
Section 3 Floating-Point Unit (FPU)
Page 68 of 1336
R01UH0025EJ0300 Rev. 3.00
Sep 24, 2010
SH7261 Group
The exponent is expressed in biased form, as follows:
e = E + bias
The range of unbiased exponent E is E
min – 1 to Emax + 1. The two values Emin – 1 and Emax + 1 are
distinguished as follows. E
min – 1 indicates zero (both positive and negative sign) and a
denormalized number, and E
max + 1 indicates positive or negative infinity or a non-number (NaN).
Table 3.1 shows E
min and Emax values.
Table 3.1
Floating-Point Number Formats and Parameters
Parameter
Single-Precision
Double-Precision
Total bit width
32 bits
64 bits
Sign bit
1 bit
Exponent field
8 bits
11 bits
Fraction field
23 bits
52 bits
Precision
24 bits
53 bits
Bias
+127
+1023
E
max
+127
+1023
E
min
–126
–1022
Floating-point number value v is determined as follows:
If E = E
max + 1 and f ≠ 0, v is a non-number (NaN) irrespective of sign s
If E = E
max + 1 and f = 0, v = (–1)
s (infinity) [positive or negative infinity]
If E
min ≤ E ≤ Emax, v = (–1)
s2E (1.f) [normalized number]
If E = E
min – 1 and f ≠ 0, v = (–1)
s2Emin (0.f) [denormalized number]
If E = E
min – 1 and f = 0, v = (–1)
s0 [positive or negative zero]
Table 3.2 shows the ranges of the various numbers in hexadecimal notation.