Math functions need some special cases

auravulpes commented

2022-11-17 05:37:39 +00:00

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What is pow(1, INFINITY)? What about sin(NAN)? log(-3)? Right now, my code takes any of those sorts of nonsensical queries and tries to legitimately calculate them, but it shouldn't. It needs special cases for that sort of stuff. I'll come in tomorrow and actually try to list out a bunch of them for the code I've already written.

auravulpes added the

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label 2022-11-17 05:37:39 +00:00

auravulpes commented

2022-11-17 23:15:06 +00:00

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Owner

Okay, so, according to IEEE 754-2019 and the C99 standard...

(nb: k is used for an arbitrary number, +k is arbitrary positive number, -k is an arbitrary negative number, v is an arbitrary even, d is an arbitrary odd, i is an arbitrary integer, r is an arbitrary non-integer, 0 can be either +0 or -0, and rules take priority from top to bottom)

pow():

k^0 = 1 (k not a signaling NaN; includes 0^0)
0^-d = INF, divByZero
0^-INF = +INF
0^+INF = 0
0^+k = 0 (matching sign)
-1^INF = 1
1^k = 1
k^+INF = 0, |k| < 1
k^+INF = +INF, |k| > 1
k^-INF = +INF, |k| < 1
k^-INF = 0, |k| > 1
+INF^-k = 0
+INF^+k = +INF
-INF^-d = -0
-INF^+d = -INF
-INF^-v = +0
-INF^+v = +INF
0^-v = +INF, divByZero
0^+v = +0
-k^r => invalid operation/domain error

exp():

exp(+INF) = +INF
exp(-INF) = +0
Range error if input too large

log():

log(+INF) = +INF
log(0) = -INF, divByZero
log(1) = +0 (might be good to include)
log(-k) => domain error

sqrt():

sqrt(-k) => domain error

I'm not sure this covers everything, but it's definitely a nice start. I'll, like, see what musl does for some other cases (e.g. sin(NaN)) later.

Okay, so, according to IEEE 754-2019 and the C99 standard... (nb: k is used for an arbitrary number, +k is arbitrary positive number, -k is an arbitrary negative number, v is an arbitrary even, d is an arbitrary odd, i is an arbitrary integer, r is an arbitrary non-integer, 0 can be either +0 or -0, and rules take priority from top to bottom) pow(): * k^0 = 1 (k not a signaling NaN; includes 0^0) * 0^-d = INF, divByZero * 0^-INF = +INF * 0^+INF = 0 * 0^+k = 0 (matching sign) * -1^INF = 1 * 1^k = 1 * k^+INF = 0, |k| < 1 * k^+INF = +INF, |k| > 1 * k^-INF = +INF, |k| < 1 * k^-INF = 0, |k| > 1 * +INF^-k = 0 * +INF^+k = +INF * -INF^-d = -0 * -INF^+d = -INF * -INF^-v = +0 * -INF^+v = +INF * 0^-v = +INF, divByZero * 0^+v = +0 * -k^r => invalid operation/domain error exp(): * exp(+INF) = +INF * exp(-INF) = +0 * Range error if input too large log(): * log(+INF) = +INF * log(0) = -INF, divByZero * log(1) = +0 (might be good to include) * log(-k) => domain error sqrt(): * sqrt(-k) => domain error I'm not sure this covers everything, but it's definitely a nice start. I'll, like, see what musl does for some other cases (e.g. sin(NaN)) later.

Math functions need some special cases #2