underflow

I'm implementing the forward algorithm for HMMs to calculate the probability of a given HMM emitting a given observation sequence. I'd like my algorithm to be robust to underflow. I can't work in log-space because the forward algorithm requires the multiplication AND addition of probabilities. What is the best way to avoid underflow? I've read some sources about this but the best suggestion I get is scaling the probabilities at each time step Section 6 Here . By the end of the algorithm you won't be left with the exact probability you want (of the observation sequence). Also, unless I'm

I need to compute the geometric mean of a large set of numbers, whose values are not a priori limited. The naive way would be double geometric_mean(std::vector<double> const&data) // failure { auto product = 1.0; for(auto x:data) product *= x; return std::pow(product,1.0/data.size()); } However, this may well fail because of underflow or overflow in the accumulated product (note: long double doesn't really avoid this problem). So, the next option is to sum-up the logarithms: double geometric_mean(std::vector<double> const&data) { auto sumlog = 0.0; for(auto x:data) sum_log += std::log(x);

We know that Java does not handle underflows and overflows , but how does Javascript handle these for integers? Does it go back to a minimum/maximum? If yes, which minimum/maximum? I need to split a string and compute a hash value based on its characters. In a simple test, when I try this: var max = Number.MAX_VALUE; var x = max + 10; var min = Number.MIN_VALUE; var y = min / 10; I find that x and max have the same value (in Chrome, IE and Firefox) so it appears that some overflows are just pegged to the max value. And, y gets pegged to 0 so some underflows seem to go to zero. Ahhh, but it is

Is there a general way to check for an overflow or an underflow of a given data type (uint32, int etc.)? I am doing something like this: uint32 a,b,c; ... //initialize a,b,c if(b < c) { a -= (c - b) } When I print a after some iterations, it displays a large number like: 4294963846. To check for over/underflow in arithmetic check the result compared to the original values. uint32 a,b; //assign values uint32 result = a + b; if (result < a) { //Overflow } For your specific the check would be: if (a > (c-b)) { //Underflow } I guess if I wanted to do that I would make a class that simulates the

I have read in many places that unsigned integer overflow is well-defined in C unlike the signed counterpart. Is underflow the same? For example: unsigned int x = -1; // Does x == UINT_MAX? Thanks. I can't recall where, but i read somewhere that arithmetic on unsigned integral types is modular, so if that were the case then -1 == UINT_MAX mod (UINT_MAX+1). Stephen Canon §6.2.5, paragraph 9: A computation involving unsigned operands can never overflow, because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the