Atmel CAVR-4 Manual De Usuario

CAVR-4

Basic data types

Reference Guide

--64bit_doubles

 --64bit_doubles

long double

double

The representation of a 32-bit floating-point number as an integer is:

The value of the number is:

(-1)

S

 * 2

(Exponent-127)

 * 1.Mantissa

The precision of the float operators (

+

, 

-

, 

*

, and 

/

) is approximately 7 decimal digits.

The representation of a 64-bit floating-point number as an integer is:

The value of the number is:

(-1)

S

 * 2

(Exponent-1023)

 * 1.Mantissa

The precision of the float operators (

+

, 

-

, 

*

, and 

/

) is approximately 15 decimal digits.

The following applies to both 32-bit and 64-bit floating-point formats:

●

Zero is represented by zero mantissa and exponent. The sign bit signifies positive or 
negative zero.

●

Infinity is represented by setting the exponent to the highest value and the mantissa 
to zero. The sign bit signifies positive or negative infinity.

●

Not a number (

NaN

) is represented by setting the exponent to the highest positive 

value and the mantissa to a non-zero value. The value of the sign bit is ignored.

●

Subnormal numbers are used for representing values smaller than what can be 
represented by normal values. The drawback is that the precision will decrease with 
smaller values. The exponent is set to 0 to signify that the number is denormalized, 
even though the number is treated as if the exponent would have been 1. Unlike 
normal numbers, denormalized numbers do not have an implicit 1 as the most 
significant bit (MSB) of the mantissa. 

S

31 30

23 22

0

Exponent

Mantissa

S

63 62

52 51

0

Exponent

Mantissa