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- #import std
- #import nat
- #comment -[
- This module contains some floating point functions and constants.
- Copyright (C) 2007-2010 Dennis Furey]-
- #library+
- eps = 5e-16
- inf = -{wgfzg]ftVjBk=hTZd@L\}-
- nan = -{wgfzg]ftVjBk=hTY<PP<}-
- ninf = -{wgfzg]ftVjBk=hT[<AA<}-
- pi = 3.14159265358979323846
- #optimize+
- abs = math..fabs
- ari = ~&?\0!! "n". ("l","h"). plus/*"l" times^(~&l,float@r)* -*iota"n" div(minus/"h" "l",float predecessor "n")
- acos = math..acos
- asin = math..asin
- atan = math..atan
- atanh = math..atanh
- bus = math..bus
- correlation = div^/covariance times+ stdev~~
- cos = math..cos
- covariance = mean+ (* times+ minus~~)^DbbIS/mean~~ ~&p
- cu_prod = :/1.; ~&ar^& ^rlfPrlart3XRC/~& times+~&alrhPX
- cu_sum = :/0.; ~&ar^& ^rlfPrlart3XRC/~& plus+~&alrhPX
- derivative = // gsldif..central
- div = math..div
- eudist = sqrt+ iprod+ ~&iiX+ minus*p
- exp = math..exp
- fleq = math..islessequal
- float = ~&/(0.,1.); ~&r->ll ^\~&rt ^\-+times/2.,~&lr+- ~&rh?/plus+~&l ~&ll
- floatz = ~&?\0.! ~&z?(~&NiX,~&NNXyX); (~&l?\~&r negative@r)^|/~& float
- geo = exp*++ ln~~;+ ari
- integral = "f". ("a","b"). gslint..qagx ("f","a","b")
- iprod = plus:-0.+ times*p
- levin_sum = ~&l+ gslevu..utrunc
- levin_limit = plus^/~&h levin_sum+ minus*typ
- ln = math..log
- max = fleq?/~&r ~&l
- mean = div^/plus:-0. float+ length
- min = fleq?/~&l ~&r
- minus = math..sub
- N = rmath..pnorm\(0.,1.,&,0)
- negative = minus/0.
- nth_deriv = "n". -++- (* "t". // gsldif..t_central\"t") (times/2.)|\x (pow/1.0e-8 div/1. float "n")!* iota "n"
- nth_diff = "n". rep"n" minus*typ
- oprod = @pbaatPahPfatPRDCaqPO minus*lihBPrrlXPrQS+ num+ iprod~~+* ~&lyPrtPXltPryPXX
- plus = math..add
- pow = math..pow
- printf = math..asprintf
- Q = rmath..qnorm\(0.,1.,&,0)
- rand = mtwist..u_cont+ 0!
- sgn = 0.?=/~& fleq/0.?/1.! -1.!
- sin = math..sin
- sqr = times+ ~&iiX
- sqrt = math..sqrt
- stdev = sqrt+ variance
- strtod = math..strtod
- tan = math..tan
- tanh = math..tanh
- times = math..mul
- variance = mean+ (sqr+ minus)^*D/mean ~&
- vid = math..vid
- Z = rand; rmath..qnorm\(0.,1.,&,0)
- zeroid = math..iszero
- root_finder = # takes ((lower bound,upper bound),function,tolerance)
- ^(^bbI/~&l ~&H~~+~&rlPlG,~&r); (fleq^/~&rr abs+ minus+ ~&lbl)->lll ^\~&r -+
- (==+ sgn~~)?rrPlllr3X/~&rllr2X ~&lll2rX,
- ^/~& ^rlrHX/~&rl div\2.+ plus+ ~&lbl+-
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