The ranges are actually –infinity to +infinity.

The largest finite float is 340282346638528859811704183484516925440. This is 2¹²⁸–2^128–24.

The largest finite double is 179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368. This is 2¹⁰²⁴–2^1024–53.

OP's approach works when calculations are done with wider precision than float in the first case and wider than double in the 2nd case.

In the first case, OP reports FLT_EVAL_METHOD == 0 so float calculations are done as float and double are done as double. Note that float step ... 1.0 + step is a double calculation.

The below code forces the calculation to double and so I can replicate OP's problem even with my FLT_EVEL_METHOD==2 (Use long double for internal calculations.)

  volatile double d = 1.0;
  volatile double last_d;
  volatile double step_d = 9.0;
  while(1) {
      last_d = d;
      d *= (1.0 + step_d);
      while (d == INFINITY) {
          step_d /= 2.0;
          volatile double sum = 1.0 + step_d;
          d  = last_d * sum;
          //d  = last_d  + step_d*last_d;
      }
      if (! (d > last_d) ) {
        break;
      }
  }

diff                 : 1.995840e+292
The expected value?  : no

Instead OP should use the following which does not form the inexact sum of 1.0 + step_d when step_d is small, rather it forms the exact product of step_d*last_d. The 2nd form results in a more accurate calculation for the new d, by providing an additional bit of calculation precision in d. Higher precision FP is not needed to employ OP's approach.

          d  = last_d  + step_d*last_d;

diff                 : 0x0p+0 0.000000e+00
The expected value?  : yes

The ranges for the signed integers are usually asymmetric — there's usually one more negative value than there are positive values.

The header <limits.h> defines the ranges for the integer types you specify.

• ULONG_MAX
• ULLONG_MAX

etc.

The header <float.h> defines the ranges for the floating point types:

• DBL_MAX
• DBL_MIN

etc.

You must print the values using the correct format specifiers.