SH7261 datasheet(100/1348 Pages) RENESAS

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Section 3 Floating-Point Unit (FPU)

Rev. 2.00 Sep. 07, 2007 Page 68 of 1312

REJ09B0320-0200

Figure 3.2 Format of Double-Precision Floating-Point Number

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

max

+127

+1023

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.

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