[r6rs-discuss] [Formal] NaN is not a real number.

From: Aubrey Jaffer <agj>
Date: Sun Sep 24 21:18:28 2006

 | From: William D Clinger <will_at_ccs.neu.edu>
 | Date: Fri, 22 Sep 2006 13:43:56 -0400
 |
 | I am posting this as an individual member of the Scheme community.
 | I am not speaking for the R6RS editors, and this message should not
 | be confused with the editors' eventual formal response.
 |
 | John Cowan wrote:
 | > This argument is quite sound theoretically, but will have unfortunate
 | > performance consequences.
 |
 | Indeed. In addition to the inefficiency cited by John, the
 | proposal would destroy the closure property of the fl procedures on
 | which flow analysis depends. The need for this closure property
 | was explained in SRFI 77, but here is a concrete example, taken
 | from the inner loops of an FFT:
 |
 | (let loop4 ((wr 1.0) (wi 0.0) (m 0))
 | (define (flvector-ref v i)
 | (real->flonum (bytes-ieee-double-native-ref v i)))
 | (define (flvector-set! v i x)
 | (bytes-ieee-double-native-set! v i x))
 | (if (< m mmax)
 | (begin
 | (let loop5 ((i m))
 | (if (< i n)
 | (let* ((j (+ i mmax))
 | (tempr (fl-
 | (fl* wr (flvector-ref data j))
 | (fl* wi (flvector-ref data (+ j 1)))))
 | (tempi (fl+
 | (fl* wr (flvector-ref data (+ j 1)))
 | (fl* wi (flvector-ref data j)))))
 | (flvector-set! data j
 | (fl- (flvector-ref data i) tempr))
 | (flvector-set! data (+ j 1)
 | (fl- (flvector-ref data (+ i 1)) tempi))
 | (flvector-set! data i
 | (fl+ (flvector-ref data i) tempr))
 | (flvector-set! data (+ i 1)
 | (fl+ (flvector-ref data (+ i 1)) tempi))
 | (loop5 (+ j mmax)))
 | (loop4 (fl+ (fl- (fl* wr wpr) (fl* wi wpi)) wr)
 | (fl+ (fl+ (fl* wi wpr) (fl* wr wpi)) wi)
 | (+ m 2)))))))
 |
 | With the semantics described in the 5.91 draft, it is easy for a
 | compiler to generate efficient machine code for the above. By
 | efficient, I mean that none of the inexact reals will be
 | heap-allocated, and all 18 of the calls to fl+, fl-, and fl* will
 | be compiled into a single machine instruction.

The term flonum doesn't seem to be defined by R5.91RS. If it means
floating-point numbers, then most flonums are real, but flonum NaNs
are not. The flonums including NaNs are closed under fl-, fl*, fl+,
etc. Thus your example code will be completely unaffected by the
realness of NaNs.

As has been established in other threads, a system can have a variety
of distinct NaNs.

 | If the proposed change were adopted, so NaNs would no longer be
 | considered real, then all intermediate values would probably have
 | to be heap-allocated,

No -- my proposal does not prevent flonums from encoding non-real
values.

I just noticed that R5.91RS has changed the meaning of the predicate
`real?'. Should my proposal have substituded "real-valued number" for
"real number"?
Received on Sun Sep 24 2006 - 21:18:01 UTC