Re: New proposal for math.e
Hi Juergen,
As I mentionned it in previous unoticed post, a math.e library should only deal
with numbers. So why find_least() use compare() to compare elements of sequence?
Those elements should be atoms and the relational operator '<' should be used.
You may argue that list may contain sub-sequence of atom, but can you give
exemples were this would be usefull?
What i propose is this:
function find_least(sequence list,integer start)
-- return the smallest element of list where list is sequence of atoms.
-- list must have length(list)>=2
-- but what should we do if length(list)<2, crash!!! ?
atom temp
ineger ret
temp = s[start]
ret = start
for i = start+1 to length(list) do
if s[i]<temp then
temp = s[i]
ret = i
end if
end for
return ret
end function
same thing for find_greatest()
regards,
Jacques Deschênes
Juergen Luethje wrote:
>
> This is my new proposal for a "math.e" standard include file,
> according to the recent discussion on this forum.
>
> Changes compared to the previous version:
> - All constant values are now truncated after the 17th digit
> (according to Matt's explanation about precision).
> - Double-checked all constant values by using a third-party
> calculator (--> no changes).
> - No user-defined type checking of the last parameter anymore in
> functions find_least(), find_greatest(), least(), greatest()
> ( with an invalid parameter, the functions will crash anyway --
> with or without type-checking 
).
> Removed the concerning user-defined type.
> - Simplified function log10() by using sequence operations.
> - Changed the names deg() and rad() to radians_to_degrees() and
> degrees_to_radians(), respectively.
>
> }}}
<eucode>
> global constant
> LN2 = 0.6931471805599453,
> LN10 = 2.3025850929940456,
> E = 2.7182818284590452,
> SQRT2 = 1.4142135623730950,
> HALF_SQRT2 = 0.7071067811865475,
> PI = 3.1415926535897932,
> HALF_PI = 1.5707963267948966,
> QUARTER_PI = 0.7853981633974483,
> TWO_PI = 6.2831853071795864
>
>
> global function log2 (object x)
> -- logarithm base 2
> -- in : (sequence of) real number(s) > 0
> -- out: (sequence of) real number(s)
> -- Note: This function returns _exact_ results for all integral
> -- powers of 2 in the half-closed interval ]0,#FFFFFFFF]
>
> if atom(x) then
> if x = #20000000 then
> return 29
> elsif x = #80000000 then
> return 31
> else
> return log(x)/LN2
> end if
> end if
>
> for i = 1 to length(x) do
> x[i] = log2(x[i])
> end for
> return x
> end function
>
> global function log10 (object x)
> -- logarithm base 10
> -- in : (sequence of) real number(s) > 0
> -- out: (sequence of) real number(s)
>
> return log(x)/LN10
> end function
>
> global function exp (object x)
> return power(E, x)
> end function
>
> global function sinh (object x)
> return (exp(x) - exp(-x)) / 2
> end function
>
> global function cosh (object x)
> return (exp(x) + exp(-x)) / 2
> end function
>
> global function tanh (object x)
> return sinh(x) / cosh(x)
> end function
>
> global function arcsinh (object x)
> return log(x + sqrt(x*x+1))
> end function
>
> type not_below_1 (object x)
> if atom(x) then
> return x >= 1.0
> end if
>
> for i = 1 to length(x) do
> if not not_below_1(x[i]) then
> return 0
> end if
> end for
> return 1
> end type
>
> global function arccosh (not_below_1 x)
> return log(x + sqrt(x*x-1))
> end function
>
> type abs_below_1 (object x)
> if atom(x) then
> return x > -1.0 and x < 1.0
> end if
>
> for i = 1 to length(x) do
> if not abs_below_1(x[i]) then
> return 0
> end if
> end for
> return 1
> end type
>
> global function arctanh (abs_below_1 x)
> return log((1+x)/(1-x)) / 2
> end function
>
> global function abs (object x)
> -- return the absolute value of (all elements of) x
>
> if atom(x) then
> if x < 0 then
> return -x
> else
> return x
> end if
> end if
>
> for i = 1 to length(x) do
> x[i] = abs(x[i])
> end for
> return x
> end function
>
> global function sign (object x)
> -- x < 0 ==> -1
> -- x = 0 ==> 0
> -- x > 0 ==> +1
>
> if atom(x) then
> return compare(x, 0)
> end if
>
> for i = 1 to length(x) do
> x[i] = sign(x[i])
> end for
> return x
> end function
>
> global function ceil (object x)
> -- the opposite of floor()
> -- Examples: ? ceil(3.2) --> 4
> -- ? ceil({-3.2,7,1.6}) --> {-3,7,2}
>
> return -floor(-x)
> end function
>
> global function sum (sequence list)
> -- Return the sum of all elements in 'list'.
> -- Note: This does not do a recursive sum of sub-sequences.
> atom ret
>
> ret = 0
> for i = 1 to length(list) do
> ret += list[i]
> end for
> return ret
> end function
>
> global function find_least (sequence list, integer start)
> -- Search for the lowest value in 'list', beginning at index 'start'.
> -- Return the index of that element.
> -- Notes: This does not do a recursive compare on sub-sequences.
> -- An empty sequence will cause a runtime error.
> object temp
> integer ret
>
> temp = list[start]
> ret = start
> for i = start+1 to length(list) do
> if compare(temp, list[i]) = 1 then
> temp = list[i]
> ret = i
> end if
> end for
> return ret
> end function
>
> global function find_greatest (sequence list, integer start)
> -- Search for the greatest value in 'list', beginning at index 'start'.
> -- Return the index of that element.
> -- Notes: This does not do a recursive compare on sub-sequences.
> -- An empty sequence will cause a runtime error.
> object temp
> integer ret
>
> temp = list[start]
> ret = start
> for i = start+1 to length(list) do
> if compare(temp, list[i]) = -1 then
> temp = list[i]
<snip>
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