Renesas M32R-FPU Manual Do Utilizador

APPENDICES

APPENDICES-19

M32R-FPU Software Manual (Rev.1.01)

APPENDIX 5

Appendix 5 IEEE754 Specification Overview

Appendix Table 5.1.1 Single Precision Floating-Point Bit Values

Exponent

Expressed value

Before adding bias

After adding bias

( =0111 1111)

0111 1111 (+127)

1111 1110

Normalized number

• • •

(The absolute value can be described for the range

1000 0010 (-126)

0000 0001

of 1. 0…0 x 2 ^ -126 to 1. 1…1 x 2 ^ 127)

(1000 0001 (-127) )

0000 0000

Fraction field = all 0:

Fraction field

≠

all 0: denormalized number

(1000 0000 (-128) )

1111 1111

Fraction field = all 0:

±∞

Fraction field

≠

all 0: NaN (the value is split into SNaN and

QNaN according to the value of high-order bit of the

fraction field)

(1) Denormalized Numbers

Denormalized numbers represent numbers (values??) that have an absolute value

less than 1. 0…0 x 2 ^ -126. Single-precision denormalized numbers are expressed as

follows:

(-1) ^ s x 0.f x 2 ^ -126

(2) NaN (Not a Number)

SNaN (Signaling NaN): a NaN in which the MSB of the decimal fraction field is "0".

When SNaN is used as the source operand in an operation, an IVLD occurs. SNaNs

are useful in identifying program bugs when used as the initial value in a variable.

However, SNaNs cannot be generated by hardware.

QNaN (Quiet NaN): a NaN in which the MSB of the decimal fraction field is "1". Even

when QNaN is used as the source operand in an operation, an IVLD will not occur

(excluding comparison and format conversion). Because a result can be checked by

the arithmetic operations, QNaN allows the user to debug without executing an EIT

processing. QNaNs are created by hardware.