If I run the following code in python 3
1.0 1e-16
I get
1.0
as a result. Im wondering why? Assuming the numbers are stored as IEE754 double precision (64 bit) then I have the following representation of these numbers:
Number 1:
- sign: 0
- exponent: 01111111111 --> 1023 as decimal number
- significand: 0...0
Number 1e-16:
- sign: 0
- exponent: 01111001101 --> 973 as decimal number
- significand: 0010000000111010111110011110111001110101011000010110
In order to add both numbers I have to increase the exponent of the the small number by 50 to fit the exponent of the representation of number 1.0. If I do that the mantissa becomes:
- 0.0...0100
After adding both mantissas my result should be:
- sign: 0
- exponent: 01111111111
- significand: 0000000000000000000000000000000000000000000000000100
and this is not euqal to 1.0. Can someone explain or give me a hint what I'm overlooking?
CodePudding user response：
It seems your conversion of 1e-16 to binary is not correct: float.hex(1e-16) produces 0x1.cd2b297d889bcp-54, meaning the (unbiased) exponent is -54 in decimal, not -50. Then the leading 1 drops off the end of the significand and you end up with zero.