This seems to be a bug in the bc library. I asked jhasler to look into it.

John Hasler said:

The example in #44995 is wrong.  "^" has higher precedence than "%" so
"4^4%3" means "(4^4)%3" or "256%3", not "4^(4%3).  The latter gives a
runtime error in bc with scale=1, as it should as fractional exponents
are not supported.

From number.c:

/* Raise BASE to the EXPO power, reduced modulo MOD.  The result is
  placed in RESULT.  If a EXPO is not an integer,
  only the integer part is used.  */
...
...
...
 /* Check the base for scale digits. */
 if (base->n_scale != 0)
     bc_rt_warn ("non-zero scale in base");

 /* Check the exponent for scale digits. */
 if (exponent->n_scale != 0)
   {
     bc_rt_warn ("non-zero scale in exponent");
     bc_divide (exponent, _one_, &exponent, 0); /*truncate */
   }

 /* Check the modulus for scale digits. */
 if (mod->n_scale != 0)
     bc_rt_warn ("non-zero scale in modulus");
...
...
...

As you can see, non-zero scale is not supported.  Thus the bug is in
bcpowmod().  It should not accept a scale, and the documentation should
say so.

Related to this...

<?php
echo bcpowmod('3234', '32345', '22345', 0) . "\r\n";
echo bcpowmod('3234', '32345', '22345', 1);
?>

That outputs the following:

17334
1140.8

It seems to me that the output of the above ought to either be this:

Warning: bcpowmod() expects at most 3 parameters, 4 given

...or this:

17334
17334.0

> As you can see, non-zero scale is not supported. Thus the bug is
> in bcpowmod(). It should not accept a scale, and the
> documentation should say so.

The documentation for the scale parameter states:

| This optional parameter is used to set the number of digits
| after the decimal place in the result.

Although the fractional part of the operation is always zero,
it still might make sense to request a certain number of decimals.
So the behavior should be fixed to match the other BCMath
operations, instead of removing this parameter.

> Expected result:
> ----------------
> 0.1

The expected result would actually be 1.0.