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Table 1: Values Represented by Bit Patterns in IEEE Single Format
Single-Format Bit Pattern Value 0
e
s^
×
e-
×
f (normal numbers) e
f 6 = 0 (at least one bit in f is nonzero)
s^
×
×
f (subnormal numbers) e
f = 0 (all bits in f are zero)
s^
×
0.0 (signed zero) s
e
f
(all bits in f are zero) +INF (positive infinity) s
e
f
(all bits in f are zero) -INF (negative infinity) s = u; e
f 6 = 0 (at least one bit in f is nonzero) NaN (Not-a-Number) Bit Patterns in Single-Storage Format and their IEEE Values Common Name Bit Pattern (Hex) Decimal Value
3f
maximum normal number 7f7fffff 3.40282347e+ minimum positive normal number
1.17549435e- maximum subnormal number 007fffff 1.17549421e- minimum positive subnormal number
1.40129846e-
7f Infinity −∞ ff -Infinity Not-a-Number 7fc NaN
Table 2: Values Represented by Bit Patterns in IEEE Double Format
Double-Format Bit Pattern Value 0
e
s^
×
e- x 1. f (normal numbers) e
f 6 = 0 (at least one bit in f is nonzero)
s^
×
x 0. f (subnormal numbers) e
f = 0 (all bits in f are zero)
s^
×
0.0 (signed zero) s
e
f
(all bits in f are zero) +INF (positive infinity) s
e
f
(all bits in f are zero) -INF (negative infinity) s = u; e
f 6 = 0 (at least one bit in f is nonzero) NaN (Not-a-Number) Bit Patterns in Double-Storage Format and their IEEE Values Common Name Bit Pattern (Hex) Decimal Value
3ff00000 00000000
max normal number 7fefffff ffffffff 1.7976931348623157e+ min positive normal number
2.2250738585072014e- max subnormal number 000fffff ffffffff 2.2250738585072009e- min positive subnormal number
4.9406564584124654e-
7ff00000 00000000 Infinity −∞ fff00000 00000000 -Infinity Not-a-Number 7ff80000 00000000 NaN
Figure 1: The floating-point number line
int main()
float y, z;
y = 838861.2;
z = 1.3;
printf("y: %18.11f\n", y);
printf("z: %18.11f\n", z);
return 0;
The output from this program should be similar to:
y: 838861.
z: 1.
Standards: POSIX, BSD 4.3, ISO 9899
acos arccosine, returns value in [0, π]
asin arcsine, returns value in [−π/ 2 , π/2]
atan arctangent, returns value in [−π/ 2 , π/2]
atan2 takes y and x to break degeneracy in atan(y/x)
ceil smallest integral value not less than x
cos Cosine
cosh Hyperbolic cosine
exp Exponentiate
fabs absolute value of floating-point number
floor largest integral value not greater than x
fmod floating-point remainder function
frexp convert floating-point number to fractional and integral components
ldexp multiply floating-point number by integral power of 2
log Natural log
log10 Log base ten
modf extract signed integral and fractional values from floating-point number
pow Raise number to a power
sin Sine
sinh Hyperbolic sine
sqrt Square root of a number
tan Tangent
tanh Hyperbolic tangent
