DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
8.3. Trapped Underflow
When an underflow trap has been implemented and is enabled, underflow shall be
signaled when tininess is detected regardless of loss of accuracy. Trapped
underflows on all operations except conversion shall deliver to the trap handler the
result obtained by multiplying the infinitely precise result by b a and then rounding.
The bias-adjust a is determined by the format's exponent bias from Table 1b:
(3/2)(bias+1) - thus 192 in the binary32 format. The bias-adjust a is 192 in the
single, 1536 in the double, 24576 in the quad § Q, and 3 × b n– 2
in the extended
format, where n is the number of bits in the exponent field. [FOOTNOTE 8:
Note that a system whose underlying hardware always traps on underflow,
producing a rounded, bias-adjusted result, shall indicate whether such a result is
rounded up in magnitude in order that the correctly subnormal denormalized §2
result may be produced in system software when the user underflow trap is
disabled.] Trapped underflows on conversion shall be handled analogously to the
handling of overflows on conversion.
A trapped underflowed result Z of a conversion or scaling operation, intended for
a binary floating-point destination, might not round to a normal number in the
destination format, even after multiplying by the bias-adjust b a . But for some
integral value n > α , Z × b n would round to a normal number z in the destination
format, 1