On 07/30/2013 02:59 PM, hemant wrote:
I have written a std code for ARM 32-bit platform using math.h library and float=powf(float,float) function. When I give input to my system as 100 ^ 4.4 it gives me answer as 630957632.0000 (as float) whereas calculator in WindowsXP gives answer as 630957344.48019324943436013662234. I just want to know which one is more accurate ???? why is difference ????? on what things accuracy depends???? Also what do we mean by "arbitrary"-precision??? I have read such word on MSDN help forums. how much accurate is my system???? how to improve accuracy??????
You should read: http://en.wikipedia.org/wiki/IEEE_754 The reason is that 4.4 is not accurately represented in binary. This is like 1/3 which isn't accurately represented in decimal. To calculate the impact of this inaccuracy, you need to consider the structure of float. Float has 23 bits fraction+one leading '1' bit. This means that you have a 24 bit significand. Assuming 'round to nearest' error= 4.4* 2.0^{-24} And the float value is around 4.4+/- error. I computed this with 'bc' using scale=100 and got 100^(4.4+error)-100^4.4 = 762.0... 100^(4.4-error)-100^4.4 = -762.0... Before even considering the inaccuracy of assigning pow's result to float, you get an answer which can be off by +/- 762. Also, since pow(b,e) is implemented, as far as I know, by exp(log(b)*e) you've got 3 operations and not one, which add up their inaccuracies. So your *theoretical* accuracy is even lower, much lower since most inaccuracies are accumulated to the argument of 'exp'. It's probably around +/-2286. This explains why you've got a result which is off by nearly 300. It could have been much worse. Michael
