Some numerical instability suggested by the Gemini AI

[Georgi Guninski <gguninski@gmail.com>]

I don't claim this is a bug, just FYI.
Suggested by Gemini, prompts by me, based on floating point instability.

Follows session:
? pre = 38;
? default(realprecision, pre);
?
? 0.1 + 0.2 == 0.3
%4 = 0
? b = default(realbitprecision);
? x = 2.0^b;
? x==x+1
%7 = 1
? x==x+2
%8 = 0

Attach is more serious floating point numbers in python.

#gemini python code about floats
import math

# 1. Non-Associativity: (a + b) + c != a + (b + c)
a, b, c = 1e16, -1e16, 1.0
(a + b) + c  # 1.0
a + (b + c)  # 0.0
(a + b) + c == a + (b + c)  # False

# 2. Binary Decimal Inexactness
0.1 + 0.2  # 0.30000000000000004
0.1 + 0.2 == 0.3  # False

# 3. The Absorption Wall (53-bit mantissa limit in float64)
x = 2.0**53  # 9007199254740992.0
x + 1.0  # 9007199254740992.0
x + 1.0 == x  # True
x + 2.0 == x  # False

# 4. NaN Breaks Reflexivity and Trichotomy
nan = float("nan")
nan == nan  # False
nan != nan  # True
nan < 1.0  # False
nan >= 1.0  # False

# 5. Signed Zero Equivalence vs. Behavior
pos_zero, neg_zero = 0.0, -0.0
pos_zero == neg_zero  # True
math.copysign(1.0, pos_zero)  # 1.0
math.copysign(1.0, neg_zero)  # -1.0

# 6. Indeterminate Forms
inf = float("inf")
inf - inf  # nan
inf * 0.0  # nan

# 7. The Container 'in' Operator Trap (identity 'is' vs equality '==')
nan_a = float("nan")
nan_b = float("nan")
nan_a in [nan_a]  # True  (checks identity 'is' first)
nan_a in [nan_b]  # False (falls back to '==', which evaluates to False!)