<commit_before>
                     
   FLOAT_FIXED_POINT  
                     



ALTERNATIVES ==>        #Floating point numbers:
                        #  - most common
                        #  - implemented hardware, i.e. faster
                        #  - low space
                        #Fixed point numbers:
                        #  - lowest space
                        #  - least variable precision
                        #String of digits:
                        #  - infinite precision
                        #  - higest space
                        #Rational numbers:
                        #  - best precision for rational numbers (not irrational) with repeating decimals
                        #Base 2 vs base 10:
                        #  - base 2 more efficient, but decimal rounding errors to represent base 10


                                             /=+===============================+=\
                                            /  :                               :  \
                                            )==:             TYPES             :==(
                                            \  :_______________________________:  /
                                             \=+===============================+=/


REPRESENTATIONS ==>     #How ℝ  is represented:
                        #  - scientific notation:
                        #     - m * bⁿ
                        #     - b ∈ ℕ and m,n ∈ ℤ
                        #  - logarithmic number system (LNS)
                        #     - bⁿ
                        #     - b ∈ ℕ and n ∈ ℚ
                        #  - string of digits
                        #     - allows for arbitrary precision (see doc for integers)
                        #  - fractions:
                        #     - two integers: nominator|denominator

RADIX ==>               #Can be:
                        #  - base 2 (binary)
                        #     - more commonly used
                        #     - more compact
                        #  - base 10 (decimal)
                        #Using 2 can lead to imprecise representation of base-10 decimal parts:<commit_msg>no commit message<commit_after>
                     
   FLOAT_FIXED_POINT  
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ALTERNATIVES ==>        #Floating point numbers:
                        #  - most common
                        #  - implemented hardware, i.e. faster
                        #  - low space
                        #Fixed point numbers:
                        #  - lowest space
                        #  - least variable precision
                        #String of digits:
                        #  - infinite precision
                        #  - higest space
                        #Rational numbers:
                        #  - best precision for rational numbers (not irrational) with repeating decimals
                        #Base 2 vs base 10:
                        #  - base 2 more efficient, but decimal rounding errors to represent base 10


                                             /=+===============================+=\
                                            /  :                               :  \
                                            )==:             TYPES             :==(
                                            \  :_______________________________:  /
                                             \=+===============================+=/


REPRESENTATIONS ==>     #How ℝ  is represented:
                        #  - scientific notation:
                        #     - m * bⁿ
                        #     - b∈ N and m,n∈ Z
                        #  - logarithmic number system (LNS)
                        #     - bⁿ
                        #     - b∈ N and n∈ Q
                        #  - string of digits
                        #     - allows for arbitrary precision (see doc for integers)
                        #  - fractions:
                        #     - two integers: nominator|denominator

RADIX ==>               #Can be:
                        #  - base 2 (binary)
                        #     - more commonly used
                        #     - more compact
                        #  - base 10 (decimal)
                        #Using 2 can lead to imprecise representation of base-10 decimal parts:
{'fraction_non_alphanumeric': 0.20193470374848851, 'fraction_numerical': 0.0048367593712212815, 'mean_word_length': 0.9051823416506718, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 9, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 28, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '2769262', 'n_tokens_mistral': 2819, 'n_tokens_neox': 2688, 'n_words': 263}