Float32List.join() produces unpredictable results

[sgrekhov]

  var l1 = new Float32List.fromList([1.11, 2.11]);
  var s1 = l1.join(',');
  print(s1); // prints 1.1100000143051147,2.109999895095825

  var l2 = new Float32List.fromList([1.25, 2.25]);
  var s2 = l2.join(',');
  print(s2); // prints 1.25,2.25

Why results are so different? Why 1.25 is printed as 1.25 but 1.11 as 1.1100000143051147?

Dart SDK version: 2.10.0-59.0.dev (dev) (Tue Aug 25 18:05:44 2020 -0700) on "windows_x64"

[whesse]

Floating point numbers can only represent fractional powers of 2 like 1/2, 1/4, 3/8, 999/1024 exactly.
1.11 as a floating point number is not exactly 1.11.
Please rewrite these tests with only numbers like 12.625 or 0.03125, or include an inaccuracy factor of about 1/100000, or whatever is needed.

[whesse]

Also the Float32x4 reciprocal square root and reciprocal tests are failing.
The error given by the hardware reciprocal square root approximation is only within 1/1000 of the correct answer, not 1/10000.
The intel doc says:
Compute the approximate reciprocal square root of the lower single-precision (32-bit) floating-point element in a, store the result in the lower element of dst, and copy the upper 3 packed elements from a to the upper elements of dst. The maximum relative error for this approximation is less than 1.5*2^-12.

Reciprocal approximation is within https://www.felixcloutier.com/x86/rcpss the same limit.

Does the spec say anything about the approximation accuracy? These two operations are specifically designed to be fast and approximate.

[sgrekhov]

dart-lang/co19@4f7d3e7