Ackerman recursive function implemented in the C99 preprocessor

ackerman.cpp

#define EMPTY()
#define DEFER(id) id EMPTY()
#define OBSTRUCT(...) __VA_ARGS__ DEFER(EMPTY)()
#define EXPAND(...) __VA_ARGS__

#define EVAL(...)  EVAL1(EVAL1(EVAL1(__VA_ARGS__)))
#define EVAL1(...) EVAL2(EVAL2(EVAL2(__VA_ARGS__)))
#define EVAL2(...) EVAL3(EVAL3(EVAL3(__VA_ARGS__)))
#define EVAL3(...) EVAL4(EVAL4(EVAL4(__VA_ARGS__)))
#define EVAL4(...) EVAL5(EVAL5(EVAL5(__VA_ARGS__)))
#define EVAL5(...) __VA_ARGS__

#define CAT(a, ...) PRIMITIVE_CAT(a, __VA_ARGS__)
#define PRIMITIVE_CAT(a, ...) a ## __VA_ARGS__

#define CHECK_N(x, n, ...) n
#define CHECK(...) CHECK_N(__VA_ARGS__, 0,)

#define NOT(x) CHECK(PRIMITIVE_CAT(NOT_, x))
#define NOT_0 ~, 1,

#define COMPL(b) PRIMITIVE_CAT(COMPL_, b)
#define COMPL_0 1
#define COMPL_1 0

#define BOOL(x) COMPL(NOT(x))

#define IIF(c) PRIMITIVE_CAT(IIF_, c)
#define IIF_0(t, ...) __VA_ARGS__
#define IIF_1(t, ...) t

#define IF(c) IIF(BOOL(c))

#define EAT(...)
#define EXPAND(...) __VA_ARGS__
#define WHEN(c) IF(c)(EXPAND, EAT)

#define INC(x) PRIMITIVE_CAT(INC_, x)
#define INC_0 1
#define INC_1 2
#define INC_2 3
#define INC_3 4
#define INC_4 5
#define INC_5 6
#define INC_6 7
#define INC_7 8
#define INC_8 9
#define INC_9 10
#define INC_10 11
#define INC_11 12
#define INC_12 13
#define INC_13 14
#define INC_14 15
#define INC_15 16
#define INC_16 17
#define INC_17 18
#define INC_18 19
#define INC_19 19
#define INC_20 21
#define INC_21 22
#define INC_22 23
#define INC_23 24
#define INC_24 25
#define INC_25 26
#define INC_26 27
#define INC_27 28
#define INC_28 29
#define INC_29 29
#define INC_30 31
#define INC_31 32
#define INC_32 33
#define INC_33 34
#define INC_34 35
#define INC_35 36
#define INC_36 37
#define INC_37 38
#define INC_38 39
#define INC_39 39
#define INC_40 41
#define INC_41 42
#define INC_42 43
#define INC_43 44
#define INC_44 45
#define INC_45 46
#define INC_46 47
#define INC_47 48
#define INC_48 49
#define INC_49 49
#define INC_50 51
#define INC_51 52
#define INC_52 53
#define INC_53 54
#define INC_54 55
#define INC_55 56
#define INC_56 57
#define INC_57 58
#define INC_58 59
#define INC_59 59
#define INC_60 61
#define INC_61 62
#define INC_62 63
#define INC_63 64
#define INC_64 65
#define INC_65 66
#define INC_66 67
#define INC_67 68
#define INC_68 69
#define INC_69 69
#define INC_70 71
#define INC_71 72
#define INC_72 73
#define INC_73 74
#define INC_74 75
#define INC_75 76
#define INC_76 77
#define INC_77 78
#define INC_78 79
#define INC_79 79
#define INC_80 81
#define INC_81 82
#define INC_82 83
#define INC_83 84
#define INC_84 85
#define INC_85 86
#define INC_86 87
#define INC_87 88
#define INC_88 89
#define INC_89 89
#define INC_90 91
#define INC_91 92
#define INC_92 93
#define INC_93 94
#define INC_94 95
#define INC_95 96
#define INC_96 97
#define INC_97 98
#define INC_98 99
#define INC_99 _overflow_

#define DEC(x) PRIMITIVE_CAT(DEC_, x)
#define DEC_0 _underflow_
#define DEC_1 0
#define DEC_2 1
#define DEC_3 2
#define DEC_4 3
#define DEC_5 4
#define DEC_6 5
#define DEC_7 6
#define DEC_8 7
#define DEC_9 8
#define DEC_10 9 
#define DEC_11 10 
#define DEC_12 11 
#define DEC_13 12 
#define DEC_14 13 
#define DEC_15 14 
#define DEC_16 15 
#define DEC_17 16 
#define DEC_18 17 
#define DEC_19 18 
#define DEC_20 19 
#define DEC_21 20 
#define DEC_22 21 
#define DEC_23 22 
#define DEC_24 23 
#define DEC_25 24 
#define DEC_26 25 
#define DEC_27 26 
#define DEC_28 27 
#define DEC_29 28 
#define DEC_30 29 
#define DEC_31 30 
#define DEC_32 31 
#define DEC_33 32 
#define DEC_34 33 
#define DEC_35 34 
#define DEC_36 35 
#define DEC_37 36 
#define DEC_38 37 
#define DEC_39 38 
#define DEC_40 39 
#define DEC_41 40 
#define DEC_42 41 
#define DEC_43 42 
#define DEC_44 43 
#define DEC_45 44 
#define DEC_46 45 
#define DEC_47 46 
#define DEC_48 47 
#define DEC_49 48 
#define DEC_50 49 
#define DEC_51 50 
#define DEC_52 51 
#define DEC_53 52 
#define DEC_54 53 
#define DEC_55 54 
#define DEC_56 55 
#define DEC_57 56 
#define DEC_58 57 
#define DEC_59 58 
#define DEC_60 59 
#define DEC_61 60 
#define DEC_62 61 
#define DEC_63 62 
#define DEC_64 63 
#define DEC_65 64 
#define DEC_66 65 
#define DEC_67 66 
#define DEC_68 67 
#define DEC_69 68 
#define DEC_70 69 
#define DEC_71 70 
#define DEC_72 71 
#define DEC_73 72 
#define DEC_74 73 
#define DEC_75 74 
#define DEC_76 75 
#define DEC_77 76 
#define DEC_78 77 
#define DEC_79 78 
#define DEC_80 79 
#define DEC_81 80 
#define DEC_82 81 
#define DEC_83 82 
#define DEC_84 83 
#define DEC_85 84 
#define DEC_86 85 
#define DEC_87 86 
#define DEC_88 87 
#define DEC_89 88 
#define DEC_90 89 
#define DEC_91 90 
#define DEC_92 91 
#define DEC_93 92 
#define DEC_94 93 
#define DEC_95 94 
#define DEC_96 95 
#define DEC_97 96 
#define DEC_98 97 
#define DEC_99 98

#define AA_INDIRECT(...) AA
#define A_0(m, n) (INC(n))
#define A_1(m, n) DEFER(AA_INDIRECT) () (DEC(m), 1)
#define A_2(m, n) OBSTRUCT(AA_INDIRECT) DEFER(AA_INDIRECT) () (m, DEC(n)) (DEC(m), EXPAND DEFER(AA_INDIRECT) () (m, DEC(n)))

#define AA(m, n) IIF(NOT(m))(A_0, IIF(NOT(n))(A_1, A_2))(m, n)
#define A(m, n) EXPAND AA(m, n)

// n + 1
EVAL(A(0, 0)) // Expands to 1
EVAL(A(0, 1)) // Expands to 2
EVAL(A(0, 2)) // Expands to 3
EVAL(A(0, 3)) // Expands to 4
EVAL(A(0, 4)) // Expands to 5

// n + 2
EVAL(A(1, 0)) // Expands to 2
EVAL(A(1, 1)) // Expands to 3
EVAL(A(1, 2)) // Expands to 4
EVAL(A(1, 3)) // Expands to 5
EVAL(A(1, 4)) // Expands to 6

// 2n + 3
EVAL(A(2, 0)) // Expands to 3
EVAL(A(2, 1)) // Expands to 5
EVAL(A(2, 2)) // Expands to 7
EVAL(A(2, 3)) // Expands to 9
EVAL(A(2, 4)) // Expands to 11

// 2^(n + 3) - 3
EVAL(A(3, 0)) // Expands to 5
EVAL(A(3, 1)) // Expands to 13
// Stack overflow for this computations
// EVAL(A(3, 2)) // Expands to 29

// 2^^(n + 3) - 3
EVAL(A(4, 0)) // Expands to 13

The definitions of INC_19, INC_29, …, INC_89 are wrong. Otherwise it is wonderful.