I can solve bigmod if range of m is <=10^9. But if range more than this range my procedure overflows. How can i solve (n^p)%m where (n,m,p)<=10^18
Related
I have the following system I'm trying to solve:
assume(x>0);
solve([x^2 = 3], x);
I expected that the answer would be [x=sqrt(3)], but maxima also gives the negative solution [x=-sqrt(3),x=sqrt(3)]. Is it possible to specify that the domain of x here is all positive real numbers?
This seems to work for me, (not yet tested in other cases):
assume(x>0)$
sublist(
solve(x^2=3,x),
lambda(
[point],
facts: subst(point, facts(initial)),
every(lambda([fact], is(fact)), facts)
)
);
In a loop like this:
cur := -999999; // represent a minimal possible value hold by a Single type
while ... do
begin
if some_value > cur then
cur := some_value;
end;
There is MaxSingle/NegInfinitydefined in System.Math
MaxSingle = 340282346638528859811704183484516925440.0;
NegInfinity = -1.0 / 0.0;
So should I use -MaxSingle or NegInfinity in this case?
I assume you are trying to find the largest value in a list.
If your values are in an array, just use the library function MaxValue(). (If you look at the implementation of MaxValue, you'll see that it takes the first value in the array as the starting point.)
If you must implement it yourself, use -MaxSingle as the starting value, which is approximately -3.40e38. This is the most negative value that can be represented in a Single.
Special values like Infinity and NaN have special rules in comparisons, so I would avoid these unless you are sure about what those rules are. (See also How do arbitrary floating point values compare to infinity?. In fact, it seems NegInfinity would work OK.)
It might help to understand the range of values that can be represented by a Single. In order, most negative to most positive, they are:
NegInfinity
-MaxSingle .. -MinSingle
0
MinSingle .. MaxSingle
Infinity
I have a textedit component and a button component. The button component will add the textedit component text value to a list if that value is greater than 0. On the textedit component I can as many decimal places as I want, but I'd like to validate two decimal places. Like If I put 00.0032 in the textedit component the validation will take that as 0. Is there a function that will allow me to do this or do I have to do this by my own code.
This is my code
if (Trim(textEdit.Text) <> '') and (StrToCurr(Trim(textEdit.Text)) <> 0) then
begin
code to add the value
end;
Reading your question two possible solutions come to my mind:
You could convert to float multiply by 100 (to shift by two decimals) and round using floor:
(Floor(StrToFloat(Trim(textEdit.Text)) * 100) <> 0)
This performs a conversion to floating point which might be slow.
An other solution could be to use string functions:
(StrToCurr(Copy(textEdit.Text, 1, Pos('.', textEdit.Text) + 2)) <> 0)
This copies the input string from beginning to two digits after the decimal separator '.'.
Don't worry if your string is shorter (for example '0.1') you won't get an error.
Which solution is ultimately fast would have to be benchmarked.
Also have in mind, that not in every region a '.' is the decimal separator.
In most of Europe for example decimal separator is ',' and thousands separator is '.'.
Find out about TFormatSettings.
PS: You don't need to Trim before using StrToCurr because it does a trim internally.
I have a record declared as
T3DVector = record
X,Y,Z: Integer;
end;
One variable V of type T3DVector holds:
V.X= -25052
V.Y= 34165
V.Z= 37730
I then try to the following line. D is declared as Double.
D:= (V.X*V.X) + (V.Y*V.Y) + (V.Z*V.Z);
The return value is: -1076564467 (0xFFFFFFFFBFD4EE0D)
The following code should be equivalent:
D:= (V.X*V.X);
D:= D + (V.Y*V.Y);
D:= D + (V.Z*V.Z);
But this,however, returns 3218402829 (0x00000000BFD4EE0D), which actually is the correct value.
By looking at the high bits, I thought this was an overflow problem. When I turned on overflow checking, the first line halted with the exception "Integer overflow". This is even more confusing to me because D is Double, and I am only storing values into D
Can anyone clarify please ?
The target of an assignment statement has no bearing on how the right side is evaluated. On the right side, all you have are of type Integer, so the expression is evaluated as that type.
If you want the right side evaluated as some other type, then at least one operand must have that type. You witnessed this when you broke the statement into multiple steps, incorporating D into the right side of the expression. The value of V.Y * V.Y is still evaluated as type Integer, but the result is promoted to have type Double so that it matches the type of the other operand in the addition term (D).
The fact that D is a double doesn't affect the type of X, Y and Z. Those are Integers, and are apparently not large enough to store the squares of such large numbers, and their multiplication is what overflows. Why don't you declare them as doubles, too?
i want to test some code to make sure it handles NAN, INF and -INF inputs properly.
i know there exists functions that return NAN, INF and -INF, but as a Double:
unit IEEE754;
...
function NAN: Double;
function PositiveInfinity: Double;
function NegativeInfinity: Double;
Except in my case i need to test when a Currency is one of these three edge-case values. Unfortunatly you cannot convert any of these to a Double:
Test(NAN);
procedure Test(const Value: Currency);
...
There's an EInvalidOp Invalid floating point operation exception when converting a Double NAN to a Currency.
Is it possible to assign a NAN to a Currency?
Perhaps, rather than it being possible to assign a NAN to a Currency, it is instead not possible - and i can just ignore this edge case.
Can i ignore this edge case?
Is it possible to "Set a Currency value to NAN, INF or -INF?"
{ David Heffernan says it's impossible for a currency to contain INF,-INF or NAN.
So there's no need to test for it.
http://stackoverflow.com/questions/7096966/set-a-currency-value-to-nan-inf-or-inf
//Handle NaN, where exponent is -32767
test(NAN, 'NAN');
//Handle +inf, where exponent is 32767 and Negative is true
test(PositiveInfinity, 'INF');
//Handle -inf, where expondent is 32767 and Negative is true
test(NegativeInfinity, '-INF');
}
Currency is not an IEEE754 float type and does not have NAN or INF values.
The documentation explains that Currency is implemented as a 64 bit integer with implicit scale of 10000 and that the range of possible values is -922337203685477.5808 to 922337203685477.5807. Since this covers the full range of a 64 bit integer it follows that there are no bit patterns available for sentinel values like NAN or INF.