Floating Point Numbers

IEEE Standard 754 Floating Point Numbers

Comparing floating point numbers

a tool: IEEE-754 Analysis

 

Float Values (b = bias)

Sign	Exponent (e)	Fraction (f)	Value
0	00..00	00..00	+0
0	00..00	00..01 : 11..11	Positive Denormalized Real 0.f × 2(-b+1)
0	00..01 : 11..10	XX..XX	Positive Normalized Real 1.f × 2(e-b)
0	11..11	00..00	+Infinity
0	11..11	00..01 : 01..11	SNaN
0	11..11	10..00 : 11..11	QNaN
1	00..00	00..00	-0
1	00..00	00..01 : 11..11	Negative Denormalized Real -0.f × 2(-b+1)
1	00..01 : 11..10	XX..XX	Negative Normalized Real -1.f × 2(e-b)
1	11..11	00..00	-Infinity
1	11..11	00..01 : 01..11	SNaN
1	11..11	10..00 : 11.11	QNaN

 

对于单精度而言，超过2^24 - 1的数的整数部分精度就开始降低为2^(n-24), n为bit位数。