Table 22-9 Fmul Family Bounce Thresholds - ARM ARM1176JZF-S Technical Reference Manual

22.12.3 FMUL and FNMUL
22.12.4 FMAC, FMSC, FNMAC, and FNMSC
ARM DDI 0301H
ID012310
Detection of a potential exception is based on the initial product exponent, that is the sum of the
multiplicand and multiplier exponents. Table 22-9 lists the result for specific values of the initial
product exponent. The exponent values in Table 22-9 are in biased format. The exponent can be
incremented by a significand overflow condition, and this is the cause for the additional bounce
values near the real overflow threshold. The one additional value in the bounce range makes the
FMUL and FNMUL overflow detection ranges identical to those in Table 22-8 on page 22-21.
Initial product exponent value
DP a SP b
> -
0x7FF
-
0x7FF
-
0x7FE
-
0x7FD
0x7FC -
> 0x47F > 0xFF
0x47F 0xFF
0x47E 0xFE
0x47D 0xFD
0x47C 0xFC
0x3FF 0x7F
0x381 0x01
0x380 0x00
< <
0x380 0x00
-
0x001
-
0x000
< 0x000 -
a. DP = double-precision.
b. SP = single-precision.
The FMAC family of operations adds to the potential overflow range by generating significand
values from zero up to but not including four. In this case it is possible for the final exponent to
require incrementing by two to normalize the significand.
The bounce thresholds for the FADD family in Table 22-8 on page 22-21 and for the FMUL
family in Table 22-9 incorporate this additional factor. Those ranges are used to detect potential
exceptions for the FMAC family.
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Table 22-9 FMUL family bounce thresholds

Condition in full-compliance mode
Float value SP
DP overflow -
DP NaN or infinity -
DP maximum normal -
DP normal -
DP normal -
SP overflow Bounce
SP NaN or infinity Bounce
SP maximum normal Bounce
SP normal Bounce
SP normal Normal
e = 0 bias value Normal
SP normal Normal
SP subnormal Bounce
SP underflow Bounce
DP normal -
DP subnormal -
DP underflow -
VFP Exception Handling
DP
Bounce
Bounce
Bounce
Bounce
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Bounce
Bounce
22-22