floating-accuracy

问题 If we use algorithms with double and float arithmetic, how can we guarantee that the results are the same running it in Python and C, in x86 and x64 Linux and Windows computers and ARM microcontrollers? We re using an algorithm that uses: double + double double + float double exp(double) float * float On the same computer, compiling it for x86 and x64 MinGW gives different results. The algorithm makes a lot of math so any small error will make a difference in the end. Right now the ARM mcu

问题 I've got the following Python script: x = 300000000.0 while (x < x + x): x = x + x print "exec: " + str(x) print "terminated" + str(x) This seemingly infinite loop, terminates pretty quickly if x is a floating point number. But if i change x to 300000000 instead, it gets into an infinite loop (runs longer than a minute in my test). I think this is to do with the fact that it's exhausting the precision of a floating point number that can be represented in memory. Can someone provide a more

问题 I've got the following Python script: x = 300000000.0 while (x < x + x): x = x + x print "exec: " + str(x) print "terminated" + str(x) This seemingly infinite loop, terminates pretty quickly if x is a floating point number. But if i change x to 300000000 instead, it gets into an infinite loop (runs longer than a minute in my test). I think this is to do with the fact that it's exhausting the precision of a floating point number that can be represented in memory. Can someone provide a more

问题 Consider the following code: 0.1 + 0.2 == 0.3 -> false 0.1 + 0.2 -> 0.30000000000000004 Why do these inaccuracies happen? 回答1: Binary floating point math is like this. In most programming languages, it is based on the IEEE 754 standard. The crux of the problem is that numbers are represented in this format as a whole number times a power of two; rational numbers (such as 0.1 , which is 1/10 ) whose denominator is not a power of two cannot be exactly represented. For 0.1 in the standard

问题 Consider the following code: 0.1 + 0.2 == 0.3 -> false 0.1 + 0.2 -> 0.30000000000000004 Why do these inaccuracies happen? 回答1: Binary floating point math is like this. In most programming languages, it is based on the IEEE 754 standard. The crux of the problem is that numbers are represented in this format as a whole number times a power of two; rational numbers (such as 0.1 , which is 1/10 ) whose denominator is not a power of two cannot be exactly represented. For 0.1 in the standard

问题 As I understand it, Ruby (1.9.2) floats have a precision of 15 decimal digits. Therefore, I would expect rounding float x to 15 decimal places would equal x . For this calculation this isn't the case. x = (0.33 * 10) x == x.round(15) # => false Incidentally, rounding to 16 places returns true. Can you please explain this to me? 回答1: Part of the problem is that 0.33 does not have an exact representation in the underlying format, because it cannot be expressed by a series of 1 / 2 n terms. So,

问题 As I understand it, Ruby (1.9.2) floats have a precision of 15 decimal digits. Therefore, I would expect rounding float x to 15 decimal places would equal x . For this calculation this isn't the case. x = (0.33 * 10) x == x.round(15) # => false Incidentally, rounding to 16 places returns true. Can you please explain this to me? 回答1: Part of the problem is that 0.33 does not have an exact representation in the underlying format, because it cannot be expressed by a series of 1 / 2 n terms. So,

问题 As I understand it, Ruby (1.9.2) floats have a precision of 15 decimal digits. Therefore, I would expect rounding float x to 15 decimal places would equal x . For this calculation this isn't the case. x = (0.33 * 10) x == x.round(15) # => false Incidentally, rounding to 16 places returns true. Can you please explain this to me? 回答1: Part of the problem is that 0.33 does not have an exact representation in the underlying format, because it cannot be expressed by a series of 1 / 2 n terms. So,

来源： https://stackoverflow.com/questions/59705590/powa-b-returning-1-less-than-the-actual-value-when-b-is-more-than-15

来源： https://stackoverflow.com/questions/59705590/powa-b-returning-1-less-than-the-actual-value-when-b-is-more-than-15