize r) + where + r = if 11*a >= 8*b then 19/29/(a+b) else 1%1 + kr512b = if 11*a >= 8*b then kr512a else (Kr512b, optimize + [L 8 - K 11 - 4 :/: L (29 * a) - K (29 * b) + M (4*b-20*a)] + [ L (2 * a) >=. K (2 * b) + M a + , 4 >. K 29 + , K 29 + L 29 >. 24 + ]) + -- |Compute Θ(a, b) for given a and b. tauab :: Integer -> Integer -> (TauabTheorem, OptimizeResult) -tauab a' b' - | d /= 1 = divideResult d $ tauab (a'`div` d) (b' `div` d) where - d = gcd a' b' -tauab a' b' = minimumBy (comparing (optimalValue . snd)) [kr511a, kr511b, kr512a, kr512b] where - a = toRational a' - b = toRational b' - kr511a = (Kr511a, optimize - [RationalForm (LinearForm 2 2 (-1)) (LinearForm 0 0 (a+b))] - [Constraint (LinearForm (-2*b) (2*a) (-a)) NonStrict]) - kr511b = (Kr511b, optimize - [RationalForm (LinearForm 1 0 0) (LinearForm b (-a) a)] - [Constraint (LinearForm (2*b) (-2*a) a) Strict]) - kr512a = (Kr512a, simulateOptimize r) where - r = if 11*a >= 8*b then 19/29/(a+b) else 1%1 - kr512b = if 11*a >= 8*b then kr512a else (Kr512b, optimize - [ - RationalForm (LinearForm (-11) 8 (-4)) (LinearForm (-29*b) (29*a) (4*b-20*a)) - ] - [ - Constraint (LinearForm (-2*b) (2*a) (-a)) NonStrict, - Constraint (LinearForm (-29) 0 4) Strict, - Constraint (LinearForm 29 29 (-24)) Strict - ]) +tauab a b + | d /= 1 = divideResult d $ tauab (a `div` d) (b `div` d) + where + d = a `gcd` b +tauab a b = tauab' a' b' + where + [a', b'] = sort $ map toRational [a, b] + -- |Special type to specify the theorem of Krätzel1988, -- which provided the best estimate of Θ(a, b, c) data TauabcTheorem @@ -113,35 +129,224 @@ pretty (Tauab t) = pretty t pretty t = pretty (show t) +tauabc' :: Rational -> Rational -> Rational -> (TauabcTheorem, OptimizeResult) +tauabc' a b c = minimumBy (comparing snd) [kr61, kr62, kr63, kr64, kr65, kr66] + where + abc = a + b + c + kr61 + | c=. K (b + c) + , M (a + b + c) >=. K (2 * c) + L (2 * c) + ]) + kr63 = (Kr63, optimize + [K 4 + L 2 + 3 :/: K (2 * abc) + M (3 * abc)] + [scaleLF (2 * a) (K 1 + L 1 + 1) >=. scaleLF (b + c) (K 2 + 1)]) + kr64 = (Kr64, simulateOptimize r) where + r = recip abc * minimum (abc:[2-4*(k-1)%(3*2^k-4) | k<-[1..maxk], (3*2^k-2*k-4)%1 * a >= 2 * (b+c), (3*2^k-8)%1 * (a+b) >= (3*2^k-4*k+4)%1 * c]) + maxk = 4 `max` floor (logBase 2 (fromRational $ b+c) :: Double) + kr65 = (Kr65, simulateOptimize r) where + r = if 7*a>=2*(b+c) && 4*(a+b)>=5*c then 3%2/abc else 1%1 + kr66 = (Kr66, simulateOptimize r) where + r = if 18*a>=7*(b+c) && 2*(a+b)>=3*c then 25%17/abc else 1%1 + -- |Compute Θ(a, b, c) for given a, b and c. tauabc :: Integer -> Integer -> Integer -> (TauabcTheorem, OptimizeResult) -tauabc a' b' c' - | d /= 1 = divideResult d $ tauabc (a'`div` d) (b' `div` d) (c' `div` d) where - d = gcd (gcd a' b') c' tauabc 1 1 1 = (Kolesnik, simulateOptimize $ 43%96) -tauabc a' b' c' = minimumBy (comparing (optimalValue . snd)) [kr61, kr62, kr63, kr64, kr65, kr66] where - a = toRational a' - b = toRational b' - c = toRational c' - kr61 - | c= 2 * (b+c), (3*2^k-8)%1 * (a+b) >= (3*2^k-4*k+4)%1 * c]) - maxk = 4 `max` floor (logBase 2 (fromRational $ b+c) :: Double) - kr65 = (Kr65, simulateOptimize r) where - r = if 7*a>=2*(b+c) && 4*(a+b)>=5*c then 3%2/(a+b+c) else 1%1 - kr66 = (Kr66, simulateOptimize r) where - r = if 18*a>=7*(b+c) && 2*(a+b)>=3*c then 25%17/(a+b+c) else 1%1 + d = a `gcd` b `gcd` c +tauabc a b c = tauabc' a' b' c' + where + [a', b', c'] = sort $ map toRational [a, b, c] + + +-- |Special type to specify the theorem of Krätzel1988, +-- which provided the best estimate of Θ(a, b, c, d) +data TauabcdTheorem + = HeathBrown + | Tauabc TauabcTheorem + | Kr611 + | Kr1992_2 + | Kr1992_31 + | Kr1992_32 + | Kr2010_1a + | Kr2010_1b + | Kr2010_2 + | Kr2010_3 + | CaoZhai + deriving (Eq, Ord, Show) + +instance Pretty TauabcdTheorem where + pretty (Tauabc t) = pretty t + pretty t = pretty (show t) + +tauabcd' :: Rational -> Rational -> Rational -> Rational -> (TauabcdTheorem, OptimizeResult) +tauabcd' a1 a2 a3 a4 = minimumBy (comparing snd) [kr611, kr1992_2, kr1992_31, kr1992_32, kr2010_1a, kr2010_1b, kr2010_2, kr2010_3] + where + a12 = a1 + a2 + a123 = a1 + a2 + a3 + a1234 = a1 + a2 + a3 + a4 + + kr611 + | optimalValue optRes3 < Finite (recip a4) = (Kr611, optimize [form] cons) + | otherwise = (Tauabc th3, optRes3) + where + (th3, optRes3) = tauabc' a1 a2 a3 + form = K 2 + L 2 + 1 :/: M (a1 + a2 + a3 + a4) -- (6.46) + cons = + [ scaleLF a1 (L 2 - 1) >. K (2 * a4) -- (6.41) + , scaleLF a3 (scaleLF a2 (K 2 + L 2) + M a4) <. M ((a1 + a2) * (a2 + a4)) -- (6.42) + , scaleLF a1 (K 2 + L 2 + 1) >=. M (a2 + a3) + , M (a1 + a2) >=. scaleLF a3 (K 2 + L 2 - 1) + ] + + kr1992_2 = (Kr1992_2, optimize [form] cons) + where + form = K 3 + L 1 + 4 :/: scaleLF a1234 (K 1 + 2) + cons = + [ scaleLF a4 (K 6 + L 2 + 8) <. scaleLF a1234 (K 2 + 4) + , scaleLF a1234 (K 2 + 2) <=. scaleLF a1 (K 6 + L 2 + 8) + ] + + kr1992_31 = (Kr1992_31, optimize [form] cons1) + where + form = K 1 + L 1 + 2 :/: K a1 + L a1 + M a1234 + cons0 = + [ scaleLF a4 (K 1 + L 1 + 2) <. K a1 + L a1 + M a1234 + , scaleLF a1 (K 2 + L 2 + 2) <=. scaleLF (a2 + a3) (K 2 + 1) + ] + cons1 = cons0 ++ + [ L a1 <=. K a2 + , scaleLF a1 (K 1 + L 1 + 1) >=. K (a2 + a3) + ] + + kr1992_32 = (Kr1992_32, simulateOptimize $ if cond then val else 1) + where + k = 32 % 205 + l = k + 1 % 2 + val = (k + l + 2) / ((k + l) * a1 + a1234) + cond = (k + l - 2) * a4 < (k + l) * a1 + a1234 + && 2 * (k + l + 1) * a1 <= (2 * k + l) * (a2 + a3) + && l * a1 >= k * a2 + && (l - k) * (2 * k + 1) * a3 <= (2 * l - 2 * k - 1) * (k + l + 1) * a1 + (2 * k * (k - l + 1) + 1) * a2 + + kr2010_1a = (Kr2010_1a, simulateOptimize $ if cond then val else 1) + where + val = 45 % 19 / a1234 + cond = 5 * a1 >= a1234 && 9 * a123 >= 34 * a1 && 9 * a12 >= 20 * a1 + + kr2010_1b = (Kr2010_1b, simulateOptimize $ if cond then val else 1) + where + val = 45 / (15 * a1 + 16 * a1234) + cond = 5 * a1 <= a1234 && a1234 <= 15%2 * a1 && 2 * a123 >= 9 * a1 && 2 * a12 >= 5 * a1 + + kr2010_2 = (Kr2010_2, simulateOptimize $ if cond then val else 1) + where + val = 35 / (11 * a4 + 16 * a123) + cond = 2 * a123 >= 3 * a4 && 34 * a1 >= 9 * a123 && 7 * a12 >= 10 * a3 + + kr2010_3 = (Kr2010_3, simulateOptimize $ if cond then val else 1) + where + val = 235 / (406 * a1 + 81 * a4) + cond = a1 == a2 && 2 * a1 == a3 && 29 * a1 >= 11 * a4 + + +-- |Compute Θ(a, b, c, d) for given a, b, c and d. +tauabcd :: Integer -> Integer -> Integer -> Integer -> (TauabcdTheorem, OptimizeResult) +tauabcd 1 1 1 1 = (HeathBrown, simulateOptimize $ 1%2) +tauabcd a1 a2 a3 a4 + | d /= 1 = divideResult d $ tauabcd (a1 `div` d) (a2 `div` d) (a3 `div` d) (a4 `div` d) + where + d = a1 `gcd` a2 `gcd` a3 `gcd` a4 +tauabcd a1 a2 a3 a4 = tauabcd' a1' a2' a3' a4' + where + [a1', a2', a3', a4'] = sort $ map toRational [a1, a2, a3, a4] + + +-- |Special type to specify the theorem of Krätzel1988, +-- which provided the best estimate of Θ(a1, a2...) +data Theorem + = NoTheorem + | Ivic + | Ab TauabTheorem + | Abc TauabcTheorem + | Abcd TauabcdTheorem + deriving (Eq, Ord, Show) + +instance Pretty Theorem where + pretty NoTheorem = text "" + pretty Ivic = text "Ivic" + pretty (Ab t) = pretty t + pretty (Abc t) = pretty t + pretty (Abcd t) = pretty t + +-- |Special type to specify the theorem of Krätzel1988, +-- which provided the best estimate of Θ(a1, a2...) +data TauAResult + = Node Theorem OptimizeResult + | Combination TauAResult TauAResult Rational + deriving (Show) + +instance Pretty TauAResult where + pretty (Node th o) = pretty th <+> pretty o + pretty (Combination t1 t2 r) = pretty t1 <+> pretty t2 <+> pretty r + + +deriveMemoizable ''Theorem +deriveMemoizable ''TauabTheorem +deriveMemoizable ''TauabcTheorem +deriveMemoizable ''TauabcdTheorem +deriveMemoizable ''TauAResult + +extractValue :: TauAResult -> Rational +extractValue (Node _ o) = toRational $ optimalValue o +extractValue (Combination _ _ r1) = r1 + +instance Eq TauAResult where + (==) = (==) `on` extractValue + +instance Ord TauAResult where + compare = compare `on` extractValue + +-- | Compute Θ(a1, a2...) for given list [a1, a2...]. +tauA :: [Integer] -> TauAResult +tauA = go' . sort + where + fi :: Integer -> Rational + fi = fromIntegral + + go' = memoize go + + go :: [Integer] -> TauAResult + go [] = Node NoTheorem (simulateOptimize 0) + go [_] = Node NoTheorem (simulateOptimize 0) + go [a, b] = (\(t, o) -> Node (Ab t) o) $ tauab a b + go [a, b, c] = (\(t, o) -> Node (Abc t) o) $ tauabc a b c + go as@[a,b,c,d] = (\(t, o) -> Node (Abcd t) o) (tauabcd a b c d) `min` go608 as + go as@(a:_) + | all (== a) as + = Node Ivic $ simulateOptimize $ reverseMOnS 1e-6 (fromIntegral $ length as) / fi a + go as = go608' as + + go608' = memoize go608 + + go608 as = minimum $ mapMaybe f [1 .. length as - 1] + where + f q = if (alphaV `max` betaV) < 1 / fi (last as) + then Just $ Combination alpha beta ret + else Nothing + where + alpha = go' $ take q as + alphaV = extractValue alpha + beta = go' $ drop q as + betaV = extractValue beta + a0 = fi $ head as + aq = fi $ as !! q + ret = (1 - a0 * aq * alphaV * betaV) / (a0 + aq - a0 * aq * (alphaV + betaV)) diff --git a/Math/ExpPairs/LinearForm.hs b/Math/ExpPairs/LinearForm.hs --- a/Math/ExpPairs/LinearForm.hs +++ b/Math/ExpPairs/LinearForm.hs @@ -12,6 +12,7 @@ -} module Math.ExpPairs.LinearForm ( LinearForm (..) + , scaleLF , evalLF , substituteLF , RationalForm (..) @@ -33,7 +34,7 @@ import Math.ExpPairs.RatioInf --- |Define an affine linear form of two variables: a*k + b*l + c*m. +-- |Define an affine linear form of three variables: a*k + b*l + c*m. -- First argument of 'LinearForm' stands for a, second for b -- and third for c. Linear forms form a monoid by addition. data LinearForm t = LinearForm !t !t !t @@ -62,6 +63,7 @@ mempty = 0 mappend = (+) +-- | Multiply a linear form by a given coefficient. scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t scaleLF 0 = const 0 scaleLF s = fmap (* s) @@ -77,26 +79,27 @@ substituteLF (k, l, m) (LinearForm a b c) = scaleLF a k + scaleLF b l + scaleLF c m -- | Define a rational form of two variables, equal to the ratio of two 'LinearForm'. -data RationalForm t = RationalForm (LinearForm t) (LinearForm t) +data RationalForm t = (LinearForm t) :/: (LinearForm t) deriving (Eq, Show, Functor, Foldable, Generic) +infix 5 :/: instance (Num t, Eq t, Pretty t) => Pretty (RationalForm t) where - pretty (RationalForm l1 l2) = parens (pretty l1) parens (pretty l2) + pretty (l1 :/: l2) = parens (pretty l1) parens (pretty l2) instance NFData t => NFData (RationalForm t) where rnf = rnf . toList instance Num t => Num (RationalForm t) where - (+) = error "Addition of RationalForm is undefined" - (*) = error "Multiplication of RationalForm is undefined" - negate (RationalForm a b) = RationalForm (negate a) b - abs = error "Absolute value of RationalForm is undefined" - signum = error "Signum of RationalForm is undefined" - fromInteger n = RationalForm (fromInteger n) 1 + (+) = error "Addition of RationalForm is undefined" + (*) = error "Multiplication of RationalForm is undefined" + negate (a :/: b) = negate a :/: b + abs = error "Absolute value of RationalForm is undefined" + signum = error "Signum of RationalForm is undefined" + fromInteger n = fromInteger n :/: 1 instance Num t => Fractional (RationalForm t) where - fromRational r = RationalForm (fromInteger $ numerator r) (fromInteger $ denominator r) - recip (RationalForm a b) = RationalForm b a + fromRational r = fromInteger (numerator r) :/: fromInteger (denominator r) + recip (a :/: b) = b :/: a mapTriple :: (a -> b) -> (a, a, a) -> (b, b, b) mapTriple f (x, y, z) = (f x, f y, f z) @@ -105,7 +108,7 @@ -- |Evaluate a rational form (a*k + b*l + c*m) \/ (a'*k + b'*l + c'*m) -- for given k, l and m. evalRF :: (Real t, Num t) => (Integer, Integer, Integer) -> RationalForm t -> RationalInf -evalRF (k, l, m) (RationalForm num den) = if denom==0 then InfPlus else Finite (numer / denom) where +evalRF (k, l, m) (num :/: den) = if denom==0 then InfPlus else Finite (numer / denom) where klm = mapTriple fromInteger (k, l, m) numer = toRational $ evalLF klm num denom = toRational $ evalLF klm den diff --git a/Math/ExpPairs/Matrix3.hs b/Math/ExpPairs/Matrix3.hs --- a/Math/ExpPairs/Matrix3.hs +++ b/Math/ExpPairs/Matrix3.hs @@ -1,4 +1,3 @@ -{-# LANGUAGE RecordWildCards, DeriveFunctor, DeriveFoldable, DeriveGeneric #-} {-| Module : Math.ExpPairs.Matrix3 Description : Implements matrices of order 3 @@ -11,6 +10,13 @@ Provides types and functions for matrices and vectors of order 3. Can be used instead of "Data.Matrix" to reduce overhead and simplify code. -} + +{-# LANGUAGE DeriveFunctor #-} +{-# LANGUAGE DeriveFoldable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE RecordWildCards #-} +{-# LANGUAGE TemplateHaskell #-} + module Math.ExpPairs.Matrix3 ( Matrix3 (..) , fromList @@ -29,6 +35,7 @@ import Data.List (transpose) import GHC.Generics (Generic (..)) import Text.PrettyPrint.Leijen +import Data.Function.Memoize (deriveMemoizable) -- |Matrix of order 3. Instances of 'Num' and 'Fractional' -- are given in terms of the multiplicative group of matrices, @@ -83,7 +90,7 @@ negate = fmap negate - abs = undefined + abs = error "abs of Matrix3 is undefined" signum = diag . signum . det @@ -299,3 +306,5 @@ a31 * a1 + a32 * a2 + a33 * a3 ) {-# INLINE multCol #-} + +deriveMemoizable ''Matrix3 diff --git a/Math/ExpPairs/MenzerNowak.hs b/Math/ExpPairs/MenzerNowak.hs --- a/Math/ExpPairs/MenzerNowak.hs +++ b/Math/ExpPairs/MenzerNowak.hs @@ -21,17 +21,14 @@ ( menzerNowak ) where -import Data.Ratio ((%)) - import Math.ExpPairs -- |Compute Θ(a, b) for given a and b. menzerNowak :: Integer -> Integer -> OptimizeResult menzerNowak a' b' = optimize - [ - RationalForm (LinearForm 1 1 0) (LinearForm (a+b) 0 (a+b)), - RationalForm (LinearForm 1 0 0) (LinearForm (a+b) (-a) a) - ] - [] where - a = a'%1 - b = b'%1 + [ K 1 + L 1 :/: K (a + b) + M (a + b) + , K 1 :/: K (a + b) - L a + M a + ] [] + where + a = fromInteger a' + b = fromInteger b' diff --git a/Math/ExpPairs/Pair.hs b/Math/ExpPairs/Pair.hs --- a/Math/ExpPairs/Pair.hs +++ b/Math/ExpPairs/Pair.hs @@ -14,6 +14,7 @@ -} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE TypeSynonymInstances #-} {-# OPTIONS_GHC -fno-warn-orphans #-} @@ -31,6 +32,7 @@ import Data.Ratio import GHC.Generics (Generic (..)) import Text.PrettyPrint.Leijen +import Data.Function.Memoize -- |Vertices of the triangle of initial exponent pairs. data Triangle @@ -63,7 +65,9 @@ -- Exactly -- 'Mix' a b = a * 'Corput16' + b * 'HuxW87b1' + (1-a-b) * 'Hux05' | Mix !t !t - deriving (Eq, Show, Generic) + deriving (Eq, Ord, Show, Generic) + +deriveMemoizable ''InitPair' -- |Exponent pair built from rational fractions of -- 'Corput16', 'HuxW87b1' and 'Hux05' diff --git a/Math/ExpPairs/PrettyProcess.hs b/Math/ExpPairs/PrettyProcess.hs --- a/Math/ExpPairs/PrettyProcess.hs +++ b/Math/ExpPairs/PrettyProcess.hs @@ -110,7 +110,7 @@ bcs = takeWhile (not . null . snd) $ iterate bcf ([head xs], tail xs) - bcf (_, []) = undefined + bcf (_, []) = error "prettify': unexpected second argument of bcf" bcf (zs, y:ys) = (zs++[y], ys) f (bs, cs) = PPWL (Sequence bsP csP) (bsW + csW) where diff --git a/Math/ExpPairs/Process.hs b/Math/ExpPairs/Process.hs --- a/Math/ExpPairs/Process.hs +++ b/Math/ExpPairs/Process.hs @@ -9,7 +9,11 @@ Provides types for sequences of /A/- and /B/-processes of van der Corput. A good account on this topic can be found in /Graham S. W., Kolesnik G. A./ Van Der Corput's Method of Exponential Sums, Cambridge University Press, 1991, especially Ch. 5. -} -{-# LANGUAGE DeriveGeneric, CPP #-} + +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE TemplateHaskell #-} + module Math.ExpPairs.Process ( Process () , Path (Path) @@ -22,19 +26,18 @@ import GHC.Generics (Generic) import Data.Monoid import Text.PrettyPrint.Leijen hiding ((<>)) +import Data.Function.Memoize (deriveMemoizable) import Math.ExpPairs.ProcessMatrix import Math.ExpPairs.PrettyProcess -- | Holds a list of 'Process' and a matrix of projective --- transformation, which they define. It also provides a fancy 'Show' --- instance. E. g., --- --- > show (mconcat $ replicate 10 aPath) == "A^10" --- +-- transformation, which they define. data Path = Path !ProcessMatrix ![Process] deriving (Eq, Show, Generic) +deriveMemoizable ''Path + instance Monoid Path where mempty = Path mempty mempty mappend (Path m1 p1) (Path m2 p2) = Path (m1 <> m2) (p1 <> p2) @@ -52,13 +55,14 @@ reads' xs = (mempty, xs) instance Ord Path where - (Path _ q1) <= (Path _ q2) = cmp q1 q2 where - cmp (A:p1) (A:p2) = cmp p1 p2 - cmp (BA:p1) (BA:p2) = cmp p2 p1 - cmp (A:_) (BA:_) = True - cmp (BA:_) (A:_) = False - cmp [] _ = True - cmp _ [] = False + compare (Path _ x) (Path _ y) = cmp x y where + cmp [] [] = EQ + cmp ( A:u) ( A:v) = cmp u v + cmp (BA:u) (BA:v) = cmp v u + cmp ( A:_) _ = LT + cmp (BA:_) _ = GT + cmp _ ( A:_) = GT + cmp _ (BA:_) = LT -- | Path consisting of a single process 'A'. aPath :: Path diff --git a/Math/ExpPairs/ProcessMatrix.hs b/Math/ExpPairs/ProcessMatrix.hs --- a/Math/ExpPairs/ProcessMatrix.hs +++ b/Math/ExpPairs/ProcessMatrix.hs @@ -40,8 +40,11 @@ deriveMemoizable ''Process +-- | Sequence of processes, represented as a matrix 3x3. newtype ProcessMatrix = ProcessMatrix (Matrix3 Integer) deriving (Eq, Num, Show, Pretty) + +deriveMemoizable ''ProcessMatrix instance Monoid ProcessMatrix where mempty = 1 diff --git a/Math/ExpPairs/RatioInf.hs b/Math/ExpPairs/RatioInf.hs --- a/Math/ExpPairs/RatioInf.hs +++ b/Math/ExpPairs/RatioInf.hs @@ -9,6 +9,11 @@ Provides types and necessary instances for rational numbers, extended with infinite values. Just use 'RationalInf' instead of 'Rational' from "Data.Ratio". -} + +{-# LANGUAGE TemplateHaskell #-} + +{-# OPTIONS_GHC -fno-warn-orphans #-} + module Math.ExpPairs.RatioInf ( RatioInf (..) , RationalInf @@ -16,6 +21,7 @@ import Data.Ratio (Ratio, numerator, denominator) import Text.PrettyPrint.Leijen +import Data.Function.Memoize (deriveMemoizable) -- |Extends a rational type with positive and negative -- infinities. @@ -27,6 +33,9 @@ -- |Positive infinity | InfPlus deriving (Eq, Ord, Show) + +deriveMemoizable ''Ratio +deriveMemoizable ''RatioInf -- |Arbitrary-precision rational numbers with positive and negative -- infinities. diff --git a/exp-pairs.cabal b/exp-pairs.cabal --- a/exp-pairs.cabal +++ b/exp-pairs.cabal @@ -1,5 +1,5 @@ name: exp-pairs -version: 0.1.4.1 +version: 0.1.5.0 synopsis: Linear programming over exponent pairs description: Package implements an algorithm to minimize rational objective function over the set of exponent pairs homepage: https://github.com/Bodigrim/exp-pairs @@ -9,7 +9,7 @@ maintainer: andrew.lelechenko@gmail.com category: Math build-type: Simple -extra-source-files: CHANGELOG.md +extra-source-files: CHANGELOG.md, tests/*.txt cabal-version: >=1.10 source-repository head @@ -47,6 +47,7 @@ Matrix3, MenzerNowak, Pair, + Process, PrettyProcess, RatioInf build-depends: base >=4 && <5, diff --git a/tests/Instances.hs b/tests/Instances.hs --- a/tests/Instances.hs +++ b/tests/Instances.hs @@ -6,9 +6,13 @@ import Test.SmallCheck.Series import Control.Applicative import Control.Monad +#if __GLASGOW_HASKELL__ < 710 +import Data.Foldable +#endif import GHC.Generics (Generic (..)) import Math.ExpPairs.LinearForm +import Math.ExpPairs.Process import Math.ExpPairs.ProcessMatrix import Math.ExpPairs.Pair (InitPair' (..)) import Math.ExpPairs.Matrix3 as M3 (Matrix3, fromList) @@ -21,11 +25,11 @@ series = cons3 LinearForm instance Arbitrary a => Arbitrary (RationalForm a) where - arbitrary = RationalForm <$> arbitrary <*> arbitrary + arbitrary = (:/:) <$> arbitrary <*> arbitrary shrink = genericShrink instance (Monad m, Serial m a) => Serial m (RationalForm a) where - series = cons2 RationalForm + series = cons2 (:/:) instance Arbitrary a => Arbitrary (Constraint a) where arbitrary = Constraint <$> arbitrary <*> arbitrary @@ -55,7 +59,7 @@ instance (Ord t, Fractional t, Arbitrary t) => Arbitrary (Ratio01 t) where arbitrary = Ratio01 <$> (arbitrary `suchThat` (\x -> 0 <= x && x <= 1)) - shrink = genericShrink + shrink (Ratio01 y) = Ratio01 <$> filter (\x -> 0 <= x && x <= 1) (shrink y) instance (Ord t, Fractional t, Serial m t) => Serial m (Ratio01 t) where series = Ratio01 <$> (series `suchThatSerial` (\x -> 0 <= x && x <= 1)) @@ -163,3 +167,9 @@ instance (Ord t, Serial m t) => Serial m (Sorted (t, t, t, t, t, t)) where series = Sorted <$> (series `suchThatSerial` (\(a, b, c, d, e, f) -> a <= b && b <= c && c <= d && d <= e && e <= f)) + +instance Arbitrary Path where + arbitrary = foldMap (\x -> if x then aPath else baPath) <$> (arbitrary :: Gen [Bool]) + +instance Monad m => Serial m Path where + series = foldMap (\x -> if x then aPath else baPath) <$> (series :: Monad m => Series m [Bool]) diff --git a/tests/Ivic.hs b/tests/Ivic.hs --- a/tests/Ivic.hs +++ b/tests/Ivic.hs @@ -6,9 +6,11 @@ import Test.Tasty import Test.Tasty.SmallCheck as SC -import Test.Tasty.QuickCheck as QC +import Test.Tasty.QuickCheck as QC hiding (Positive) import Test.Tasty.HUnit +import Debug.Trace + import Instances import Etalon (testEtalon) @@ -56,26 +58,45 @@ testMOnSInf (Ratio01 a') = a < 1 || (optimalValue . mOnS) a == InfPlus where a = fromMinus3To3 a' -testZetaReverse :: Ratio01 Rational -> Bool -testZetaReverse (Ratio01 s') = abs (s - t) <= 5 % 1000 where - s = s' / 2 +testZetaReverse1 :: Ratio01 Rational -> Bool +testZetaReverse1 (Ratio01 s') = if t <= s + 2e-2 && s <= t + 2e-3 then True else trace (show $ fromRational $ s-t) False where + s = fromHalfToOne s' zs = zetaOnS s t = toRational $ optimalValue $ reverseZetaOnS $ toRational $ optimalValue zs --- Convexity tests - they fail and it is OK -testZetaConvex :: Sorted (Ratio01 Rational, Ratio01 Rational, Ratio01 Rational) -> Bool -testZetaConvex (Sorted (Ratio01 a, Ratio01 b, Ratio01 c)) = a == b || b == c || zb <= k * Finite b + l where - [za, zb, zc] = map (optimalValue . zetaOnS) [a, b, c] - k = (za - zc) / Finite (a - c) - l = za - k * Finite a +testZetaReverse2 :: Ratio01 Rational -> Bool +testZetaReverse2 (Ratio01 s') = if t <= s + 1e-10 && s <= t + 4e-3 then True else trace (show $ fromRational $ s-t) False where + s = s' * 32 / 205 + zs = reverseZetaOnS s + t = toRational $ optimalValue $ zetaOnS $ toRational $ optimalValue zs --- Ivic, Th. 8.1, p. 205 -testMConvex :: Sorted (Ratio01 Rational, Ratio01 Rational, Ratio01 Rational) -> Bool -testMConvex (Sorted (Ratio01 a', Ratio01 b', Ratio01 c')) = a==b || b==c || za==InfPlus || zc==InfPlus - || zb>= za*zc*Finite(c-a)/(zc*Finite(c-b) + za*Finite(b-a)) where - [a,b,c] = map fromHalfToOne [a', b', c'] - [za, zb, zc] = map (optimalValue . mOnS) [a,b,c] :: [RationalInf] +testMOnSReverse1 :: Ratio01 Rational -> Bool +testMOnSReverse1 (Ratio01 s') = + if t <= s + 4e-2 && s <= t + 1e-3 then True else trace (show $ fromRational $ s-t) False + where + s = fromHalfToOne s' + zs = mOnS s + t = toRational $ reverseMOnS 1e-3 $ optimalValue zs +testMOnSReverse2 :: Ratio01 Rational -> Bool +testMOnSReverse2 (Ratio01 s') = s' == 0 || if recip t <= recip s + 1e-3 && recip s <= recip t + 1e-3 then True else trace (show $ fromRational $ recip s - recip t) False where + s = 4 * recip s' + zs = reverseMOnS 1e-3 (Finite s) + t = toRational $ optimalValue $ mOnS $ toRational zs + +testMBigOnHalfReverse1 :: Positive Rational -> Bool +testMBigOnHalfReverse1 (Positive s') = if recip t <= recip s + 2e-3 && recip s <= recip t + 1e-10 then True else trace (show $ fromRational $ recip s - recip t) False where + s = s' + 4 + zs = mBigOnHalf s + t = toRational $ optimalValue $ reverseMBigOnHalf $ toRational $ optimalValue zs + +testMBigOnHalfReverse2 :: Positive Rational -> Bool +testMBigOnHalfReverse2 (Positive s') = if recip t <= recip s + 2e-3 && recip s <= recip t + 1e-10 then True else trace (show $ fromRational $ recip s - recip t) False where + s = s' + 1 + zs = reverseMBigOnHalf s + t = toRational $ optimalValue $ mBigOnHalf $ toRational $ optimalValue zs + + etalonZetaOnS :: Integer -> Integer -> Integer -> Integer -> Bool etalonZetaOnS a b c d = Finite (c%d) >= optimalValue (zetaOnS $ a%b) @@ -100,8 +121,24 @@ , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `div` 2)) $ SC.testProperty "mOnS strict monotonic" testMOnS2 , QC.testProperty "mOnS strict monotonic" testMOnS2 - , SC.testProperty "zetaOnS reverse" testZetaReverse - , QC.testProperty "zetaOnS reverse" testZetaReverse + + , SC.testProperty "reverseZetaOnS . zetaOnS == id" testZetaReverse1 + , QC.testProperty "reverseZetaOnS . zetaOnS == id" testZetaReverse1 + , SC.testProperty "zetaOnS . reverseZetaOnS == id" testZetaReverse2 + , QC.testProperty "zetaOnS . reverseZetaOnS == id" testZetaReverse2 + + , SC.testProperty "reverseMOnS . mOnS == id" testMOnSReverse1 + , adjustOption (\(QC.QuickCheckTests n) -> QC.QuickCheckTests (n `min` 100)) $ + QC.testProperty "reverseMOnS . mOnS == id" testMOnSReverse1 + , SC.testProperty "mOnS . reverseMOnS == id" testMOnSReverse2 + , adjustOption (\(QC.QuickCheckTests n) -> QC.QuickCheckTests (n `min` 100)) $ + QC.testProperty "mOnS . reverseMOnS == id" testMOnSReverse2 + + , SC.testProperty "reverseMBigOnHalf . mBigOnHalf == id" testMBigOnHalfReverse1 + , QC.testProperty "reverseMBigOnHalf . mBigOnHalf == id" testMBigOnHalfReverse1 + , SC.testProperty "mBigOnHalf . reverseMBigOnHalf == id" testMBigOnHalfReverse2 + , QC.testProperty "mBigOnHalf . reverseMBigOnHalf == id" testMBigOnHalfReverse2 + , SC.testProperty "zetaOnS symmetry" testZetaOnSsym , QC.testProperty "zetaOnS symmetry" testZetaOnSsym , SC.testProperty "zetaOnS above s=1" testZetaOnSZero diff --git a/tests/Process.hs b/tests/Process.hs new file mode 100644 --- /dev/null +++ b/tests/Process.hs @@ -0,0 +1,29 @@ +module Process where + +import Math.ExpPairs.Process + +import Test.Tasty +import Test.Tasty.SmallCheck as SC +import Test.Tasty.QuickCheck as QC hiding (Positive) + +import Instances () + +testReadShow :: Path -> Bool +testReadShow p@(Path _ xs) = read (concatMap show xs) == p + +testOrd :: Path -> Path -> Bool +testOrd p1 p2 = compare p1 p2 == compare (x1 / z1) (x2 / z2) + && compare (y2 / z2) (y1 / z1) == compare (x1 / z1) (x2 / z2) + where + (x1, y1, z1) = evalPath p1 (1, 4, 6) + (x2, y2, z2) = evalPath p2 (1, 4, 6) + +testSuite :: TestTree +testSuite = testGroup "Process" + [ adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `min` 13)) $ + SC.testProperty "read . show == id" testReadShow + , QC.testProperty "read . show == id" testReadShow + , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `min` 8)) $ + SC.testProperty "Ord of Processes" testOrd + , QC.testProperty "Ord of Processes" testOrd + ] diff --git a/tests/Tests.hs b/tests/Tests.hs --- a/tests/Tests.hs +++ b/tests/Tests.hs @@ -3,6 +3,7 @@ import qualified RatioInf (testSuite) import qualified Pair (testSuite) import qualified PrettyProcess (testSuite) +import qualified Process (testSuite) import qualified Ivic (testSuite) import qualified Kratzel (testSuite) @@ -20,6 +21,7 @@ , RatioInf.testSuite , Pair.testSuite , PrettyProcess.testSuite + , Process.testSuite , Ivic.testSuite , Kratzel.testSuite , MenzerNowak.testSuite diff --git a/tests/etalon-mOnS.txt b/tests/etalon-mOnS.txt new file mode 100644 --- /dev/null +++ b/tests/etalon-mOnS.txt @@ -0,0 +1,791 @@ +101 132 477435698018201574 29229448099906007 +101 140 2423764 192441 +101 144 47394576 4153039 +101 158 66682636 7708275 +101 160 3877826508800 467138272673 +103 104 57752214 55831 +103 112 138502457443 1852958281 +103 142 3569603670778024952 277562542967901079 +103 144 243093168 19623695 +107 108 1080 1 +107 152 44215128 3819271 +107 160 26752454981667520 2724371422927733 +109 140 341350796332861 19126491351885 +109 144 5510389341894498 355393196283539 +109 152 371104431997769372695423927 30193707971262898992038820 +109 154 66486252 5617019 +111 112 1120 1 +111 116 28362 169 +111 136 23398462378211570722978426649046405157798741091526 995047397952694751322305782904094250618613818729 +111 176 9856 1191 +11 12 1791162 25177 +11 14 43827931168 2335831431 +11 15 105869142730 7868949657 +11 16 359841 33722 +11 17 20944 2337 +113 140 5843450521859968583685242480 266309045050759864594080921 +113 146 1718921875 99273206 +113 158 9877212 797779 +113 160 295203680 25165257 +113 164 43170113218986677272587413 4017391584083859861113156 +115 116 1160 1 +115 124 2507996038 29268543 +115 154 748172292 51367657 +117 136 335336919557660005133413929827 9584642445059238255029573073 +117 184 659662470722564432 77545998724611569 +119 120 1200 1 +119 122 4287124887654307936 12704712105579945 +119 146 81329531557608761051020307905944429 3488122975460256846283462130582794 +119 184 54468416 6085663 +121 128 12002304 96755 +121 144 3146768714778 109602391783 +121 148 59944283723935906584746 2521482319636978522669 +121 166 67091403785273409357752595805616324 5113537259107081891678204893301255 +121 168 5442171 435290 +121 172 56568091 4899018 +121 184 328094 35007 +121 190 590792964488 69115505345 +12 17 106570076 9104117 +12 19 138385981018496 16640880070721 +123 124 1240 1 +123 136 25233168 422683 +123 176 32030384 2845817 +125 134 332543177 3502316 +125 158 1178581078579747775528950337135750 60431177943897038270524308858699 +125 176 10903472 907943 +125 182 13153062261804556 1236501981034245 +125 192 478990065080 52471840941 +127 128 1280 1 +127 136 1258 13 +127 140 205800 3349 +127 142 221099981451189103646 4281813901441949301 +127 176 933024 74005 +127 178 197456468 16119225 +127 190 57203066580523168790739060 5833561417508198158671383 +127 196 41893607982226 4645158828459 +129 160 24139850074160 1107656219813 +129 184 4203176 368927 +131 132 1320 1 +131 140 4175106830 41537119 +131 146 19662204195899690 367177721494067 +131 160 2342216752506 97612749097 +131 182 25139507848 2015829341 +131 184 1715272 141345 +131 208 32676635180800 3967963243431 +13 14 407120838053575044 4650281458640375 +13 16 428248 18733 +13 17 1957065543705534118807383728 120158143510689856918705771 +13 18 4012164 316981 +13 20 2771652460 304875553 +133 160 1095324960 41295451 +133 172 85104456001281365114 4944040805429554319 +133 184 285113 22440 +133 202 170062184 18084261 +135 136 1360 1 +135 152 791650662519381537319151 16549897323467996115082 +137 146 128550557445609287225650482 1212132752642594243040755 +137 152 772160637396130765507734 13698856816799099515369 +137 164 2316619392 82319363 +137 192 430805568 35155781 +137 194 1157184004 98683377 +137 208 811828784 86243003 +137 216 2615476608 310010273 +139 140 1400 1 +139 144 2198713190698771206 9980492035236655 +139 154 68146873565001 1189714248304 +139 160 5484544160 143378181 +139 192 9539008 745405 +139 196 14846167 1243990 +141 200 230096600 19756739 +14 17 960823884 38571391 +14 19 9957026 725169 +143 144 1440 1 +143 152 62065039 556333 +143 160 229157221166565 4472359950724 +143 200 39057800 3158451 +145 202 40401232787624911845727251380191785224650465838464 3274349623873850766446446327538887881181568246785 +145 208 36907 3308 +147 176 121247984 4317343 +147 208 1637168 139175 +149 184 355408350400912698 15874550404628441 +149 206 526479556 41312757 +149 212 3503406 304535 +151 152 1520 1 +151 214 40187916 3438635 +151 216 265446936 23557387 +15 16 112662 1081 +15 19 41390132050806 2147937279967 +153 184 7876051 295817 +153 224 1198015475769393977521 114574951397326311947 +153 232 505882844 53554021 +155 164 52541336 428733 +155 218 210599772 17454403 +157 166 1129381 9070 +157 172 10432914870390074768786720537025771353289952454 156105846494533281838012066745967945531027123 +157 214 9929479732 736700701 +157 216 175017487293 13495080112 +157 220 1224495 99866 +157 224 572886944 50338137 +159 160 1600 1 +159 224 582407392 48615769 +161 208 20934921072 1208341375 +16 25 27229803600 3135869143 +163 172 14101979786814 108007134491 +163 196 3289344912 123353273 +163 214 43424044675946205325276328 2718220043629888112306295 +163 232 10274584 894345 +165 224 333481821301384392 24320729872434985 +165 232 313167752 25924133 +165 248 15209445584566382329163794 1571648480042242034289365 +167 168 1680 1 +167 170 10540 21 +167 200 215206725 7688837 +167 206 180363931262177 8000684081816 +167 208 4925545045855249259704 231855938346296187777 +167 236 2083762 176215 +169 232 5178965812 395767995 +169 240 661658160 57082463 +171 184 4209084814685247176576471104698 47386152772799265182124975229 +171 208 13268022576 538545073 +17 18 1566 13 +17 22 496509160719146676 28943421368007515 +17 24 119064 10027 +17 25 13924640525 1349905747 +17 26 192189671000435108 20820142690014595 +173 206 470852758 16396007 +173 208 1852514768 69375525 +173 212 1810639 77084 +173 224 342840288 20033135 +173 240 2964800 236269 +175 176 1760 1 +175 244 17464606216105999303 1420120666481329676 +175 248 354218152 30301713 +175 256 9896675584 944108777 +177 200 12750 277 +177 248 35948840 2930543 +179 200 647275138250 12435628269 +179 206 22734618659 592159974 +179 208 270436102768 7706499055 +179 216 19892772739790482810438143298971 766638753445383241928999059936 +179 240 124542480 8602009 +179 248 11891011 942086 +179 256 3044608 269985 +179 272 770334736 82029075 +181 192 14487255882725688 124721818224613 +181 256 252269824 21407863 +181 280 243299491120 27218165543 +183 184 1840 1 +183 256 767689984 62140957 +185 248 85248482407222372883 5883350078319962076 +185 256 152279808 11998109 +185 264 36161688 3179807 +187 208 100163013728205552459867042836 1828872118454352651167661649 +187 224 2159032736 77340939 +191 192 1920 1 +191 236 82477650992 3696884723 +191 264 1228629 96298 +191 272 282260112 24621461 +19 21 188748 3127 +19 24 73065837669880734497772 3732179061729095618641 +19 27 267742044 23159305 +19 28 4668246380 455440723 +19 30 202660 24139 +193 208 6735883823118853 77930724560337 +193 232 1152644556 43065521 +193 272 171668176 14352303 +195 248 18202633506134726 966176488026525 +197 218 2542534 43581 +197 236 4792534128 171869861 +197 240 34794596676804944434135843550675 1426573469166311964455524985602 +197 272 57463264 4481571 +197 280 224899640 19468053 +197 288 5372635104 511434073 +197 296 8577797288777503766951795088 885558989812068294124748375 +199 200 2000 1 +199 220 44019800 734287 +199 224 1626616092696 33908029885 +199 280 151916520 12613213 +201 256 29957220096 1602877169 +20 21 874314 5917 +20 31 52922704 5952351 +203 248 6390818576531769165 266761449073011433 +203 260 1764247355 97350653 +203 272 433953597084324531697076154 29885482591279493946440903 +203 284 314903886 25498805 +203 288 954011808 81979241 +205 232 1492378834184816721989710656 32946675896978398502566387 +205 272 93832050073063 6176472673708 +205 288 966252384 79696241 +205 292 325203758 28391337 +207 208 2080 1 +207 248 1322932316 47490751 +209 280 10196976895 701785793 +209 296 33667336 2872849 +209 332 7104800 864167 +211 268 420247286416337388021079534346 22145396112379653686357376831 +211 280 1938100290805 127658111022 +211 292 264135316 20818201 +21 29 125387532 9786919 +21 31 2581277 253123 +213 256 2807516416 104696879 +215 216 2160 1 +215 256 142032 4943 +215 288 86317776864 5936280899 +217 240 818550 13817 +217 272 291309264020 14233651479 +217 304 360181328 29342589 +221 296 15198949244 1044541659 +221 320 4495307840 415255091 +22 23 405452726614689376234058744095027158 2442098019903115439532582107475961 +22 31 118951092 9937855 +223 224 2240 1 +223 268 6154349856 229317335 +223 272 2895564151 119636061 +223 288 13383898848 770644883 +223 316 4853602 415081 +225 256 1870580016281574720 43623405321409177 +225 272 15020006970898237967 585712761878448750 +227 232 1020379587 2571128 +227 272 3182149488 114432385 +227 288 582692695250760 30514684343827 +227 320 395871680 33133119 +227 332 4757051376 453490589 +229 256 374170397077642871125796352 7231150774521216153947917 +229 316 310457044 24147753 +229 328 203687016 18164893 +229 340 2396671519058288 239072814877305 +229 352 5861500190515124912 643310405461818945 +231 232 2320 1 +23 24 708390 4039 +23 28 301201173072555 12291654197303 +23 30 918131960 55665693 +233 248 1047118 9639 +233 280 839799170 31268259 +233 332 42020991 3673628 +233 368 1939342336 231222295 +23 34 38289508 3770459 +23 36 924 107 +235 304 3592520731728558622420 209014807517728002843 +237 272 689673 17531 +239 240 2400 1 +239 280 108640756427 3325971461 +239 288 5918538 226025 +239 320 35541730880 2438001373 +239 332 220542081496 17674581195 +239 356 12271107112 1235733429 +241 340 446450430 37489061 +241 376 26968034134655664044656 3091422157882426773631 +24 31 1063141776 61277657 +245 332 1299977374664 94066639307 +245 344 114963768 9458837 +247 248 2480 1 +247 352 6133408 536511 +251 356 34719701 2980172 +25 28 2039237959472 40243915413 +253 256 7206535168 8748903 +253 280 35652400 612949 +253 304 3960329904 147259513 +253 364 79600749513628707 7203482368536955 +25 34 9453969210232 694752094189 +25 36 71882325 6523522 +25 38 135260848 14414887 +255 256 2560 1 +257 284 73356632 1208837 +257 308 741691104 26727829 +257 332 35560459576 2051440701 +257 356 392137204 31041385 +257 368 4460720 397383 +259 304 28066422736 872991355 +26 29 751390 14157 +263 264 2640 1 +263 280 2969969359526396237501668338630 27471057441287251708087987699 +263 296 516492928214639902231 10750845717411348937 +263 368 3283376 266057 +265 376 135488968 11647627 +269 380 278363395 23503068 +271 272 2720 1 +271 280 11879690 49183 +271 376 3897757 310788 +271 388 285173307 25393135 +271 412 3532388296 376650753 +27 32 2136145140 71989639 +27 38 26852092 2231983 +27 40 65181560 6460247 +275 392 36594768 3204167 +275 416 463022560 48708299 +277 340 6320747110291362964823064747330 271842930290020455494724423281 +277 388 117367478 9555437 +279 280 2800 1 +28 31 1674 29 +283 292 347322904 1353781 +283 304 3846441813419317880358782306 42025932375000856638525615 +283 340 9909508080 367867157 +283 364 77851075111545267940295010499408669 4395607836721280366692416938785680 +283 400 616424400 52167269 +283 436 5495495573213776754 606672758011739615 +287 288 2880 1 +287 344 62045388 2239597 +287 404 316081419 26293732 +289 400 24778400 1954207 +289 412 323348827 28323465 +29 32 3545707803058539871484 58693166330428562925 +293 356 1238555462712441745354916 49912886117803707110443 +293 416 662834848 57131899 +29 36 166530437165727 7681634711762 +29 40 186645 14488 +29 41 41434436 3510303 +29 44 11018776 1168407 +29 46 5132 621 +295 328 298874543 5432877 +295 412 664208478 53367647 +295 448 6274565696 667046319 +299 380 32398980643785097731413344933675 1713002339224210365698938536413 +299 428 694193102 61765911 +301 424 69567800 5804163 +301 436 48838649 4516870 +305 428 356191979 29233196 +307 424 34895359 2725114 +307 436 363916883 31402595 +311 344 53813296 911099 +311 440 33860840 2877033 +31 32 76326933880257 305628965932 +31 33 198359227576623978 1830612693488581 +313 376 757555917 28085108 +313 436 378258385547214676071376685377398561601 30644883569917283820491390403098407566 +313 448 760675776 67658327 +31 36 276431485450691503504083 7834269710947693115701 +31 40 23955 1376 +31 43 91380676 7277885 +31 44 404630 34833 +31 46 17574639969593918558 1750166620134216445 +31 48 1633788216 183227851 +317 356 550532322919319520377112338 11190669014692523233071645 +317 380 12414823440 448728137 +317 404 475472298447179 25530820250077 +317 440 678985 54236 +319 364 4004799653574646985786 96152512552532104205 +319 412 54777235048 3155033975 +319 448 779716672 64213591 +325 328 3280 3 +329 332 3320 3 +329 464 831827184 69755153 +329 512 79805497266176 9079971092297 +331 412 162720636 7627951 +331 472 424239736 37199043 +331 520 8483926034287817572476480320 994000814681544504944449651 +33 46 417246074 33895163 +33 50 2893820148687953002065572200 305759302273331365882937469 +335 428 414140582752 22544164191 +335 464 166559296 13178763 +337 340 3400 3 +337 472 54283776 4417697 +341 344 3440 3 +341 488 64482856 5732025 +341 512 17318488576 1784328215 +343 412 14554819584 539002739 +347 416 7438370784 269154403 +347 440 2829228387234155054244827106200 147699439919128374187041437667 +347 488 46175048 3825659 +349 352 3520 3 +349 496 26887664 2326727 +353 356 3560 3 +353 428 15858971087934494636780013744371543 630446207869643028542667527767840 +353 440 1198666478240 56629636513 +353 488 46169131 3621514 +353 536 2045443 217359 +35 36 221381073251018730 763170344336593 +35 47 194591254769385909106 13532824604979581343 +355 496 962149232 77450313 +359 464 4958438096 287050351 +359 512 998198784 87574175 +361 364 3640 3 +361 388 23283810320717309486474 256876949536804008345 +365 368 3680 3 +365 404 148444952 2560383 +365 512 145708544 11938401 +367 520 259610520 22192601 +371 512 203728384 15853799 +373 376 3760 3 +373 448 8605641408 318395095 +37 50 3747763700 267958669 +37 52 10494926 867027 +37 56 94183246199 9921958800 +37 58 4297764236 499799437 +377 380 3800 3 +377 536 34325708 2974925 +379 388 8640447567913182114 23818845519019789 +383 536 560601864 45461017 +383 560 1895530224 180528595 +383 608 20575619840 2496730751 +385 388 3880 3 +385 544 1140600992 96402963 +389 392 3920 3 +389 488 2770811596345800695872 136039289675162182885 +39 44 18320264094 391459753 +395 404 105906142255157616043255142370 277803905583887299290150637 +39 62 992 121 +397 400 4000 3 +397 568 30585096 2716229 +401 404 4040 3 +401 440 1715250543000828927983855015270 26247108088374587786209863149 +401 536 2430191007829500997 165538531856087008 +401 560 1227232720 98572861 +403 568 623772488 52166561 +40 43 91495493697425270 1012876217298531 +407 488 2558524098 92738683 +409 412 4120 3 +409 436 1322279 12540 +413 416 4160 3 +413 464 709710743308 14490862185 +413 584 656612808 55668625 +41 48 3520672 107133 +41 50 4134065975 170607724 +41 52 81259944312534 4247413612877 +41 53 136685728 7921575 +415 592 1334112848 117147117 +41 56 566953786 42428933 +41 58 310702636 26387235 +41 62 5879956 617937 +41 64 853592 98007 +419 536 1061048355042883465970589239779801 58162241677679044736536051651472 +421 424 4240 3 +421 520 63928712357260768810 2859100006978301771 +421 544 2807242912 162237459 +421 592 1359274032 112560881 +421 640 12786962560 1363187007 +425 428 4280 3 +425 608 223136 19809 +425 632 289395259810755 29001720221552 +427 472 5959472 99047 +427 520 896055805775 36645800536 +427 592 270799744 21520211 +431 560 1066100298758105213176308 63404226704792381853719 +431 608 1427804704 119853475 +433 436 4360 3 +433 520 5797956060 214201103 +433 616 1080184 93847 +43 48 141637307220936 2692816292717 +43 61 456565236 39220363 +43 62 641785374793382723146404234184 58487205704605428744938648163 +43 64 25728 2585 +43 66 2968413459918477916 324571505267984029 +43 67 51124510117136 5837642671863 +437 440 4400 3 +439 616 838516 68799 +439 664 589931132 62035655 +443 632 274920 24149 +445 448 4480 3 +445 616 6676649 526892 +449 608 3531736804299238779836 254759755835339732779 +449 632 80264 6675 +451 544 132998508684555768884 5111842745745408469 +451 640 224269440 19290833 +451 712 39382018901275408222464 4688484806862877739737 +45 52 5787535 156849 +455 512 25498229384824680313685190784 529724353597504276289361357 +455 608 1724901950874094 117336319968435 +45 56 228636542418452 10706435977925 +45 62 10093209303979794708164 782827997797329937175 +45 64 46960576 4075309 +4 5 673781 32397 +457 640 26181760 2129659 +461 464 4640 3 +461 656 1643436784 142925593 +461 680 105405865 10312341 +463 640 63536000 4981347 +463 664 73830623804 6611940795 +46 61 53702056242663292526 3525694286080552779 +467 536 2455353820241744746 62451709154832515 +467 560 13474898640 489047941 +467 632 9197059933840593096278645051 661732279615861153367727222 +467 656 238759728 19682675 +469 472 4720 3 +469 496 120148064 952893 +469 664 423737576 36106647 +469 712 7928052004 842029635 +473 488 485039792 1869697 +473 608 25465205762887566277872914 1432933868656272952719597 +473 656 5448736 433671 +47 48 17562322278 42480791 +47 50 4181719286668267000 38107671710464229 +47 52 7377864 125779 +47 53 49452710 1051183 +475 592 2170194549824 102423504865 +47 56 17383856 610087 +475 664 17583384 1418671 +475 712 3051063913 312861352 +47 65 41917460 3293921 +47 66 36926724 3039845 +47 70 574463720820456250 57830319169531099 +479 680 110709440 9537801 +479 728 8275293572 881640531 +481 664 1403779 109388 +481 688 1795558224 159302285 +485 488 4880 3 +485 536 130647856 2158349 +485 752 708138530646452608 79718780135739361 +487 688 364959920 30822989 +487 712 175719286 16730369 +491 680 2555525 202106 +491 704 274438976 24557259 +493 496 4960 3 +493 592 15031259472 554702197 +49 58 139520885 4653428 +49 60 5390413405045623683458094821970 228351068618392413063126876531 +49 68 42823068 3417803 +497 704 173095488 14780149 +497 776 375584 43157 +499 712 241146568 21194805 +503 608 225005112408 8767528901 +503 704 175815616 14263125 +505 616 38020179467965039431064594866019 1571466014496981278887933256265 +505 664 50915140441 3209773230 +505 712 979716984 82050451 +50 71 88248172 7610793 +509 512 5120 3 +509 704 34918976 2745109 +509 728 502648328 44583459 +515 728 1020767384 86428031 +517 520 5200 3 +517 736 89894432 7830965 +517 784 6418343792 679588311 +521 728 259059528 20862325 +523 736 91254496 7581933 +52 55 1890988 15105 +52 73 2705380 222427 +527 632 108612516 3945785 +527 656 84975398208 3985420019 +527 728 102844651 8039502 +527 752 2151842736 189176057 +527 800 953314400 101232543 +52 79 3120084776 332048283 +529 640 153718637852977985011469832 6024760822792568916592673 +529 760 164177229749195 14788334099736 +533 536 5360 3 +533 752 436760848 36685617 +533 800 13134605948590567475 1351926685839808641 +535 592 19921688 340987 +53 58 472749283122 6962332795 +53 60 2927872620 64854623 +53 71 2152052600 148055431 +53 74 24497404 1965855 +53 76 11608427264 1039157717 +53 84 1152 139 +541 544 5440 3 +541 592 243558547444687 3583655693577 +541 760 140191120 11560351 +545 704 559118656 32239961 +545 752 439583104 34180267 +545 776 164134088 14308277 +551 776 582714696 48574427 +553 664 4727920866 174323767 +55 56 15397336114007656515 31081495413387976 +55 58 928 7 +55 62 11307814659606 239474697473 +55 67 11521782387824312813 472161068762439591 +55 68 76837359829638624163 3457263548507678710 +55 72 2373551010 146495297 +557 560 5600 3 +55 76 2560972 200471 +559 784 2392047504 195844373 +559 880 287836396486949032800 33947288213944818491 +5 6 206054 7543 +563 800 2448696800 211753299 +565 568 5680 3 +565 784 474425056 37847363 +565 808 1238569464 109808851 +56 89 92551391475 11276988589 +569 800 354671200 29352133 +569 872 322994023716 35175661205 +571 688 1688125874146648233833 64427639483502543132 +571 808 627870136 53389765 +5 7 18348988 1490457 +575 656 131573469 3153577 +575 704 134804032 5706235 +57 58 28074262 54223 +575 872 2977300447 315289893 +57 64 354359856 7187551 +577 664 472439855848 12294575421 +577 808 353096 28713 +57 80 74650960 6131107 +581 584 5840 3 +581 824 8138442 698401 +583 760 619452429740 37450567491 +583 808 126170311 10011004 +583 832 526731712 46326411 +58 67 1649028443012092 44555675261197 +587 608 106572027049832112414 480643244838332939 +587 704 1935612096 70373909 +587 824 1319661544 108464877 +58 85 54934011149712678782000 5269825788607836690257 +589 592 5920 3 +589 832 2669020224 225303215 +593 656 48923824 831049 +593 848 2728649456 241870017 +595 832 2704381888 218494687 +59 71 3449508588 130529263 +59 76 7411374208219496963 421834109077670761 +59 83 854530484 70894067 +59 84 40392681 3519997 +59 92 45872672 5249863 +599 848 2764691152 235520941 +601 832 76553152 6043017 +601 856 349370408 30493001 +605 608 6080 3 +605 728 566713329 21427174 +605 848 2800732848 228692177 +607 712 1213956368088 37543259599 +607 784 99170743280 5713907697 +607 856 1415672488 118672485 +611 848 554904064 44307075 +611 872 723201048 63617609 +613 616 6160 3 +613 736 1010312352 37225253 +613 856 716931672 57566561 +61 70 1601707428486458895049 40666387345350552332 +617 872 1464932968 123925581 +61 80 711875910101206912226682801530 44329062975930287890417190417 +61 88 13721941750340872535111 1252638412336324244440 +619 856 141999379 11154668 +619 880 269186640 23323051 +623 872 74173192 6018805 +625 808 862470916 50015591 +62 77 226501542093442 10476590586397 +62 95 3883869938060071286980 422790254480350650149 +629 632 6320 3 +629 848 22872510254352162199999392778 1618589258548885335643978905 +629 872 146897011 11670400 +637 640 6400 3 +637 712 22425908472252330466481206 432681307420269112741067 +637 880 30784 2407 +63 80 211987100 11156141 +63 88 4131304 332173 +63 92 405320053355454565329068529858570906247772102611 38458528259602065757217406740369621389921333902 +643 736 2349612950193993636339516635588 58189747605535213164784539673 +64 67 189878 1187 +647 776 3233470653 117635606 +64 91 202606404 17565491 +653 656 6560 3 +653 800 184407247200 7835559329 +655 784 5294965872 187891325 +655 856 3297515140088500321 201833821852521154 +65 83 3657548716 198513737 +65 84 2275425096 131605931 +65 86 4325905632866773677677941204 280980356243247679229813691 +65 92 707613 60227 +659 680 941793200 3699963 +661 664 6640 3 +6 7 10705450028 316037291 +673 712 495157552 4014129 +673 808 52059036 1917025 +67 70 1866014677730 11035422619 +677 680 6800 3 +67 94 274973124 22546777 +685 688 6880 3 +68 95 1129604340 90893383 +697 784 3404362107124972 70417119108897 +69 88 1847403 99592 +701 704 7040 3 +70 73 139301082 780289 +707 848 30888874032 1124349577 +707 872 34236240847352 1517502001011 +709 712 7120 3 +70 97 465591076 36915973 +709 784 69878704 1173299 +7 10 3039620 268397 +71 100 58055425 4840929 +71 101 1247154868 108324171 +71 110 20680 2323 +715 856 3155192460 112260067 +71 74 9957884 54819 +71 84 9310905778962470332154771 309312691722716040540357 +71 98 119397124 9298405 +725 728 7280 3 +725 872 3254279148 122397847 +73 103 1310906132 110134499 +73 104 61864504 5404935 +73 116 160840452406736 19586683322813 +733 736 7360 3 +733 808 163216 2653 +733 880 274573680 10106041 +73 84 2520531076 65498273 +73 88 458809560621687 17565069102308 +73 91 29294569304 1385139607 +73 92 2586364317931361819012254201976 130392844500272639499029255823 +739 880 2147997280 74834783 +74 101 4340374 323843 +74 89 5424360252 203907565 +749 752 7520 3 +75 104 6266637 498406 +751 808 14929152531424038 167732593950845 +751 832 1619914041356 28264167781 +757 760 7600 3 +761 848 102666787178648940581728 1913748583083825691785 +767 848 40876568 683237 +76 91 5704292412 203304145 +77 108 13616613 1115159 +773 776 7760 3 +77 92 1189629123140424431 42749743513159851 +77 95 762173074384307211512753 33848741696267119943389 +77 96 3802911616 180041871 +779 824 663189808 5320197 +779 872 4845927232 95011785 +7 8 157422 3839 +781 784 7840 3 +787 832 77736869437764506961663263190404 622281702698477841687285348597 +79 109 591106564 45951341 +79 112 48137264 4124745 +79 118 26999574638029333921808 2740797596939325889839 +79 120 675061980 71810303 +791 872 1330672 21677 +7 9 5178505770 291766481 +797 800 8000 3 +805 808 8080 3 +809 848 106044014668699221902585698 686086151112096112942293 +81 112 29175552 2290657 +81 116 21840886 1946677 +81 128 113880836608 13602779789 +817 832 3155607 6439 +821 824 8240 3 +82 85 16555923093433771246695490 76655763495343125744361 +829 832 8320 3 +83 104 92475429528357926581830238378374 4509163544371135900175725017247 +83 116 26302739 2120087 +83 86 25703969906 117339971 +845 848 8480 3 +85 118 171859684 13737597 +85 132 8393576287888 949095058129 +853 856 8560 3 +857 872 3172892336 6064601 +85 94 4018171 67639 +869 872 8720 3 +87 124 175791514 15384937 +87 136 289083240704 33339684607 +877 880 8800 3 +87 88 26185523330110 30669672971 +89 104 529896063229 15863762521 +89 107 7844288556 293578747 +89 112 162876368368 8142684563 +89 132 2948337891148056 293186575939535 +89 136 162959514140233742 17613617940340169 +89 140 37782021474067360 4444920405809809 +9 10 95850 1729 +91 108 206351848812177421119 7031173753139727287 +91 109 8180207148 292854643 +91 120 232189600025045660868782025 14845201675228847355463606 +91 128 190562432 15800565 +9 11 37508576518761587924246383733296 1570175268289310200702148989751 +9 13 30214121666138076014729719 2769380327578530456720327 +9 14 41608 4727 +91 97 2386394 22599 +93 136 4191546316 399406251 +94 103 26041339024866 390694663201 +95 112 2671325482 86216455 +95 134 554906596 46559889 +95 136 52562504 4678491 +95 98 11416872577951540099547 44514448262602980906 +97 136 36005048 2943755 +97 144 48341915904665622 4820481061106971 +97 154 83717592 10162333 +99 140 226387210 19198933 +99 152 728396312 79707025 diff --git a/tests/etalon-tauab.txt b/tests/etalon-tauab.txt new file mode 100644 --- /dev/null +++ b/tests/etalon-tauab.txt @@ -0,0 +1,974 @@ +1 2 269 1217 +1 3 1486 8647 +1 4 1448 10331 +1 6 669 6305 +1 10 150509 2096993 +1 11 1048 15811 +1 12 64 1037 +1 13 2516635 43324033 +1 14 75 1373 +1 16 15 307 +1 17 223719847217121 4818899500742111 +1 18 11576873 261780300 +1 19 275869 6532095 +1 21 1771 45681 +1 22 13 349 +1 23 239355515695 6676324696363 +1 24 247 7147 +1 26 13336 413975 +1 27 13336 428823 +1 28 64 2125 +1 29 64 2189 +1 31 31868239 1155220065 +1 32 93607 3490915 +1 33 14299 548165 +1 36 2844315012 117898533653 +1 37 35 1487 +1 38 269 11708 +1 43 108159466379 5266052621833 +1 45 638073389 32378276423 +1 46 57 2951 +2 3 269 2047 +2 4 269 2434 +2 6 743 8647 +2 7 724 9363 +2 8 724 10331 +2 9 32 493 +2 11 218024379851983 3853043458377914 +2 12 669 12610 +2 13 11081 222023 +2 15 14857678 331509943 +2 17 625865993 15373292652 +2 19 1094143543 29296160013 +2 20 150509 4193986 +2 21 524 15187 +2 22 524 15811 +2 23 524 16435 +2 24 32 1037 +2 25 32 1069 +2 26 2516635 86648066 +2 27 1035509 36783338 +2 28 75 2746 +2 29 48968995 1846162586 +2 32 15 614 +2 33 32705 1374481 +2 34 223719847217121 9637799001484222 +2 35 13 574 +2 36 11576873 523560600 +2 37 4981 230578 +2 38 275869 13064190 +2 39 901 43624 +2 42 1771 91362 +2 43 95746813491517 5040237686324834 +2 44 13 698 +2 45 353949443 19374944132 +2 46 239355515695 13352649392726 +2 48 247 14294 +3 4 19 203 +3 5 269 3264 +3 6 269 3651 +3 7 5867 87301 +3 9 1486 25941 +3 10 1448 27121 +3 11 1448 29057 +3 12 1448 30993 +3 13 64 1447 +3 14 64 1511 +3 17 1409 38185 +3 18 223 6305 +3 19 1583 46589 +3 20 24763 757447 +3 22 1859 61155 +3 23 27 919 +3 25 269 9761 +3 28 279451496671 11070173646688 +3 30 150509 6290979 +3 31 1048 44937 +3 32 1048 46185 +3 33 1048 47433 +3 34 1048 48681 +3 35 64 3047 +3 36 64 3111 +3 37 64 3175 +3 38 64 3239 +3 39 2516635 129972099 +3 40 5832435759679 307592990483371 +3 41 743 39994 +3 42 25 1373 +3 44 1366604910835973 78022928423524953 +3 46 272079231 16121387395 +3 48 5 307 +4 5 16 221 +4 6 269 4094 +4 7 269 4481 +4 8 269 4868 +4 9 349 6768 +4 11 2985 65761 +4 12 743 17294 +4 13 362 8879 +4 14 362 9363 +4 15 362 9847 +4 16 362 10331 +4 17 16 477 +4 18 16 493 +4 19 16 509 +4 22 218024379851983 7706086916755828 +4 24 669 25220 +4 25 81872031 3181281076 +4 26 11081 444046 +4 27 427 17581 +4 30 7428839 331509943 +4 31 7763609 355259308 +4 33 14873 714151 +4 34 625865993 30746585304 +4 35 11517061 578651566 +4 38 1094143543 58592320026 +4 40 150509 8387972 +4 41 21209515 1204939858 +4 42 262 15187 +4 43 262 15499 +4 44 262 15811 +4 45 262 16123 +4 46 262 16435 +4 47 16 1021 +4 48 16 1037 +5 6 64 1089 +5 7 269 4924 +5 8 269 5311 +5 9 269 5698 +5 10 269 6085 +5 11 1494957 35728459 +5 12 31958 806765 +5 13 56902130353 1510899511886 +5 14 154 4285 +5 15 1486 43235 +5 16 1448 43911 +5 17 1448 45847 +5 18 1448 47783 +5 19 1448 49719 +5 20 1448 51655 +5 21 1448 53591 +5 22 64 2433 +5 23 64 2497 +5 24 64 2561 +5 27 37131637 1618420011 +5 30 669 31525 +5 31 67537 3260867 +5 32 11081 548146 +5 33 269 13617 +5 37 67 3699 +5 39 589495295338445 33885343036099771 +5 41 30550 1824549 +5 44 11763209026574867668144257331007414 742037223603544333737920966312790157 +5 47 17281 1147457 +6 7 32 647 +6 8 19 406 +6 9 269 6141 +6 10 269 6528 +6 11 269 6915 +6 12 269 7302 +6 13 15387 437072 +6 14 5867 174602 +6 18 743 25941 +6 20 724 27121 +6 21 724 28089 +6 22 724 29057 +6 23 724 30025 +6 24 724 30993 +6 25 724 31961 +6 26 32 1447 +6 27 32 1479 +6 28 32 1511 +6 29 32 1543 +6 31 22571 1143139 +6 33 218024379851983 11559130375133742 +6 34 1409 76370 +6 36 223 12610 +6 38 1583 93178 +6 39 11081 666069 +6 40 24763 1514894 +6 43 20 1293 +6 44 1859 122310 +6 45 14857678 994529829 +6 46 27 1838 +7 8 64 1499 +7 9 64 1563 +7 10 269 6971 +7 11 269 7358 +7 12 269 7745 +7 13 269 8132 +7 14 269 8519 +7 16 4487779 153815515 +7 17 219685 7822664 +7 19 199 7604 +7 20 68074509 2686722241 +7 21 1486 60529 +7 22 136149018 5713817027 +7 23 1448 62637 +7 24 1448 64573 +7 25 1448 66509 +7 26 1448 68445 +7 27 1448 70381 +7 28 1448 72317 +7 29 1448 74253 +7 30 64 3355 +7 31 64 3419 +7 32 64 3483 +7 33 64 3547 +7 36 22571 1328884 +7 37 4270734388451 256506021665323 +7 39 1832403 114429617 +7 40 12908791557077 821347302331963 +7 42 669 44135 +7 44 44906995144 3066566729547 +7 45 11081 770169 +7 46 269 19010 +8 9 8 213 +8 10 8 221 +8 11 1 29 +8 12 269 8188 +8 13 269 8575 +8 14 269 8962 +8 15 269 9349 +8 16 269 9736 +8 18 349 13536 +8 19 6725252666082473912 269837142815144165315 +8 22 2985 131522 +8 23 94 4257 +8 24 743 34588 +8 25 47 2246 +8 26 181 8879 +8 27 181 9121 +8 28 181 9363 +8 29 181 9605 +8 30 181 9847 +8 31 181 10089 +8 32 181 10331 +8 33 181 10573 +8 34 8 477 +8 35 8 485 +8 36 8 493 +8 37 8 501 +8 38 8 509 +8 39 8927 577503 +8 41 22571 1514629 +8 44 218024379851983 15412173833511656 +8 48 669 50440 +9 10 64 1909 +9 11 64 1973 +9 12 19 609 +9 13 269 9018 +9 14 269 9405 +9 15 269 9792 +9 16 269 10179 +9 17 269 10566 +9 18 269 10953 +9 19 2846636445243 119319375184511 +9 21 5867 261903 +9 25 269 13412 +9 26 213398 10906091 +9 27 1486 77823 +9 28 106699 5719793 +9 29 1448 79427 +9 30 1448 81363 +9 31 1448 83299 +9 32 1448 85235 +9 33 1448 87171 +9 34 1448 89107 +9 35 8 503 +9 36 1448 92979 +9 37 1448 94915 +9 38 64 4277 +9 39 64 4341 +9 40 64 4405 +9 41 64 4469 +9 42 64 4533 +9 43 64 4597 +9 46 22571 1700374 +10 11 32 1057 +10 12 32 1089 +10 13 19 667 +10 14 269 9848 +10 15 269 10235 +10 16 269 10622 +10 17 269 11009 +10 18 269 11396 +10 19 269 11783 +10 20 269 12170 +10 21 22391 1039389 +10 22 1494957 71456918 +10 23 90047 4426279 +10 24 15979 806765 +10 26 56902130353 3021799023772 +10 27 2985 162359 +10 28 77 4285 +10 30 743 43235 +10 32 724 43911 +10 33 724 44879 +10 34 724 45847 +10 35 724 46815 +10 36 724 47783 +10 37 724 48751 +10 38 724 49719 +10 39 724 50687 +10 40 724 51655 +10 41 724 52623 +10 42 724 53591 +10 43 32 2401 +10 44 32 2433 +10 45 32 2465 +10 46 32 2497 +10 47 32 2529 +10 48 32 2561 +11 12 64 2319 +11 13 64 2383 +11 14 64 2447 +11 15 19 754 +11 16 269 11065 +11 17 269 11452 +11 18 269 11839 +11 19 269 12226 +11 20 269 12613 +11 21 269 13000 +11 22 269 13387 +11 23 22391 1140187 +11 24 11439 598352 +11 25 32026 1718785 +11 26 743 40878 +11 27 3 169 +11 29 4915 289628 +11 30 2985 179821 +11 31 211021 12971783 +11 33 1486 95117 +11 35 211021 14026888 +11 36 1448 98153 +11 37 1448 100089 +11 38 1448 102025 +11 39 1448 103961 +11 40 1448 105897 +11 41 1448 107833 +11 42 1448 109769 +11 43 1448 111705 +11 44 1448 113641 +11 45 1448 115577 +11 46 1448 117513 +11 47 64 5263 +11 48 64 5327 +12 13 16 631 +12 14 16 647 +12 15 16 663 +12 16 19 812 +12 17 269 11895 +12 18 269 12282 +12 19 269 12669 +12 20 269 13056 +12 21 269 13443 +12 22 269 13830 +12 23 269 14217 +12 24 269 14604 +12 25 22391 1240985 +12 26 15387 874144 +12 27 349 20304 +12 28 5867 349204 +12 29 1937 117873 +12 33 995 65761 +12 35 619 42442 +12 36 743 51882 +12 37 1238 87979 +12 39 362 26637 +12 40 362 27121 +12 41 362 27605 +12 42 362 28089 +12 43 362 28573 +12 44 362 29057 +12 45 362 29541 +12 46 362 30025 +12 47 362 30509 +12 48 362 30993 +13 14 64 2729 +13 15 64 2793 +13 16 64 2857 +13 17 19 870 +13 18 269 12725 +13 19 269 13112 +13 20 269 13499 +13 21 269 13886 +13 22 269 14273 +13 23 269 14660 +13 24 269 15047 +13 25 269 15434 +13 26 269 15821 +13 27 22391 1341783 +13 30 9785 626588 +13 32 1036934989772687 69159480605522577 +13 33 16359 1112516 +13 35 2985 210658 +13 36 269 19343 +13 37 35 2559 +13 38 62327 4636164 +13 39 1486 112411 +13 40 124654 9583963 +13 41 35 2734 +13 42 1448 114943 +13 43 1448 116879 +13 44 1448 118815 +13 45 1448 120751 +13 46 1448 122687 +13 47 1448 124623 +13 48 1448 126559 +14 15 32 1467 +14 16 32 1499 +14 17 32 1531 +14 18 32 1563 +14 19 19 957 +14 20 269 13942 +14 21 269 14329 +14 22 269 14716 +14 23 269 15103 +14 24 269 15490 +14 25 269 15877 +14 26 269 16264 +14 27 269 16651 +14 28 269 17038 +14 29 22391 1442581 +14 32 4487779 307631030 +14 33 5867 410129 +14 34 219685 15645328 +14 37 325085403505815839 24418612227393898801 +14 38 199 15208 +14 39 269 20893 +14 40 68074509 5373444482 +14 42 743 60529 +14 44 68074509 5713817027 +14 45 724 61669 +14 46 724 62637 +14 47 724 63605 +14 48 724 64573 +15 16 64 3139 +15 17 64 3203 +15 18 64 3267 +15 19 64 3331 +15 20 19 1015 +15 21 269 14772 +15 22 269 15159 +15 23 269 15546 +15 24 269 15933 +15 25 269 16320 +15 26 269 16707 +15 27 269 17094 +15 28 269 17481 +15 29 269 17868 +15 30 269 18255 +15 31 22391 1543379 +15 33 498319 35728459 +15 34 2122540708227654350851 155072213378569359073777 +15 35 5867 436505 +15 36 31958 2420295 +15 37 689201 53108763 +15 38 16359 1281935 +15 39 56902130353 4532698535658 +15 41 2985 245582 +15 42 154 12855 +15 43 7113 602861 +15 45 1486 129705 +15 47 7113 638426 +15 48 1448 131733 +16 17 4 209 +16 18 4 213 +16 19 4 217 +16 20 4 221 +16 21 19 1073 +16 22 1 58 +16 23 269 15989 +16 24 269 16376 +16 25 269 16763 +16 26 269 17150 +16 27 269 17537 +16 28 269 17924 +16 29 269 18311 +16 30 269 18698 +16 31 269 19085 +16 32 269 19472 +16 33 22391 1644177 +16 35 11439 871787 +16 36 349 27072 +16 38 3362626333041236956 269837142815144165315 +16 43 995 86319 +16 44 2985 263044 +16 45 112450 10041383 +16 46 47 4257 +16 47 6340524178 582318638983 +16 48 743 69176 +17 18 64 3549 +17 19 64 3613 +17 20 64 3677 +17 21 64 3741 +17 22 19 1131 +17 23 19 1160 +17 24 269 16819 +17 25 269 17206 +17 26 269 17593 +17 27 269 17980 +17 28 269 18367 +17 29 269 18754 +17 30 269 19141 +17 31 269 19528 +17 32 269 19915 +17 33 269 20302 +17 34 269 20689 +17 35 22391 1744975 +17 36 2654453 210576825 +17 37 11439 923269 +17 40 5867 497430 +17 42 599 52365 +17 46 2985 276419 +17 47 269 25274 +17 48 854 81231 +18 19 32 1877 +18 20 32 1909 +18 21 32 1941 +18 22 32 1973 +18 23 32 2005 +18 24 19 1218 +18 25 269 17649 +18 26 269 18036 +18 27 269 18423 +18 28 269 18810 +18 29 269 19197 +18 30 269 19584 +18 31 269 19971 +18 32 269 20358 +18 33 269 20745 +18 34 269 21132 +18 35 269 21519 +18 36 269 21906 +18 37 269 22175 +18 38 2846636445243 238638750369022 +18 39 5129 437072 +18 42 5867 523806 +19 20 64 3959 +19 21 64 4023 +19 22 64 4087 +19 23 64 4151 +19 24 64 4215 +19 25 19 1276 +19 26 19 1305 +19 27 269 18866 +19 28 269 19253 +19 29 269 19640 +19 30 269 20027 +19 31 269 20414 +19 32 269 20801 +19 33 269 21188 +19 34 269 21575 +19 35 269 21962 +19 36 269 22349 +19 37 269 22736 +19 38 269 23123 +19 39 269 23392 +19 40 28458415 2513830036 +19 45 73 6944 +19 46 68248986 6583441727 +20 21 16 1041 +20 22 16 1057 +20 23 16 1073 +20 24 16 1089 +20 25 16 1105 +20 26 19 1334 +20 27 19 1363 +20 28 269 19696 +20 29 269 20083 +20 30 269 20470 +20 31 269 20857 +20 32 269 21244 +20 33 269 21631 +20 34 269 22018 +20 35 269 22405 +20 36 269 22792 +20 37 269 23179 +20 38 269 23566 +20 39 269 23953 +20 40 269 24340 +20 41 269 24609 +20 42 22391 2078778 +20 44 1494957 142913836 +20 45 349 33840 +20 46 90047 8852558 +20 47 5867 584731 +20 48 15979 1613530 +21 22 64 4369 +21 23 64 4433 +21 24 64 4497 +21 25 64 4561 +21 26 64 4625 +21 27 64 4689 +21 28 19 1421 +21 29 269 20526 +21 30 269 20913 +21 31 269 21300 +21 32 269 21687 +21 33 269 22074 +21 34 269 22461 +21 35 269 22848 +21 36 269 23235 +21 37 269 23622 +21 38 269 24009 +21 39 269 24396 +21 40 269 24783 +21 41 269 25170 +21 42 269 25557 +21 43 269 25826 +21 44 22391 2179576 +21 46 585 58564 +21 47 7500512497 761087553559 +21 48 4487779 461446545 +22 23 32 2287 +22 24 32 2319 +22 25 32 2351 +22 26 32 2383 +22 27 32 2415 +22 28 32 2447 +22 29 19 1479 +22 30 19 1508 +22 31 269 21743 +22 32 269 22130 +22 33 269 22517 +22 34 269 22904 +22 35 269 23291 +22 36 269 23678 +22 37 269 24065 +22 38 269 24452 +22 39 269 24839 +22 40 269 25226 +22 41 269 25613 +22 42 269 26000 +22 43 269 26387 +22 44 269 26774 +22 45 269 27043 +22 46 22391 2280374 +22 48 11439 1196704 +23 24 64 4779 +23 25 64 4843 +23 26 64 4907 +23 27 64 4971 +23 28 64 5035 +23 29 64 5099 +23 30 19 1537 +23 31 19 1566 +23 32 269 22573 +23 33 269 22960 +23 34 269 23347 +23 35 269 23734 +23 36 269 24121 +23 37 269 24508 +23 38 269 24895 +23 39 269 25282 +23 40 269 25669 +23 41 269 26056 +23 42 269 26443 +23 43 269 26830 +23 44 269 27217 +23 45 269 27604 +23 46 269 27991 +23 47 269 28260 +23 48 22391 2381172 +24 25 8 623 +24 26 8 631 +24 27 8 639 +24 28 8 647 +24 29 8 655 +24 30 8 663 +24 31 19 1595 +24 32 19 1624 +24 33 1 87 +24 34 269 23790 +24 35 269 24177 +24 36 269 24564 +24 37 269 24951 +24 38 269 25338 +24 39 269 25725 +24 40 269 26112 +24 41 269 26499 +24 42 269 26886 +24 43 269 27273 +24 44 269 27660 +24 45 269 28047 +24 46 269 28434 +24 47 269 28821 +24 48 269 29208 +25 26 64 5189 +25 27 64 5253 +25 28 64 5317 +25 29 64 5381 +25 30 64 5445 +25 31 64 5509 +25 32 64 5573 +25 33 19 1682 +25 34 19 1711 +25 35 269 24620 +25 36 269 25007 +25 37 269 25394 +25 38 269 25781 +25 39 269 26168 +25 40 269 26555 +25 41 269 26942 +25 42 269 27329 +25 43 269 27716 +25 44 269 28103 +25 45 269 28490 +25 46 269 28877 +25 47 269 29264 +25 48 269 29651 +26 27 32 2697 +26 28 32 2729 +26 29 32 2761 +26 30 32 2793 +26 31 32 2825 +26 32 32 2857 +26 33 32 2889 +26 34 19 1740 +26 35 19 1769 +26 36 269 25450 +26 37 269 25837 +26 38 269 26224 +26 39 269 26611 +26 40 269 26998 +26 41 269 27385 +26 42 269 27772 +26 43 269 28159 +26 44 269 28546 +26 45 269 28933 +26 46 269 29320 +26 47 269 29707 +26 48 269 30094 +27 28 64 5599 +27 29 64 5663 +27 30 64 5727 +27 31 64 5791 +27 32 64 5855 +27 33 64 5919 +27 34 64 5983 +27 35 19 1798 +27 36 19 1827 +27 37 19 1856 +27 38 269 26667 +27 39 269 27054 +27 40 269 27441 +27 41 269 27828 +27 42 269 28215 +27 43 269 28602 +27 44 269 28989 +27 45 269 29376 +27 46 269 29763 +27 47 269 30150 +27 48 269 30537 +28 29 16 1451 +28 30 16 1467 +28 31 16 1483 +28 32 16 1499 +28 33 16 1515 +28 34 16 1531 +28 35 16 1547 +28 36 16 1563 +28 37 19 1885 +28 38 19 1914 +28 39 269 27497 +28 40 269 27884 +28 41 269 28271 +28 42 269 28658 +28 43 269 29045 +28 44 269 29432 +28 45 269 29819 +28 46 269 30206 +28 47 269 30593 +28 48 269 30980 +29 30 64 6009 +29 31 64 6073 +29 32 64 6137 +29 33 64 6201 +29 34 64 6265 +29 35 64 6329 +29 36 64 6393 +29 37 64 6457 +29 38 19 1943 +29 39 19 1972 +29 40 269 28327 +29 41 269 28714 +29 42 269 29101 +29 43 269 29488 +29 44 269 29875 +29 45 269 30262 +29 46 269 30649 +29 47 269 31036 +29 48 269 31423 +30 31 32 3107 +30 32 32 3139 +30 33 32 3171 +30 34 32 3203 +30 35 32 3235 +30 36 32 3267 +30 37 32 3299 +30 38 32 3331 +30 39 19 2001 +30 40 19 2030 +30 41 19 2059 +30 42 269 29544 +30 43 269 29931 +30 44 269 30318 +30 45 269 30705 +30 46 269 31092 +30 47 269 31479 +30 48 269 31866 +31 32 64 6419 +31 33 64 6483 +31 34 64 6547 +31 35 64 6611 +31 36 64 6675 +31 37 64 6739 +31 38 64 6803 +31 39 64 6867 +31 40 19 2059 +31 41 19 2088 +31 42 19 2117 +31 43 269 30374 +31 44 269 30761 +31 45 269 31148 +31 46 269 31535 +31 47 269 31922 +31 48 269 32309 +32 33 2 207 +32 34 2 209 +32 35 2 211 +32 36 2 213 +32 37 2 215 +32 38 2 217 +32 39 2 219 +32 40 2 221 +32 41 2 223 +32 42 19 2146 +32 43 19 2175 +32 44 1 116 +32 45 269 31591 +32 46 269 31978 +32 47 269 32365 +32 48 269 32752 +33 34 64 6829 +33 35 64 6893 +33 36 64 6957 +33 37 64 7021 +33 38 64 7085 +33 39 64 7149 +33 40 64 7213 +33 41 64 7277 +33 42 64 7341 +33 43 1 116 +33 44 19 2233 +33 45 19 2262 +33 46 269 32421 +33 47 269 32808 +33 48 269 33195 +34 35 32 3517 +34 36 32 3549 +34 37 32 3581 +34 38 32 3613 +34 39 32 3645 +34 40 32 3677 +34 41 32 3709 +34 42 32 3741 +34 43 32 3773 +34 44 19 2262 +34 45 19 2291 +34 46 19 2320 +34 47 269 33251 +34 48 269 33638 +35 36 64 7239 +35 37 64 7303 +35 38 64 7367 +35 39 64 7431 +35 40 64 7495 +35 41 64 7559 +35 42 64 7623 +35 43 64 7687 +35 44 64 7751 +35 45 64 7815 +35 46 19 2349 +35 47 19 2378 +35 48 19 2407 +36 37 16 1861 +36 38 16 1877 +36 39 16 1893 +36 40 16 1909 +36 41 16 1925 +36 42 16 1941 +36 43 16 1957 +36 44 16 1973 +36 45 16 1989 +36 46 16 2005 +36 47 19 2407 +36 48 19 2436 +37 38 64 7649 +37 39 64 7713 +37 40 64 7777 +37 41 64 7841 +37 42 64 7905 +37 43 64 7969 +37 44 64 8033 +37 45 64 8097 +37 46 64 8161 +37 47 64 8225 +37 48 19 2465 +38 39 32 3927 +38 40 32 3959 +38 41 32 3991 +38 42 32 4023 +38 43 32 4055 +38 44 32 4087 +38 45 32 4119 +38 46 32 4151 +38 47 32 4183 +38 48 32 4215 +39 40 64 8059 +39 41 64 8123 +39 42 64 8187 +39 43 64 8251 +39 44 64 8315 +39 45 64 8379 +39 46 64 8443 +39 47 64 8507 +39 48 64 8571 +40 41 8 1033 +40 42 8 1041 +40 43 8 1049 +40 44 8 1057 +40 45 8 1065 +40 46 8 1073 +40 47 8 1081 +40 48 8 1089 +41 42 64 8469 +41 43 64 8533 +41 44 64 8597 +41 45 64 8661 +41 46 64 8725 +41 47 64 8789 +41 48 64 8853 +42 43 32 4337 +42 44 32 4369 +42 45 32 4401 +42 46 32 4433 +42 47 32 4465 +42 48 32 4497 +43 44 64 8879 +43 45 64 8943 +43 46 64 9007 +43 47 64 9071 +43 48 64 9135 +44 45 16 2271 +44 46 16 2287 +44 47 16 2303 +44 48 16 2319 +45 46 64 9289 +45 47 64 9353 +45 48 64 9417 +46 47 32 4747 +46 48 32 4779 +47 48 64 9699 diff --git a/tests/etalon-tauabc.txt b/tests/etalon-tauabc.txt new file mode 100644 --- /dev/null +++ b/tests/etalon-tauabc.txt @@ -0,0 +1,966 @@ +1 2 2 333 1025 +1 2 3 2293 8301 +1 3 3 669 2818 +1 5 5 150509 973242 +1 5 6 269 1896 +1 6 6 56101 423967 +1 6 7 2516635 20403699 +1 7 7 75 649 +1 8 8 15 146 +1 8 9 223719847217121 2297589826762495 +1 9 9 23153746 250203427 +1 9 10 275869 3128113 +1 10 11 1771 21955 +1 11 11 13 168 +1 11 12 239355515695 3218484590334 +1 12 12 247 3450 +1 13 13 1819 27324 +1 13 14 1819 28336 +1 15 16 31868239 561675913 +1 16 16 93607 1698654 +1 16 17 14299 266933 +1 18 18 5688630024 115054218641 +1 18 19 37163 770843 +1 19 19 122549345354977673 2605376534034571879 +2 3 3 743 3920 +2 3 4 10133 57826 +2 3 5 333 2050 +2 4 4 333 2050 +2 4 5 4586 30437 +2 4 6 2293 16602 +2 5 5 2293 16602 +2 5 6 218024379851983 1708497349336974 +2 5 7 669 5636 +2 6 6 669 5636 +2 6 7 2024 18255 +2 7 8 29715356 301794587 +2 8 9 625865993 7060780333 +2 9 10 2188287086 27107872927 +2 9 11 150509 1946484 +2 10 10 150509 1946484 +2 10 11 269 3634 +2 10 12 269 3792 +2 11 11 269 3792 +2 11 12 269 3950 +2 11 13 56101 847934 +2 12 12 56101 847934 +2 12 14 2516635 40807398 +2 13 13 2516635 40807398 +2 13 14 1035509 17356160 +2 13 15 75 1298 +2 14 14 75 1298 +2 14 15 48968995 874112298 +2 15 17 15 292 +2 16 16 15 292 +2 16 17 4727 94605 +2 16 18 223719847217121 4595179653524990 +2 17 17 223719847217121 4595179653524990 +2 17 18 13 274 +2 17 19 11576873 250203427 +2 18 18 11576873 250203427 +2 18 19 4981 110308 +2 18 20 275869 6256226 +2 19 19 275869 6256226 +2 19 20 901 20911 +3 4 4 92 679 +3 4 5 743 5880 +3 4 7 1283 11207 +3 5 6 1283 11207 +3 5 7 111 1025 +3 5 8 43 416 +3 6 6 111 1025 +3 6 7 43 416 +3 6 8 4586 47039 +3 6 9 2293 24903 +3 7 7 4586 47039 +3 7 8 2293 24903 +3 7 9 16051 183882 +3 7 10 1409 16979 +3 8 8 16051 183882 +3 8 9 1409 16979 +3 8 10 223 2818 +3 8 11 92 1217 +3 9 9 223 2818 +3 9 10 92 1217 +3 9 11 24763 341579 +3 10 10 24763 341579 +3 10 12 6213 92875 +3 10 13 27 419 +3 11 11 6213 92875 +3 11 12 27 419 +3 11 14 53 882 +3 12 13 53 882 +3 13 15 558902993342 10231819156675 +3 14 14 558902993342 10231819156675 +3 14 16 150509 2919726 +3 14 17 269 5372 +3 15 15 150509 2919726 +3 15 16 269 5372 +3 15 17 269 5530 +3 15 18 269 5688 +3 16 16 269 5530 +3 16 17 269 5688 +3 16 18 269 5846 +3 16 19 103 2280 +3 17 17 269 5846 +3 17 18 103 2280 +3 17 19 56101 1271901 +3 18 18 56101 1271901 +3 18 21 2516635 61211097 +3 19 20 2516635 61211097 +3 19 21 5832435759679 145047841602167 +4 5 6 1012 10185 +4 5 7 743 7840 +4 5 8 2293 25262 +4 5 9 10133 115652 +4 6 6 743 7840 +4 6 7 2293 25262 +4 6 8 10133 115652 +4 6 9 4 47 +4 6 10 333 4100 +4 7 7 10133 115652 +4 7 8 4 47 +4 7 9 333 4100 +4 7 10 43 546 +4 7 11 2293 30437 +4 8 8 333 4100 +4 8 9 43 546 +4 8 10 2293 30437 +4 8 11 4586 63641 +4 8 12 2293 33204 +4 9 9 2293 30437 +4 9 10 4586 63641 +4 9 11 2293 33204 +4 9 12 3093 46625 +4 9 13 218024379851983 3416994698673948 +4 10 10 2293 33204 +4 10 11 3093 46625 +4 10 12 218024379851983 3416994698673948 +4 10 13 11888 193347 +4 10 14 669 11272 +4 11 11 218024379851983 3416994698673948 +4 11 12 11888 193347 +4 11 13 669 11272 +4 11 14 2024 35293 +4 11 15 1012 18255 +4 12 12 669 11272 +4 12 13 2024 35293 +4 12 14 1012 18255 +4 13 13 1012 18255 +4 13 17 14857678 301794587 +4 14 16 14857678 301794587 +4 14 17 7763609 162102436 +4 15 15 14857678 301794587 +4 15 16 7763609 162102436 +4 15 18 1249 27491 +4 15 19 625865993 14121560666 +4 16 17 1249 27491 +4 16 18 625865993 14121560666 +4 16 19 11517061 266291661 +4 17 17 625865993 14121560666 +4 17 18 11517061 266291661 +4 17 21 1094143543 27107872927 +4 18 20 1094143543 27107872927 +4 18 22 150509 3892968 +4 19 19 1094143543 27107872927 +4 19 21 150509 3892968 +4 19 22 269 7110 +4 19 23 269 7268 +5 6 6 15979 183584 +5 6 7 56902130353 688811679299 +5 6 8 77 974 +5 6 9 743 9800 +5 6 10 77 1051 +5 7 7 77 974 +5 7 8 743 9800 +5 7 9 77 1051 +5 7 11 455217042824 6575189113303 +5 7 12 111 1640 +5 8 8 77 1051 +5 8 10 455217042824 6575189113303 +5 8 11 111 1640 +5 8 12 333 5125 +5 8 13 333 5330 +5 9 9 455217042824 6575189113303 +5 9 10 111 1640 +5 9 11 333 5125 +5 9 12 333 5330 +5 9 13 4586 74709 +5 9 14 2293 38738 +5 10 10 333 5125 +5 10 11 333 5330 +5 10 12 4586 74709 +5 10 13 2293 38738 +5 10 14 4586 80243 +5 10 15 2293 41505 +5 11 11 4586 74709 +5 11 12 2293 38738 +5 11 13 4586 80243 +5 11 14 2293 41505 +5 11 15 3093 57815 +5 11 16 37131637 716380913 +5 12 12 4586 80243 +5 12 13 2293 41505 +5 12 14 3093 57815 +5 12 15 37131637 716380913 +5 13 13 3093 57815 +5 13 14 37131637 716380913 +5 13 17 669 14090 +5 13 18 506 10953 +5 14 16 669 14090 +5 14 17 506 10953 +5 14 18 2024 45029 +5 15 15 669 14090 +5 15 16 506 10953 +5 15 17 2024 45029 +5 16 16 2024 45029 +5 16 21 67 1682 +5 17 20 67 1682 +5 17 22 589495295338445 15468933279703773 +5 18 19 67 1682 +5 18 21 589495295338445 15468933279703773 +5 18 23 1249 34178 +5 19 20 589495295338445 15468933279703773 +5 19 22 1249 34178 +6 7 7 1249 16910 +6 7 9 46 679 +6 7 11 743 11760 +6 8 8 46 679 +6 8 10 743 11760 +6 8 13 10133 173478 +6 8 14 1283 22414 +6 9 9 743 11760 +6 9 12 10133 173478 +6 9 13 1283 22414 +6 9 14 333 5945 +6 9 15 111 2050 +6 10 11 10133 173478 +6 10 12 1283 22414 +6 10 13 333 5945 +6 10 14 111 2050 +6 10 15 333 6355 +6 10 16 43 832 +6 11 11 1283 22414 +6 11 12 333 5945 +6 11 13 111 2050 +6 11 14 333 6355 +6 11 15 43 832 +6 11 16 4586 91311 +6 11 17 2293 47039 +6 12 12 111 2050 +6 12 13 333 6355 +6 12 14 43 832 +6 12 15 4586 91311 +6 12 16 2293 47039 +6 12 17 4586 96845 +6 12 18 2293 49806 +6 13 13 43 832 +6 13 14 4586 91311 +6 13 15 2293 47039 +6 13 16 4586 96845 +6 13 17 2293 49806 +6 13 18 4586 102379 +6 13 19 16051 367764 +6 14 14 2293 47039 +6 14 15 4586 96845 +6 14 16 2293 49806 +6 14 17 4586 102379 +6 14 18 16051 367764 +6 14 19 218024379851983 5125492048010922 +6 14 20 1409 33958 +6 15 15 2293 49806 +6 15 16 4586 102379 +6 15 17 16051 367764 +6 15 18 218024379851983 5125492048010922 +6 15 19 1409 33958 +6 15 21 223 5636 +6 16 16 16051 367764 +6 16 17 218024379851983 5125492048010922 +6 16 18 1409 33958 +6 16 20 223 5636 +6 16 21 2024 52331 +6 16 22 46 1217 +6 17 17 1409 33958 +6 17 19 223 5636 +6 17 20 2024 52331 +6 17 21 46 1217 +6 17 22 2024 54765 +6 17 23 24763 683158 +6 18 18 223 5636 +6 18 19 2024 52331 +6 18 20 46 1217 +6 18 21 2024 54765 +6 18 22 24763 683158 +6 19 19 46 1217 +6 19 20 2024 54765 +6 19 21 24763 683158 +6 19 24 40 1173 +6 19 25 6213 185750 +7 8 8 2498 38893 +7 8 9 219685 3562653 +7 8 11 506 8827 +7 8 12 68074509 1220899433 +7 8 13 743 13720 +7 8 14 68074509 1288973942 +7 9 10 506 8827 +7 9 11 68074509 1220899433 +7 9 12 743 13720 +7 9 13 68074509 1288973942 +7 9 16 4919 99200 +7 10 10 68074509 1220899433 +7 10 11 743 13720 +7 10 12 68074509 1288973942 +7 10 15 4919 99200 +7 10 17 333 6970 +7 11 11 68074509 1288973942 +7 11 14 4919 99200 +7 11 16 333 6970 +7 11 17 333 7175 +7 11 18 37 820 +7 12 13 4919 99200 +7 12 15 333 6970 +7 12 16 333 7175 +7 12 17 37 820 +7 12 18 43 962 +7 12 19 2293 52573 +7 13 14 333 6970 +7 13 15 333 7175 +7 13 16 37 820 +7 13 17 43 962 +7 13 18 2293 52573 +7 13 19 4586 107913 +7 13 20 2293 55340 +7 14 14 333 7175 +7 14 15 37 820 +7 14 16 43 962 +7 14 17 2293 52573 +7 14 18 4586 107913 +7 14 19 2293 55340 +7 14 20 4586 113447 +7 14 21 2293 58107 +7 15 15 43 962 +7 15 16 2293 52573 +7 15 17 4586 107913 +7 15 18 2293 55340 +7 15 19 4586 113447 +7 15 20 2293 58107 +7 15 21 4586 118981 +7 15 22 4270734388451 113305440473083 +7 16 16 4586 107913 +7 16 17 2293 55340 +7 16 18 4586 113447 +7 16 19 2293 58107 +7 16 20 4586 118981 +7 16 21 4270734388451 113305440473083 +7 16 23 1832403 50801398 +7 17 17 4586 113447 +7 17 18 2293 58107 +7 17 19 4586 118981 +7 17 20 4270734388451 113305440473083 +7 17 22 1832403 50801398 +7 17 23 12908791557077 365492880716212 +7 17 24 2113 61068 +7 18 18 4586 118981 +7 18 19 4270734388451 113305440473083 +7 18 21 1832403 50801398 +7 18 22 12908791557077 365492880716212 +7 18 23 2113 61068 +7 18 24 669 19726 +7 19 20 1832403 50801398 +7 19 21 12908791557077 365492880716212 +7 19 22 2113 61068 +7 19 23 669 19726 +7 19 25 2024 62067 +7 19 26 506 15821 +8 9 9 1249 21983 +8 9 10 18395 335664 +8 9 13 506 10185 +8 9 14 47 967 +8 9 15 743 15680 +8 9 16 47 1014 +8 9 17 2293 50524 +8 10 12 506 10185 +8 10 13 47 967 +8 10 14 743 15680 +8 10 15 47 1014 +8 10 16 2293 50524 +8 10 17 21499 482368 +8 10 18 10133 231304 +8 11 11 506 10185 +8 11 12 47 967 +8 11 13 743 15680 +8 11 14 47 1014 +8 11 15 2293 50524 +8 11 16 21499 482368 +8 11 17 10133 231304 +8 11 19 2 47 +8 12 12 743 15680 +8 12 13 47 1014 +8 12 14 2293 50524 +8 12 15 21499 482368 +8 12 16 10133 231304 +8 12 18 2 47 +8 12 19 111 2665 +8 12 20 333 8200 +8 13 13 2293 50524 +8 13 14 21499 482368 +8 13 15 10133 231304 +8 13 17 2 47 +8 13 18 111 2665 +8 13 19 333 8200 +8 13 20 333 8405 +8 13 21 43 1092 +8 14 14 10133 231304 +8 14 16 2 47 +8 14 17 111 2665 +8 14 18 333 8200 +8 14 19 333 8405 +8 14 20 43 1092 +8 14 21 1 26 +8 14 22 2293 60874 +8 15 15 2 47 +8 15 16 111 2665 +8 15 17 333 8200 +8 15 18 333 8405 +8 15 19 43 1092 +8 15 20 1 26 +8 15 21 2293 60874 +8 15 22 4586 124515 +8 15 23 2293 63641 +8 16 16 333 8200 +8 16 17 333 8405 +8 16 18 43 1092 +8 16 19 1 26 +8 16 20 2293 60874 +8 16 21 4586 124515 +8 16 22 2293 63641 +8 16 23 4586 130049 +8 16 24 2293 66408 +8 17 17 43 1092 +8 17 18 1 26 +8 17 19 2293 60874 +8 17 20 4586 124515 +8 17 21 2293 63641 +8 17 22 4586 130049 +8 17 23 2293 66408 +8 17 24 4586 135583 +8 17 25 3093 93250 +8 18 18 2293 60874 +8 18 19 4586 124515 +8 18 20 2293 63641 +8 18 21 4586 130049 +8 18 22 2293 66408 +8 18 23 4586 135583 +8 18 24 3093 93250 +8 18 26 218024379851983 6833989397347896 +8 19 19 2293 63641 +8 19 20 4586 130049 +8 19 21 2293 66408 +8 19 22 4586 135583 +8 19 23 3093 93250 +8 19 25 218024379851983 6833989397347896 +8 19 27 5944 193347 +9 10 10 2498 49039 +9 10 11 1249 25365 +9 10 14 92 2037 +9 10 15 3 68 +9 10 16 106699 2476870 +9 10 17 743 17640 +9 10 18 106699 2583569 +9 11 13 92 2037 +9 11 14 3 68 +9 11 15 106699 2476870 +9 11 16 743 17640 +9 11 17 106699 2583569 +9 12 12 92 2037 +9 12 13 3 68 +9 12 14 106699 2476870 +9 12 15 743 17640 +9 12 16 106699 2583569 +9 12 21 1283 33621 +9 13 13 106699 2476870 +9 13 14 743 17640 +9 13 15 106699 2583569 +9 13 20 1283 33621 +9 13 22 333 9020 +9 14 14 106699 2583569 +9 14 19 1283 33621 +9 14 21 333 9020 +9 14 22 37 1025 +9 14 23 333 9430 +9 15 18 1283 33621 +9 15 20 333 9020 +9 15 21 37 1025 +9 15 22 333 9430 +9 15 23 43 1222 +9 15 24 43 1248 +9 16 17 1283 33621 +9 16 19 333 9020 +9 16 20 37 1025 +9 16 21 333 9430 +9 16 22 43 1222 +9 16 23 43 1248 +9 16 24 4586 135583 +9 16 25 2293 69175 +9 17 18 333 9020 +9 17 19 37 1025 +9 17 20 333 9430 +9 17 21 43 1222 +9 17 22 43 1248 +9 17 23 4586 135583 +9 17 24 2293 69175 +9 17 25 4586 141117 +9 17 26 2293 71942 +9 18 18 37 1025 +9 18 19 333 9430 +9 18 20 43 1222 +9 18 21 43 1248 +9 18 22 4586 135583 +9 18 23 2293 69175 +9 18 24 4586 141117 +9 18 25 2293 71942 +9 18 26 4586 146651 +9 18 27 2293 74709 +9 19 19 43 1222 +9 19 20 43 1248 +9 19 21 4586 135583 +9 19 22 2293 69175 +9 19 23 4586 141117 +9 19 24 2293 71942 +9 19 25 4586 146651 +9 19 26 2293 74709 +9 19 27 4586 152185 +9 19 28 3093 104440 +10 11 11 1249 27056 +10 11 12 2498 55803 +10 11 13 15979 367168 +10 11 15 56902130353 1377623358598 +10 11 16 1012 25123 +10 11 17 77 1948 +10 11 19 743 19600 +10 11 21 77 2102 +10 12 12 15979 367168 +10 12 14 56902130353 1377623358598 +10 12 15 1012 25123 +10 12 16 77 1948 +10 12 18 743 19600 +10 12 20 77 2102 +10 13 13 56902130353 1377623358598 +10 13 14 1012 25123 +10 13 15 77 1948 +10 13 17 743 19600 +10 13 19 77 2102 +10 13 22 10133 289130 +10 13 23 227608521412 6575189113303 +10 14 14 77 1948 +10 14 16 743 19600 +10 14 18 77 2102 +10 14 21 10133 289130 +10 14 22 227608521412 6575189113303 +10 14 23 1494957 43689865 +10 14 24 111 3280 +10 15 15 743 19600 +10 15 17 77 2102 +10 15 20 10133 289130 +10 15 21 227608521412 6575189113303 +10 15 22 1494957 43689865 +10 15 23 111 3280 +10 15 24 333 10045 +10 15 25 333 10250 +10 16 16 77 2102 +10 16 19 10133 289130 +10 16 20 227608521412 6575189113303 +10 16 21 1494957 43689865 +10 16 22 111 3280 +10 16 23 333 10045 +10 16 24 333 10250 +10 16 25 111 3485 +10 16 26 333 10660 +10 17 18 10133 289130 +10 17 19 227608521412 6575189113303 +10 17 20 1494957 43689865 +10 17 21 111 3280 +10 17 22 333 10045 +10 17 23 333 10250 +10 17 24 111 3485 +10 17 25 333 10660 +10 17 26 43 1378 +10 17 27 2293 74709 +10 18 18 227608521412 6575189113303 +10 18 19 1494957 43689865 +10 18 20 111 3280 +10 18 21 333 10045 +10 18 22 333 10250 +10 18 23 111 3485 +10 18 24 333 10660 +10 18 25 43 1378 +10 18 26 2293 74709 +10 18 27 4586 152185 +10 18 28 2293 77476 +10 19 19 111 3280 +10 19 20 333 10045 +10 19 21 333 10250 +10 19 22 111 3485 +10 19 23 333 10660 +10 19 24 43 1378 +10 19 25 2293 74709 +10 19 26 4586 152185 +10 19 27 2293 77476 +10 19 28 4586 157719 +10 19 29 2293 80243 +11 12 12 2498 59185 +11 12 13 1249 30438 +11 12 14 18395 459984 +11 12 15 3 77 +11 12 16 791 20787 +11 12 17 1771 47560 +11 12 18 1012 27839 +11 12 19 211021 5896571 +11 12 21 743 21560 +11 12 23 211021 6318613 +11 13 13 18395 459984 +11 13 14 3 77 +11 13 15 791 20787 +11 13 16 1771 47560 +11 13 17 1012 27839 +11 13 18 211021 5896571 +11 13 20 743 21560 +11 13 22 211021 6318613 +11 14 14 791 20787 +11 14 15 1771 47560 +11 14 16 1012 27839 +11 14 17 211021 5896571 +11 14 19 743 21560 +11 14 21 211021 6318613 +11 14 25 44950934202285 1418801946268517 +11 15 15 1012 27839 +11 15 16 211021 5896571 +11 15 18 743 21560 +11 15 20 211021 6318613 +11 15 24 44950934202285 1418801946268517 +11 15 25 12 383 +11 16 17 743 21560 +11 16 19 211021 6318613 +11 16 23 44950934202285 1418801946268517 +11 16 24 12 383 +11 16 26 333 10865 +11 16 27 37 1230 +11 17 18 211021 6318613 +11 17 22 44950934202285 1418801946268517 +11 17 23 12 383 +11 17 25 333 10865 +11 17 26 37 1230 +11 17 27 333 11275 +11 17 28 333 11480 +11 18 21 44950934202285 1418801946268517 +11 18 22 12 383 +11 18 24 333 10865 +11 18 25 37 1230 +11 18 26 333 11275 +11 18 27 333 11480 +11 18 28 111 3895 +11 18 29 43 1508 +11 19 20 44950934202285 1418801946268517 +11 19 21 12 383 +11 19 23 333 10865 +11 19 24 37 1230 +11 19 25 333 11275 +11 19 26 333 11480 +11 19 27 111 3895 +11 19 28 43 1508 +11 19 29 43 1534 +11 19 30 2293 83010 +12 13 13 1249 32129 +12 13 14 2498 65949 +12 13 15 1249 33820 +12 13 16 1937 53668 +12 13 19 23 679 +12 13 20 1012 30555 +12 13 22 619 19270 +12 13 23 743 23520 +12 13 24 619 19889 +12 14 14 1249 33820 +12 14 15 1937 53668 +12 14 18 23 679 +12 14 19 1012 30555 +12 14 21 619 19270 +12 14 22 743 23520 +12 14 23 619 19889 +12 14 25 2293 75786 +12 15 17 23 679 +12 15 18 1012 30555 +12 15 20 619 19270 +12 15 21 743 23520 +12 15 22 619 19889 +12 15 24 2293 75786 +12 15 26 70188 2376259 +12 15 27 10133 346956 +12 16 16 23 679 +12 16 17 1012 30555 +12 16 19 619 19270 +12 16 20 743 23520 +12 16 21 619 19889 +12 16 23 2293 75786 +12 16 25 70188 2376259 +12 16 26 10133 346956 +12 16 28 1283 44828 +12 17 18 619 19270 +12 17 19 743 23520 +12 17 20 619 19889 +12 17 22 2293 75786 +12 17 24 70188 2376259 +12 17 25 10133 346956 +12 17 27 1283 44828 +12 17 28 4 141 +12 17 29 333 11890 +12 18 18 743 23520 +12 18 19 619 19889 +12 18 21 2293 75786 +12 18 23 70188 2376259 +12 18 24 10133 346956 +12 18 26 1283 44828 +12 18 27 4 141 +12 18 28 333 11890 +12 18 29 333 12095 +12 18 30 111 4100 +12 19 20 2293 75786 +12 19 22 70188 2376259 +12 19 23 10133 346956 +12 19 25 1283 44828 +12 19 26 4 141 +12 19 27 333 11890 +12 19 28 333 12095 +12 19 29 111 4100 +12 19 30 333 12505 +12 19 31 333 12710 +13 14 14 2498 69331 +13 14 15 1249 35511 +13 14 16 2498 72713 +13 14 17 18395 547008 +13 14 18 1036934989772687 31514657264458393 +13 14 19 6213 192694 +13 14 21 253 8148 +13 14 22 3 98 +13 14 23 35 1163 +13 14 24 62327 2104723 +13 14 25 743 25480 +13 14 26 62327 2167050 +13 14 27 35 1233 +13 15 15 2498 72713 +13 15 16 18395 547008 +13 15 17 1036934989772687 31514657264458393 +13 15 18 6213 192694 +13 15 20 253 8148 +13 15 21 3 98 +13 15 22 35 1163 +13 15 23 62327 2104723 +13 15 24 743 25480 +13 15 25 62327 2167050 +13 15 26 35 1233 +13 15 28 3886795819 140271950650 +13 16 16 1036934989772687 31514657264458393 +13 16 17 6213 192694 +13 16 19 253 8148 +13 16 20 3 98 +13 16 21 35 1163 +13 16 22 62327 2104723 +13 16 23 743 25480 +13 16 24 62327 2167050 +13 16 25 35 1233 +13 16 27 3886795819 140271950650 +13 17 18 253 8148 +13 17 19 3 98 +13 17 20 35 1163 +13 17 21 62327 2104723 +13 17 22 743 25480 +13 17 23 62327 2167050 +13 17 24 35 1233 +13 17 26 3886795819 140271950650 +13 17 30 8 301 +13 18 18 3 98 +13 18 19 35 1163 +13 18 20 62327 2104723 +13 18 21 743 25480 +13 18 22 62327 2167050 +13 18 23 35 1233 +13 18 25 3886795819 140271950650 +13 18 29 8 301 +13 19 19 62327 2104723 +13 19 20 743 25480 +13 19 21 62327 2167050 +13 19 22 35 1233 +13 19 24 3886795819 140271950650 +13 19 28 8 301 +13 19 31 37 1435 +13 19 32 333 13120 +14 15 15 1249 37202 +14 15 16 2498 76095 +14 15 17 1249 38893 +14 15 18 2498 79477 +14 15 19 219685 7125306 +14 15 22 325085403505815839 11127317648113160278 +14 15 23 253 8827 +14 15 24 3 106 +14 15 25 68074509 2441798866 +14 15 27 743 27440 +14 15 29 68074509 2577947884 +14 16 16 1249 38893 +14 16 17 2498 79477 +14 16 18 219685 7125306 +14 16 21 325085403505815839 11127317648113160278 +14 16 22 253 8827 +14 16 23 3 106 +14 16 24 68074509 2441798866 +14 16 26 743 27440 +14 16 28 68074509 2577947884 +14 16 29 1819951438032391 69706840889366278 +14 17 17 219685 7125306 +14 17 20 325085403505815839 11127317648113160278 +14 17 21 253 8827 +14 17 22 3 106 +14 17 23 68074509 2441798866 +14 17 25 743 27440 +14 17 27 68074509 2577947884 +14 17 28 1819951438032391 69706840889366278 +14 18 19 325085403505815839 11127317648113160278 +14 18 20 253 8827 +14 18 21 3 106 +14 18 22 68074509 2441798866 +14 18 24 743 27440 +14 18 26 68074509 2577947884 +14 18 27 1819951438032391 69706840889366278 +14 18 31 10133 404782 +14 18 32 4919 198400 +14 19 19 253 8827 +14 19 20 3 106 +14 19 21 68074509 2441798866 +14 19 23 743 27440 +14 19 25 68074509 2577947884 +14 19 26 1819951438032391 69706840889366278 +14 19 30 10133 404782 +14 19 31 4919 198400 +14 19 32 878740 35722659 +15 16 16 2498 79477 +15 16 17 1249 40584 +15 16 18 2498 82859 +15 16 19 1249 42275 +15 16 20 15979 550752 +15 16 21 689201 24202607 +15 16 22 6213 222017 +15 16 23 56902130353 2066435037897 +15 16 24 92 3395 +15 16 25 253 9506 +15 16 26 77 2922 +15 16 27 7113 273919 +15 16 29 743 29400 +15 16 31 7113 288145 +15 17 17 2498 82859 +15 17 18 1249 42275 +15 17 19 15979 550752 +15 17 20 689201 24202607 +15 17 21 6213 222017 +15 17 22 56902130353 2066435037897 +15 17 23 92 3395 +15 17 24 253 9506 +15 17 25 77 2922 +15 17 26 7113 273919 +15 17 28 743 29400 +15 17 30 7113 288145 +15 17 31 77 3153 +15 18 18 15979 550752 +15 18 19 689201 24202607 +15 18 20 6213 222017 +15 18 21 56902130353 2066435037897 +15 18 22 92 3395 +15 18 23 253 9506 +15 18 24 77 2922 +15 18 25 7113 273919 +15 18 27 743 29400 +15 18 29 7113 288145 +15 18 30 77 3153 +15 19 19 6213 222017 +15 19 20 56902130353 2066435037897 +15 19 21 92 3395 +15 19 22 253 9506 +15 19 23 77 2922 +15 19 24 7113 273919 +15 19 26 743 29400 +15 19 28 7113 288145 +15 19 29 77 3153 +16 17 17 1249 42275 +16 17 18 2498 86241 +16 17 19 1249 43966 +16 17 20 2498 89623 +16 17 21 18395 671328 +16 17 26 1012 40061 +16 17 27 253 10185 +16 17 28 56225 2282333 +16 17 29 47 1934 +16 17 30 3170262089 132141422345 +16 17 31 743 31360 +16 17 32 3170262089 135311684434 +16 17 33 47 2028 +16 18 18 1249 43966 +16 18 19 2498 89623 +16 18 20 18395 671328 +16 18 25 1012 40061 +16 18 26 253 10185 +16 18 27 56225 2282333 +16 18 28 47 1934 +16 18 29 3170262089 132141422345 +16 18 30 743 31360 +16 18 31 3170262089 135311684434 +16 18 32 47 2028 +16 18 33 56225 2451008 +16 18 34 2293 101048 +16 19 19 18395 671328 +16 19 24 1012 40061 +16 19 25 253 10185 +16 19 26 56225 2282333 +16 19 27 47 1934 +16 19 28 3170262089 132141422345 +16 19 29 743 31360 +16 19 30 3170262089 135311684434 +16 19 31 47 2028 +16 19 32 56225 2451008 +16 19 33 2293 101048 +16 19 34 326645851 14519806250 +16 19 35 21499 964736 +17 18 18 2498 89623 +17 18 19 1249 45657 +17 18 20 2498 93005 +17 18 21 1249 47348 +17 18 22 2498 96387 +17 18 23 1439 56405 +17 18 24 599 23865 +17 18 25 2071 83780 +17 18 28 1012 42777 +17 18 29 3 128 +17 18 31 6815 298452 +17 18 33 743 33320 +17 19 19 2498 93005 +17 19 20 1249 47348 +17 19 21 2498 96387 +17 19 22 1439 56405 +17 19 23 599 23865 +17 19 24 2071 83780 +17 19 27 1012 42777 +17 19 28 3 128 +17 19 30 6815 298452 +17 19 32 743 33320 +17 19 35 16051 742163 +17 19 36 2293 106992 +18 19 19 1249 47348 +18 19 20 2498 96387 +18 19 21 1249 49039 +18 19 22 2498 99769 +18 19 23 1249 50730 +18 19 24 18395 758352 +18 19 29 46 2037 +18 19 30 1012 45493 +18 19 31 3 136 +18 19 33 106699 4953740 +18 19 34 6258413099 293873117617 +18 19 35 743 35280 +18 19 36 6258413099 300131530716 +18 19 37 106699 5167138 diff --git a/tests/etalon-zetaOnS.txt b/tests/etalon-zetaOnS.txt new file mode 100644 --- /dev/null +++ b/tests/etalon-zetaOnS.txt @@ -0,0 +1,894 @@ +101 106 9210542615639205 1432875253204022774 +101 132 12093276003271 227788219785852 +101 138 223 3450 +101 140 23 336 +101 142 3141 44872 +101 144 1705 22752 +101 166 45075 404044 +101 168 47099 408912 +101 178 451061 3445368 +101 180 18001 134280 +10 19 15897 105146 +103 104 1801 1879982 +103 112 34961477 2780235885 +103 114 2545 158688 +103 138 13433441014093830750443840177663 225933938932347489300134610051186 +103 142 16174030823839 241111139555130 +103 144 1547 22752 +103 146 3363 46136 +103 156 71510732950909227809816265846391 790730200392651666134106160283736 +103 162 30152 300915 +103 170 46689 413780 +105 148 829 11692 +105 164 68302723 694398796 +105 172 46279 418648 +105 176 677195 5771744 +107 108 6362302118623 6948722511187650 +107 126 6405961 221944086 +107 148 601 8880 +107 150 3269 47400 +107 152 1769 24016 +107 160 223107970103 2561073739840 +107 176 47893 428384 +107 178 49917 433252 +109 140 656162865 13441576162 +109 144 175156824191 3138959104488 +109 146 54403 916442 +109 152 2243217531297392198517 31916765979576876078500 +109 154 3491 48664 +109 156 235 3081 +109 162 10282123 120159855 +109 180 49507 438120 +111 116 1 174 +111 136 80459885012751253442411723368973417208588487 2134362058821206290584928475054586893470746380 +111 154 1271 18480 +111 158 47 632 +111 164 8867 105452 +11 12 1481 112302 +11 14 3544509 76158670 +11 15 707703 11039050 +11 16 13 162 +11 17 14924 156145 +11 18 1 9 +11 19 103943 829008 +11 20 15423 110680 +11 21 8858 58107 +113 140 1730526841104691463289 43057123810665785054360 +113 146 9908 197319 +113 154 49310046338004123673455235199618887037217290071 771093564492191219151577850592347792761532423082 +113 156 209 3120 +113 158 43 632 +113 160 1833 25280 +113 164 1127847160046002206938 14150282143126497498907 +113 176 105245349227 1078121994576 +115 122 4634391223 562840218630 +115 124 496077 44999414 +115 154 28649 483329 +115 162 3619 51192 +115 164 243 3239 +117 136 695093367543639006093957 26773170960540871143525602 +117 148 3666241457290288 81370118576599513 +117 154 188852860101419 3441750981980850 +117 164 893 12956 +117 166 3841 52456 +117 172 57 688 +119 122 846980807038663 292100624718962034 +119 130 113079 8402290 +119 146 263493199536203115748864037663 6935392361502897193614931138186 +119 174 93731 1150140 +119 178 59685 684499 +119 180 227 2520 +121 128 523 67840 +121 144 23626297 754392036 +121 148 186679671254681167 5002508081890159612 +121 158 5398501748548991 102102579908422146 +121 162 60193 1016874 +121 166 252383261394160302634529632955 3839203422877840634510928999434 +121 168 29 420 +121 170 3747 53720 +121 172 251 3397 +12 17 781 10744 +12 23 19535 127282 +123 136 2213 141984 +123 148 5065 149776 +123 170 55 816 +123 172 925 13588 +123 176 2119 27808 +125 134 875579 87690270 +125 148 1136589275 37737598626 +125 158 6107596563827829050889680513 136108629520164028986786485222 +125 166 45397262569 794512660934 +125 174 4250739461 60922730838 +125 176 1961 27808 +125 178 4191 56248 +127 136 1 102 +127 140 17 1120 +127 142 129751936407331797 7238400231476713874 +127 164 44333 886584 +127 176 361 5280 +127 178 3875 56248 +127 180 259 3555 +129 160 6311899 156050960 +129 164 4935739265 106671534586 +129 178 1427 21360 +131 140 619957 65598670 +131 146 21598689499651 1247275852581046 +131 148 39879 1998296 +131 156 625 19968 +131 160 6664351 180124196 +131 166 123375 2713436 +13 14 930056291728075 86131034650507882 +13 16 13 336 +13 17 8782848001658494036891 164983975083330937057700 +13 18 49 720 +13 20 745417 7895680 +13 21 141814380293367034145076111 1319625357659765692126461374 +13 22 34462894030490579197 287493488567963085342 +13 24 19061 132816 +13 25 10677 69175 +133 156 115979 4148664 +133 160 2731 80960 +133 172 10489775111239825 207602349026713028 +135 152 235306597016132646186 12205380627567410387773 +137 146 34632364361216978372593 3859194757777237761976622 +137 152 192941645307029570639 11696825856111373377598 +137 164 5257 165968 +137 178 289163 5598812 +139 144 47300910119605 10735548280375286 +139 154 297428562076 18307027855655 +139 160 8667 363200 +139 180 421 8280 +141 170 2292 66895 +14 17 12241 342431 +14 19 561 8930 +14 23 3119 27991 +14 25 18587 138350 +14 27 433 2808 +143 148 140350767417 32906003028622 +143 152 7621 891765 +143 160 20055425788 1110603240265 +143 172 5859 174064 +143 178 3027 73336 +147 158 17572021 1681776806 +147 176 257 8096 +151 162 733 72414 +15 16 47 5150 +15 19 345272027 7607380170 +15 26 7881687332158312 62386002265082821 +15 28 22699 154952 +15 29 467 3016 +153 154 3569 5905438 +155 164 5427 695360 +155 166 1437927189487 146430143549506 +157 162 3521 922752 +157 166 907 118026 +157 170 299334341415631 25369053065480674 +157 172 1927232672772015825160642799332937599148483 137604884943049314435654357944440011537786962 +159 172 46385 3996936 +161 166 1333 358560 +161 178 11555 743328 +16 27 248792207830437092147 2088742160942844847587 +16 29 22225 160486 +16 31 501 3224 +163 172 1301290777 177329035838 +165 166 27887583 50286583682 +167 170 1 510 +17 18 1 126 +17 22 35253862811215 695466782309706 +17 24 271 3792 +17 25 1960957 23645375 +17 26 8278386755473 89110334913964 +17 28 7647 68152 +17 31 12022 85777 +17 32 26337 177088 +17 33 535 3432 +175 176 44976606361084912792135061 86617999042811308605386837302 +18 35 569 3640 +19 21 901 58464 +19 24 2007627252140449499 44901201575192280012 +19 27 1259 17064 +19 28 309613 3710224 +19 33 12029 94798 +19 34 25389 188156 +19 35 13841 96845 +19 36 29975 199224 +19 37 603 3848 +20 21 97 14910 +20 31 45113388387 468240353554 +20 33 4528 40161 +20 37 29501 204758 +20 39 49 312 +21 29 467 6960 +21 31 13 155 +21 37 187411 1432344 +21 38 29027 210292 +21 40 33613 221360 +21 41 671 4264 +22 23 255144569243609075772060817198981 43932526749072849662306705128861450 +22 31 1387 19592 +22 39 38567 290940 +22 41 33139 226894 +22 43 705 4472 +23 24 577 104814 +23 28 1795410163651 49474854757286 +23 30 32121 610630 +23 34 1771 21029 +23 38 10465 92492 +23 41 41023 305860 +23 42 32665 232428 +23 43 17479 118981 +23 44 37251 243496 +23 45 739 4680 +24 31 16793 335172 +24 43 32191 237962 +24 47 773 4888 +25 28 3095685801 169625414056 +25 34 164516243 2595491442 +25 36 547 7029 +25 38 1289 14117 +25 41 11067 99794 +25 43 7850528083131 63185647491542 +25 44 6822205 52259592 +25 46 36303 254564 +25 47 19298 130049 +25 48 40889 265632 +25 49 807 5096 +26 29 1573 90074 +26 37 1737 23384 +26 41 38464076341899338121 381149475193059339586 +26 43 5937 52331 +26 47 35829 260098 +26 49 40415 271166 +26 51 841 5304 +27 32 23081 760456 +27 37 2087 31894 +27 38 845 12008 +27 40 8293 97840 +27 41 11087 121852 +27 49 18824 135583 +27 50 39941 276700 +27 52 2 13 +27 53 875 5512 +28 31 1 62 +28 39 13438421 192121098 +28 45 2033 19170 +28 51 39467 282234 +28 53 44053 293302 +28 55 909 5720 +29 32 3912877755361904195 253483355901182923308 +29 36 4092506506 100682981595 +29 39 20692411 342467086 +29 40 1 15 +29 41 1865 25912 +29 44 5931 65384 +29 46 205081 2001184 +29 48 13283 116832 +29 49 88524837 741088838 +29 51 153481537 1177679454 +29 52 38993 287768 +29 53 20643 146651 +29 54 43579 298836 +29 55 22936 152185 +29 56 225 1456 +29 57 943 5928 +30 59 977 6136 +31 32 6502743956 1668409045349 +31 33 96348036499399 10961405924475378 +31 36 6426800419153152679 249538037115920074146 +31 39 13096284289053021879569878345 299340374583620159563482398742 +31 40 1 20 +31 43 709 10320 +31 44 255 3476 +31 45 1202215622439829057 15074300827295459325 +31 46 228282602626202145 2680437547589667163 +31 51 13885 124134 +31 52 1206782156626159 10268214942194404 +31 53 93041 759066 +31 55 10897 82060 +31 56 42631 309904 +31 57 22462 157719 +31 58 47217 320972 +31 59 24755 163253 +31 60 121 780 +31 61 1011 6344 +32 45 1993 28440 +32 53 7346 64501 +32 57 56941 425220 +32 59 46743 326506 +32 61 51329 337574 +32 63 1045 6552 +33 46 191228 2725247 +33 47 2215 29704 +33 49 991771 11622408 +33 50 20630139820074985890489 227857747492148193733150 +33 58 666650797 5121789084 +33 59 21988 163253 +33 61 24281 168787 +33 62 50855 343108 +33 64 259 1664 +33 65 83 520 +34 47 761 11280 +34 59 57842 456719 +34 61 45795 337574 +34 63 50381 348642 +34 65 54967 359710 +34 67 1113 6968 +3 5 1409 12170 +35 36 14399440459181 4279819492388934 +35 47 1130278510396691 18824907933438670 +35 58 16101 141172 +35 62 7652 57815 +35 64 49907 354176 +35 66 54493 365244 +35 67 28393 185389 +35 68 69 442 +35 69 1147 7176 +36 59 7948 71803 +36 65 49433 359710 +36 67 54019 370778 +36 71 1181 7384 +37 50 14201 230200 +37 51 1379975279400427 20587899165190714 +37 52 287 4108 +37 53 2565 33496 +37 56 9540345 105707392 +37 58 378923 3814718 +37 61 16703 148474 +37 62 238371 2033228 +37 63 724008412670854187 5957774348526525042 +37 66 8266 61545 +37 67 25626 185389 +37 68 53545 376312 +37 69 27919 190923 +37 70 58131 387380 +37 71 30212 196457 +37 72 293 1872 +37 73 1215 7592 +38 63 8755 76671 +38 65 57121 465465 +38 69 53071 381846 +38 71 57657 392914 +38 73 62243 403982 +38 75 1249 7800 +39 41 15237 2272097 +39 43 21 1376 +39 44 6417373 326001522 +39 55 2471 34760 +39 59 335 3717 +39 64 17305 155776 +39 70 52597 387380 +39 71 27445 196457 +39 73 29738 201991 +39 74 61769 409516 +39 76 155 988 +39 77 1283 8008 +40 43 24704297982891 2358009579577514 +40 57 2693 36024 +40 59 69548081850496431 831221420062648288 +40 69 1087 8694 +40 71 70403 529660 +40 73 56709 403982 +40 77 65881 426118 +40 79 1317 8216 +41 48 67 2432 +41 50 148613 4053200 +41 52 62523569 1368290170 +41 53 545 10812 +41 56 98443 1525104 +41 58 1323 18328 +41 62 703 7812 +41 67 830757549667 7503420200894 +41 68 18919 165512 +41 69 2938463 24820266 +41 70 15627 127820 +41 71 235876249157030738094379838482285933 1870823362662469677326742321268065250 +41 73 72859 544580 +41 74 56235 409516 +41 75 29264 207525 +41 76 60821 420584 +41 77 31557 213059 +41 78 65407 431652 +41 79 1265 8216 +41 80 327 2080 +41 81 1351 8424 +42 47 17 940 +42 53 33 742 +42 59 2599 37288 +42 79 64933 437186 +42 83 1385 8632 +43 48 40191287951 2281793268264 +43 61 2821 38552 +43 62 2855402319221082299708961 36547931805636723559501754 +43 64 11 128 +43 66 17085408499657 182127444712102 +43 69 49460585 468259392 +43 71 19521 172814 +43 73 3795089307 31436334706 +43 75 83651 653325 +43 76 2446426647413733 18572766566479870 +43 77 28790 213059 +43 78 59873 431652 +43 79 31083 218593 +43 80 64459 442720 +43 81 33376 224127 +43 82 69045 453788 +43 83 1333 8632 +43 84 43 273 +43 85 1419 8840 +44 61 1003 14640 +44 63 3043 39816 +44 67 671114894 7310753307 +44 69 7479017268963752068938 75213242591420145344129 +44 73 10164 88841 +44 79 59399 437186 +44 81 63985 448254 +44 83 68571 459322 +44 85 1367 8840 +44 87 1453 9048 +4 5 3 71 +45 52 147 5954 +45 56 175472195 4256446012 +45 59 116342939523199601753579613985931203966074251 2159021834056451937114354400723634832245315266 +45 62 34781534535803525 519841969978905278 +45 64 749 10112 +45 74 20123 180116 +45 77 1759 14322 +45 82 63511 453788 +45 83 32902 229661 +45 86 72683 475924 +45 88 361 2288 +45 89 1487 9256 +46 61 221365874683277 3899502162550850 +46 63 191 2926 +46 65 2949 41080 +46 83 63037 459322 +46 85 67623 470390 +46 87 72209 481458 +46 89 1435 9256 +47 48 598321 252029070 +47 50 38107671710464229 4388658895863272050 +47 52 1723 108576 +47 53 150169 7666662 +47 56 113 3584 +47 63 938935 15760374 +47 65 211 3120 +47 66 1451 20856 +47 67 3171 42344 +47 70 2682421224061 31153535189245 +47 77 20725 187418 +47 78 21737 189852 +47 80 28007 230640 +47 82 183033 1428604 +47 83 400072 3042697 +4 7 8379415 64974378 +47 84 62563 464856 +47 85 32428 235195 +47 86 67149 475924 +47 87 34721 240729 +47 88 71735 486992 +47 89 37014 246263 +47 90 76321 498060 +47 92 189 1196 +48 73 19849 216956 +48 79 10766 96143 +48 85 16773 126820 +48 89 71261 492526 +49 58 821 27318 +49 60 125398719724542785866626511 3338391723097516156574302820 +49 68 281 4080 +49 69 3077 43608 +49 74 22719055891720660 253346931347317211 +49 75 671269 7210200 +49 81 22339 197154 +49 87 86321 649020 +49 88 66201 486992 +49 89 34247 246263 +49 90 70787 498060 +49 92 75373 509128 +49 94 79959 520196 +49 96 395 2496 +50 63 364621540975444682275729 8265551600712043552057542 +50 69 123 1840 +50 71 3299 44872 +50 73 4965 61174 +50 83 11573 101011 +50 89 88777 663940 +51 100 103 650 +51 73 3521 46136 +51 89 99382 775279 +51 92 69839 509128 +51 94 74425 520196 +51 98 83597 542332 +52 55 285 37312 +52 73 3205 46136 +52 79 21399 234788 +52 87 924458759 7912152012 +52 89 78322 637329 +53 100 82649 553400 +53 102 87235 564468 +53 104 33 208 +53 57 1341925 127129494 +53 58 169812995 12311161722 +53 60 17971763 882191820 +53 61 8243 346175 +53 71 105911 1782668 +53 74 1579 23384 +53 75 3427 47400 +53 76 81817 1065064 +53 78 161270 1940289 +53 82 5055 52726 +53 87 23543 211758 +53 88 24555 214192 +53 94 23263 175310 +53 96 73477 531264 +53 98 78063 542332 +54 77 3649 48664 +54 85 16151 160820 +54 89 12175 108313 +55 102 81701 564468 +55 104 86287 575536 +55 106 849 5512 +55 108 223 1404 +55 56 1123427545062216 565611564035581049 +55 58 13 1798 +55 62 5569179011 285331871210 +55 63 693725650197475009937 30408617520822620835630 +55 67 191390785878573 5253767526509591 +55 68 285017604988267 7176412217389707 +55 71 38287 767652 +55 72 81071 1515312 +55 76 307 4560 +55 78 1801 24648 +55 81 286808 3443553 +55 86 2346 23779 +55 92 2765884768122378463233 23683599925238346328888 +55 96 214495 1672512 +55 98 24491 182770 +5 6 397 12144 +56 73 561137 10698004 +56 75 111701 1883100 +56 79 45 632 +56 85 22949 252620 +56 87 66173717325395 682567865540836 +57 104 80753 575536 +57 106 85339 586604 +57 110 883 5720 +57 112 463 2912 +5 7 303 4424 +57 58 3783 1989632 +57 61 619823778270139274276571 63965476645212965021681828 +57 64 80759 4311312 +57 79 1297 18960 +57 80 877 12640 +57 92 37917303 353599628 +57 94 25759 228796 +57 98 149566 1204861 +5 8 13 124 +58 67 3238763921 131555713236 +58 81 3461 51192 +58 83 3999 52456 +58 85 291488787466554383 3550708974195979020 +59 104 131825 1006512 +59 106 79805 586604 +59 108 84391 597672 +59 110 88977 608740 +59 112 93563 619808 +59 114 917 5928 +59 116 60 377 +5 9 3401 24903 +59 71 9733 287408 +59 76 26805242999153 540886845485098 +59 78 96815667381239908180769 1729454049788804599382070 +59 79 117491 1983532 +59 83 3683 52456 +59 84 247 3318 +59 98 27373 238532 +60 83 1349 19920 +61 100 26963 243400 +61 110 83443 608740 +61 112 88029 619808 +61 114 92615 630876 +61 116 97201 641944 +61 118 951 6136 +61 120 497 3120 +6 11 8621 60874 +61 70 10166596836337638083 438089841184784685722 +61 75 1 26 +61 80 5539055726094000736026139 102657160428359089756628920 +61 86 1929 27176 +61 87 4127 54984 +61 88 2846905482582555101 36380669292699633770 +62 77 62187791 1526018802 +62 87 3811 54984 +63 104 28577 253136 +63 110 245957 1916420 +63 116 91667 641944 +63 118 96253 653012 +63 122 985 6344 +63 124 257 1612 +63 65 8371 2221440 +63 71 498441 25604872 +63 80 321 6980 +63 88 941 13904 +63 89 4033 56248 +63 92 29905542970141575238893784401531587394962157 368178967925701239264834919541462278276372163 +64 67 1187 197114 +64 77 87 2576 +64 81 906986164713158724569 20072773435265702999622 +65 108 30191 262872 +65 116 58169 432680 +65 118 90719 653012 +65 122 99891 675148 +65 124 104477 686216 +65 126 1019 6552 +65 128 531 3328 +65 83 8521 179944 +65 84 7613 151368 +65 86 523240886858934225753843 9313275514522864597542914 +65 92 263 3634 +66 71 1278113937 120535456222 +66 73 9595 609696 +66 79 10117 319792 +67 104 8742581 90387232 +67 110 29781 267740 +67 116 2036177855 16157014296 +67 118 298583 2284008 +67 120 89771 664080 +67 122 94357 675148 +67 124 98943 686216 +67 126 103529 697284 +67 128 108115 708352 +67 130 81 520 +67 132 137 858 +6 7 224299 8379210 +67 69 38461225688834595868997083 10845713886039135532613596938 +67 70 649142507 113785918890 +67 74 2468307543367272909997626518347864592467 157950900276401786851381240979990475452746 +67 75 10093 556275 +67 94 2057 29704 +67 98 52867 647780 +68 81 1303 41472 +69 118 207283 1689996 +69 124 93409 686216 +69 128 102581 708352 +69 130 107167 719420 +69 134 1087 6968 +69 136 565 3536 +69 73 9611 1238080 +69 74 1037 103082 +69 83 11321 335984 +69 86 5787 139363 +69 88 59 1254 +69 98 2279 30968 +70 73 780289 144216902 +7 10 239 3160 +71 100 279 3950 +71 106 938078 10818413 +7 11 1 10 +71 118 33009 287212 +71 126 15611 117495 +71 128 97047 708352 +71 130 101633 719420 +71 132 106219 730488 +71 134 110805 741556 +71 136 115391 752624 +71 138 1121 7176 +71 140 291 1820 +7 12 233805 1895396 +7 13 5220 35971 +71 74 6091 1145002 +71 84 564645293396706901315 18859336899670066368954 +71 85 10911 344080 +71 98 787 11760 +72 89 1270954505533 32038484832316 +73 102 2185 32232 +73 104 1227 16432 +73 110 4094886911 45961338335 +73 118 113409 1053563 +73 120 32599 292080 +73 126 2217539 17713332 +73 130 649 4849 +73 132 100685 730488 +73 134 105271 741556 +73 136 109857 752624 +73 138 114443 763692 +73 140 119029 774760 +73 142 1155 7384 +73 144 599 3744 +73 74 19947 14035580 +73 77 150997030519567521 20769024486688463678 +73 81 46655 2825667 +73 84 22609 953400 +73 87 1409 44544 +73 88 7423951438 216884914895 +73 92 4007032497473115131650203 90728680101849187418453872 +74 89 12115 360272 +75 104 107 1560 +75 106 2407 33496 +75 118 43971 438370 +75 124 34213 301816 +75 128 28549 233728 +75 134 99737 741556 +75 136 104323 752624 +75 142 118081 785828 +75 146 1189 7592 +75 148 77 481 +75 83 11081 693216 +75 98 9374271 176739374 +77 108 295 4266 +77 118 453503 4855228 +77 120 1331983 13623024 +77 128 35827 311552 +77 138 103375 763692 +77 142 112547 785828 +77 144 117133 796896 +77 146 121719 807964 +77 148 126305 819032 +77 150 1223 7800 +77 152 633 3952 +77 78 310065899948556945711259 232254462528343272220640970 +77 92 4847459293929 150233216472058 +77 96 25915 622272 +7 8 349 15630 +79 102 45 901 +79 112 1291 17696 +79 118 227697731738749347 2622263140525281194 +79 120 16243 178320 +79 122 3887 40748 +79 126 3894456818741 37458472073904 +79 130 35417 316420 +79 132 3349901 28756200 +79 140 2767 20888 +79 142 107013 785828 +79 144 111599 796896 +79 146 116185 807964 +79 148 120771 819032 +79 150 125357 830100 +79 152 129943 841168 +79 154 1257 8008 +79 156 25 156 +7 9 39001 794718 +79 83 17233831 2608893682 +81 112 227 3360 +81 116 701 9164 +81 118 284908261789 3533725258137 +81 134 37031 326156 +81 140 14756090150676449 117520289793946180 +81 146 110651 807964 +81 148 115237 819032 +81 152 124409 841168 +81 154 128995 852236 +81 158 1291 8216 +81 160 667 4160 +8 15 12259 83010 +81 89 143628208391843 9848867188229114 +82 85 923563415606543683667 205593816862374004990490 +82 87 9512774402371595651 1153118171073255248826 +83 104 327108430398662879449117225 7641368101019751345198328793 +83 112 4856833521367002050433551689797519956852826137729 79220723384788890141402270840371148555585514231080 +83 116 311 4582 +83 118 2757 37288 +83 126 8509 93618 +83 132 1436179045987629556 13918192629634808031 +83 136 36621 331024 +83 138 38645 335892 +83 142 249685 2033724 +83 144 1964833 15521184 +83 148 74087 552040 +83 150 114289 830100 +83 152 118875 841168 +83 154 123461 852236 +83 156 128047 863304 +83 158 132633 874372 +83 160 641 4160 +83 162 1325 8424 +83 164 171 1066 +83 86 16762853 3783515218 +83 87 6499471702095844561311 1044182350361305138876738 +85 118 977 14160 +85 122 40139811361148520453740473 520937315226744763514201007 +85 152 113341 841168 +85 154 117927 852236 +85 156 122513 863304 +85 158 127099 874372 +85 162 136271 896508 +85 164 329 2132 +85 166 1359 8632 +85 168 701 4368 +85 94 6149 392544 +87 122 2663 38552 +87 124 733 9796 +87 154 25695707 194448716 +87 158 121565 874372 +87 160 126151 885440 +87 164 135323 907576 +87 166 139909 918644 +87 170 1393 8840 +87 172 359 2236 +87 88 702358923 606090887434 +89 104 1520537 56054310 +89 106 851 27136 +89 112 5791 132160 +89 126 2885 39816 +89 132 157204598359 1848531160344 +89 136 3563345729383 38447327517952 +89 140 4171 41608 +89 146 39439 355364 +89 148 41463 360232 +89 158 39181 294670 +89 160 120617 885440 +89 162 125203 896508 +89 164 129789 907576 +89 166 134375 918644 +89 168 138961 929712 +89 170 143547 940780 +89 172 173 1118 +89 174 1427 9048 +89 176 735 4576 +89 94 753 100768 +9 10 247 14740 +91 108 2009480924018213 65518380855328770 +91 120 1249806505744135995577 22585668753337155128580 +91 122 2898 48617 +91 128 1419 20224 +91 138 4642 51267 +91 146 1329539 12592354 +91 150 41053 365100 +91 160 81265263147697872907275791212241018708640569 623844120448361834836718828259604131400963360 +91 162 40409 302130 +91 164 124255 907576 +91 166 128841 918644 +91 170 138013 940780 +91 172 142599 951848 +91 174 147185 962916 +91 176 709 4576 +9 11 780793271153311884983664341 21016436699918950523107607876 +91 178 1461 9256 +91 180 94 585 +9 13 323639164143803956611 4119880849210379275087 +9 14 10603 108990 +9 16 7959 59680 +9 17 7039 47039 +93 118 44877045 979977374 +93 130 2791 41080 +93 136 73299 898960 +93 154 42667 374836 +93 160 1712967 13779520 +93 166 41637 309590 +93 170 132479 940780 +93 172 137065 951848 +93 176 146237 973984 +93 178 150823 985052 +95 112 7813 268212 +95 134 3013 42344 +95 136 1641 21488 +95 142 390465640939943913957 4487370651059355869741 +95 156 42257 379704 +95 158 44281 384572 +95 168 899953 6824202 +95 172 131531 951848 +95 174 136117 962916 +95 176 140703 973984 +95 178 145289 985052 +95 98 7419074710433830151 1953931347399288914930 +97 122 21892903537503429221957324895 501112498788984911962793920274 +97 126 106621103 2066659938 +97 134 1081 16080 +97 136 1483 21488 +97 138 3235 43608 +97 144 431671985413 5061846176616 +97 156 1580863 14880216 +97 160 43871 389440 +97 166 292087 2377452 +97 170 445711 3445220 +97 172 85093 641560 +97 174 130583 962916 +97 176 135169 973984 +97 178 139755 985052 +97 180 144341 996120 +99 118 957 30208 +99 140 797 11060 +99 152 14585 155344 +99 158 181 1738 +99 164 45485 399176 +99 178 134221 985052