Hello,

I am fooling around IEEE 754 (don't ask why) and I started asking questions to various CL impleentations about the usual corner cases. Take for example the function ACOS.

prompt> (acos 42.0) #C(0.0 4.430675)

Seems legit, according to CLHS. Now, suppose you do (e.g. in CCL)

CCL prompt> (acos 1D++0) ; 1D++0 is positive infinity Error: FLOATING-POINT-INVALID-OPERATION detected performing * on (0.0D0 1D++0) While executing: CCL::%DOUBLE-FLOAT*-2!, in process Listener(4). Type cmd-. to abort, cmd-\ for a list of available restarts. Type :? for other options. 1 >

SBCL prompt> (acos 1D++0) ; No, you can't write that in SBCL, but ber with me. arithmetic error FLOATING-POINT-INEXACT signalled [Condition of type FLOATING-POINT-INEXACT]

Restarts: 0: [RETRY] Retry SLIME REPL evaluation request. 1: [*ABORT] Return to SLIME's top level. 2: [REMOVE-FD-HANDLER] Remove #<SB-IMPL::HANDLER INPUT on descriptor 8: #<CLOSURE (LABELS SWANK/SBCL::RUN :IN SWANK/BACKEND:ADD-FD-HANDLER) {12974D1D}>> 3: [ABORT] Exit debugger, returning to top level.

LW prompt> (acos 1D++0) #C(6.283185307179586D0 1D+-0 #| 1D+-0 is double-float not-a-number |#)

ACOS (and friends) also take complex numbers.

CL-USER 19 > (acos #C( 42 42)) #C(0.785469 -4.7773905)

Things get even more interesting when you pass to ACOS (and friends) a complex number with an infinity RE or IM part.

LW prompt> (acos (complex 42 1D++0)) #C(1D+-0 #| 1D+-0 is double-float not-a-number |# -1D++0 #| -1D++0 is double-float minus-infinity |#)

CCL prompt> (acos (complex 1.0 1D++0)) #C(1.5707963267948966D0 -1D++0)

SCBL prompt> (acos (complex 1.0 1D++0)) arithmetic error FLOATING-POINT-INEXACT signalled [Condition of type FLOATING-POINT-INEXACT]

Restarts: 0: [RETRY] Retry SLIME REPL evaluation request. 1: [*ABORT] Return to SLIME's top level. 2: [REMOVE-FD-HANDLER] Remove #<SB-IMPL::HANDLER INPUT on descriptor 8: #<CLOSURE (LABELS SWANK/SBCL::RUN :IN SWANK/BACKEND:ADD-FD-HANDLER) {12974D1D}>> 3: [ABORT] Exit debugger, returning to top level.

Now, now, now. We do not like this state of affairs, do we?

So, the question is: what should ACOS (and friends) do in these cases?

What about the LIA ISO/IEC 10967 standards?

All the best

Marco

-- Marco Antoniotti, Associate Professor tel. +39 - 02 64 48 79 01 DISCo, Università Milano Bicocca U14 2043 http://bimib.disco.unimib.it Viale Sarca 336 I-20126 Milan (MI) ITALY

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