Makes sense to me :) kinda

 perl -Mbignum -E " for $x( -1,0,1){ $y = 0;  sub F{say $x % $y} F; $x
+->bdiv; F;} "
-1
-inf
0
NaN
1
inf
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The bdiv seems to force/convert the numeric representation to stringy value via binf/bnan

Its a bit odd but details of division by zero are in comments https://metacpan.org/source/PJACKLAM/Math-BigInt-1.999726/lib/Math/BigInt.pm

    # Divide by zero and modulo zero.
    #
    # Division: Use the common convention that x / 0 is inf with the s
+ame sign
    # as x, except when x = 0, where we return NaN. This is also what 
+earlier
    # versions did.
    #
    # Modulo: In modular arithmetic, the congruence relation z = x (mo
+d y)
    # means that there is some integer k such that z - x = k y. If y =
+ 0, we
    # get z - x = 0 or z = x. This is also what earlier versions did, 
+except
    # that 0 % 0 returned NaN.
    #
    #     inf /    0 =  inf                  inf %    0 =  inf
    #       5 /    0 =  inf                    5 %    0 =    5
    #       0 /    0 =  NaN                    0 %    0 =    0
    #      -5 /    0 = -inf                   -5 %    0 =   -5
    #    -inf /    0 = -inf                 -inf %    0 = -inf
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