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| From: William D Clinger <will@xxxxxxxxxxx>
| Date: Wed, 21 Jun 2006 09:29:44 -0400
|
| Aubrey Jaffer wrote:
| ...
| > Does SRFI-77 (or R5RS) mandate that floating-point procedures
| > work for arguments generating the full range of possible outputs?
|
| No. Neither mandates that ... implementations
| of the standard procedures be of high quality.
R5RS Section 6.2.6 "Numerical Input and Output" places a stringent
constraint on the quality of NUMBER->STRING:
If Z is inexact, the radix is 10, and the above expression can be
satisfied by a result that contains a decimal point, then the
result contains a decimal point and IS EXPRESSED USING THE
MINIMUM NUMBER OF DIGITS (exclusive of exponent and trailing
zeroes) NEEDED TO MAKE THE ABOVE EXPRESSION TRUE [howtoprint],
[howtoread]; otherwise the format of the result is unspecified.
The operations for computing complex MAGNITUDE and / are:
magnitude flonum operations
sum product quotient abs <
naive: 1 2 0 0 0
correct: 1 2 1 2 1
/ flonum operations
sum product quotient abs <
naive: 3 6 2 0 0
correct: 3 3 3 2 1
Floating-point ABS involves just flipping one bit; it should be very
fast.
The correct versions are unlikely to be much slower than naive ones;
correct-/ is perhaps faster. So the arguments for implementing these
procedures incorrectly are weak.