g_math 0.4.2

Multi-domain fixed-point arithmetic with geometric extension: Lie groups, manifolds, ODE solvers, tensors, fiber bundles — zero-float, 0 ULP transcendentals
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235

// AUTO-GENERATED by scripts/generate_ulp_references.py
// Q64.64 (128-bit two's complement)
// mpmath precision: 250 decimal places
//
// Format: (input_qformat, expected_output_qformat, label)
// All values are exact Q64.64 representations:
//   value_q = round(value_real * 2^64)

const EXP_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000000000000000000000_i128, 0x00000000000000010000000000000000_i128, "0"),
    (0x00000000000000008000000000000000_i128, 0x0000000000000001A61298E1E069BC97_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000002B7E151628AED2A6B_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x000000000000000763992E35376B730D_i128, "2.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x00000000000000005E2D58D8B3BCDF1B_i128, "-1.0"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0x00000000000000009B4597E37CB04FF4_i128, "-0.5"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x00000000000000010041919B7EE33CE8_i128, "0.001"),
    (0x0000000000000000B17217F7D1CF79AC_i128, 0x00000000000000020000000000000000_i128, "ln2"),
    (0x00000000000000030000000000000000_i128, 0x000000000000001415E5BF6FB105F2D5_i128, "3.0"),
    (0x000000000000000A0000000000000000_i128, 0x000000000000560A773E54157E7C1FAA_i128, "10.0"),
    (0xFFFFFFFFFFFFFFF60000000000000000_u128 as i128, 0x00000000000000000002F9AF36AC8F93_i128, "-10.0"),
    (0x0000000000000000FFBE76C8B4395810_i128, 0x0000000000000002B72F42FA823252F3_i128, "0.999"),
];

const LN_REFS: &[(i128, i128, &str)] = &[
    (0x0000000000000000004189374BC6A7F0_i128, 0xFFFFFFFFFFFFFFF9179D599C0017EEED_u128 as i128, "0.001"),
    (0x0000000000000000199999999999999A_i128, 0xFFFFFFFFFFFFFFFDB289C889555D4FA4_u128 as i128, "0.1"),
    (0x00000000000000008000000000000000_i128, 0xFFFFFFFFFFFFFFFF4E8DE8082E308654_u128 as i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000000000000000000000_i128, "1.0"),
    (0x0000000000000001004189374BC6A7F0_i128, 0x0000000000000000004180D53E30FAFC_i128, "1.001"),
    (0x00000000000000020000000000000000_i128, 0x0000000000000000B17217F7D1CF79AC_i128, "2.0"),
    (0x0000000000000002B7E151628AED2A6B_i128, 0x00000000000000010000000000000000_i128, "e"),
    (0x00000000000000030000000000000000_i128, 0x0000000000000001193EA7AAD030A977_i128, "3.0"),
    (0x000000000000000A0000000000000000_i128, 0x00000000000000024D763776AAA2B05C_i128, "10.0"),
    (0x00000000000000640000000000000000_i128, 0x00000000000000049AEC6EED554560B7_i128, "100.0"),
    (0x00000000000004000000000000000000_i128, 0x0000000000000006EE74EFAE321AC0B6_i128, "1024.0"),
];

const SQRT_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000004000000000000000_i128, 0x00000000000000008000000000000000_i128, "0.25"),
    (0x00000000000000008000000000000000_i128, 0x0000000000000000B504F333F9DE6484_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000010000000000000000_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x00000000000000016A09E667F3BCC909_i128, "2.0"),
    (0x00000000000000030000000000000000_i128, 0x0000000000000001BB67AE8584CAA73B_i128, "3.0"),
    (0x00000000000000040000000000000000_i128, 0x00000000000000020000000000000000_i128, "4.0"),
    (0x00000000000000050000000000000000_i128, 0x00000000000000023C6EF372FE94F82C_i128, "5.0"),
    (0x000000000000000A0000000000000000_i128, 0x0000000000000003298B075B4B6A5241_i128, "10.0"),
    (0x00000000000000640000000000000000_i128, 0x000000000000000A0000000000000000_i128, "100.0"),
    (0x0000000000000000028F5C28F5C28F5C_i128, 0x0000000000000000199999999999999A_i128, "0.01"),
    (0x000000000000000100068DB8BAC710CB_i128, 0x0000000000000001000346D6FF11672B_i128, "1.0001"),
];

const SIN_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000007ABBA1D12C17BFA2_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000000D76AA47848677021_i128, "1.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF28955B87B7988FDF_u128 as i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x00000000000000000041893694862988_i128, "0.001"),
    (0x0000000000000000860A91C16B9B2C23_i128, 0x00000000000000008000000000000000_i128, "pi/6"),
    (0x0000000000000000C90FDAA22168C235_i128, 0x0000000000000000B504F333F9DE6484_i128, "pi/4"),
    (0x00000000000000010C152382D7365846_i128, 0x0000000000000000DDB3D742C265539E_i128, "pi/3"),
    (0x0000000000000001921FB54442D1846A_i128, 0x00000000000000010000000000000000_i128, "pi/2"),
    (0x0000000000000003243F6A8885A308D3_i128, 0x00000000000000000000000000000000_i128, "pi"),
    (0x00000000000000030000000000000000_i128, 0x0000000000000000242070DB6DAAB69E_i128, "3.0"),
    (0x000000000000000A0000000000000000_i128, 0xFFFFFFFFFFFFFFFF74BB085065856D32_u128 as i128, "10.0"),
];

const COS_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x0000000000000000E0A94032DBEA7CEE_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000008A51407DA8345C92_i128, "1.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x00000000000000008A51407DA8345C92_i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x0000000000000000FFFFF79C843B5F70_i128, "0.001"),
    (0x0000000000000000860A91C16B9B2C23_i128, 0x0000000000000000DDB3D742C265539E_i128, "pi/6"),
    (0x0000000000000000C90FDAA22168C235_i128, 0x0000000000000000B504F333F9DE6484_i128, "pi/4"),
    (0x00000000000000010C152382D7365846_i128, 0x00000000000000008000000000000000_i128, "pi/3"),
    (0x0000000000000001921FB54442D1846A_i128, 0x00000000000000000000000000000000_i128, "pi/2"),
    (0x0000000000000003243F6A8885A308D3_i128, 0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, "pi"),
    (0x00000000000000030000000000000000_i128, 0xFFFFFFFFFFFFFFFF028FDA0BD0D16CF8_u128 as i128, "3.0"),
    (0x000000000000000A0000000000000000_i128, 0xFFFFFFFFFFFFFFFF29329BB79CA706FB_u128 as i128, "10.0"),
];

const TAN_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000008BDA7ADF9A3A5219_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000018EB245CBEE3A5B8B_i128, "1.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFE714DBA3411C5A475_u128 as i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x000000000000000000418938BA47AF8E_i128, "0.001"),
    (0x0000000000000000C90FDAA22168C235_i128, 0x00000000000000010000000000000000_i128, "pi/4"),
    (0x0000000000000000860A91C16B9B2C23_i128, 0x000000000000000093CD3A2C8198E269_i128, "pi/6"),
    (0x00000000000000010C152382D7365846_i128, 0x0000000000000001BB67AE8584CAA73B_i128, "pi/3"),
    (0x00000000000000018000000000000000_i128, 0x000000000000000E19F6A85C43BBAD2F_i128, "1.5"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF7425852065C5ADE7_u128 as i128, "-0.5"),
    (0x00000000000000004000000000000000_i128, 0x0000000000000000415E1690F1315799_i128, "0.25"),
];

const ATAN_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x000000000000000076B19C1586ED3DA3_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000000C90FDAA22168C235_i128, "1.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF36F0255DDE973DCB_u128 as i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x000000000000000000418935DD45B856_i128, "0.001"),
    (0x00000000000000020000000000000000_i128, 0x00000000000000011B6E192EBBE446C7_i128, "2.0"),
    (0x000000000000000A0000000000000000_i128, 0x0000000000000001789BD2C16005382F_i128, "10.0"),
    (0x00000000000000640000000000000000_i128, 0x00000000000000018F905EB2DEF218BF_i128, "100.0"),
    (0xFFFFFFFFFFFFFFF60000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFE87642D3E9FFAC7D1_u128 as i128, "-10.0"),
    (0x00000000000000006A09E667F3BCC909_i128, 0x00000000000000006487ED5110B4611A_i128, "tan_pi_8"),
    (0x0000000000000000199999999999999A_i128, 0x00000000000000001983E282E2CC4C3B_i128, "0.1"),
];

const ASIN_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x0000000000000000860A91C16B9B2C23_i128, "0.5"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF79F56E3E9464D3DD_u128 as i128, "-0.5"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x00000000000000000041893803072C59_i128, "0.001"),
    (0x0000000000000000199999999999999A_i128, 0x000000000000000019A49276037883C0_i128, "0.1"),
    (0x0000000000000000B504F333F9DE6484_i128, 0x0000000000000000C90FDAA22168C235_i128, "sqrt2/2"),
    (0x0000000000000000DDB3D742C265539E_i128, 0x00000000000000010C152382D7365846_i128, "sqrt3/2"),
    (0x0000000000000000FFBE76C8B4395810_i128, 0x000000000000000186AC9AD18F803716_i128, "0.999"),
    (0x0000000000000000E666666666666666_i128, 0x00000000000000011EA93705FA171F47_i128, "0.9"),
    (0xFFFFFFFFFFFFFFFF199999999999999A_u128 as i128, 0xFFFFFFFFFFFFFFFEE156C8FA05E8E0B9_u128 as i128, "-0.9"),
    (0x00000000000000004000000000000000_i128, 0x000000000000000040AFA7382E1F3479_i128, "0.25"),
];

const ACOS_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000010C152382D7365846_i128, "0.5"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0x0000000000000002182A4705AE6CB08D_i128, "-0.5"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x000000000000000191DE2C0C3FCA5811_i128, "0.001"),
    (0x0000000000000000199999999999999A_i128, 0x0000000000000001787B22CE3F5900A9_i128, "0.1"),
    (0x0000000000000000B504F333F9DE6484_i128, 0x0000000000000000C90FDAA22168C235_i128, "sqrt2/2"),
    (0x0000000000000000DDB3D742C265539E_i128, 0x0000000000000000860A91C16B9B2C23_i128, "sqrt3/2"),
    (0x0000000000000000FFBE76C8B4395810_i128, 0x00000000000000000B731A72B3514D54_i128, "0.999"),
    (0x0000000000000000E666666666666666_i128, 0x000000000000000073767E3E48BA6522_i128, "0.9"),
    (0xFFFFFFFFFFFFFFFF199999999999999A_u128 as i128, 0x0000000000000002B0C8EC4A3CE8A3B1_i128, "-0.9"),
    (0x00000000000000004000000000000000_i128, 0x000000000000000151700E0C14B24FF0_i128, "0.25"),
];

const SINH_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000008566807F31DCB652_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000012CD9FC44EB9825A8_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x0000000000000003A079EC76DC33EDE7_i128, "2.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFED32603BB1467DA58_u128 as i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x0000000000000000004189380307278B_i128, "0.001"),
    (0x00000000000000030000000000000000_i128, 0x000000000000000A04937384A4D6CDB8_i128, "3.0"),
    (0x00000000000000050000000000000000_i128, 0x000000000000004A34059BC1CDD1E1EB_i128, "5.0"),
    (0xFFFFFFFFFFFFFFFD0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFF5FB6C8C7B5B293248_u128 as i128, "-3.0"),
    (0x0000000000000000B17217F7D1CF79AC_i128, 0x0000000000000000C000000000000000_i128, "ln2"),
    (0x0000000000000000199999999999999A_i128, 0x000000000000000019A487337B59B2D7_i128, "0.1"),
];

const COSH_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x000000000000000120AC1862AE8D0646_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000018B07551D9F5504C3_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x0000000000000003C31F41BE5B378526_i128, "2.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x00000000000000018B07551D9F5504C3_i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x0000000000000001000008637BDC155D_i128, "0.001"),
    (0x00000000000000030000000000000000_i128, 0x000000000000000A11524BEB0C2F251D_i128, "3.0"),
    (0x00000000000000050000000000000000_i128, 0x000000000000004A35BF2FBFCEA7194D_i128, "5.0"),
    (0xFFFFFFFFFFFFFFFD0000000000000000_u128 as i128, 0x000000000000000A11524BEB0C2F251D_i128, "-3.0"),
    (0x0000000000000000B17217F7D1CF79AC_i128, 0x00000000000000014000000000000000_i128, "ln2"),
    (0x0000000000000000199999999999999A_i128, 0x00000000000000010147F40224B386D8_i128, "0.1"),
];

const TANH_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x0000000000000000764D4F5D5A2BCD94_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000000C2F7D5A8A79CA2AC_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x0000000000000000F6CA82F0DE1E9E9A_i128, "2.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF3D082A5758635D54_u128 as i128, "-1.0"),
    (0xFFFFFFFFFFFFFFFE0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF09357D0F21E16166_u128 as i128, "-2.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x000000000000000000418935DD45B388_i128, "0.001"),
    (0x00000000000000030000000000000000_i128, 0x0000000000000000FEBBE888D057FF10_i128, "3.0"),
    (0x00000000000000050000000000000000_i128, 0x0000000000000000FFFA0CB346F889A8_i128, "5.0"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF89B2B0A2A5D4326C_u128 as i128, "-0.5"),
    (0x0000000000000000199999999999999A_i128, 0x00000000000000001983D7795F4139DC_i128, "0.1"),
];

const ASINH_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000007B30B2BB14582653_i128, "0.5"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000000E1A1B30BCEA13661_i128, "1.0"),
    (0x00000000000000020000000000000000_i128, 0x0000000000000001719218313D0872F9_i128, "2.0"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF1E5E4CF4315EC99F_u128 as i128, "-1.0"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x00000000000000000041893694862E56_i128, "0.001"),
    (0x000000000000000A0000000000000000_i128, 0x0000000000000002FF8B8A0DA57B5AA4_i128, "10.0"),
    (0xFFFFFFFFFFFFFFF60000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFD007475F25A84A55C_u128 as i128, "-10.0"),
    (0x0000000000000000199999999999999A_i128, 0x0000000000000000198EB9E7E5FC3E13_i128, "0.1"),
    (0x00000000000000640000000000000000_i128, 0x00000000000000054C602A4F4F0A7CEE_i128, "100.0"),
    (0x00000000000000004000000000000000_i128, 0x00000000000000003F59F64733CC6DD2_i128, "0.25"),
];

const ACOSH_REFS: &[(i128, i128, &str)] = &[
    (0x0000000000000001004189374BC6A7F0_i128, 0x00000000000000000B729D65E6F682CD_i128, "1.001"),
    (0x00000000000000018000000000000000_i128, 0x0000000000000000F661657628B04CA6_i128, "1.5"),
    (0x00000000000000020000000000000000_i128, 0x000000000000000151242719804349BE_i128, "2.0"),
    (0x00000000000000030000000000000000_i128, 0x0000000000000001C34366179D426CC2_i128, "3.0"),
    (0x00000000000000050000000000000000_i128, 0x00000000000000024ADCCD491476BDA3_i128, "5.0"),
    (0x000000000000000A0000000000000000_i128, 0x0000000000000002FE43DA39C0BA87F9_i128, "10.0"),
    (0x00000000000000640000000000000000_i128, 0x00000000000000054C5CE372F189A288_i128, "100.0"),
    (0x000000000000000100068DB8BAC710CB_i128, 0x0000000000000000039ECFAFD81AD4C6_i128, "1.0001"),
    (0x0000000000000002B7E151628AED2A6B_i128, 0x0000000000000001A84EEF63326E7A6B_i128, "e"),
    (0x0000000000000001199999999999999A_i128, 0x0000000000000000718DB06A20BCA24E_i128, "1.1"),
];

const ATANH_REFS: &[(i128, i128, &str)] = &[
    (0x00000000000000008000000000000000_i128, 0x00000000000000008C9F53D5681854BB_i128, "0.5"),
    (0xFFFFFFFFFFFFFFFF8000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF7360AC2A97E7AB45_u128 as i128, "-0.5"),
    (0x0000000000000000E666666666666666_i128, 0x000000000000000178E360604B32C720_i128, "0.9"),
    (0xFFFFFFFFFFFFFFFF199999999999999A_u128 as i128, 0xFFFFFFFFFFFFFFFE871C9F9FB4CD38E0_u128 as i128, "-0.9"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x000000000000000000418938BA47B45C_i128, "0.001"),
    (0x0000000000000000199999999999999A_i128, 0x000000000000000019AF93CD23441205_i128, "0.1"),
    (0xFFFFFFFFFFFFFFFFE666666666666666_u128 as i128, 0xFFFFFFFFFFFFFFFFE6506C32DCBBEDFB_u128 as i128, "-0.1"),
    (0x0000000000000000FD70A3D70A3D70A4_i128, 0x0000000000000002A58B0332F9B0C4C1_i128, "0.99"),
    (0x00000000000000004000000000000000_i128, 0x00000000000000004162BBEA0451469D_i128, "0.25"),
    (0x0000000000000000C000000000000000_i128, 0x0000000000000000F913957192D2BAA3_i128, "0.75"),
];

const ATAN2_REFS: &[(i128, i128, i128, &str)] = &[
    (0x00000000000000010000000000000000_i128, 0x00000000000000010000000000000000_i128, 0x0000000000000000C90FDAA22168C235_i128, "1_1"),
    (0x00000000000000010000000000000000_i128, 0x00000000000000000000000000000000_i128, 0x0000000000000001921FB54442D1846A_i128, "1_0"),
    (0x00000000000000000000000000000000_i128, 0x00000000000000010000000000000000_i128, 0x00000000000000000000000000000000_i128, "0_1"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x00000000000000010000000000000000_i128, 0xFFFFFFFFFFFFFFFF36F0255DDE973DCB_u128 as i128, "-1_1"),
    (0x00000000000000010000000000000000_i128, 0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x00000000000000025B2F8FE6643A469E_i128, "1_-1"),
    (0x00000000000000000000000000000000_i128, 0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0x0000000000000003243F6A8885A308D3_i128, "0_-1"),
    (0x0000000000000001BB67AE8584CAA73B_i128, 0x00000000000000010000000000000000_i128, 0x00000000000000010C152382D7365846_i128, "sqrt3_1"),
    (0x00000000000000010000000000000000_i128, 0x0000000000000001BB67AE8584CAA73B_i128, 0x0000000000000000860A91C16B9B2C23_i128, "1_sqrt3"),
    (0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFF0000000000000000_u128 as i128, 0xFFFFFFFFFFFFFFFDA4D070199BC5B962_u128 as i128, "-1_-1"),
    (0x0000000000000000004189374BC6A7F0_i128, 0x00000000000000010000000000000000_i128, 0x000000000000000000418935DD45B856_i128, "0.001_1"),
];

const POW_REFS: &[(i128, i128, i128, &str)] = &[
    (0x00000000000000020000000000000000_i128, 0x000000000000000A0000000000000000_i128, 0x00000000000004000000000000000000_i128, "2^10"),
    (0x00000000000000020000000000000000_i128, 0x00000000000000008000000000000000_i128, 0x00000000000000016A09E667F3BCC909_i128, "2^0.5"),
    (0x000000000000000A0000000000000000_i128, 0x00000000000000030000000000000000_i128, 0x00000000000003E80000000000000000_i128, "10^3"),
    (0x00000000000000020000000000000000_i128, 0x00000000000000038000000000000000_i128, 0x000000000000000B504F333F9DE64846_i128, "2.0^3.5"),
    (0x00000000000000018000000000000000_i128, 0x00000000000000028000000000000000_i128, 0x0000000000000002C173FAD148AA8994_i128, "1.5^2.5"),
    (0x00000000000000008000000000000000_i128, 0x00000000000000020000000000000000_i128, 0x00000000000000004000000000000000_i128, "0.5^2"),
    (0x00000000000000008000000000000000_i128, 0x00000000000000030000000000000000_i128, 0x00000000000000002000000000000000_i128, "0.5^3"),
    (0x00000000000000030000000000000000_i128, 0x00000000000000008000000000000000_i128, 0x0000000000000001BB67AE8584CAA73B_i128, "3^0.5"),
    (0x0000000000000001004189374BC6A7F0_i128, 0x00000000000000640000000000000000_i128, 0x00000000000000011AE8DCC401C58517_i128, "1.001^100"),
    (0x0000000000000002B7E151628AED2A6B_i128, 0x00000000000000010000000000000000_i128, 0x0000000000000002B7E151628AED2A6B_i128, "e^1"),
];