[rdeviti]

In binary circuits, the function mpc_math.log2_fx can return wrong values at small precisions. I found this while testing #1796, which fixed popcnt returning a count one bit too short for some lengths, so I checked log2_fx, which uses popcnt in binary circuits. For instance, with Scripts/compile-run.py -E replicated, the following snippet prints -5.5 for log2(8):

from Compiler import mpc_math
sfix.set_precision(2, 7)
for x in (1, 2, 4, 8):
    print_ln("log2(%s) = %s", x, mpc_math.log2_fx(sfix(x)).reveal())

It prints -0.5, 0.5, 1.5 and -5.5. The first three are 0.5 below the exact values, but -5.5 is far off. With this PR, log2(8) gives 2.5, which is consistent with the other outputs as log2_fx is only approximate with 2 fractional bits.

Cause

log2_fx calls floatingpoint.Int2FL, which computes the exponent as a.popcnt_bits(b) - lam. In binary circuits, a is an sbitintvec of k bits, 7 in the snippet. But sbitintvec.popcnt_bits returns the count as a 3-bit number, just wide enough for counts up to 6, so the exponent overflows.

Fix

I patched sbitintvec.popcnt_bits so it behaves like sbitint.popcnt_bits, returning the count with as many bits as the integer it is called on.

Testing

• I added a check to test_gc.mpc that the count has as many bits as the integer.
• I tested log2_fx with 21 precisions, with k from 5 to 31, on up to six powers of two, from 2**-f to the largest that fits: without the fix, 3 precisions give a value off by 1 or more, all with k of 12 or less: (k, f) = (7, 2), (11, 2) and (12, 2). With the fix, none does, and the values that were right before are unchanged.
• With this PR, including the new check, Scripts/compile-run.py -E ring test_gc and -E replicated test_gc print the same output as master's test_gc.