content
stringlengths 10
1.02M
| lang
stringclasses 87
values | size
int64 10
1.02M
| ext
stringclasses 189
values | max_stars_count
int64 1
82k
⌀ | avg_line_length
float64 1.89
277k
| max_line_length
int64 1
417k
| alphanum_fraction
float64 0.1
1
|
|---|---|---|---|---|---|---|---|
vcpkg_from_github(
OUT_SOURCE_PATH SOURCE_PATH
REPO eyalz800/zpp_bits
REF v.4.4.4
SHA512 172300f1547b985702698d7f10ac5bd804421226a8c20b26b60608aaa10bf4f9682fd1a3e49e75c309c9cb30b888f623aa5eb7ace5705d85601a2c67c8829b3f
HEAD_REF master
)
file(INSTALL "${SOURCE_PATH}/zpp_bits.h" DESTINATION "${CURRENT_PACKAGES_DIR}/include")
file(INSTALL "${SOURCE_PATH}/LICENSE" DESTINATION "${CURRENT_PACKAGES_DIR}/share/${PORT}" RENAME copyright)
| CMake | 465 | cmake | 5,585 | 38.75 | 140 | 0.797849 |
defmodule Default do
def go(x \\ 42_000), do: x
def gogo(a, x \\ 666_000, y \\ 1_000), do: a + x + y
end
| Elixir | 110 | ex | 16 | 18.333333 | 54 | 0.572727 |
lexer grammar LGFileLexer;
@parser::header {#pragma warning disable 3021} // Disable StyleCop warning CS3021 re CLSCompliant attribute in generated files.
@lexer::header {#pragma warning disable 3021} // Disable StyleCop warning CS3021 re CLSCompliant attribute in generated files.
@lexer::members {
bool startTemplate = false;
}
fragment WHITESPACE : ' '|'\t'|'\ufeff'|'\u00a0';
NEWLINE : '\r'? '\n';
OPTION : WHITESPACE* '>' WHITESPACE* '!#' ~('\r'|'\n')+ { !startTemplate }?;
COMMENT : WHITESPACE* '>' ~('\r'|'\n')* { !startTemplate }?;
IMPORT : WHITESPACE* '[' ~[\r\n[\]]*? ']' '(' ~[\r\n()]*? ')' ~('\r'|'\n')* { !startTemplate }?;
TEMPLATE_NAME_LINE : WHITESPACE* '#' ~('\r'|'\n')* { TokenStartColumn == 0}? { startTemplate = true; };
INLINE_MULTILINE: WHITESPACE* '-' WHITESPACE* '```' ~('\r'|'\n')* '```' WHITESPACE* { startTemplate && TokenStartColumn == 0 }?;
MULTILINE_PREFIX: WHITESPACE* '-' WHITESPACE* '```' ~('\r'|'\n')* { startTemplate && TokenStartColumn == 0 }? -> pushMode(MULTILINE_MODE);
TEMPLATE_BODY : ~('\r'|'\n')+ { startTemplate }?;
INVALID_LINE : ~('\r'|'\n')+ { !startTemplate }?;
mode MULTILINE_MODE;
MULTILINE_SUFFIX : '```' -> popMode;
ESCAPE_CHARACTER : '\\' ~[\r\n]?;
MULTILINE_TEXT : .+?; | ANTLR | 1,241 | g4 | null | 34.472222 | 138 | 0.618856 |
5 13 16 39 5 1 19 27 22 4 14 4 36 49 32 2 17 16 22 4 2 40 47 24 25 4 14 29 29 9 21 6 50 34 12 42 14 45 8 27 48 17 47 24 48 25 50 36 13 19 1 1 13 7 27 16 14 24 28 5 48 42 7 40 50 35 6 40 39 8 13 38 4 2 12 12 34 9 50 47 20 30 25 12 12 12 24 39 9 45 34 39 16 48 13 17 16 16 33 34
27 42 19 21 5 23 13 44 12 11 31 24 15 47 2 10 6 35 43 30 48 35 40 12 32 2 46 3 14 2 7 12 4 22 30 14 33 20 17 20 18 43 5 34 27 24 2 47 45 42 13 23 3 24 13 21 18 30 41 28 15 27 13 21 29 37 15 9 47 45 19 20 24 19 36 9 26 4 46 25 9 33 36 29 1 38 45 14 40 25 45 10 31 44 11 17 17 2 24 8
34 19 20 14 48 7 43 44 50 6 16 33 33 7 36 24 27 26 12 18 6 16 16 23 28 37 44 23 49 10 42 11 50 35 9 41 12 42 37 15 42 33 22 23 11 16 10 33 47 8 28 36 28 47 40 18 34 19 43 28 9 32 45 23 7 45 42 23 29 10 11 43 20 17 2 28 47 48 10 46 7 28 50 14 16 34 15 35 16 9 44 17 19 10 18 2 37 19 13 28
1 27 28 12 9 7 24 15 3 13 50 36 15 31 18 6 37 50 9 9 8 18 23 44 49 36 48 19 25 32 18 38 24 1 27 44 29 35 45 7 34 40 24 11 6 27 2 36 33 45 32 12 18 44 45 12 33 5 7 30 10 3 25 46 30 1 21 1 15 1 39 22 50 7 48 12 6 31 35 34 25 5 37 19 38 21 9 5 46 44 12 22 22 21 34 11 39 7 46 6
9 17 37 23 46 15 49 17 46 32 31 21 42 40 21 16 16 6 50 3 49 29 11 9 24 14 4 37 24 40 4 42 21 16 39 31 46 23 39 4 21 48 32 16 40 35 48 33 40 2 34 44 46 23 8 32 16 48 24 6 36 18 50 47 45 30 22 46 47 44 37 27 36 27 1 43 41 32 7 3 9 33 13 15 25 27 42 24 6 32 49 38 36 4 39 33 19 32 40 27
46 16 37 13 15 14 14 2 27 41 2 17 49 5 44 21 18 19 34 34 22 7 21 41 9 16 3 34 34 46 36 29 31 37 20 43 31 8 39 47 38 2 32 48 46 34 23 35 38 16 39 28 42 16 12 17 34 32 28 13 10 42 21 41 43 45 37 38 3 17 8 49 5 37 43 3 39 28 40 40 2 33 28 50 27 21 21 24 32 8 7 38 45 42 29 37 24 41 1 50
47 23 45 11 5 19 9 12 20 29 17 42 38 38 28 40 50 2 18 40 16 15 43 30 8 16 22 5 15 22 36 23 17 44 44 17 15 40 22 29 30 37 8 37 5 47 49 48 13 3 38 48 7 31 2 14 37 44 14 30 24 20 32 36 47 42 42 3 28 28 40 8 50 5 6 22 5 30 42 14 48 35 47 17 11 10 11 32 18 21 13 40 39 47 21 21 50 19 30 18
30 13 4 7 20 30 26
2 2 5 5 4 4 3 5 5 5 5 1 4 4 5 4 3 4 1 3 1 4 4 3 2 2 3 2 1 5 4 3 2 4 4 1 5 1 2 3 4 3 5 4 3 1 1 2 4 5 3 3 2 5 1 3 1 2 5 1 5 5 1 3 4 5 4 5 2 5 1 3 4 1 3 3 2 3 5 2 1 4 2 4 4 5 4 4 3 5 3 1 4 3 3 5 3 3 4 3
3 4 3 4 3 4 1 3 1 2 2 4 3 3 2 3 5 2 5 1 5 2 1 2 3 3 5 1 2 1 5 5 1 4 1 2 4 5 5 3 2 1 2 2 1 1 1 1 2 2 5 5 1 5 2 4 4 4 1 5 4 2 2 3 5 1 2 5 4 1 3 1 5 2 3 1 5 4 1 4 2 1 3 3 4 3 3 4 4 5 2 2 4 2 1 5 2 2 1 3 5 5 5 1 5 4 2 2 4 1
2 1 5 4 2 1 3 2 3 3 1 5 4 1 1 3 3 4 5 5 4 4 2 1 1 2 3 4 4 3 1 4 5 1 1 3 1 3 3 1 1 4 4 1 4 1 3 2 1 5 5 5 3 5 2 5 5 3 4 5 5 2 5 1 1 2 5 2 2 5 5 3 5 2 3 3 4 3 2 1 5 5 3 3 1 2 1 5 4 2 2 2 4 4 4 1 3 3 5 2 1 5 3 2 3 5 1 4 5 5
3 1 5 5 3 5 2 3 5 4 4 1 4 5 2 3 1 5 2 1 5 4 2 2 5 5 2 3 2 3 5 1 3 5 3 2 2 5 3 5 4 4 2 5 1 3 4 3 1 5 5 3 1 4 4 5 4 5 2 1 5 1 2 4 2 1 4 1 1 1 5 5 5 5 3 2 4 3 1 2 5 3 1 4 1 4 2 2 4 3 1 1 3 4 1 3 3 4 2 4 1 2 3 3 3 4 1 4 3 5
1 5 2 3 3 5 4 1 2 5 2 2 5 3 5 1 1 4 5 4 1 1 2 2 5 4 2 5 2 5 3 3 4 5 5 4 2 2 4 4 4 2 3 5 5 2 5 1 5 2 3 2 5 1 1 3 3 4 2 1 5 4 5 1 3 1 3 2 4 4 3 2 5 4 1 1 2 4 3 1 2 2 5 5 2 4 3 2 4 5 2 4 2 4 5 4 1 3 2 5 1 5 5 2 5 2 2 3 3 1
1 4 1 5 2 5 3 4 2 3 5 2 4 4 4 2 5 5 3 3 1 2 2 2 3 3 2 1 5 4 2 5 2 2 3 2 4 5 4 2 2 5 2 2 5 4 3 2 2 5 4 4 5 3 5 4 4 2 5 2 2 5 4 4 5 2 5 4 2 3 1 4 2 3 2 3 1 4 1 3 5 2 1 1 4 4 2 5 2 2 3 1 1 4 4 4 2 5 4 4 4 3 2 2 5 5 1 5 3 3
5 4 5 4 1 3 5 5 2 5 5 1 1 4 3 5 3 4 4 4 5 3 1 2 3 5 4 3 1 2 1 4 2 5 2 1 3 1 4 4 4 2 5 3 1 4 4 2 3 3 2 4 5 3 4 2 3 4 2 3 1 2 5 3 1 5 1 5 1 5 1 3 2 3 2 1 5 3 3 3 3 2 4 5 3 1 5 5 5 2 4 2 1 3 3 1 1 5 4 5 1 3 1 1 1 3 3 3 3 1
2 1 1 4 1 3 1 2 5 1 4 2 5 5 3 5 1 2 1 3 1 4 3 1 1 1 2 5 2 1 2 3 2 1 4 5 2 2 4 2 2 5 1 1 4 1 4 5 5 4 3 1 2 3 5 5 1 2 3 3 1 2 1 2 1 3 3 4 3 5 2 5 1 4 2 5 5 1 2 4 4 1 4 3 4 4 5 5 4 1 5 4 5 5 5 5 3 5 3 5 1 3 5 4 4 3 3 1 4 2
3 4 2 5 2 5 2 2 5 5 3 4 5 3 1 4 2 4 3 4 4 4 3 4 5 2 1 3 1 2 1 2 5 4 5 5 1 3 4 5 3 4 2 5 3 5 5 5 1 2 2 5 3 2 5 1 3 3 3 3 2 1 3 2 1 1 2 1 4 5 3 5 5 2 4 2 2 2 3 4 4 4 4 3 1 4 4 2 5 4 2 4 5 2 1 3 2 4 5 4 3 3 3 3 3 4 3 3 2 5
5 2 4 3 2 4 2 4 5 3 3 5 5 5 4 2 5 5 4 1 2 2 5 2 3 4 1 3 5 1 1 3 3 2 5 5 1 2 5 1 1 4 3 4 4 5 4 4 5 2 2 3 2 2 4 2 2 4 3 5 5 1 2 5 2 3 4 3 3 2 3 4 2 1 3 3 4 3 2 4 4 5 3 2 3 2 1 5 2 1 4 4 2 1 1 2 2 5 4 4 5 5 2 2 3 2 3 3 1 4
4 1 2 5 2 3 1 1 4 5 1 4 4 1 5 5 4 5 2 4 4 1 3 1 3 2 1 1 3 4 3 2 5 1 5 4 4 5 3 3 2 4 3 5 4 5 4 5 2 5 4 3 1 5 1 5 4 2 3 4 1 5 1 2 4 5 4 5 1 2 4 3 4 3 3 1 4 3 5 3 1 1 3 3 4 5 3 3 2 3 5 3 2 1 3 1 4 4 2 2 1 3 1 1 2 2 5 1 2 1
2 2 5 4 1 3 3 2 2 3 5 3 3 1 5 1 5 5 2 1 2 4 5 5 1 3 5 2 5 1 2 4 5 4 3 3 3 3 1 4 3 4 2 2 3 2 2 3 5 3 4 4 1 1 2 4 3 4 3 1 3 1 2 5 5 1 5 5 2 3 5 4 4 2 5 1 4 2 4 5 2 3 2 3 5 2 4 3 4 4 3 4 3 2 1 1 3 3 1 4 4 4 5 1 1 3 4 5 1 1
5 5 1 5 3 4 2 5 1 5 4 2 4 2 3 2 4 3 1 5 3 1 1 2 1 2 2 5 2 4 5 5 4 2 2 4 1 3 1 5 1 3 2 4 4 4 4 3 3 3 2 1 4 5 5 2 2 5 5 4 2 5 5 4 5 3 4 2 1 1 4 2 1 5 2 5 2 1 4 4 4 5 5 5 3 1 3 4 2 2 4 1 5 3 4 2 3 5 4 1 4 5 2 5 3 5 4 5 3 3
3 5 5 4 3 2 2 3 4 2 4 2 3 3 2 3 5 5 1 3 1 1 2 2 2 5 4 4 1 1 2 1 2 5 1 2 3 2 3 4 4 5 5 2 5 3 1 5 3 3 3 4 3 3 2 2 4 5 2 1 3 2 5 1 4 4 3 1 4 4 3 3 1 3 5 3 4 2 2 1 1 5 5 3 5 5 2 5 2 5 4 2 4 3 5 3 2 5 5 4 2 1 3 1 5 3 3 2 1 4
1 4 4 3 4 3 2 5 5 5 4 1 4 1 3 3 4 2 4 5 3 3 4 1 2 5 2 4 2 5 3 5 3 1 1 1 2 2 5 1 2 1 4 4 3 3 4 4 4 4 3 3 1 3 1 4 5 1 2 3 2 4 2 1 4 4 2 4 3 2 1 3 3 5 1 3 2 3 5 2 5 4 4 3 5 3 3 2 4 2 1 4 2 5 1 5 3 2 2 5 2 3 1 4 3 1 1 2 3 2
2 5 4 5 5 1 4 5 4 1 2 2 4 2 2 3 3 5 2 2 2 1 3 2 1 4 5 2 3 5 4 2 3 4 5 1 4 4 1 5 2 2 2 2 3 4 1 5 1 3 4 4 4 3 1 5 5 3 4 5 2 1 4 4 4 1 4 3 2 4 3 5 5 4 5 3 5 2 5 4 1 3 3 5 3 3 5 5 1 1 1 3 1 5 1 1 3 2 5 3 1 2 2 1 5 3 3 1 5 4
1 2 4 2 5 5 5 5 4 1 2 2 1 1 1 1 1 1 4 5 5 1 5 2 5 2 1 4 5 2 1 4 2 2 2 2 1 1 1 4 2 5 2 4 1 2 5 2 4 1 1 2 1 3 1 1 2 3 1 1 4 3 3 3 2 5 1 2 5 2 2 5 2 5 5 3 4 2 2 2 3 2 3 3 5 4 5 5 4 3 5 4 5 4 4 3 2 3 2 2 5 1 3 1 1 5 2 1 2 1
5 3 2 5 2 2 5 1 1 2 2 1 4 4 1 3 2 5 4 3 1 5 2 5 1 2 5 5 2 1 5 5 4 2 4 3 2 4 5 4 4 2 4 5 2 2 2 2 5 3 2 3 5 5 1 2 2 5 3 2 4 4 2 2 1 1 4 3 1 2 4 3 1 2 4 1 2 3 5 1 5 4 1 2 2 2 4 1 2 5 4 4 1 5 4 1 5 2 1 4 3 1 5 2 2 5 1 5 5 2
2 1 1 4 1 1 5 4 1 1 2 5 3 1 4 4 2 5 3 3 4 4 3 1 4 5 5 3 4 1 5 4 5 2 4 1 3 5 1 4 5 2 3 4 3 4 1 4 4 1 2 3 5 1 1 3 2 3 4 3 3 4 5 2 5 3 3 1 1 2 4 1 3 5 5 2 3 3 2 4 1 5 1 1 5 5 5 2 2 1 3 1 1 3 1 5 4 4 2 5 3 1 1 2 4 5 5 1 3 2
1 2 5 2 3 4 1 1 1 3 3 5 2 1 3 1 1 4 3 3 2 4 4 4 5 3 1 3 3 4 3 3 2 5 1 2 1 4 1 4 3 4 4 2 3 4 3 5 1 4 1 3 5 4 1 3 5 5 2 5 4 5 3 3 2 4 2 2 1 2 5 5 2 2 1 2 2 5 4 3 5 5 1 1 2 1 1 5 1 2 3 1 4 2 3 3 4 4 4 1 5 3 3 4 4 4 1 3 3 5
4 2 5 4 2 3 2 5 3 2 3 5 1 4 2 3 1 1 2 5 5 5 3 2 3 3 3 1 2 3 5 1 5 3 3 1 3 5 1 1 3 4 2 2 2 5 3 2 5 4 3 3 3 3 2 1 2 3 5 5 2 1 2 4 1 3 2 4 3 3 1 2 5 4 1 3 3 2 1 3 2 1 3 1 3 3 4 4 3 4 2 3 2 5 4 4 5 1 2 5 5 4 1 2 5 1 5 4 4 2
1 3 3 1 2 4 2 1 2 1 5 3 3 5 1 1 5 3 3 5 4 5 4 3 5 5 1 5 3 5 5 5 1 3 1 3 4 2 1 5 2 4 4 1 1 5 4 1 2 2 2 3 2 2 5 5 2 2 2 2 5 3 3 5 3 2 2 4 3 2 2 5 4 5 2 2 2 2 2 3 1 5 2 1 5 1 3 1 3 5 5 4 1 3 4 3 1 3 4 4 3 3 3 4 5 2 2 5 1 3
4 1 5 2 1 2 4 4 2 5 4 2 1 3 2 5 2 4 4 4 2 4 3 1 4 3 2 1 2 3 5 1 5 2 3 5 1 1 4 1 3 5 3 3 4 2 1 2 3 3 1 4 3 3 1 2 2 2 3 4 5 2 5 4 1 5 3 2 5 5 4 2 4 4 2 4 2 3 4 5 4 3 4 1 4 1 3 3 3 5 4 2 4 2 4 4 5 3 4 4 3 3 2 5 4 4 4 5 2 1
1 4 3 2 4 4 3 2 1 1 4 3 3 4 5 4 1 5 4 1 1 1 3 5 4 2 4 4 3 5 2 5 4 4 2 3 3 5 1 4 1 4 3 4 1 2 3 4 4 3 5 3 2 5 3 3 5 1 5 4 5 4 2 2 4 4 1 2 2 5 3 2 1 5 1 4 4 4 1 4 4 5 2 5 5 1 3 4 4 1 5 3 3 4 1 4 3 2 4 5 1 3 4 1 3 4 3 1 2 4
3 4 2 4 4 3 4 5 5 5 5 5 5 4 4 4 1 3 3 5 5 2 4 3 2 4 4 4 5 2 4 1 3 3 4 5 2 2 4 2 2 1 5 1 3 1 4 3 1 5 4 3 3 2 1 4 5 5 4 2 1 2 5 2 5 5 5 4 2 1 4 4 3 3 3 3 2 4 1 2 3 3 5 2 5 3 4 1 3 1 1 1 5 2 5 5 2 5 3 2 1 3 4 4 4 1 5 1 4 2
4 1 1 2 4 1 1 3 3 1 1 1 3 4 4 4 4 5 2 5 2 2 4 1 5 3 3 2 3 1 5 5 1 3 2 4 5 4 2 4 5 4 4 1 4 4 1 3 1 4 2 3 4 2 1 5 1 2 4 4 1 3 3 5 5 2 2 1 1 4 1 5 1 3 3 2 2 4 1 2 1 3 1 5 3 1 1 5 2 5 4 3 3 2 3 1 2 5 4 1 4 5 4 1 4 4 3 1 3 1
1 3 1 3 4 1 5 5 4 2 4 4 5 4 5 3 5 5 2 5 3 4 3 3 4 1 5 2 5 1 1 5 4 5 1 1 1 4 1 4 2 4 4 4 2 3 1 4 3 4 3 5 2 4 1 2 1 1 5 3 3 2 4 1 1 5 4 5 1 4 3 2 4 1 5 5 4 2 3 2 4 3 5 3 4 2 5 2 2 4 1 4 3 5 3 3 3 2 3 5 5 5 5 1 2 2 3 2 4 4
1 1 4 1 1 5 2 2 2 2 2 3 5 4 1 5 1 4 1 2 1 3 1 1 3 2 1 3 4 2 3 1 3 4 2 1 5 4 5 5 5 3 3 5 4 1 3 4 4 5 4 2 5 2 4 4 1 1 1 3 4 4 5 2 5 3 4 2 1 2 5 5 5 1 1 4 5 4 5 5 3 4 2 2 2 1 5 4 3 2 2 5 1 5 1 1 3 1 1 5 4 1 5 3 2 3 5 3 2 5
2 4 5 1 3 4 4 3 1 1 4 2 3 2 5 3 2 3 4 4 2 3 3 5 4 3 2 3 5 5 2 4 3 2 1 1 3 2 1 5 4 5 4 5 4 2 2 4 3 3 1 2 5 3 1 5 1 1 3 4 4 3 2 1 4 4 3 4 2 3 1 5 5 2 2 1 3 2 2 4 2 2 3 4 2 5 1 4 3 2 5 1 5 2 4 4 5 2 4 4 4 5 4 1 5 5 3 3 4 4
2 5 2 2 1 4 5 2 3 4 4 1 5 4 4 4 4 5 4 2 1 3 2 2 5 2 5 4 5 3 1 1 3 4 3 5 2 3 3 5 1 2 4 3 3 5 3 4 1 4 3 3 2 4 2 3 3 4 4 2 2 4 2 2 4 2 1 2 2 3 2 2 2 5 4 3 5 3 4 5 1 1 3 5 1 2 1 2 1 1 3 4 2 5 5 1 4 2 2 3 1 3 1 2 3 2 2 5 3 4
4 1 4 2 3 2 2 5 3 4 3 3 5 2 1 3 3 2 1 4 4 5 1 1 5 5 3 3 5 1 3 3 2 4 4 3 5 2 2 4 4 4 4 3 1 5 4 5 1 2 2 2 4 3 2 2 1 2 4 1 2 4 4 2 2 4 4 5 2 4 4 4 5 5 3 2 4 4 4 5 3 1 5 1 3 5 1 1 5 3 5 4 1 2 2 5 1 1 1 4 3 1 3 3 1 1 3 3 2 4
2 3 5 3 1 5 4 3 1 5 1 2 5 1 1 1 5 1 3 5 2 4 5 4 2 4 2 3 2 2 5 1 3 4 2 5 5 3 3 3 3 2 5 2 1 4 2 3 1 5 1 2 3 5 3 5 4 2 2 2 2 1 2 4 1 3 5 4 1 2 2 5 2 2 4 2 4 1 4 1 5 3 4 3 2 1 3 4 1 3 2 4 5 1 3 3 3 5 5 3 4 4 3 4 5 5 1 2 1 4
5 4 1 5 2 1 3 5 3 1 1 1 1 4 4 3 1 4 5 3 4 3 3 5 3 4 3 1 4 1 2 2 3 1 3 2 1 2 3 1 3 4 4 1 1 5 1 1 1 1 1 5 3 5 5 1 5 1 1 2 5 1 2 3 3 2 1 4 3 2 5 3 1 5 5 4 1 1 4 1 2 2 1 1 2 5 4 4 5 3 5 3 3 5 1 4 1 1 3 5 3 5 1 1 4 2 5 5 4 5
3 5 2 2 4 4 4 5 3 4 4 2 4 3 4 1 5 4 4 4 2 1 5 3 4 3 4 2 2 5 2 2 2 3 2 2 2 2 4 2 2 1 4 4 4 5 1 2 2 5 3 3 1 1 1 3 3 1 5 4 4 2 2 2 1 3 1 3 4 4 5 5 2 4 2 1 3 4 2 5 4 2 2 3 4 1 4 2 4 3 4 3 4 5 1 1 4 5 4 2 4 3 5 1 1 1 2 2 2 1
4 3 4 2 2 3 3 4 2 2 4 1 1 1 5 4 1 4 4 4 3 4 5 4 3 1 1 3 4 2 5 4 4 4 4 5 1 4 1 1 2 2 2 3 4 2 5 2 2 4 1 3 4 2 2 1 1 5 2 3 3 3 3 1 2 4 4 4 1 2 2 3 3 1 1 1 3 3 1 1 3 4 1 1 1 3 1 1 2 1 2 1 2 1 4 3 3 1 4 5 1 4 2 4 5 2 4 1 5 2
5 1 1 4 1 3 1 5 1 5 1 4 4 1 3 4 2 2 4 3 5 2 3 5 2 1 3 3 4 5 1 3 1 3 3 1 2 1 1 1 1 3 1 5 5 4 2 2 4 3 4 3 2 3 3 5 2 3 5 2 5 4 4 5 4 1 3 3 3 5 3 5 1 3 1 3 1 5 4 1 3 3 1 5 5 2 2 3 5 4 1 5 3 2 1 1 1 3 4 3 5 5 4 5 5 2 5 5 2 4
4 1 1 2 4 2 1 3 2 4 1 1 5 1 2 2 3 4 1 4 2 3 3 5 5 1 4 2 3 3 2 3 3 3 3 3 1 3 1 4 4 5 2 2 5 4 1 3 2 5 5 4 3 2 1 4 2 4 2 2 3 3 4 4 5 3 3 1 2 4 2 1 1 5 5 4 3 2 3 3 2 5 4 3 3 5 1 2 4 2 1 2 4 2 5 2 1 4 5 3 1 5 3 3 1 5 5 5 5 2
3 2 3 5 5 1 2 4 3 2 2 5 2 2 5 2 2 1 2 2 1 2 1 1 5 1 2 3 2 2 3 3 3 1 2 3 1 1 1 1 2 5 4 5 5 4 4 4 3 2 5 3 2 1 3 3 1 2 5 4 2 4 4 2 2 2 1 4 5 4 2 2 3 3 5 5 2 2 1 1 5 4 3 1 4 1 4 2 5 3 4 3 3 2 4 5 3 3 4 5 3 1 4 1 3 5 4 2 5 4
3 4 3 2 3 1 5 2 3 3 3 2 5 4 1 2 3 2 5 4 1 5 4 2 5 4 1 4 4 3 2 1 3 5 2 4 2 2 1 5 4 2 5 3 4 1 3 5 1 1 3 3 5 3 5 1 4 5 4 5 1 5 4 3 2 3 1 5 5 5 5 2 3 5 5 2 5 3 1 3 3 5 4 1 3 2 4 5 2 5 1 5 2 2 2 5 5 3 2 3 5 2 1 1 5 4 3 4 4 3
1 1 4 2 4 4 1 3 4 3 4 1 5 1 2 1 5 3 5 5 1 4 1 4 3 2 5 4 3 5 3 1 5 3 2 4 3 5 1 4 2 2 4 4 5 2 4 3 3 2 3 3 2 4 3 4 2 5 4 1 1 2 4 5 1 4 4 5 2 3 4 2 5 1 1 5 1 2 1 3 4 5 2 1 5 1 1 2 1 5 2 1 3 2 3 4 5 3 5 2 1 1 1 1 4 3 2 3 5 5
4 3 1 1 5 1 1 3 3 1 2 4 4 4 3 3 2 4 4 3 1 5 4 5 4 5 3 2 1 1 5 2 1 3 1 2 2 2 5 3 5 2 3 1 3 2 2 5 5 2 4 3 3 2 1 5 4 5 1 3 4 4 3 3 5 2 5 4 5 4 4 4 3 1 5 1 4 2 4 3 5 1 5 3 3 4 2 3 3 3 4 1 5 3 3 5 4 2 2 4 3 2 2 4 1 4 3 3 1 3
2 5 3 1 5 5 2 1 4 4 5 2 5 4 3 2 5 3 2 2 1 2 3 4 2 4 3 2 3 3 2 1 1 4 4 2 5 4 1 4 3 1 1 4 2 5 2 3 3 3 3 5 5 5 3 1 1 4 4 5 4 4 4 4 3 1 2 5 3 4 1 1 1 5 4 1 4 4 1 4 1 1 1 5 4 4 1 4 1 5 3 1 5 3 2 4 2 5 2 5 3 4 2 2 1 5 1 3 2 5
5 3 1 5 4 2 1 4 1 5 1 5 5 1 1 3 2 5 1 5 3 1 1 2 2 3 5 1 4 3 3 2 5 2 4 3 3 5 3 5 1 2 3 1 5 4 4 4 5 3 3 2 3 4 4 1 1 4 3 1 5 5 5 5 1 5 1 1 1 4 3 4 3 3 2 1 4 2 3 5 2 5 2 1 4 2 2 4 2 2 3 1 5 5 3 1 3 1 4 4 3 4 2 3 5 2 1 1 5 2
2 4 3 5 3 2 5 3 5 4 2 5 2 5 3 5 1 4 3 4 5 3 5 2 3 5 4 5 3 3 4 3 2 4 2 2 5 1 5 4 3 5 4 5 4 2 2 1 4 5 1 1 2 4 3 1 3 4 4 4 1 4 5 4 5 2 1 1 4 3 5 3 2 4 4 4 4 5 2 3 2 5 4 3 2 3 4 2 1 5 5 2 4 5 5 4 4 5 4 3 1 1 5 1 3 1 5 5 1 2
4 1 2 4 4 3 3 1 4 5 4 5 5 3 5 3 3 5 5 3 2 4 5 2 4 4 3 5 5 5 1 2 2 1 1 2 2 2 1 5 5 5 3 2 4 5 3 4 1 1 5 4 5 2 1 3 2 4 5 5 4 4 4 4 1 3 5 5 1 1 3 5 2 4 4 3 2 4 1 1 1 1 4 4 2 3 3 3 2 5 3 5 4 2 3 2 5 2 2 4 4 3 3 3 4 4 4 4 5 5
2 2 2 4 2 3 4 4 3 5 4 2 5 4 1 3 5 1 5 1 2 5 5 3 5 3 4 5 2 5 4 5 5 3 4 5 2 3 4 4 2 1 5 1 1 5 1 4 4 4 4 4 5 1 4 1 3 3 4 2 4 1 1 3 4 2 3 4 4 1 2 1 2 3 2 1 4 2 3 1 2 4 4 2 2 1 1 3 2 2 5 5 3 1 4 5 3 4 5 1 1 5 5 4 1 5 5 4 1 1
5 1 4 1 2 4 3 2 4 4 4 2 1 5 1 1 5 2 3 3 3 2 1 5 4 3 4 4 2 3 2 3 4 3 2 5 3 5 1 5 5 5 4 2 3 2 1 3 5 2 4 1 5 2 1 5 4 4 3 1 4 3 1 4 2 4 4 4 5 1 4 5 1 3 4 4 2 5 1 4 1 1 1 2 4 3 3 4 4 1 3 3 5 1 3 3 3 5 2 5 3 1 5 3 3 3 2 2 5 5
2 5 1 1 4 2 4 1 2 4 4 5 1 4 5 4 4 5 5 1 1 4 2 1 2 3 4 3 3 2 4 5 4 2 5 1 2 1 1 3 3 3 2 1 1 4 2 4 2 1 1 1 5 2 4 3 5 2 4 2 4 2 2 4 4 4 2 2 5 1 2 3 2 2 3 4 1 5 3 2 2 2 2 3 1 4 3 4 1 3 5 3 1 3 2 2 3 4 5 2 1 5 4 3 5 3 2 5 1 2
4 4 5 1 2 1 3 1 2 3 1 4 2 4 4 5 1 2 5 1 4 1 5 3 2 5 2 3 5 4 5 2 1 3 3 1 2 2 1 5 2 3 5 2 4 2 1 2 5 3 4 3 2 5 3 2 1 1 5 2 3 1 1 5 1 5 4 4 4 1 1 4 5 1 5 1 3 4 2 4 5 4 1 1 1 4 5 3 3 4 5 4 5 1 1 4 1 4 4 4 4 1 5 1 1 4 4 1 4 2
2 2 1 3 1 2 4 2 5 3 1 1 4 4 1 5 2 2 2 2 5 2 1 5 5 5 5 2 2 2 2 1 3 1 1 2 3 2 5 2 3 5 4 1 2 1 2 4 5 4 2 2 5 1 4 2 3 1 2 1 5 5 3 4 3 2 3 1 1 2 3 3 1 4 2 3 3 3 1 4 5 1 5 4 5 2 3 3 4 2 5 4 2 1 3 2 2 4 2 4 5 5 4 1 1 1 1 4 2 2
5 4 4 4 5 3 5 4 3 2 3 3 2 1 4 1 5 3 2 5 1 2 5 4 2 2 5 2 4 2 2 4 2 1 5 3 3 1 4 2 5 4 1 5 2 1 3 5 5 3 2 5 3 1 1 1 2 1 2 1 2 3 3 5 4 1 2 4 1 4 3 4 4 5 5 1 3 5 1 3 4 4 1 5 2 1 2 2 1 2 1 1 2 3 3 5 4 5 3 4 2 2 1 3 4 5 1 2 3 5
5 5 5 5 3 4 3 1 4 2 2 2 2 1 4 2 2 2 5 3 2 5 3 2 4 3 5 3 1 2 1 1 4 4 1 3 3 4 1 1 1 2 4 2 1 2 1 5 1 3 5 1 3 1 1 3 1 5 2 5 4 5 4 5 2 4 2 5 2 5 3 5 5 1 2 1 2 1 1 4 4 1 1 1 4 4 1 3 2 4 1 5 2 4 4 2 1 1 4 5 5 4 5 1 5 3 5 3 4 3
1 1 3 1 2 5 1 2 2 4 2 4 4 3 3 3 3 3 3 1 5 3 5 2 5 2 5 2 3 3 4 1 1 1 3 1 1 4 5 3 3 1 1 4 4 3 2 4 4 5 5 3 4 3 1 3 1 1 5 4 4 3 1 2 1 5 3 4 4 2 3 1 2 3 1 5 3 4 4 3 1 3 3 2 4 3 2 2 3 4 5 1 5 5 1 5 1 2 2 4 4 3 1 1 1 4 4 3 1 1
5 3 3 3 3 5 5 3 3 4 2 3 3 2 3 1 4 2 3 5 3 5 5 5 1 4 5 5 1 2 2 2 5 4 1 1 5 5 5 3 3 3 2 5 3 2 2 2 4 5 4 1 5 5 1 3 3 3 3 3 1 1 1 1 3 4 1 4 3 1 4 4 5 1 2 3 4 2 5 2 1 1 3 3 3 5 3 5 1 2 5 4 1 3 4 4 4 5 2 3 2 3 1 3 4 3 5 1 5 2
1 3 3 4 4 5 5 2 2 2 2 2 4 4 1 5 2 4 5 3 4 4 2 3 5 2 5 3 2 4 2 3 1 4 4 1 3 4 1 2 5 5 2 5 5 4 1 4 4 2 4 4 1 4 2 3 3 3 2 2 5 2 4 4 4 1 4 2 2 5 2 5 5 5 2 4 4 3 1 2 3 1 3 4 5 1 1 3 3 3 1 1 5 3 5 2 5 4 5 3 5 4 2 1 3 5 2 2 1 5
5 4 1 3 1 1 4 4 3 2 5 1 5 5 2 5 5 1 3 3 3 3 1 2 1 4 1 4 1 1 2 4 3 2 4 1 5 5 1 1 4 3 2 2 3 3 5 1 4 4 4 4 1 1 2 3 1 5 5 4 4 5 1 3 3 4 2 5 5 1 1 2 5 3 2 3 3 3 2 5 4 2 1 4 1 1 5 2 4 5 4 4 5 5 3 4 1 2 3 4 1 1 4 5 5 2 2 3 3 1
3 3 5 3 3 3 4 5 1 5 5 2 2 3 5 3 4 2 3 5 1 5 3 1 4 3 4 3 4 3 5 4 1 4 2 5 4 5 2 5 5 5 1 3 1 4 1 1 1 4 1 2 2 4 1 5 2 1 1 1 1 1 5 3 5 1 4 3 5 3 3 1 1 3 3 1 2 4 1 1 2 4 5 4 4 1 4 5 5 1 3 5 5 4 1 2 5 2 5 4 5 5 4 4 3 4 4 4 2 2
1 4 4 2 1 2 3 4 4 4 4 4 4 1 4 2 2 5 4 2 2 5 2 1 1 3 1 4 5 4 2 2 5 4 3 2 5 5 2 4 3 1 1 3 2 3 3 4 5 2 3 2 2 2 4 1 1 5 3 5 4 3 5 3 1 2 4 4 5 2 3 1 2 5 4 4 1 2 5 1 3 4 5 3 1 3 5 1 5 3 2 1 1 3 3 5 4 2 1 3 4 1 3 5 3 2 4 3 1 1
1 5 4 4 2 5 2 1 3 1 2 2 3 4 4 2 3 4 4 4 4 5 3 2 4 3 2 2 5 4 2 1 4 3 4 2 3 3 4 2 4 1 3 5 2 4 5 3 4 4 1 5 5 3 3 5 1 3 3 2 4 3 1 4 1 3 5 2 3 5 1 4 1 3 1 2 5 2 1 3 4 1 1 5 2 3 1 5 2 1 5 4 2 2 1 3 5 5 3 3 3 3 4 5 3 1 2 3 5 5
3 3 3 4 3 4 5 1 5 3 5 2 3 5 2 3 5 4 3 3 5 5 3 5 1 4 1 1 2 3 1 2 3 3 4 3 2 1 1 4 4 1 3 1 1 5 2 5 3 4 5 1 4 3 3 5 3 4 3 4 1 2 3 2 5 3 2 4 5 5 5 4 1 2 2 4 5 2 5 4 1 2 3 1 3 4 3 5 1 4 2 3 4 3 3 3 3 5 3 4 5 5 4 5 5 1 4 5 3 3
3 3 4 1 1 3 1 1 1 1 5 5 4 4 2 3 2 5 4 2 4 2 1 2 1 2 5 3 4 3 5 4 2 1 2 4 1 4 3 4 1 1 5 5 2 3 1 1 3 5 4 1 2 2 1 3 5 4 5 3 2 4 4 2 5 1 4 5 1 3 2 5 3 3 1 5 1 5 2 4 2 3 3 2 2 1 2 5 5 5 4 5 3 2 1 2 5 3 1 2 1 1 1 2 4 1 3 1 3 3
5 2 4 1 1 5 4 1 3 5 1 1 5 3 2 2 4 3 2 3 1 2 2 1 3 1 5 1 1 1 2 4 2 5 5 4 3 2 2 1 5 2 1 4 5 1 4 1 3 3 2 1 1 2 2 5 5 1 5 2 3 1 1 5 3 5 5 1 2 2 3 1 4 4 2 2 5 2 4 5 2 5 5 4 1 1 1 3 2 2 2 3 5 3 1 1 4 2 2 2 2 4 1 3 3 5 5 3 5 1
4 3 4 4 5 3 3 3 2 2 2 3 2 5 2 1 4 1 4 3 2 5 3 5 5 5 2 1 2 3 1 2 4 5 3 3 5 2 3 5 5 2 5 1 1 5 2 5 2 1 5 4 2 2 5 1 2 1 1 5 1 2 3 2 3 1 5 4 4 5 3 5 2 4 1 5 1 5 2 3 1 1 2 3 3 1 4 1 4 1 4 3 2 4 5 3 5 2 1 2 3 5 2 5 5 2 5 3 1 2
1 2 4 1 2 4 2 4 3 4 3 5 2 2 2 5 4 1 4 4 4 5 5 1 4 2 5 1 3 5 1 5 5 5 4 3 5 1 5 1 4 1 5 2 1 2 1 4 1 4 4 2 4 5 2 1 4 1 4 4 1 3 2 2 2 1 1 5 2 2 2 2 2 1 1 3 3 3 4 2 3 4 4 2 3 1 4 5 3 4 5 4 4 4 5 4 3 3 3 1 1 2 4 1 4 4 1 3 4 3
4 2 2 1 4 1 1 5 3 3 5 1 2 1 4 2 1 4 2 3 1 3 3 4 4 5 3 1 4 2 3 3 3 4 4 2 3 2 5 2 4 4 3 1 4 4 2 3 3 3 5 5 3 4 2 5 1 1 1 1 2 4 5 3 2 1 2 2 3 3 1 5 3 2 2 3 4 5 5 5 1 3 2 5 1 4 5 3 1 2 2 5 3 3 2 2 3 1 3 5 3 2 3 1 5 5 2 1 4 3
2 3 2 3 2 3 5 5 5 4 2 3 1 5 4 1 5 2 3 2 3 2 3 1 2 2 3 2 3 4 1 3 4 1 3 5 3 5 3 2 1 2 4 4 3 3 2 3 4 1 3 2 1 2 5 2 5 5 3 3 4 5 5 3 2 2 4 3 3 2 3 5 3 2 2 4 3 4 3 5 3 5 2 4 5 1 2 5 2 5 4 2 5 1 3 1 3 1 1 4 5 4 3 2 2 1 4 1 2 2
3 5 1 1 1 5 5 1 1 2 1 5 3 5 4 2 5 3 3 3 2 2 4 5 1 2 2 2 2 2 5 1 2 5 5 4 1 2 3 1 5 4 2 3 3 1 2 1 2 1 1 5 3 1 1 1 1 3 5 3 2 3 5 2 3 5 4 3 5 1 4 5 4 1 3 3 1 1 5 3 1 5 2 2 2 3 1 4 1 5 4 4 1 5 5 1 1 4 4 2 1 2 1 2 1 3 2 1 1 3
1 5 2 5 2 2 2 3 4 1 1 1 4 5 4 4 2 1 3 5 4 2 5 2 3 2 4 5 4 1 5 1 4 2 4 3 5 1 4 3 4 2 3 5 1 2 3 3 3 3 1 2 1 3 1 5 3 1 3 4 3 5 1 3 3 2 4 5 5 1 5 4 3 1 5 4 4 5 1 5 2 5 2 4 3 5 3 3 5 5 2 1 4 4 3 2 4 5 3 5 5 1 5 4 5 4 1 1 5 5
1 1 1 4 5 2 1 2 1 2 5 3 2 1 1 1 4 4 1 2 5 5 1 1 2 2 5 4 4 2 1 2 4 4 5 5 4 5 3 3 3 5 2 3 2 4 1 4 3 5 5 5 5 2 2 3 5 1 5 2 2 5 1 4 5 1 3 3 1 5 5 2 1 1 1 1 3 1 3 2 2 4 5 1 3 2 4 4 5 5 2 4 3 3 1 2 5 2 3 1 1 1 3 5 4 5 3 2 4 1
2 1 4 2 3 2 1 4 2 4 5 3 1 4 4 1 1 3 2 1 2 4 3 3 2 3 1 5 1 3 2 1 4 3 1 3 1 2 3 3 3 4 1 2 3 1 1 2 1 4 1 1 5 5 3 3 1 4 3 3 5 2 3 1 5 2 3 4 1 4 4 2 4 3 3 5 1 4 5 2 3 2 3 2 2 4 1 3 2 2 4 4 1 5 2 5 2 1 5 4 1 3 5 3 5 1 1 3 4 3
2 4 4 1 1 5 3 1 1 3 3 4 5 2 5 2 3 2 3 1 5 5 4 3 5 2 2 2 4 4 4 1 1 3 2 1 2 3 2 5 2 1 3 5 1 4 4 3 3 2 3 5 2 4 2 4 5 4 4 1 5 3 5 1 4 2 4 5 2 3 1 2 3 5 1 4 2 2 2 3 5 2 2 1 2 4 4 3 1 5 4 4 1 3 4 3 3 5 3 2 3 4 1 4 1 5 4 4 1 2
2 2 3 2 4 5 3 3 5 3 5 2 1 3 5 4 4 4 2 1 1 2 2 1 2 3 4 1 3 1 3 3 1 2 1 3 2 2 1 1 3 5 4 1 1 3 4 3 1 5 2 2 3 1 3 1 5 2 5 5 2 1 2 4 3 1 1 4 1 2 3 5 1 3 2 1 5 3 5 3 2 3 5 1 3 3 5 2 1 1 5 4 3 3 4 5 5 1 3 2 3 4 3 2 3 1 1 5 5 5
1 3 1 2 3 5 5 4 1 5 5 2 1 5 5 5 1 3 2 1 5 1 2 3 1 1 5 4 2 3 4 2 5 1 3 1 5 4 1 3 1 2 5 5 4 3 3 5 4 2 4 1 1 5 5 3 3 4 3 4 4 1 5 3 3 5 3 3 4 5 3 5 2 1 1 4 2 2 4 3 3 5 1 3 1 3 4 4 1 4 2 4 4 5 3 1 3 2 4 4 3 4 5 1 5 5 1 1 3 3
2 5 2 4 4 3 1 1 3 5 5 4 5 5 3 5 5 4 3 1 1 1 3 5 2 1 3 3 1 1 2 4 4 4 1 3 5 2 5 5 1 5 5 2 5 4 1 1 2 3 5 5 3 2 3 3 5 4 5 5 5 3 1 4 2 3 1 2 2 1 4 4 3 1 2 4 1 4 3 5 5 1 5 4 3 1 1 1 4 2 2 2 5 5 3 2 1 1 4 3 3 3 5 2 3 5 3 4 5 1
2 1 5 3 5 5 4 5 3 2 3 2 1 1 2 3 1 4 1 5 3 3 2 1 5 3 4 3 5 4 3 1 5 1 4 2 2 5 4 3 4 5 2 2 1 1 1 4 2 2 2 3 1 1 4 2 2 1 5 3 3 1 4 1 2 1 2 5 5 5 4 4 3 5 2 4 4 5 4 4 2 4 1 3 2 5 4 1 5 5 4 5 4 1 1 5 4 3 5 1 3 3 3 5 5 3 5 5 3 4
4 4 5 1 1 2 5 2 5 4 4 3 3 2 3 5 5 5 2 3 1 4 5 4 1 4 5 1 3 5 4 4 1 1 5 2 2 2 2 1 4 5 4 3 5 2 5 4 4 2 4 1 3 3 3 3 3 4 4 2 2 2 4 1 4 4 1 4 5 1 5 4 2 4 5 5 3 1 5 2 3 3 5 2 3 3 5 1 3 2 3 2 3 5 5 4 4 5 1 3 1 5 3 1 5 3 3 1 1 4
5 2 4 2 2 1 1 5 3 3 2 1 2 5 1 5 5 5 5 3 1 4 1 5 2 4 4 2 4 4 5 4 5 2 1 4 3 1 5 5 1 5 3 1 3 3 1 2 1 1 2 1 4 4 2 1 3 1 4 2 1 1 5 1 4 3 2 1 2 1 4 4 3 4 3 2 5 2 4 2 1 3 3 1 2 3 3 3 3 1 3 4 2 5 4 3 3 5 5 1 4 3 5 1 5 5 1 1 2 4
4 2 4 3 1 2 4 2 2 3 1 5 1 4 4 3 3 4 1 2 3 4 5 2 1 1 4 5 4 1 4 2 2 2 1 2 5 3 3 1 1 2 1 3 4 3 5 2 2 1 2 4 4 3 2 1 1 2 4 1 4 5 4 4 5 4 4 1 2 4 1 5 3 1 4 5 2 3 1 5 3 1 3 4 1 4 2 1 2 2 1 5 1 3 2 2 2 5 2 5 3 3 1 3 2 5 2 4 2 4
3 4 5 5 5 2 4 3 5 2 4 2 5 5 2 3 3 3 2 5 5 3 1 2 2 2 2 2 1 4 1 2 2 3 1 2 3 4 3 1 3 3 5 3 1 5 3 4 1 1 5 4 3 2 4 3 1 5 5 4 3 3 5 2 2 2 1 2 5 3 3 5 1 1 2 2 1 1 4 2 3 2 3 5 2 3 4 2 1 5 3 1 1 1 2 3 4 3 3 3 4 1 4 1 5 1 2 5 4 3
5 2 2 4 1 5 4 5 4 4 4 2 3 4 4 3 1 2 3 3 3 5 2 3 2 1 5 3 4 3 5 2 1 3 5 3 5 4 2 5 2 5 2 3 1 1 5 5 2 4 4 3 1 2 4 5 2 5 4 5 5 4 3 3 5 1 3 4 2 5 1 4 3 5 5 3 1 3 2 5 2 1 5 3 3 1 3 4 1 4 5 5 1 5 3 2 1 2 2 4 1 4 1 1 4 2 1 3 1 4
2 5 5 3 3 4 5 1 3 1 4 2 2 2 5 4 1 1 5 2 4 4 1 4 1 5 4 1 3 5 5 2 5 1 3 3 3 5 1 4 4 3 1 4 4 2 4 1 5 3 3 3 4 5 4 5 5 4 4 2 3 5 3 4 2 5 4 4 2 4 5 1 3 3 2 5 4 5 1 4 5 1 2 4 1 3 3 3 3 3 1 5 4 2 2 2 1 2 1 2 1 5 2 3 5 3 2 1 3 4
2 3 4 1 3 4 2 4 2 4 3 3 5 5 3 2 2 5 1 4 2 3 4 5 4 3 5 3 1 5 5 3 5 2 5 3 4 1 2 2 4 3 4 2 3 1 4 3 5 1 4 3 2 3 4 5 1 2 4 3 4 4 2 4 1 3 4 1 4 5 4 2 2 4 1 1 5 1 5 3 3 5 4 3 2 5 5 1 1 1 4 3 3 2 2 5 2 4 4 3 2 4 3 5 4 1 5 5 1 5
1 1 4 2 5 2 1 5 4 5 1 5 4 3 1 1 5 3 2 4 4 2 5 5 5 1 2 5 5 3 2 4 3 5 4 3 5 4 3 4 5 4 3 2 3 2 5 3 4 4 3 4 3 1 3 5 5 1 4 3 3 1 3 5 2 1 2 3 4 4 5 2 3 3 2 1 1 4 4 3 3 5 3 1 3 1 4 4 3 2 2 5 1 1 3 5 1 4 4 2 3 1 4 3 1 4 3 2 3 2
5 4 2 2 4 2 5 3 1 2 3 2 2 3 5 3 1 4 1 5 3 3 4 2 2 2 1 3 1 3 3 4 5 3 5 5 1 1 3 1 2 5 4 3 1 5 3 2 3 2 4 2 3 5 1 1 1 5 5 4 2 1 3 1 1 1 1 5 1 1 1 3 3 1 1 1 3 2 3 2 4 1 5 4 2 2 5 4 2 4 4 5 1 5 1 1 4 2 2 2 5 1 3 1 3 1 4 3 1 3
1 5 3 2 1 1 5 1 2 4 5 3 2 4 1 2 4 3 2 5 2 1 1 4 4 3 3 1 1 1 2 5 4 2 3 2 1 4 1 3 2 3 3 2 5 1 4 4 1 1 1 2 1 3 5 4 5 4 5 1 1 1 3 2 2 5 3 2 1 5 3 1 1 1 3 3 5 3 2 5 1 1 4 3 2 3 2 4 4 3 3 1 1 5 2 2 1 2 3 5 5 4 3 3 1 2 2 1 1 1
4 3 1 3 3 4 4 5 3 5 5 4 5 4 5 5 2 2 2 5 4 1 4 5 1 5 4 2 4 2 1 2 5 4 5 5 4 5 2 4 1 3 1 1 1 4 3 4 5 1 3 2 5 1 4 3 1 4 4 1 1 3 1 4 2 2 4 2 5 3 5 2 3 1 1 5 2 5 1 2 2 2 1 3 1 3 1 1 3 3 5 5 4 5 3 5 3 2 4 2 5 3 3 3 5 2 1 4 5 5
2 1 1 1 4 3 5 5 3 1 1 1 1 4 3 4 5 5 2 4 5 3 2 3 2 3 5 1 4 5 4 3 4 3 2 3 3 4 3 4 1 1 2 4 4 1 3 1 3 5 1 1 1 4 3 4 2 1 3 3 1 5 1 2 1 3 4 5 3 1 5 3 4 4 5 4 5 1 2 4 5 3 4 1 4 1 4 3 5 3 5 2 4 3 5 5 3 1 4 3 5 2 4 3 2 3 4 4 4 2
3 2 1 1 1 1 4 3 3 3 4 1 4 3 4 2 2 4 2 1 4 2 2 5 1 2 4 4 5 4 1 2 2 4 4 2 5 2 2 1 4 3 3 3 4 5 1 3 3 1 4 5 4 4 3 3 3 4 4 3 3 3 2 5 4 5 2 1 2 3 5 2 5 1 2 3 5 5 2 3 5 3 1 2 2 1 1 4 2 3 1 2 2 1 2 3 5 3 4 4 3 3 1 5 5 2 3 5 3 4
5 1 2 3 2 1 2 3 3 2 4 4 3 4 3 4 3 5 2 4 3 2 5 3 1 4 5 4 1 5 1 2 1 5 4 5 1 3 4 5 3 2 1 5 4 1 1 3 3 3 3 5 5 2 2 3 5 1 2 4 2 5 3 5 5 3 5 4 2 5 5 4 5 3 2 3 5 1 2 4 4 4 3 2 2 1 2 4 4 1 3 1 4 5 5 1 4 3 5 1 4 3 3 4 5 4 5 2 5 3
5 4 1 3 5 2 2 5 4 2 5 4 4 2 4 2 4 4 1 1 3 4 4 5 3 3 2 1 4 1 2 1 5 2 5 1 4 1 4 3 3 4 2 5 1 3 1 4 4 2 2 3 5 5 5 5 2 5 4 2 1 2 4 3 1 4 4 4 1 5 1 3 3 5 1 4 4 5 1 5 1 2 4 5 5 1 1 2 5 2 2 5 1 2 4 2 3 1 5 3 5 3 3 1 1 2 2 3 4 5
4 2 2 1 1 1 3 2 1 4 2 3 5 5 2 1 3 2 5 4 5 5 4 5 4 3 1 4 1 3 1 5 2 4 2 5 3 3 1 3 3 1 2 3 4 3 4 3 2 4 1 1 3 4 1 5 5 3 4 3 2 4 1 3 4 1 4 4 3 5 3 1 2 5 2 3 2 2 3 1 3 2 2 2 2 3 1 1 4 3 5 1 2 2 1 3 4 2 1 3 4 4 4 2 1 5 4 4 2 3
5 2 1 4 3 5 4 2 4 5 3 1 4 5 1 3 5 2 4 4 4 5 3 5 3 3 5 4 4 5 3 2 2 3 5 4 3 5 5 2 3 1 1 3 4 2 5 3 4 3 5 1 3 3 3 4 5 1 2 5 1 3 5 5 1 1 3 1 4 3 1 5 2 5 2 4 4 1 4 4 5 2 3 2 3 5 1 3 2 3 5 4 1 4 2 2 1 4 1 4 2 1 4 3 3 3 2 5 1 4
3 5 5 1 2 1 3 1 3 1 5 4 3 4 2 5 3 5 1 5 3 5 5 5 3 1 3 5 5 3 4 3 2 2 4 2 1 1 4 2 2 2 1 2 2 2 3 1 2 1 2 2 4 1 4 5 2 2 4 3 1 2 1 4 5 5 5 3 3 4 5 2 2 1 1 3 4 3 1 3 3 5 5 4 3 5 5 4 4 2 2 5 3 1 4 3 4 2 3 4 4 4 4 5 5 1 4 5 5 3
1 2 3 2 4 2 3 1 3 3 4 1 1 2 2 5 5 2 4 3 3 1 4 3 3 4 2 3 5 2 3 4 5 3 3 5 3 3 2 1 1 2 2 2 3 1 4 1 3 3 1 3 4 4 3 5 2 2 1 4 4 4 4 5 4 3 2 5 3 1 2 3 1 5 1 3 3 5 5 5 1 4 3 2 1 1 1 3 3 4 1 1 4 5 5 2 2 2 4 2 5 4 4 3 4 5 5 2 4 1
3 3 4 1 2 5 3 2 2 1 2 4 5 2 4 5 5 5 4 5 3 1 5 4 3 5 3 1 3 5 1 3 2 3 1 2 1 5 5 5 4 1 3 5 2 1 5 1 3 1 4 3 3 5 1 4 3 4 3 5 5 1 1 5 1 2 3 5 1 3 1 3 4 3 4 1 3 3 4 4 4 4 1 3 1 4 3 2 4 1 4 1 4 3 1 5 3 5 5 2 5 3 5 2 1 2 4 3 5 1
3 2 4 4 3 4 3 1 3 3 5 1 2 3 2 4 2 2 3 3 3 3 3 2 3 5 2 5 5 4 5 5 5 2 2 4 3 5 4 2 4 5 3 1 1 5 3 3 1 5 5 3 5 1 2 5 2 3 3 4 3 2 2 5 4 1 2 5 5 3 5 3 4 5 4 1 5 1 4 2 4 5 3 4 1 1 5 5 5 3 4 2 2 2 3 4 5 5 2 4 4 4 1 2 2 3 4 5 1 1
5 3 3 4 2 1 3 3 5 2 3 4 5 5 4 3 4 4 4 1 1 4 1 5 4 5 5 4 4 3 2 1 3 3 5 3 1 4 3 4 2 1 3 2 3 1 2 3 3 4 5 3 1 4 3 2 1 3 2 5 5 4 1 2 5 3 4 2 2 4 5 5 3 1 1 4 4 4 2 3 3 3 5 5 3 5 2 4 1 2 5 1 1 2 5 3 3 4 4 3 5 5 4 2 3 2 5 1 1 3
4 4 3 2 4 4 4 5 3 2 1 2 2 3 3 5 4 2 5 4 1 3 1 5 3 5 4 3 2 1 3 2 2 4 3 1 4 5 2 4 3 5 2 2 4 3 4 4 4 4 2 5 3 1 5 5 4 2 1 1 4 4 3 4 1 2 5 3 3 3 4 5 3 5 1 5 4 2 2 2 3 1 2 3 2 3 3 3 4 3 4 1 2 4 4 2 2 3 3 1 4 2 4 4 1 3 5 2 3 3
3 4 2 5 3 4 3 1 5 1 4 1 2 1 5 1 5 2 5 5 1 1 4 4 2 2 5 4 3 5 1 4 2 4 5 4 5 1 2 4 1 4 2 3 3 1 2 4 1 4 4 4 5 3 5 5 4 1 1 1 3 1 4 5 4 4 5 3 1 3 4 3 4 5 4 1 2 5 3 1 3 5 5 2 1 1 2 4 1 4 4 1 3 3 4 4 3 3 1 1 3 3 2 2 3 1 2 1 1 1
2 1 4 3 4 4 2 4 1 2 4 1 5 3 4 3 1 5 3 2 4 5 3 1 4 2 1 5 5 5 4 1 1 4 1 4 4 2 1 5 5 1 2 3 3 5 3 5 2 3 2 4 2 4 5 1 1 3 2 4 3 1 2 3 2 2 3 5 1 2 3 3 4 2 2 5 3 3 5 2 3 4 1 5 3 2 4 5 3 4 2 2 5 3 4 4 2 3 5 3 4 5 1 2 3 1 2 4 1 4
3 2 1 1 5 1 4 3 5 4 1 3 3 3 5 4 5 4 2 1 5 1 5 5 4 1 1 3 3 2 3 3 2 4 5 3 1 2 1 1 1 4 3 2 2 5 1 1 4 4 5 2 1 4 2 5 2 5 4 2 5 1 2 2 3 5 2 4 4 5 5 4 2 3 2 5 4 1 4 2 5 1 4 5 5 5 3 4 4 2 3 2 4 4 2 4 2 5 2 4 1 4 1 5 2 1 2 3 5 4
| Matlab | 24,197 | matlab | null | 214.132743 | 287 | 0.511923 |
/******************************************************************************
* The MIT License (MIT)
*
* Copyright (c) 2016-2019 Baldur Karlsson
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
******************************************************************************/
#pragma once
#include "driver/shaders/dxbc/dxbc_container.h"
#include "d3d12_device.h"
#include "d3d12_manager.h"
class TrackedResource12
{
public:
TrackedResource12()
{
m_ID = ResourceIDGen::GetNewUniqueID();
m_pRecord = NULL;
}
ResourceId GetResourceID() { return m_ID; }
D3D12ResourceRecord *GetResourceRecord() { return m_pRecord; }
void SetResourceRecord(D3D12ResourceRecord *record) { m_pRecord = record; }
protected:
TrackedResource12(const TrackedResource12 &);
TrackedResource12 &operator=(const TrackedResource12 &);
ResourceId m_ID;
D3D12ResourceRecord *m_pRecord;
};
extern const GUID RENDERDOC_ID3D12ShaderGUID_ShaderDebugMagicValue;
template <typename NestedType, typename NestedType1 = NestedType, typename NestedType2 = NestedType1>
class WrappedDeviceChild12 : public RefCounter12<NestedType>,
public NestedType2,
public TrackedResource12
{
protected:
WrappedID3D12Device *m_pDevice;
ULONG m_InternalRefcount;
WrappedDeviceChild12(NestedType *real, WrappedID3D12Device *device)
: RefCounter12(real), m_pDevice(device)
{
m_InternalRefcount = 0;
m_pDevice->SoftRef();
if(real)
{
bool ret = m_pDevice->GetResourceManager()->AddWrapper(this, real);
if(!ret)
RDCERR("Error adding wrapper for type %s", ToStr(__uuidof(NestedType)).c_str());
}
m_pDevice->GetResourceManager()->AddCurrentResource(GetResourceID(), this);
}
virtual void Shutdown()
{
if(m_pReal)
m_pDevice->GetResourceManager()->RemoveWrapper(m_pReal);
m_pDevice->GetResourceManager()->ReleaseCurrentResource(GetResourceID());
m_pDevice->ReleaseResource((NestedType *)this);
SAFE_RELEASE(m_pReal);
m_pDevice = NULL;
}
virtual ~WrappedDeviceChild12()
{
// should have already called shutdown (needs to be called from child class to ensure
// vtables are still in place when we call ReleaseResource)
RDCASSERT(m_pDevice == NULL && m_pReal == NULL);
}
public:
typedef NestedType InnerType;
// some applications wrongly check refcount return values and expect them to
// match D3D's values. When we have some internal refs we need to hide, we
// add them here and they're subtracted from return values
void AddInternalRef() { InterlockedIncrement(&m_InternalRefcount); }
void ReleaseInternalRef() { InterlockedDecrement(&m_InternalRefcount); }
NestedType *GetReal() { return m_pReal; }
ULONG STDMETHODCALLTYPE AddRef()
{
ULONG ret = RefCounter12::SoftRef(m_pDevice);
if(ret >= m_InternalRefcount)
ret -= m_InternalRefcount;
return ret;
}
ULONG STDMETHODCALLTYPE Release()
{
ULONG ret = RefCounter12::SoftRelease(m_pDevice);
if(ret >= m_InternalRefcount)
ret -= m_InternalRefcount;
return ret;
}
HRESULT STDMETHODCALLTYPE QueryInterface(REFIID riid, void **ppvObject)
{
if(riid == __uuidof(IUnknown))
{
*ppvObject = (IUnknown *)(NestedType *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(NestedType))
{
*ppvObject = (NestedType *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(NestedType1))
{
if(!m_pReal)
return E_NOINTERFACE;
// check that the real interface supports this
NestedType1 *dummy = NULL;
HRESULT check = m_pReal->QueryInterface(riid, (void **)&dummy);
SAFE_RELEASE(dummy);
if(FAILED(check))
return check;
*ppvObject = (NestedType1 *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(NestedType2))
{
if(!m_pReal)
return E_NOINTERFACE;
// check that the real interface supports this
NestedType2 *dummy = NULL;
HRESULT check = m_pReal->QueryInterface(riid, (void **)&dummy);
SAFE_RELEASE(dummy);
if(FAILED(check))
return check;
*ppvObject = (NestedType2 *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(ID3D12Pageable))
{
// not all child classes support this, so check it on the real interface
if(!m_pReal)
return E_NOINTERFACE;
// check that the real interface supports this
ID3D12Pageable *dummy = NULL;
HRESULT check = m_pReal->QueryInterface(riid, (void **)&dummy);
SAFE_RELEASE(dummy);
if(FAILED(check))
return check;
*ppvObject = (ID3D12Pageable *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(ID3D12Object))
{
*ppvObject = (ID3D12DeviceChild *)this;
AddRef();
return S_OK;
}
else if(riid == __uuidof(ID3D12DeviceChild))
{
*ppvObject = (ID3D12DeviceChild *)this;
AddRef();
return S_OK;
}
// for DXGI object queries, just make a new throw-away WrappedDXGIObject
// and return.
if(riid == __uuidof(IDXGIObject) || riid == __uuidof(IDXGIDeviceSubObject) ||
riid == __uuidof(IDXGIResource) || riid == __uuidof(IDXGIKeyedMutex) ||
riid == __uuidof(IDXGISurface) || riid == __uuidof(IDXGISurface1) ||
riid == __uuidof(IDXGIResource1) || riid == __uuidof(IDXGISurface2))
{
if(m_pReal == NULL)
return E_NOINTERFACE;
// ensure the real object has this interface
void *outObj;
HRESULT hr = m_pReal->QueryInterface(riid, &outObj);
IUnknown *unk = (IUnknown *)outObj;
SAFE_RELEASE(unk);
if(FAILED(hr))
{
return hr;
}
auto dxgiWrapper = new WrappedDXGIInterface<WrappedDeviceChild12>(this, m_pDevice);
// anything could happen outside of our wrapped ecosystem, so immediately mark dirty
m_pDevice->GetResourceManager()->MarkDirtyResource(GetResourceID());
if(riid == __uuidof(IDXGIObject))
{
*ppvObject = (IDXGIObject *)(IDXGIKeyedMutex *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGIDeviceSubObject))
{
*ppvObject = (IDXGIDeviceSubObject *)(IDXGIKeyedMutex *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGIResource))
{
*ppvObject = (IDXGIResource *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGIKeyedMutex))
{
*ppvObject = (IDXGIKeyedMutex *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGISurface))
{
*ppvObject = (IDXGISurface *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGISurface1))
{
*ppvObject = (IDXGISurface1 *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGIResource1))
{
*ppvObject = (IDXGIResource1 *)dxgiWrapper;
}
else if(riid == __uuidof(IDXGISurface2))
{
*ppvObject = (IDXGISurface2 *)dxgiWrapper;
}
else
{
RDCWARN("Unexpected guid %s", ToStr(riid).c_str());
SAFE_DELETE(dxgiWrapper);
}
return S_OK;
}
return RefCounter12::QueryInterface(riid, ppvObject);
}
//////////////////////////////
// implement ID3D12Object
HRESULT STDMETHODCALLTYPE GetPrivateData(REFGUID guid, UINT *pDataSize, void *pData)
{
if(!m_pReal)
{
if(pDataSize)
*pDataSize = 0;
return S_OK;
}
return m_pReal->GetPrivateData(guid, pDataSize, pData);
}
HRESULT STDMETHODCALLTYPE SetPrivateData(REFGUID guid, UINT DataSize, const void *pData)
{
if(guid == RENDERDOC_ID3D12ShaderGUID_ShaderDebugMagicValue)
return m_pDevice->SetShaderDebugPath(this, (const char *)pData);
if(guid == WKPDID_D3DDebugObjectName)
{
m_pDevice->SetName(this, (const char *)pData);
}
else if(guid == WKPDID_D3DDebugObjectNameW)
{
rdcwstr wName((const wchar_t *)pData, DataSize / 2);
rdcstr sName = StringFormat::Wide2UTF8(wName);
m_pDevice->SetName(this, sName.c_str());
}
if(!m_pReal)
return S_OK;
return m_pReal->SetPrivateData(guid, DataSize, pData);
}
HRESULT STDMETHODCALLTYPE SetPrivateDataInterface(REFGUID guid, const IUnknown *pData)
{
if(!m_pReal)
return S_OK;
return m_pReal->SetPrivateDataInterface(guid, pData);
}
HRESULT STDMETHODCALLTYPE SetName(LPCWSTR Name)
{
rdcstr utf8 = Name ? StringFormat::Wide2UTF8(Name) : "";
m_pDevice->SetName(this, utf8.c_str());
if(!m_pReal)
return S_OK;
return m_pReal->SetName(Name);
}
//////////////////////////////
// implement ID3D12DeviceChild
virtual HRESULT STDMETHODCALLTYPE GetDevice(REFIID riid, _COM_Outptr_opt_ void **ppvDevice)
{
return m_pDevice->GetDevice(riid, ppvDevice);
}
};
class WrappedID3D12CommandAllocator : public WrappedDeviceChild12<ID3D12CommandAllocator>
{
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12CommandAllocator);
enum
{
TypeEnum = Resource_CommandAllocator,
};
WrappedID3D12CommandAllocator(ID3D12CommandAllocator *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
}
virtual ~WrappedID3D12CommandAllocator() { Shutdown(); }
//////////////////////////////
// implement ID3D12CommandAllocator
virtual HRESULT STDMETHODCALLTYPE Reset() { return m_pReal->Reset(); }
};
class WrappedID3D12CommandSignature : public WrappedDeviceChild12<ID3D12CommandSignature>
{
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12CommandSignature);
D3D12CommandSignature sig;
enum
{
TypeEnum = Resource_CommandSignature,
};
WrappedID3D12CommandSignature(ID3D12CommandSignature *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
}
virtual ~WrappedID3D12CommandSignature() { Shutdown(); }
};
struct D3D12Descriptor;
class WrappedID3D12DescriptorHeap : public WrappedDeviceChild12<ID3D12DescriptorHeap>
{
D3D12_CPU_DESCRIPTOR_HANDLE realCPUBase;
D3D12_GPU_DESCRIPTOR_HANDLE realGPUBase;
UINT increment : 24;
UINT resident : 8;
UINT numDescriptors;
D3D12Descriptor *descriptors;
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12DescriptorHeap);
enum
{
TypeEnum = Resource_DescriptorHeap,
};
WrappedID3D12DescriptorHeap(ID3D12DescriptorHeap *real, WrappedID3D12Device *device,
const D3D12_DESCRIPTOR_HEAP_DESC &desc);
virtual ~WrappedID3D12DescriptorHeap();
D3D12Descriptor *GetDescriptors() { return descriptors; }
UINT GetNumDescriptors() { return numDescriptors; }
bool Resident() { return resident != 0; }
void SetResident(bool r) { resident = r ? 1 : 0; }
//////////////////////////////
// implement ID3D12DescriptorHeap
virtual D3D12_DESCRIPTOR_HEAP_DESC STDMETHODCALLTYPE GetDesc() { return m_pReal->GetDesc(); }
virtual D3D12_CPU_DESCRIPTOR_HANDLE STDMETHODCALLTYPE GetCPUDescriptorHandleForHeapStart()
{
D3D12_CPU_DESCRIPTOR_HANDLE handle;
handle.ptr = (SIZE_T)descriptors;
return handle;
}
virtual D3D12_GPU_DESCRIPTOR_HANDLE STDMETHODCALLTYPE GetGPUDescriptorHandleForHeapStart()
{
D3D12_GPU_DESCRIPTOR_HANDLE handle;
handle.ptr = (UINT64)descriptors;
return handle;
}
D3D12_CPU_DESCRIPTOR_HANDLE GetCPU(uint32_t idx)
{
D3D12_CPU_DESCRIPTOR_HANDLE handle = realCPUBase;
handle.ptr += idx * increment;
return handle;
}
D3D12_GPU_DESCRIPTOR_HANDLE GetGPU(uint32_t idx)
{
D3D12_GPU_DESCRIPTOR_HANDLE handle = realGPUBase;
handle.ptr += idx * increment;
return handle;
}
};
class WrappedID3D12Fence1 : public WrappedDeviceChild12<ID3D12Fence, ID3D12Fence1>
{
ID3D12Fence1 *m_pReal1 = NULL;
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12Fence1);
enum
{
TypeEnum = Resource_Fence,
};
WrappedID3D12Fence1(ID3D12Fence *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
real->QueryInterface(__uuidof(ID3D12Fence1), (void **)&m_pReal1);
}
virtual ~WrappedID3D12Fence1()
{
SAFE_RELEASE(m_pReal1);
Shutdown();
}
//////////////////////////////
// implement ID3D12Fence
virtual UINT64 STDMETHODCALLTYPE GetCompletedValue() { return m_pReal->GetCompletedValue(); }
virtual HRESULT STDMETHODCALLTYPE SetEventOnCompletion(UINT64 Value, HANDLE hEvent)
{
return m_pReal->SetEventOnCompletion(Value, hEvent);
}
virtual HRESULT STDMETHODCALLTYPE Signal(UINT64 Value) { return m_pReal->Signal(Value); }
//////////////////////////////
// implement ID3D12Fence1
virtual D3D12_FENCE_FLAGS STDMETHODCALLTYPE GetCreationFlags()
{
return m_pReal1->GetCreationFlags();
}
};
class WrappedID3D12ProtectedResourceSession
: public WrappedDeviceChild12<ID3D12ProtectedResourceSession>
{
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12ProtectedResourceSession);
enum
{
TypeEnum = Resource_ProtectedResourceSession,
};
WrappedID3D12ProtectedResourceSession(ID3D12ProtectedResourceSession *real,
WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
}
virtual ~WrappedID3D12ProtectedResourceSession() { Shutdown(); }
//////////////////////////////
// implement ID3D12ProtectedSession
virtual HRESULT STDMETHODCALLTYPE GetStatusFence(REFIID riid, _COM_Outptr_opt_ void **ppFence)
{
if(riid != __uuidof(ID3D12Fence) && riid != __uuidof(ID3D12Fence1))
{
RDCERR("Unsupported fence interface %s", ToStr(riid).c_str());
return E_NOINTERFACE;
}
void *iface = NULL;
HRESULT ret = m_pReal->GetStatusFence(riid, &iface);
if(ret != S_OK)
return ret;
ID3D12Fence *fence = NULL;
if(riid == __uuidof(ID3D12Fence))
fence = (ID3D12Fence *)iface;
else if(riid == __uuidof(ID3D12Fence1))
fence = (ID3D12Fence *)(ID3D12Fence1 *)iface;
// if we already have this fence wrapped, return the existing wrapper
if(m_pDevice->GetResourceManager()->HasWrapper(fence))
{
*ppFence =
(ID3D12Fence *)m_pDevice->GetResourceManager()->GetWrapper((ID3D12DeviceChild *)fence);
return S_OK;
}
// if not, record its creation
*ppFence = m_pDevice->CreateProtectedSessionFence(fence);
return S_OK;
}
virtual D3D12_PROTECTED_SESSION_STATUS STDMETHODCALLTYPE GetSessionStatus(void)
{
return m_pReal->GetSessionStatus();
}
//////////////////////////////
// implement ID3D12ProtectedResourceSession
virtual D3D12_PROTECTED_RESOURCE_SESSION_DESC STDMETHODCALLTYPE GetDesc(void)
{
return m_pReal->GetDesc();
}
};
class WrappedID3D12Heap1 : public WrappedDeviceChild12<ID3D12Heap, ID3D12Heap1>
{
ID3D12Heap1 *m_pReal1 = NULL;
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12Heap1);
enum
{
TypeEnum = Resource_Heap,
};
WrappedID3D12Heap1(ID3D12Heap *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
real->QueryInterface(__uuidof(ID3D12Heap1), (void **)&m_pReal1);
}
virtual ~WrappedID3D12Heap1()
{
SAFE_RELEASE(m_pReal1);
Shutdown();
}
//////////////////////////////
// implement ID3D12Heap
virtual D3D12_HEAP_DESC STDMETHODCALLTYPE GetDesc() { return m_pReal->GetDesc(); }
//////////////////////////////
// implement ID3D12Heap1
virtual HRESULT STDMETHODCALLTYPE
GetProtectedResourceSession(REFIID riid, _COM_Outptr_opt_ void **ppProtectedSession)
{
void *iface = NULL;
HRESULT ret = m_pReal1->GetProtectedResourceSession(riid, &iface);
if(ret != S_OK)
return ret;
if(riid == __uuidof(ID3D12ProtectedResourceSession))
{
*ppProtectedSession = new WrappedID3D12ProtectedResourceSession(
(ID3D12ProtectedResourceSession *)iface, m_pDevice);
}
else
{
RDCERR("Unsupported interface %s", ToStr(riid).c_str());
return E_NOINTERFACE;
}
return S_OK;
}
};
class WrappedID3D12PipelineState : public WrappedDeviceChild12<ID3D12PipelineState>
{
public:
static const int AllocPoolCount = 65536;
static const int AllocMaxByteSize = 5 * 1024 * 1024;
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12PipelineState, AllocPoolCount, AllocMaxByteSize);
D3D12_EXPANDED_PIPELINE_STATE_STREAM_DESC *graphics = NULL;
D3D12_EXPANDED_PIPELINE_STATE_STREAM_DESC *compute = NULL;
void Fill(D3D12_EXPANDED_PIPELINE_STATE_STREAM_DESC &desc)
{
if(graphics)
{
desc = *graphics;
if(VS())
desc.VS = VS()->GetDesc();
if(HS())
desc.HS = HS()->GetDesc();
if(DS())
desc.DS = DS()->GetDesc();
if(GS())
desc.GS = GS()->GetDesc();
if(PS())
desc.PS = PS()->GetDesc();
}
else
{
desc = *compute;
desc.CS = CS()->GetDesc();
}
}
bool IsGraphics() { return graphics != NULL; }
bool IsCompute() { return compute != NULL; }
struct DXBCKey
{
DXBCKey(const D3D12_SHADER_BYTECODE &byteCode)
{
byteLen = (uint32_t)byteCode.BytecodeLength;
DXBC::DXBCContainer::GetHash(hash, byteCode.pShaderBytecode, byteCode.BytecodeLength);
}
// assume that byte length + hash is enough to uniquely identify a shader bytecode
uint32_t byteLen;
uint32_t hash[4];
bool operator<(const DXBCKey &o) const
{
if(byteLen != o.byteLen)
return byteLen < o.byteLen;
for(size_t i = 0; i < 4; i++)
if(hash[i] != o.hash[i])
return hash[i] < o.hash[i];
return false;
}
bool operator==(const DXBCKey &o) const
{
return byteLen == o.byteLen && hash[0] == o.hash[0] && hash[1] == o.hash[1] &&
hash[2] == o.hash[2] && hash[3] == o.hash[3];
}
};
class ShaderEntry : public WrappedDeviceChild12<ID3D12DeviceChild>
{
public:
static const int AllocPoolCount = 16384;
static const int AllocMaxByteSize = 10 * 1024 * 1024;
ALLOCATE_WITH_WRAPPED_POOL(ShaderEntry, AllocPoolCount, AllocMaxByteSize);
static bool m_InternalResources;
static void InternalResources(bool internalResources)
{
m_InternalResources = internalResources;
}
ShaderEntry(const D3D12_SHADER_BYTECODE &byteCode, WrappedID3D12Device *device)
: WrappedDeviceChild12(NULL, device), m_Key(byteCode)
{
m_Bytecode.assign((const byte *)byteCode.pShaderBytecode, byteCode.BytecodeLength);
m_DebugInfoSearchPaths = NULL;
m_DXBCFile = NULL;
device->GetResourceManager()->AddLiveResource(GetResourceID(), this);
if(!m_InternalResources)
{
device->AddResource(GetResourceID(), ResourceType::Shader, "Shader");
ResourceDescription &desc = device->GetResourceDesc(GetResourceID());
// this will be appended to in the function above.
desc.initialisationChunks.clear();
// since these don't have live IDs, let's use the first uint of the hash as the name. Slight
// chance of collision but not that bad.
desc.name = StringFormat::Fmt("Shader {%08x}", m_Key.hash[0]);
}
m_Built = false;
}
virtual ~ShaderEntry()
{
m_Shaders.erase(m_Key);
m_Bytecode.clear();
SAFE_DELETE(m_DXBCFile);
Shutdown();
}
static ShaderEntry *AddShader(const D3D12_SHADER_BYTECODE &byteCode,
WrappedID3D12Device *device, WrappedID3D12PipelineState *pipeline)
{
DXBCKey key(byteCode);
ShaderEntry *shader = m_Shaders[key];
if(shader == NULL)
shader = m_Shaders[key] = new ShaderEntry(byteCode, device);
else
shader->AddRef();
return shader;
}
static void ReleaseShader(ShaderEntry *shader)
{
if(shader == NULL)
return;
shader->Release();
}
DXBCKey GetKey() { return m_Key; }
void SetDebugInfoPath(rdcarray<rdcstr> *searchPaths, const rdcstr &path)
{
m_DebugInfoSearchPaths = searchPaths;
m_DebugInfoPath = path;
}
D3D12_SHADER_BYTECODE GetDesc()
{
D3D12_SHADER_BYTECODE ret;
ret.BytecodeLength = m_Bytecode.size();
ret.pShaderBytecode = (const void *)&m_Bytecode[0];
return ret;
}
DXBC::DXBCContainer *GetDXBC()
{
if(m_DXBCFile == NULL && !m_Bytecode.empty())
{
TryReplaceOriginalByteCode();
m_DXBCFile = new DXBC::DXBCContainer((const void *)&m_Bytecode[0], m_Bytecode.size());
}
return m_DXBCFile;
}
ShaderReflection &GetDetails()
{
if(!m_Built && GetDXBC() != NULL)
BuildReflection();
m_Built = true;
return m_Details;
}
const ShaderBindpointMapping &GetMapping()
{
if(!m_Built && GetDXBC() != NULL)
BuildReflection();
m_Built = true;
return m_Mapping;
}
private:
ShaderEntry(const ShaderEntry &e);
void TryReplaceOriginalByteCode();
ShaderEntry &operator=(const ShaderEntry &e);
void BuildReflection();
DXBCKey m_Key;
rdcstr m_DebugInfoPath;
rdcarray<rdcstr> *m_DebugInfoSearchPaths;
rdcarray<byte> m_Bytecode;
bool m_Built;
DXBC::DXBCContainer *m_DXBCFile;
ShaderReflection m_Details;
ShaderBindpointMapping m_Mapping;
static std::map<DXBCKey, ShaderEntry *> m_Shaders;
};
enum
{
TypeEnum = Resource_PipelineState,
};
ShaderEntry *VS() { return (ShaderEntry *)graphics->VS.pShaderBytecode; }
ShaderEntry *HS() { return (ShaderEntry *)graphics->HS.pShaderBytecode; }
ShaderEntry *DS() { return (ShaderEntry *)graphics->DS.pShaderBytecode; }
ShaderEntry *GS() { return (ShaderEntry *)graphics->GS.pShaderBytecode; }
ShaderEntry *PS() { return (ShaderEntry *)graphics->PS.pShaderBytecode; }
ShaderEntry *CS() { return (ShaderEntry *)compute->CS.pShaderBytecode; }
WrappedID3D12PipelineState(ID3D12PipelineState *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
if(IsReplayMode(m_pDevice->GetState()))
m_pDevice->GetPipelineList().push_back(this);
}
virtual ~WrappedID3D12PipelineState()
{
if(IsReplayMode(m_pDevice->GetState()))
m_pDevice->GetPipelineList().removeOne(this);
Shutdown();
if(graphics)
{
ShaderEntry::ReleaseShader(VS());
ShaderEntry::ReleaseShader(HS());
ShaderEntry::ReleaseShader(DS());
ShaderEntry::ReleaseShader(GS());
ShaderEntry::ReleaseShader(PS());
SAFE_DELETE_ARRAY(graphics->InputLayout.pInputElementDescs);
SAFE_DELETE_ARRAY(graphics->StreamOutput.pSODeclaration);
SAFE_DELETE_ARRAY(graphics->StreamOutput.pBufferStrides);
SAFE_DELETE(graphics);
}
if(compute)
{
ShaderEntry::ReleaseShader(CS());
SAFE_DELETE(compute);
}
}
//////////////////////////////
// implement ID3D12PipelineState
virtual HRESULT STDMETHODCALLTYPE GetCachedBlob(ID3DBlob **ppBlob)
{
return m_pReal->GetCachedBlob(ppBlob);
}
};
typedef WrappedID3D12PipelineState::ShaderEntry WrappedID3D12Shader;
class WrappedID3D12QueryHeap : public WrappedDeviceChild12<ID3D12QueryHeap>
{
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12QueryHeap);
enum
{
TypeEnum = Resource_QueryHeap,
};
WrappedID3D12QueryHeap(ID3D12QueryHeap *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
}
virtual ~WrappedID3D12QueryHeap() { Shutdown(); }
};
class WrappedID3D12Resource1 : public WrappedDeviceChild12<ID3D12Resource, ID3D12Resource1>
{
ID3D12Resource1 *m_pReal1 = NULL;
static GPUAddressRangeTracker m_Addresses;
bool resident;
WriteSerialiser &GetThreadSerialiser();
public:
static const int AllocPoolCount = 16384;
static const int AllocMaxByteSize = 1536 * 1024;
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12Resource1, AllocPoolCount, AllocMaxByteSize, false);
static void RefBuffers(D3D12ResourceManager *rm);
static void GetResIDFromAddr(D3D12_GPU_VIRTUAL_ADDRESS addr, ResourceId &id, UINT64 &offs)
{
m_Addresses.GetResIDFromAddr(addr, id, offs);
}
// overload to just return the id in case the offset isn't needed
static ResourceId GetResIDFromAddr(D3D12_GPU_VIRTUAL_ADDRESS addr)
{
ResourceId id;
UINT64 offs;
m_Addresses.GetResIDFromAddr(addr, id, offs);
return id;
}
enum
{
TypeEnum = Resource_Resource,
};
WrappedID3D12Resource1(ID3D12Resource *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
if(IsReplayMode(device->GetState()))
device->GetResourceList()[GetResourceID()] = this;
real->QueryInterface(__uuidof(ID3D12Resource1), (void **)&m_pReal1);
SetResident(true);
// assuming only valid for buffers
if(m_pReal->GetDesc().Dimension == D3D12_RESOURCE_DIMENSION_BUFFER)
{
D3D12_GPU_VIRTUAL_ADDRESS addr = m_pReal->GetGPUVirtualAddress();
GPUAddressRange range;
range.start = addr;
range.end = addr + m_pReal->GetDesc().Width;
range.id = GetResourceID();
m_Addresses.AddTo(range);
}
}
virtual ~WrappedID3D12Resource1();
bool Resident() { return resident; }
void SetResident(bool r) { resident = r; }
byte *GetMap(UINT Subresource);
byte *GetShadow(UINT Subresource);
void AllocShadow(UINT Subresource, size_t size);
void FreeShadow();
virtual uint64_t GetGPUVirtualAddressIfBuffer()
{
if(m_pReal->GetDesc().Dimension == D3D12_RESOURCE_DIMENSION_BUFFER)
return m_pReal->GetGPUVirtualAddress();
return 0;
}
//////////////////////////////
// implement ID3D12Resource
virtual D3D12_RESOURCE_DESC STDMETHODCALLTYPE GetDesc() { return m_pReal->GetDesc(); }
virtual D3D12_GPU_VIRTUAL_ADDRESS STDMETHODCALLTYPE GetGPUVirtualAddress()
{
return m_pReal->GetGPUVirtualAddress();
}
virtual HRESULT STDMETHODCALLTYPE GetHeapProperties(D3D12_HEAP_PROPERTIES *pHeapProperties,
D3D12_HEAP_FLAGS *pHeapFlags)
{
return m_pReal->GetHeapProperties(pHeapProperties, pHeapFlags);
}
virtual HRESULT STDMETHODCALLTYPE Map(UINT Subresource, const D3D12_RANGE *pReadRange,
void **ppData);
virtual void STDMETHODCALLTYPE Unmap(UINT Subresource, const D3D12_RANGE *pWrittenRange);
virtual HRESULT STDMETHODCALLTYPE WriteToSubresource(UINT DstSubresource, const D3D12_BOX *pDstBox,
const void *pSrcData, UINT SrcRowPitch,
UINT SrcDepthPitch);
virtual HRESULT STDMETHODCALLTYPE ReadFromSubresource(void *pDstData, UINT DstRowPitch,
UINT DstDepthPitch, UINT SrcSubresource,
const D3D12_BOX *pSrcBox)
{
// don't have to do anything here
return m_pReal->ReadFromSubresource(pDstData, DstRowPitch, DstDepthPitch, SrcSubresource,
pSrcBox);
}
//////////////////////////////
// implement ID3D12Resource1
virtual HRESULT STDMETHODCALLTYPE
GetProtectedResourceSession(REFIID riid, _COM_Outptr_opt_ void **ppProtectedSession)
{
void *iface = NULL;
HRESULT ret = m_pReal1->GetProtectedResourceSession(riid, &iface);
if(ret != S_OK)
return ret;
if(riid == __uuidof(ID3D12ProtectedResourceSession))
{
*ppProtectedSession = new WrappedID3D12ProtectedResourceSession(
(ID3D12ProtectedResourceSession *)iface, m_pDevice);
}
else
{
RDCERR("Unsupported interface %s", ToStr(riid).c_str());
return E_NOINTERFACE;
}
return S_OK;
}
};
class WrappedID3D12RootSignature : public WrappedDeviceChild12<ID3D12RootSignature>
{
public:
static const int AllocPoolCount = 8192;
static const int AllocMaxByteSize = 2 * 1024 * 1024;
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12RootSignature, AllocPoolCount, AllocMaxByteSize);
D3D12RootSignature sig;
enum
{
TypeEnum = Resource_RootSignature,
};
WrappedID3D12RootSignature(ID3D12RootSignature *real, WrappedID3D12Device *device)
: WrappedDeviceChild12(real, device)
{
}
virtual ~WrappedID3D12RootSignature() { Shutdown(); }
};
class WrappedID3D12PipelineLibrary1 : public WrappedDeviceChild12<ID3D12PipelineLibrary1>
{
public:
ALLOCATE_WITH_WRAPPED_POOL(WrappedID3D12PipelineLibrary1);
enum
{
TypeEnum = Resource_PipelineLibrary,
};
WrappedID3D12PipelineLibrary1(WrappedID3D12Device *device) : WrappedDeviceChild12(NULL, device) {}
virtual ~WrappedID3D12PipelineLibrary1() { Shutdown(); }
virtual HRESULT STDMETHODCALLTYPE StorePipeline(_In_opt_ LPCWSTR pName,
_In_ ID3D12PipelineState *pPipeline)
{
// do nothing
return S_OK;
}
virtual HRESULT STDMETHODCALLTYPE
LoadGraphicsPipeline(_In_ LPCWSTR pName, _In_ const D3D12_GRAPHICS_PIPELINE_STATE_DESC *pDesc,
REFIID riid, _COM_Outptr_ void **ppPipelineState)
{
// pretend we don't have it - assume that the application won't store then
// load in the same run, or will handle that if it happens
return E_INVALIDARG;
}
virtual HRESULT STDMETHODCALLTYPE
LoadComputePipeline(_In_ LPCWSTR pName, _In_ const D3D12_COMPUTE_PIPELINE_STATE_DESC *pDesc,
REFIID riid, _COM_Outptr_ void **ppPipelineState)
{
// pretend we don't have it - assume that the application won't store then
// load in the same run, or will handle that if it happens
return E_INVALIDARG;
}
static const SIZE_T DummyBytes = 32;
virtual SIZE_T STDMETHODCALLTYPE GetSerializedSize(void)
{
// simple dummy serialisation since applications might not expect 0 bytes
return DummyBytes;
}
virtual HRESULT STDMETHODCALLTYPE Serialize(_Out_writes_(DataSizeInBytes) void *pData,
SIZE_T DataSizeInBytes)
{
if(DataSizeInBytes < DummyBytes)
return E_INVALIDARG;
memset(pData, 0, DummyBytes);
return S_OK;
}
//////////////////////////////
// implement ID3D12PipelineLibrary1
virtual HRESULT STDMETHODCALLTYPE LoadPipeline(LPCWSTR pName,
const D3D12_PIPELINE_STATE_STREAM_DESC *pDesc,
REFIID riid, void **ppPipelineState)
{
// pretend we don't have it - assume that the application won't store then
// load in the same run, or will handle that if it happens
return E_INVALIDARG;
}
};
#define ALL_D3D12_TYPES \
D3D12_TYPE_MACRO(ID3D12CommandAllocator); \
D3D12_TYPE_MACRO(ID3D12CommandSignature); \
D3D12_TYPE_MACRO(ID3D12DescriptorHeap); \
D3D12_TYPE_MACRO(ID3D12Fence1); \
D3D12_TYPE_MACRO(ID3D12Heap1); \
D3D12_TYPE_MACRO(ID3D12PipelineState); \
D3D12_TYPE_MACRO(ID3D12QueryHeap); \
D3D12_TYPE_MACRO(ID3D12Resource1); \
D3D12_TYPE_MACRO(ID3D12RootSignature); \
D3D12_TYPE_MACRO(ID3D12PipelineLibrary1); \
D3D12_TYPE_MACRO(ID3D12ProtectedResourceSession);
// template magic voodoo to unwrap types
template <typename inner>
struct UnwrapHelper
{
};
#undef D3D12_TYPE_MACRO
#define D3D12_TYPE_MACRO(iface) \
template <> \
struct UnwrapHelper<iface> \
{ \
typedef CONCAT(Wrapped, iface) Outer; \
static bool IsAlloc(void *ptr) { return Outer::IsAlloc(ptr); } \
static D3D12ResourceType GetTypeEnum() { return (D3D12ResourceType)Outer::TypeEnum; } \
static Outer *FromHandle(iface *wrapped) { return (Outer *)wrapped; } \
}; \
template <> \
struct UnwrapHelper<CONCAT(Wrapped, iface)> \
{ \
typedef CONCAT(Wrapped, iface) Outer; \
static bool IsAlloc(void *ptr) { return Outer::IsAlloc(ptr); } \
static D3D12ResourceType GetTypeEnum() { return (D3D12ResourceType)Outer::TypeEnum; } \
static Outer *FromHandle(iface *wrapped) { return (Outer *)wrapped; } \
};
ALL_D3D12_TYPES;
// extra helpers here for '1' or '2' extended interfaces
#define D3D12_UNWRAP_EXTENDED(iface, ifaceX) \
template <> \
struct UnwrapHelper<iface> \
{ \
typedef CONCAT(Wrapped, ifaceX) Outer; \
static bool IsAlloc(void *ptr) { return Outer::IsAlloc(ptr); } \
static D3D12ResourceType GetTypeEnum() { return (D3D12ResourceType)Outer::TypeEnum; } \
static Outer *FromHandle(iface *wrapped) { return (Outer *)wrapped; } \
};
D3D12_UNWRAP_EXTENDED(ID3D12Fence, ID3D12Fence1);
D3D12_UNWRAP_EXTENDED(ID3D12PipelineLibrary, ID3D12PipelineLibrary1);
D3D12_UNWRAP_EXTENDED(ID3D12Heap, ID3D12Heap1);
D3D12_UNWRAP_EXTENDED(ID3D12Resource, ID3D12Resource1);
D3D12ResourceType IdentifyTypeByPtr(ID3D12Object *ptr);
#define WRAPPING_DEBUG 0
template <typename iface>
typename UnwrapHelper<iface>::Outer *GetWrapped(iface *obj)
{
if(obj == NULL)
return NULL;
typename UnwrapHelper<iface>::Outer *wrapped = UnwrapHelper<iface>::FromHandle(obj);
#if WRAPPING_DEBUG
if(obj != NULL && !wrapped->IsAlloc(wrapped))
{
RDCERR("Trying to unwrap invalid type");
return NULL;
}
#endif
return wrapped;
}
class WrappedID3D12GraphicsCommandList;
template <typename ifaceptr>
ifaceptr Unwrap(ifaceptr obj)
{
if(obj == NULL)
return NULL;
return GetWrapped(obj)->GetReal();
}
template <typename ifaceptr>
ResourceId GetResID(ifaceptr obj)
{
if(obj == NULL)
return ResourceId();
return GetWrapped(obj)->GetResourceID();
}
template <typename ifaceptr>
D3D12ResourceRecord *GetRecord(ifaceptr obj)
{
if(obj == NULL)
return NULL;
return GetWrapped(obj)->GetResourceRecord();
}
// specialisations that use the IsAlloc() function to identify the real type
template <>
ResourceId GetResID(ID3D12Object *ptr);
template <>
ID3D12Object *Unwrap(ID3D12Object *ptr);
template <>
D3D12ResourceRecord *GetRecord(ID3D12Object *ptr);
template <>
ResourceId GetResID(ID3D12DeviceChild *ptr);
template <>
ResourceId GetResID(ID3D12Pageable *ptr);
template <>
ResourceId GetResID(ID3D12CommandList *ptr);
template <>
ResourceId GetResID(ID3D12GraphicsCommandList *ptr);
template <>
ResourceId GetResID(ID3D12CommandQueue *ptr);
template <>
ID3D12DeviceChild *Unwrap(ID3D12DeviceChild *ptr);
template <>
D3D12ResourceRecord *GetRecord(ID3D12DeviceChild *ptr);
| C | 36,366 | h | 1 | 29.638142 | 101 | 0.657592 |
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<xsl:apply-templates select="root/linkedview[@AnalyzerType='npvchangeyr'
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<div data-role="collapsible" data-collapsed="false" data-theme="b" data-content-theme="d" >
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<strong>Output Group Details</strong>
</h4>
<div class="ui-grid-a">
<div class="ui-block-a">
Date : <xsl:value-of select="@Date"/>
</div>
<div class="ui-block-b">
Observations : <xsl:value-of select="@Observations"/>; Alternative : <xsl:value-of select="@AlternativeType"/>
</div>
<div class="ui-block-a">
Ben Total : <xsl:value-of select="@TAMR"/>
</div>
<div class="ui-block-b">
Ben AmountChange : <xsl:value-of select="@TAMRAmountChange"/>
</div>
<div class="ui-block-a">
Ben PercentChange : <xsl:value-of select="@TAMRPercentChange"/>
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Ben BaseChange : <xsl:value-of select="@TAMRBaseChange"/>
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<div data-role="collapsible" data-theme="b" data-content-theme="d" >
<h4 class="ui-bar-b">
<strong>Output Details</strong>
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<div class="ui-grid-a">
<div class="ui-block-a">
Date : <xsl:value-of select="@Date"/>
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<div class="ui-block-b">
Observations : <xsl:value-of select="@Observations"/>; Alternative : <xsl:value-of select="@AlternativeType"/>
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Ben Total : <xsl:value-of select="@TAMR"/>
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<div class="ui-block-a">
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RPrice Total : <xsl:value-of select="@TRPrice"/>
</div>
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RPrice AmountChange : <xsl:value-of select="@TRPriceAmountChange"/>
</div>
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RPrice PercentChange : <xsl:value-of select="@TRPricePercentChange"/>
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RPrice BaseChange : <xsl:value-of select="@TRPriceBaseChange"/>
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RPrice BasePercentChange : <xsl:value-of select="@TRPriceBasePercentChange"/>
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| XSLT | 9,452 | xslt | null | 39.714286 | 149 | 0.5803 |
********************************************************************************
*! combreg, v4, GCerulli, 12/10/2018
********************************************************************************
program combreg, eclass
version 14
#delimit ;
syntax varlist [if] [in] [fweight pweight iweight] ,
model(string)
s(numlist max=1 integer)
k(numlist max=1 integer)
seed(numlist max=1)
[
factors(varlist numeric)
vce(string)
graph
];
#delimit cr
********************************************************************************
quietly{ // open quietly
********************************************************************************
marksample touse
markout `touse' `factors'
********************************************************************************
* Keep only the "if", and save the initial dataset into "mydata"
********************************************************************************
tempfile mydata
qui save `mydata' , replace
keep if `touse'
********************************************************************************
* Generate dummies for factor variables
********************************************************************************
foreach V of local factors{
levelsof `V' , local(L)
local M: word count of `L'
local H=`M'-1
forvalues i=1/`M'{
cap drop _`V'`i'
}
qui tab `V' if `touse' , gen(_`V') mis
local sum_`V' ""
forvalues i=1/`H'{
local sum_`V' `sum_`V'' _`V'`i'
}
}
********************************************************************************
local sum_tot ""
foreach V of local factors{
local sum_tot `sum_tot' `sum_`V''
}
********************************************************************************
tokenize `varlist' `sum_tot'
local y `1'
local w `2'
macro shift
macro shift
local xvars `*'
********************************************************************************
local m=`s'
********************************************************************************
preserve
set seed `seed'
local varlist `xvars'
local N : word count `varlist' // N = # of covariates
********************************************************************************
* Warning 1
********************************************************************************
if `s'>=`N'{
break
di _newline(2)
di as result in red "**********************************************************"
di as result in red "Warning: 's' must be lower than the number of covariates "
di as result in red "considered in the benchmark model. "
di as result in red "**********************************************************"
exit
}
********************************************************************************
clear
********************************************************************************
set obs `N'
tempvar X
gen `X'="."
********************************************************************************
local i=1
foreach x of local varlist{
replace `X'="`x'" in `i'
local i=`i'+1
}
replace `X'="" if `X'=="."
qui save `X' , replace
levelsof `X' , local(L) clean
di `"`L'"'
********************************************************************************
* K = number of re-samples
********************************************************************************
forvalues j=`s'/`m'{
tempfile D`j'
}
********************************************************************************
forvalues j=`s'/`m'{
forvalues i=1/`k'{
tempfile S_`j'_`i'
}
}
********************************************************************************
forvalues j=`s'/`m'{
use `X' , clear
sample `j' , count
cap drop id
gen id = _n
drop `X'
save `D`j'' , replace
forvalues i=1/`k'{
use `X' , clear
sample `j' , count
cap drop id
gen id = _n
rename `X' `X'`j'`i'
save `S_`j'_`i'' , replace
use `D`j'' , clear
merge 1:1 id using `S_`j'_`i''
drop _merge
save `D`j'' , replace
}
}
********************************************************************************
forvalues j=`s'/`m'{
use `D`j'' , clear
forvalues i=1/`k'{
levelsof `X'`j'`i' , local(" L`j'`i'") clean
di `"L`j'`i'"'
}
}
cap erase `X'.dta
restore
********************************************************************************
* Model with all variables (Baseline model)
********************************************************************************
if "`model'"=="reg"{
xi: reg `y' `w' `varlist' if `touse' [`weight'`exp'] , vce(`vce')
local ATET_original=_b[`w']
local se_att=_se[`w']
local Tstud_original=abs(_b[`w']/_se[`w'])
local lim=1.96*_se[`w']
local upper=_b[`w']+`lim'
local lower=_b[`w']-`lim'
********************************************************************************
local B=`k'*(`m'-`s'+1)
********************************************************************************
tempname J
mat `J'=J(`B',2,.)
********************************************************************************
* Run the regressions/matchings for estimating ATET
local h=1
forvalues j=`s'/`m'{
forvalues i=1/`k'{
xi: reg `y' `w' `L`j'`i'' if `touse' [`weight'`exp'] , vce(`vce')
********************************************************************************
mat `J'[`h',1] = _b[`w']
mat `J'[`h',2] = abs(_b[`w']/_se[`w'])
local h=`h'+1
}
}
}
********************************************************************************
else if "`model'"=="match"{
xi: psmatch2 `w' `varlist' if `touse' , out(`y') ate
local ATET_original=r(att)
local se_att=r(seatt)
local Tstud_original=r(att)/r(seatt)
local lim=1.96*`se_att'
local upper=`ATET_original'+`lim'
local lower=`ATET_original'-`lim'
********************************************************************************
local B=`k'*(`m'-`s'+1)
********************************************************************************
tempname J
mat `J'=J(`B',2,.)
********************************************************************************
* Run the regressions/matchings for estimating ATET
local h=1
forvalues j=`s'/`m'{
forvalues i=1/`k'{
xi: psmatch2 `w' `L`j'`i'' if `touse' , out(`y') ate
*cap drop near_obs*
*teffects psmatch (`y') (`w' `L`j'`i'' , probit) , atet generate(near_obs) atet
mat `J'[`h',1] = r(att)
mat `J'[`h',2] = r(att)/r(seatt)
local h=`h'+1
}
}
}
********************************************************************************
* Simulation results
********************************************************************************
cap drop _ATET*
svmat `J', names(_ATET)
local ate_bench=round(`ATET_original',0.01)
local Tstud_bench=round(`Tstud_original',0.01)
if "`graph'"=="graph"{
kdensity _ATET1 if `touse' , xline(`ATET_original',lpattern(dash)) xtitle("ATET") note("Number of simulations: `k'" ///
"Number of covariates: `s' out of `N'" "Reference ATET: `ate_bench'" ) scheme(s1mono) title("")
}
********************************************************************************
* Testing whether there are differences between model Ho and the
* average of the simulated models
********************************************************************************
qui reg _ATET1 if `touse'
test _cons=`ATET_original'
********************************************************************************
* Returns
********************************************************************************
ereturn clear
qui sum _ATET1 if `touse' , d
local mean_b_sim=r(mean)
ereturn scalar mean_b_sim = r(mean)
ereturn scalar median_b_sim = r(p50)
ereturn scalar sd_b_sim = r(sd)
ereturn scalar b_bench = `ate_bench'
ereturn scalar t_bench = `Tstud_bench'
local delta=abs((`mean_b_sim'-`ate_bench')/`ate_bench')
ereturn scalar delta = `delta'
ereturn scalar upci = `upper'
ereturn scalar lowci = `lower'
cap drop _ATET1
********************************************************************************
qui sum _ATET2 if `touse' , d
local mean_Tstud_sim=r(mean)
ereturn scalar mean_Tstud_sim = r(mean)
cap drop _ATET2
********************************************************************************
} // end quietly
********************************************************************************
qui use `mydata' , clear
end
********************************************************************************
* END
********************************************************************************
| Stata | 8,140 | ado | 1 | 34.201681 | 119 | 0.36683 |
(define (make-vect x y)
(cons x y))
(define (xcor-vect v)
(car v))
(define (ycor-vect v)
(cdr v))
(define (add-vect v1 v2)
(cons (+ (xcor-vect v1) (xcor-vect v2))
(+ (ycor-vect v1) (ycor-vect v2))))
(define (sub-vect v1 v2)
(cons (- (xcor-vect v1) (xcor-vect v2))
(- (ycor-vect v1) (ycor-vect v2))))
(define (scale-vect s v)
(cons (* s (xcor-vect v))
(* s (ycor-vect v))))
| Scheme | 415 | scm | null | 18.863636 | 43 | 0.537349 |
/-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.polynomial.degree.card_pow_degree
import field_theory.finite.basic
import number_theory.class_number.admissible_absolute_value
/-!
# Admissible absolute values on polynomials
This file defines an admissible absolute value
`polynomial.card_pow_degree_is_admissible` which we use to show the class number
of the ring of integers of a function field is finite.
## Main results
* `polynomial.card_pow_degree_is_admissible` shows `card_pow_degree`,
mapping `p : polynomial 𝔽_q` to `q ^ degree p`, is admissible
-/
namespace polynomial
open absolute_value real
variables {Fq : Type*} [field Fq] [fintype Fq]
/-- If `A` is a family of enough low-degree polynomials over a finite field, there is a
pair of equal elements in `A`. -/
lemma exists_eq_polynomial {d : ℕ} {m : ℕ} (hm : fintype.card Fq ^ d ≤ m) (b : polynomial Fq)
(hb : nat_degree b ≤ d) (A : fin m.succ → polynomial Fq) (hA : ∀ i, degree (A i) < degree b) :
∃ i₀ i₁, i₀ ≠ i₁ ∧ A i₁ = A i₀ :=
begin
-- Since there are > q^d elements of A, and only q^d choices for the highest `d` coefficients,
-- there must be two elements of A with the same coefficients at
-- `0`, ... `degree b - 1` ≤ `d - 1`.
-- In other words, the following map is not injective:
set f : fin m.succ → (fin d → Fq) := λ i j, (A i).coeff j,
have : fintype.card (fin d → Fq) < fintype.card (fin m.succ),
{ simpa using lt_of_le_of_lt hm (nat.lt_succ_self m) },
-- Therefore, the differences have all coefficients higher than `deg b - d` equal.
obtain ⟨i₀, i₁, i_ne, i_eq⟩ := fintype.exists_ne_map_eq_of_card_lt f this,
use [i₀, i₁, i_ne],
ext j,
-- The coefficients higher than `deg b` are the same because they are equal to 0.
by_cases hbj : degree b ≤ j,
{ rw [coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj),
coeff_eq_zero_of_degree_lt (lt_of_lt_of_le (hA _) hbj)] },
-- So we only need to look for the coefficients between `0` and `deg b`.
rw not_le at hbj,
apply congr_fun i_eq.symm ⟨j, _⟩,
exact lt_of_lt_of_le (coe_lt_degree.mp hbj) hb
end
/-- If `A` is a family of enough low-degree polynomials over a finite field,
there is a pair of elements in `A` (with different indices but not necessarily
distinct), such that their difference has small degree. -/
lemma exists_approx_polynomial_aux {d : ℕ} {m : ℕ} (hm : fintype.card Fq ^ d ≤ m)
(b : polynomial Fq) (A : fin m.succ → polynomial Fq) (hA : ∀ i, degree (A i) < degree b) :
∃ i₀ i₁, i₀ ≠ i₁ ∧ degree (A i₁ - A i₀) < ↑(nat_degree b - d) :=
begin
have hb : b ≠ 0,
{ rintro rfl,
specialize hA 0,
rw degree_zero at hA,
exact not_lt_of_le bot_le hA },
-- Since there are > q^d elements of A, and only q^d choices for the highest `d` coefficients,
-- there must be two elements of A with the same coefficients at
-- `degree b - 1`, ... `degree b - d`.
-- In other words, the following map is not injective:
set f : fin m.succ → (fin d → Fq) := λ i j, (A i).coeff (nat_degree b - j.succ),
have : fintype.card (fin d → Fq) < fintype.card (fin m.succ),
{ simpa using lt_of_le_of_lt hm (nat.lt_succ_self m) },
-- Therefore, the differences have all coefficients higher than `deg b - d` equal.
obtain ⟨i₀, i₁, i_ne, i_eq⟩ := fintype.exists_ne_map_eq_of_card_lt f this,
use [i₀, i₁, i_ne],
refine (degree_lt_iff_coeff_zero _ _).mpr (λ j hj, _),
-- The coefficients higher than `deg b` are the same because they are equal to 0.
by_cases hbj : degree b ≤ j,
{ refine coeff_eq_zero_of_degree_lt (lt_of_lt_of_le _ hbj),
exact lt_of_le_of_lt (degree_sub_le _ _) (max_lt (hA _) (hA _)) },
-- So we only need to look for the coefficients between `deg b - d` and `deg b`.
rw [coeff_sub, sub_eq_zero],
rw [not_le, degree_eq_nat_degree hb, with_bot.coe_lt_coe] at hbj,
have hj : nat_degree b - j.succ < d,
{ by_cases hd : nat_degree b < d,
{ exact lt_of_le_of_lt (nat.sub_le_self _ _) hd },
{ rw not_lt at hd,
have := lt_of_le_of_lt hj (nat.lt_succ_self j),
rwa [nat.sub_lt_iff hd hbj] at this } },
have : j = b.nat_degree - (nat_degree b - j.succ).succ,
{ rw [← nat.succ_sub hbj, nat.succ_sub_succ, nat.sub_sub_self hbj.le] },
convert congr_fun i_eq.symm ⟨nat_degree b - j.succ, hj⟩
end
/-- If `A` is a family of enough low-degree polynomials over a finite field,
there is a pair of elements in `A` (with different indices but not necessarily
distinct), such that the difference of their remainders is close together. -/
lemma exists_approx_polynomial {b : polynomial Fq} (hb : b ≠ 0)
{ε : ℝ} (hε : 0 < ε)
(A : fin (fintype.card Fq ^ nat_ceil (- log ε / log (fintype.card Fq))).succ → polynomial Fq) :
∃ i₀ i₁, i₀ ≠ i₁ ∧ (card_pow_degree (A i₁ % b - A i₀ % b) : ℝ) < card_pow_degree b • ε :=
begin
have hbε : 0 < card_pow_degree b • ε,
{ rw [algebra.smul_def, ring_hom.eq_int_cast],
exact mul_pos (int.cast_pos.mpr (absolute_value.pos _ hb)) hε },
have one_lt_q : 1 < fintype.card Fq := fintype.one_lt_card,
have one_lt_q' : (1 : ℝ) < fintype.card Fq, { assumption_mod_cast },
have q_pos : 0 < fintype.card Fq, { linarith },
have q_pos' : (0 : ℝ) < fintype.card Fq, { assumption_mod_cast },
-- If `b` is already small enough, then the remainders are equal and we are done.
by_cases le_b : b.nat_degree ≤ nat_ceil (-log ε / log ↑(fintype.card Fq)),
{ obtain ⟨i₀, i₁, i_ne, mod_eq⟩ := exists_eq_polynomial (le_refl _) b le_b (λ i, A i % b)
(λ i, euclidean_domain.mod_lt (A i) hb),
refine ⟨i₀, i₁, i_ne, _⟩,
simp only at mod_eq,
rwa [mod_eq, sub_self, absolute_value.map_zero, int.cast_zero] },
-- Otherwise, it suffices to choose two elements whose difference is of small enough degree.
rw not_le at le_b,
obtain ⟨i₀, i₁, i_ne, deg_lt⟩ := exists_approx_polynomial_aux (le_refl _) b (λ i, A i % b)
(λ i, euclidean_domain.mod_lt (A i) hb),
simp only at deg_lt,
use [i₀, i₁, i_ne],
-- Again, if the remainders are equal we are done.
by_cases h : A i₁ % b = A i₀ % b,
{ rwa [h, sub_self, absolute_value.map_zero, int.cast_zero] },
have h' : A i₁ % b - A i₀ % b ≠ 0 := mt sub_eq_zero.mp h,
-- If the remainders are not equal, we'll show their difference is of small degree.
-- In particular, we'll show the degree is less than the following:
suffices : (nat_degree (A i₁ % b - A i₀ % b) : ℝ) <
b.nat_degree + log ε / log (fintype.card Fq),
{ rwa [← real.log_lt_log_iff (int.cast_pos.mpr (card_pow_degree.pos h')) hbε,
card_pow_degree_nonzero _ h', card_pow_degree_nonzero _ hb,
algebra.smul_def, ring_hom.eq_int_cast,
int.cast_pow, int.cast_coe_nat, int.cast_pow, int.cast_coe_nat,
log_mul (pow_ne_zero _ q_pos'.ne') hε.ne',
← rpow_nat_cast, ← rpow_nat_cast, log_rpow q_pos', log_rpow q_pos',
← lt_div_iff (log_pos one_lt_q'), add_div, mul_div_cancel _ (log_pos one_lt_q').ne'] },
-- And that result follows from manipulating the result from `exists_approx_polynomial_aux`
-- to turn the `- ceil (- stuff)` into `+ stuff`.
refine lt_of_lt_of_le (nat.cast_lt.mpr (with_bot.coe_lt_coe.mp _)) _,
swap, { convert deg_lt, rw degree_eq_nat_degree h' },
rw [← sub_neg_eq_add, neg_div],
refine le_trans _ (sub_le_sub_left (le_nat_ceil _) (b.nat_degree : ℝ)),
rw ← neg_div,
exact le_of_eq (nat.cast_sub le_b.le)
end
/-- If `x` is close to `y` and `y` is close to `z`, then `x` and `z` are at least as close. -/
lemma card_pow_degree_anti_archimedean {x y z : polynomial Fq} {a : ℤ}
(hxy : card_pow_degree (x - y) < a) (hyz : card_pow_degree (y - z) < a) :
card_pow_degree (x - z) < a :=
begin
have ha : 0 < a := lt_of_le_of_lt (absolute_value.nonneg _ _) hxy,
by_cases hxy' : x = y,
{ rwa hxy' },
by_cases hyz' : y = z,
{ rwa ← hyz' },
by_cases hxz' : x = z,
{ rwa [hxz', sub_self, absolute_value.map_zero] },
rw [← ne.def, ← sub_ne_zero] at hxy' hyz' hxz',
refine lt_of_le_of_lt _ (max_lt hxy hyz),
rw [card_pow_degree_nonzero _ hxz', card_pow_degree_nonzero _ hxy',
card_pow_degree_nonzero _ hyz'],
have : (1 : ℤ) ≤ fintype.card Fq, { exact_mod_cast (@fintype.one_lt_card Fq _ _).le },
simp only [int.cast_pow, int.cast_coe_nat, le_max_iff],
refine or.imp (pow_le_pow this) (pow_le_pow this) _,
rw [nat_degree_le_iff_degree_le, nat_degree_le_iff_degree_le, ← le_max_iff,
← degree_eq_nat_degree hxy', ← degree_eq_nat_degree hyz'],
convert degree_add_le (x - y) (y - z) using 2,
exact (sub_add_sub_cancel _ _ _).symm
end
/-- A slightly stronger version of `exists_partition` on which we perform induction on `n`:
for all `ε > 0`, we can partition the remainders of any family of polynomials `A`
into equivalence classes, where the equivalence(!) relation is "closer than `ε`". -/
lemma exists_partition_polynomial_aux (n : ℕ) {ε : ℝ} (hε : 0 < ε)
{b : polynomial Fq} (hb : b ≠ 0) (A : fin n → polynomial Fq) :
∃ (t : fin n → fin (fintype.card Fq ^ nat_ceil (-log ε / log ↑(fintype.card Fq)))),
∀ (i₀ i₁ : fin n),
t i₀ = t i₁ ↔ (card_pow_degree (A i₁ % b - A i₀ % b) : ℝ) < card_pow_degree b • ε :=
begin
have hbε : 0 < card_pow_degree b • ε,
{ rw [algebra.smul_def, ring_hom.eq_int_cast],
exact mul_pos (int.cast_pos.mpr (absolute_value.pos _ hb)) hε },
-- We go by induction on the size `A`.
induction n with n ih,
{ refine ⟨fin_zero_elim, fin_zero_elim⟩ },
-- Show `anti_archimedean` also holds for real distances.
have anti_archim' : ∀ {i j k} {ε : ℝ}, (card_pow_degree (A i % b - A j % b) : ℝ) < ε →
(card_pow_degree (A j % b - A k % b) : ℝ) < ε → (card_pow_degree (A i % b - A k % b) : ℝ) < ε,
{ intros i j k ε,
rw [← lt_ceil, ← lt_ceil, ← lt_ceil],
exact card_pow_degree_anti_archimedean },
obtain ⟨t', ht'⟩ := ih (fin.tail A),
-- We got rid of `A 0`, so determine the index `j` of the partition we'll re-add it to.
suffices : ∃ j,
∀ i, t' i = j ↔ (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε,
{ obtain ⟨j, hj⟩ := this,
refine ⟨fin.cons j t', λ i₀ i₁, _⟩,
refine fin.cases _ (λ i₀, _) i₀; refine fin.cases _ (λ i₁, _) i₁,
{ simpa using hbε },
{ rw [fin.cons_succ, fin.cons_zero, eq_comm, absolute_value.map_sub],
exact hj i₁ },
{ rw [fin.cons_succ, fin.cons_zero],
exact hj i₀ },
{ rw [fin.cons_succ, fin.cons_succ],
exact ht' i₀ i₁ } },
-- `exists_approx_polynomial` guarantees that we can insert `A 0` into some partition `j`,
-- but not that `j` is uniquely defined (which is needed to keep the induction going).
obtain ⟨j, hj⟩ : ∃ j, ∀ (i : fin n), t' i = j →
(card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε,
{ by_contra this, push_neg at this,
obtain ⟨j₀, j₁, j_ne, approx⟩ := exists_approx_polynomial hb hε
(fin.cons (A 0) (λ j, A (fin.succ (classical.some (this j))))),
revert j_ne approx,
refine fin.cases _ (λ j₀, _) j₀; refine fin.cases (λ j_ne approx, _) (λ j₁ j_ne approx, _) j₁,
{ exact absurd rfl j_ne },
{ rw [fin.cons_succ, fin.cons_zero, ← not_le, absolute_value.map_sub] at approx,
have := (classical.some_spec (this j₁)).2,
contradiction },
{ rw [fin.cons_succ, fin.cons_zero, ← not_le] at approx,
have := (classical.some_spec (this j₀)).2,
contradiction },
{ rw [fin.cons_succ, fin.cons_succ] at approx,
rw [ne.def, fin.succ_inj] at j_ne,
have : j₀ = j₁ :=
(classical.some_spec (this j₀)).1.symm.trans
(((ht' (classical.some (this j₀)) (classical.some (this j₁))).mpr approx).trans
(classical.some_spec (this j₁)).1),
contradiction } },
-- However, if one of those partitions `j` is inhabited by some `i`, then this `j` works.
by_cases exists_nonempty_j : ∃ j, (∃ i, t' i = j) ∧
∀ i, t' i = j → (card_pow_degree (A 0 % b - A i.succ % b) : ℝ) < card_pow_degree b • ε,
{ obtain ⟨j, ⟨i, hi⟩, hj⟩ := exists_nonempty_j,
refine ⟨j, λ i', ⟨hj i', λ hi', trans ((ht' _ _).mpr _) hi⟩⟩,
apply anti_archim' _ hi',
rw absolute_value.map_sub,
exact hj _ hi },
-- And otherwise, we can just take any `j`, since those are empty.
refine ⟨j, λ i, ⟨hj i, λ hi, _⟩⟩,
have := exists_nonempty_j ⟨t' i, ⟨i, rfl⟩, λ i' hi', anti_archim' hi ((ht' _ _).mp hi')⟩,
contradiction
end
/-- For all `ε > 0`, we can partition the remainders of any family of polynomials `A`
into classes, where all remainders in a class are close together. -/
lemma exists_partition_polynomial (n : ℕ) {ε : ℝ} (hε : 0 < ε)
{b : polynomial Fq} (hb : b ≠ 0) (A : fin n → polynomial Fq) :
∃ (t : fin n → fin (fintype.card Fq ^ nat_ceil (-log ε / log ↑(fintype.card Fq)))),
∀ (i₀ i₁ : fin n), t i₀ = t i₁ →
(card_pow_degree (A i₁ % b - A i₀ % b) : ℝ) < card_pow_degree b • ε :=
begin
obtain ⟨t, ht⟩ := exists_partition_polynomial_aux n hε hb A,
exact ⟨t, λ i₀ i₁ hi, (ht i₀ i₁).mp hi⟩
end
/-- `λ p, fintype.card Fq ^ degree p` is an admissible absolute value.
We set `q ^ degree 0 = 0`. -/
noncomputable def card_pow_degree_is_admissible :
is_admissible (card_pow_degree : absolute_value (polynomial Fq) ℤ) :=
{ card := λ ε, fintype.card Fq ^ (nat_ceil (- log ε / log (fintype.card Fq))),
exists_partition' := λ n ε hε b hb, exists_partition_polynomial n hε hb,
.. @card_pow_degree_is_euclidean Fq _ _ }
end polynomial
| Lean | 13,364 | lean | null | 49.680297 | 98 | 0.657662 |
; A182769: Beatty sequence for (4 + sqrt(2))/2.
; 2,5,8,10,13,16,18,21,24,27,29,32,35,37,40,43,46,48,51,54,56,59,62,64,67,70,73,75,78,81,83,86,89,92,94,97,100,102,105,108,110,113,116,119,121,124,127,129,132,135,138,140,143,146,148,151,154,157,159,162,165,167,170,173,175,178,181,184,186,189,192,194,197,200,203,205,208,211,213,216,219,221,224,227,230,232,235,238,240,243,246,249,251,254,257,259,262,265,268,270,273,276,278,281,284,286,289,292,295,297,300,303,305,308,311,314,316,319,322,324,327,330,332,335,338,341,343,346,349,351,354,357,360,362,365,368,370,373,376,378,381,384,387,389,392,395,397,400,403,406,408,411,414,416,419,422,425,427,430,433,435,438,441,443,446,449,452,454,457,460,462,465,468,471,473,476,479,481,484,487,489,492,495,498,500,503,506,508,511,514,517,519,522,525,527,530,533,536,538,541,544,546,549,552,554,557,560,563,565,568,571,573,576,579,582,584,587,590,592,595,598,600,603,606,609,611,614,617,619,622,625,628,630,633,636,638,641,644,646,649,652,655,657,660,663,665,668,671,674,676
mov $7,$0
mov $8,$0
add $0,1
pow $0,2
mov $2,$0
mov $3,1
lpb $2
add $3,1
mov $4,$2
trn $4,2
lpb $4
add $3,4
trn $4,$3
add $5,2
lpe
sub $2,$2
lpe
mov $1,$5
mov $6,$7
mul $6,2
add $1,$6
div $1,2
add $1,2
add $1,$8
| Assembly | 1,248 | asm | 1 | 44.571429 | 962 | 0.685897 |
/-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import algebra.group.pi
import algebra.big_operators.order
import algebra.module.basic
import algebra.module.pi
import group_theory.submonoid.basic
import data.fintype.card
import data.finset.preimage
import data.multiset.antidiagonal
import data.indicator_function
/-!
# Type of functions with finite support
For any type `α` and a type `M` with zero, we define the type `finsupp α M` (notation: `α →₀ M`)
of finitely supported functions from `α` to `M`, i.e. the functions which are zero everywhere
on `α` except on a finite set.
Functions with finite support are used (at least) in the following parts of the library:
* `monoid_algebra R M` and `add_monoid_algebra R M` are defined as `M →₀ R`;
* polynomials and multivariate polynomials are defined as `add_monoid_algebra`s, hence they use
`finsupp` under the hood;
* the linear combination of a family of vectors `v i` with coefficients `f i` (as used, e.g., to
define linearly independent family `linear_independent`) is defined as a map
`finsupp.total : (ι → M) → (ι →₀ R) →ₗ[R] M`.
Some other constructions are naturally equivalent to `α →₀ M` with some `α` and `M` but are defined
in a different way in the library:
* `multiset α ≃+ α →₀ ℕ`;
* `free_abelian_group α ≃+ α →₀ ℤ`.
Most of the theory assumes that the range is a commutative additive monoid. This gives us the big
sum operator as a powerful way to construct `finsupp` elements.
Many constructions based on `α →₀ M` use `semireducible` type tags to avoid reusing unwanted type
instances. E.g., `monoid_algebra`, `add_monoid_algebra`, and types based on these two have
non-pointwise multiplication.
## Notations
This file adds `α →₀ M` as a global notation for `finsupp α M`. We also use the following convention
for `Type*` variables in this file
* `α`, `β`, `γ`: types with no additional structure that appear as the first argument to `finsupp`
somewhere in the statement;
* `ι` : an auxiliary index type;
* `M`, `M'`, `N`, `P`: types with `has_zero` or `(add_)(comm_)monoid` structure; `M` is also used
for a (semi)module over a (semi)ring.
* `G`, `H`: groups (commutative or not, multiplicative or additive);
* `R`, `S`: (semi)rings.
## TODO
* This file is currently ~2K lines long, so possibly it should be splitted into smaller chunks;
* Add the list of definitions and important lemmas to the module docstring.
## Implementation notes
This file is a `noncomputable theory` and uses classical logic throughout.
## Notation
This file defines `α →₀ β` as notation for `finsupp α β`.
-/
noncomputable theory
open_locale classical big_operators
open finset
variables {α β γ ι M M' N P G H R S : Type*}
/-- `finsupp α M`, denoted `α →₀ M`, is the type of functions `f : α → M` such that
`f x = 0` for all but finitely many `x`. -/
structure finsupp (α : Type*) (M : Type*) [has_zero M] :=
(support : finset α)
(to_fun : α → M)
(mem_support_to_fun : ∀a, a ∈ support ↔ to_fun a ≠ 0)
infixr ` →₀ `:25 := finsupp
namespace finsupp
/-! ### Basic declarations about `finsupp` -/
section basic
variable [has_zero M]
instance : has_coe_to_fun (α →₀ M) := ⟨λ _, α → M, to_fun⟩
@[simp] lemma coe_mk (f : α → M) (s : finset α) (h : ∀ a, a ∈ s ↔ f a ≠ 0) :
⇑(⟨s, f, h⟩ : α →₀ M) = f := rfl
instance : has_zero (α →₀ M) := ⟨⟨∅, 0, λ _, ⟨false.elim, λ H, H rfl⟩⟩⟩
@[simp] lemma coe_zero : ⇑(0 : α →₀ M) = 0 := rfl
lemma zero_apply {a : α} : (0 : α →₀ M) a = 0 := rfl
@[simp] lemma support_zero : (0 : α →₀ M).support = ∅ := rfl
instance : inhabited (α →₀ M) := ⟨0⟩
@[simp] lemma mem_support_iff {f : α →₀ M} : ∀{a:α}, a ∈ f.support ↔ f a ≠ 0 :=
f.mem_support_to_fun
@[simp, norm_cast] lemma fun_support_eq (f : α →₀ M) : function.support f = f.support :=
set.ext $ λ x, mem_support_iff.symm
lemma not_mem_support_iff {f : α →₀ M} {a} : a ∉ f.support ↔ f a = 0 :=
not_iff_comm.1 mem_support_iff.symm
lemma coe_fn_injective : @function.injective (α →₀ M) (α → M) coe_fn
| ⟨s, f, hf⟩ ⟨t, g, hg⟩ h :=
begin
change f = g at h, subst h,
have : s = t, { ext a, exact (hf a).trans (hg a).symm },
subst this
end
@[simp, norm_cast] lemma coe_fn_inj {f g : α →₀ M} : (f : α → M) = g ↔ f = g :=
coe_fn_injective.eq_iff
@[simp, norm_cast] lemma coe_eq_zero {f : α →₀ M} : (f : α → M) = 0 ↔ f = 0 :=
by rw [← coe_zero, coe_fn_inj]
@[ext] lemma ext {f g : α →₀ M} (h : ∀a, f a = g a) : f = g := coe_fn_injective (funext h)
lemma ext_iff {f g : α →₀ M} : f = g ↔ (∀a:α, f a = g a) :=
⟨by rintros rfl a; refl, ext⟩
lemma ext_iff' {f g : α →₀ M} : f = g ↔ f.support = g.support ∧ ∀ x ∈ f.support, f x = g x :=
⟨λ h, h ▸ ⟨rfl, λ _ _, rfl⟩, λ ⟨h₁, h₂⟩, ext $ λ a,
if h : a ∈ f.support then h₂ a h else
have hf : f a = 0, from not_mem_support_iff.1 h,
have hg : g a = 0, by rwa [h₁, not_mem_support_iff] at h,
by rw [hf, hg]⟩
@[simp] lemma support_eq_empty {f : α →₀ M} : f.support = ∅ ↔ f = 0 :=
by exact_mod_cast @function.support_eq_empty_iff _ _ _ f
lemma support_nonempty_iff {f : α →₀ M} : f.support.nonempty ↔ f ≠ 0 :=
by simp only [finsupp.support_eq_empty, finset.nonempty_iff_ne_empty, ne.def]
lemma nonzero_iff_exists {f : α →₀ M} : f ≠ 0 ↔ ∃ a : α, f a ≠ 0 :=
by simp [← finsupp.support_eq_empty, finset.eq_empty_iff_forall_not_mem]
lemma card_support_eq_zero {f : α →₀ M} : card f.support = 0 ↔ f = 0 :=
by simp
instance finsupp.decidable_eq [decidable_eq α] [decidable_eq M] : decidable_eq (α →₀ M) :=
assume f g, decidable_of_iff (f.support = g.support ∧ (∀a∈f.support, f a = g a)) ext_iff'.symm
lemma finite_support (f : α →₀ M) : set.finite (function.support f) :=
f.fun_support_eq.symm ▸ f.support.finite_to_set
lemma support_subset_iff {s : set α} {f : α →₀ M} :
↑f.support ⊆ s ↔ (∀a∉s, f a = 0) :=
by simp only [set.subset_def, mem_coe, mem_support_iff];
exact forall_congr (assume a, not_imp_comm)
/-- Given `fintype α`, `equiv_fun_on_fintype` is the `equiv` between `α →₀ β` and `α → β`.
(All functions on a finite type are finitely supported.) -/
def equiv_fun_on_fintype [fintype α] : (α →₀ M) ≃ (α → M) :=
⟨λf a, f a, λf, mk (finset.univ.filter $ λa, f a ≠ 0) f (by simp only [true_and, finset.mem_univ,
iff_self, finset.mem_filter, finset.filter_congr_decidable, forall_true_iff]),
begin intro f, ext a, refl end,
begin intro f, ext a, refl end⟩
end basic
/-! ### Declarations about `single` -/
section single
variables [has_zero M] {a a' : α} {b : M}
/-- `single a b` is the finitely supported function which has
value `b` at `a` and zero otherwise. -/
def single (a : α) (b : M) : α →₀ M :=
⟨if b = 0 then ∅ else {a}, λ a', if a = a' then b else 0, λ a', begin
by_cases hb : b = 0; by_cases a = a';
simp only [hb, h, if_pos, if_false, mem_singleton],
{ exact ⟨false.elim, λ H, H rfl⟩ },
{ exact ⟨false.elim, λ H, H rfl⟩ },
{ exact ⟨λ _, hb, λ _, rfl⟩ },
{ exact ⟨λ H _, h H.symm, λ H, (H rfl).elim⟩ }
end⟩
lemma single_apply : single a b a' = if a = a' then b else 0 :=
rfl
lemma single_eq_indicator : ⇑(single a b) = set.indicator {a} (λ _, b) :=
by { ext, simp [single_apply, set.indicator, @eq_comm _ a] }
@[simp] lemma single_eq_same : (single a b : α →₀ M) a = b :=
if_pos rfl
@[simp] lemma single_eq_of_ne (h : a ≠ a') : (single a b : α →₀ M) a' = 0 :=
if_neg h
lemma single_eq_update : ⇑(single a b) = function.update 0 a b :=
by rw [single_eq_indicator, ← set.piecewise_eq_indicator, set.piecewise_singleton]
lemma single_eq_pi_single : ⇑(single a b) = pi.single a b :=
single_eq_update
@[simp] lemma single_zero : (single a 0 : α →₀ M) = 0 :=
coe_fn_injective $ by simpa only [single_eq_update, coe_zero]
using function.update_eq_self a (0 : α → M)
lemma single_of_single_apply (a a' : α) (b : M) :
single a ((single a' b) a) = single a' (single a' b) a :=
begin
rw [single_apply, single_apply],
ext,
split_ifs,
{ rw h, },
{ rw [zero_apply, single_apply, if_t_t], },
end
lemma support_single_ne_zero (hb : b ≠ 0) : (single a b).support = {a} :=
if_neg hb
lemma support_single_subset : (single a b).support ⊆ {a} :=
show ite _ _ _ ⊆ _, by split_ifs; [exact empty_subset _, exact subset.refl _]
lemma single_apply_mem (x) : single a b x ∈ ({0, b} : set M) :=
by rcases em (a = x) with (rfl|hx); [simp, simp [single_eq_of_ne hx]]
lemma range_single_subset : set.range (single a b) ⊆ {0, b} :=
set.range_subset_iff.2 single_apply_mem
lemma single_injective (a : α) : function.injective (single a : M → α →₀ M) :=
assume b₁ b₂ eq,
have (single a b₁ : α →₀ M) a = (single a b₂ : α →₀ M) a, by rw eq,
by rwa [single_eq_same, single_eq_same] at this
lemma single_apply_eq_zero {a x : α} {b : M} : single a b x = 0 ↔ (x = a → b = 0) :=
by simp [single_eq_indicator]
lemma mem_support_single (a a' : α) (b : M) :
a ∈ (single a' b).support ↔ a = a' ∧ b ≠ 0 :=
by simp [single_apply_eq_zero, not_or_distrib]
lemma eq_single_iff {f : α →₀ M} {a b} : f = single a b ↔ f.support ⊆ {a} ∧ f a = b :=
begin
refine ⟨λ h, h.symm ▸ ⟨support_single_subset, single_eq_same⟩, _⟩,
rintro ⟨h, rfl⟩,
ext x,
by_cases hx : a = x; simp only [hx, single_eq_same, single_eq_of_ne, ne.def, not_false_iff],
exact not_mem_support_iff.1 (mt (λ hx, (mem_singleton.1 (h hx)).symm) hx)
end
lemma single_eq_single_iff (a₁ a₂ : α) (b₁ b₂ : M) :
single a₁ b₁ = single a₂ b₂ ↔ ((a₁ = a₂ ∧ b₁ = b₂) ∨ (b₁ = 0 ∧ b₂ = 0)) :=
begin
split,
{ assume eq,
by_cases a₁ = a₂,
{ refine or.inl ⟨h, _⟩,
rwa [h, (single_injective a₂).eq_iff] at eq },
{ rw [ext_iff] at eq,
have h₁ := eq a₁,
have h₂ := eq a₂,
simp only [single_eq_same, single_eq_of_ne h, single_eq_of_ne (ne.symm h)] at h₁ h₂,
exact or.inr ⟨h₁, h₂.symm⟩ } },
{ rintros (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩),
{ refl },
{ rw [single_zero, single_zero] } }
end
lemma single_left_inj (h : b ≠ 0) :
single a b = single a' b ↔ a = a' :=
⟨λ H, by simpa only [h, single_eq_single_iff,
and_false, or_false, eq_self_iff_true, and_true] using H,
λ H, by rw [H]⟩
lemma support_single_ne_bot (i : α) (h : b ≠ 0) :
(single i b).support ≠ ⊥ :=
begin
have : i ∈ (single i b).support := by simpa using h,
intro H,
simpa [H]
end
lemma support_single_disjoint {b' : M} (hb : b ≠ 0) (hb' : b' ≠ 0) {i j : α} :
disjoint (single i b).support (single j b').support ↔ i ≠ j :=
by simpa [support_single_ne_zero, hb, hb'] using ne_comm
@[simp] lemma single_eq_zero : single a b = 0 ↔ b = 0 :=
by simp [ext_iff, single_eq_indicator]
lemma single_swap (a₁ a₂ : α) (b : M) : single a₁ b a₂ = single a₂ b a₁ :=
by simp only [single_apply]; ac_refl
instance [nonempty α] [nontrivial M] : nontrivial (α →₀ M) :=
begin
inhabit α,
rcases exists_ne (0 : M) with ⟨x, hx⟩,
exact nontrivial_of_ne (single (default α) x) 0 (mt single_eq_zero.1 hx)
end
lemma unique_single [unique α] (x : α →₀ M) : x = single (default α) (x (default α)) :=
ext $ unique.forall_iff.2 single_eq_same.symm
lemma unique_ext [unique α] {f g : α →₀ M} (h : f (default α) = g (default α)) : f = g :=
ext $ λ a, by rwa [unique.eq_default a]
lemma unique_ext_iff [unique α] {f g : α →₀ M} : f = g ↔ f (default α) = g (default α) :=
⟨λ h, h ▸ rfl, unique_ext⟩
@[simp] lemma unique_single_eq_iff [unique α] {b' : M} :
single a b = single a' b' ↔ b = b' :=
by rw [unique_ext_iff, unique.eq_default a, unique.eq_default a', single_eq_same, single_eq_same]
lemma support_eq_singleton {f : α →₀ M} {a : α} :
f.support = {a} ↔ f a ≠ 0 ∧ f = single a (f a) :=
⟨λ h, ⟨mem_support_iff.1 $ h.symm ▸ finset.mem_singleton_self a,
eq_single_iff.2 ⟨subset_of_eq h, rfl⟩⟩, λ h, h.2.symm ▸ support_single_ne_zero h.1⟩
lemma support_eq_singleton' {f : α →₀ M} {a : α} :
f.support = {a} ↔ ∃ b ≠ 0, f = single a b :=
⟨λ h, let h := support_eq_singleton.1 h in ⟨_, h.1, h.2⟩,
λ ⟨b, hb, hf⟩, hf.symm ▸ support_single_ne_zero hb⟩
lemma card_support_eq_one {f : α →₀ M} : card f.support = 1 ↔ ∃ a, f a ≠ 0 ∧ f = single a (f a) :=
by simp only [card_eq_one, support_eq_singleton]
lemma card_support_eq_one' {f : α →₀ M} : card f.support = 1 ↔ ∃ a (b ≠ 0), f = single a b :=
by simp only [card_eq_one, support_eq_singleton']
end single
/-! ### Declarations about `on_finset` -/
section on_finset
variables [has_zero M]
/-- `on_finset s f hf` is the finsupp function representing `f` restricted to the finset `s`.
The function needs to be `0` outside of `s`. Use this when the set needs to be filtered anyways,
otherwise a better set representation is often available. -/
def on_finset (s : finset α) (f : α → M) (hf : ∀a, f a ≠ 0 → a ∈ s) : α →₀ M :=
⟨s.filter (λa, f a ≠ 0), f, by simpa⟩
@[simp] lemma on_finset_apply {s : finset α} {f : α → M} {hf a} :
(on_finset s f hf : α →₀ M) a = f a :=
rfl
@[simp] lemma support_on_finset_subset {s : finset α} {f : α → M} {hf} :
(on_finset s f hf).support ⊆ s :=
filter_subset _ _
@[simp] lemma mem_support_on_finset
{s : finset α} {f : α → M} (hf : ∀ (a : α), f a ≠ 0 → a ∈ s) {a : α} :
a ∈ (finsupp.on_finset s f hf).support ↔ f a ≠ 0 :=
by rw [finsupp.mem_support_iff, finsupp.on_finset_apply]
lemma support_on_finset
{s : finset α} {f : α → M} (hf : ∀ (a : α), f a ≠ 0 → a ∈ s) :
(finsupp.on_finset s f hf).support = s.filter (λ a, f a ≠ 0) :=
rfl
end on_finset
section of_support_finite
variables [has_zero M]
/-- The natural `finsupp` induced by the function `f` given that it has finite support. -/
noncomputable def of_support_finite
(f : α → M) (hf : (function.support f).finite) : α →₀ M :=
{ support := hf.to_finset,
to_fun := f,
mem_support_to_fun := λ _, hf.mem_to_finset }
lemma of_support_finite_coe {f : α → M} {hf : (function.support f).finite} :
(of_support_finite f hf : α → M) = f := rfl
instance : can_lift (α → M) (α →₀ M) :=
{ coe := coe_fn,
cond := λ f, (function.support f).finite,
prf := λ f hf, ⟨of_support_finite f hf, rfl⟩ }
end of_support_finite
/-! ### Declarations about `map_range` -/
section map_range
variables [has_zero M] [has_zero N]
/-- The composition of `f : M → N` and `g : α →₀ M` is
`map_range f hf g : α →₀ N`, well-defined when `f 0 = 0`. -/
def map_range (f : M → N) (hf : f 0 = 0) (g : α →₀ M) : α →₀ N :=
on_finset g.support (f ∘ g) $
assume a, by rw [mem_support_iff, not_imp_not]; exact λ H, (congr_arg f H).trans hf
@[simp] lemma map_range_apply {f : M → N} {hf : f 0 = 0} {g : α →₀ M} {a : α} :
map_range f hf g a = f (g a) :=
rfl
@[simp] lemma map_range_zero {f : M → N} {hf : f 0 = 0} : map_range f hf (0 : α →₀ M) = 0 :=
ext $ λ a, by simp only [hf, zero_apply, map_range_apply]
lemma support_map_range {f : M → N} {hf : f 0 = 0} {g : α →₀ M} :
(map_range f hf g).support ⊆ g.support :=
support_on_finset_subset
@[simp] lemma map_range_single {f : M → N} {hf : f 0 = 0} {a : α} {b : M} :
map_range f hf (single a b) = single a (f b) :=
ext $ λ a', show f (ite _ _ _) = ite _ _ _, by split_ifs; [refl, exact hf]
end map_range
/-! ### Declarations about `emb_domain` -/
section emb_domain
variables [has_zero M] [has_zero N]
/-- Given `f : α ↪ β` and `v : α →₀ M`, `emb_domain f v : β →₀ M`
is the finitely supported function whose value at `f a : β` is `v a`.
For a `b : β` outside the range of `f`, it is zero. -/
def emb_domain (f : α ↪ β) (v : α →₀ M) : β →₀ M :=
begin
refine ⟨v.support.map f, λa₂,
if h : a₂ ∈ v.support.map f then v (v.support.choose (λa₁, f a₁ = a₂) _) else 0, _⟩,
{ rcases finset.mem_map.1 h with ⟨a, ha, rfl⟩,
exact exists_unique.intro a ⟨ha, rfl⟩ (assume b ⟨_, hb⟩, f.injective hb) },
{ assume a₂,
split_ifs,
{ simp only [h, true_iff, ne.def],
rw [← not_mem_support_iff, not_not],
apply finset.choose_mem },
{ simp only [h, ne.def, ne_self_iff_false] } }
end
@[simp] lemma support_emb_domain (f : α ↪ β) (v : α →₀ M) :
(emb_domain f v).support = v.support.map f :=
rfl
@[simp] lemma emb_domain_zero (f : α ↪ β) : (emb_domain f 0 : β →₀ M) = 0 :=
rfl
@[simp] lemma emb_domain_apply (f : α ↪ β) (v : α →₀ M) (a : α) :
emb_domain f v (f a) = v a :=
begin
change dite _ _ _ = _,
split_ifs; rw [finset.mem_map' f] at h,
{ refine congr_arg (v : α → M) (f.inj' _),
exact finset.choose_property (λa₁, f a₁ = f a) _ _ },
{ exact (not_mem_support_iff.1 h).symm }
end
lemma emb_domain_notin_range (f : α ↪ β) (v : α →₀ M) (a : β) (h : a ∉ set.range f) :
emb_domain f v a = 0 :=
begin
refine dif_neg (mt (assume h, _) h),
rcases finset.mem_map.1 h with ⟨a, h, rfl⟩,
exact set.mem_range_self a
end
lemma emb_domain_injective (f : α ↪ β) :
function.injective (emb_domain f : (α →₀ M) → (β →₀ M)) :=
λ l₁ l₂ h, ext $ λ a, by simpa only [emb_domain_apply] using ext_iff.1 h (f a)
@[simp] lemma emb_domain_inj {f : α ↪ β} {l₁ l₂ : α →₀ M} :
emb_domain f l₁ = emb_domain f l₂ ↔ l₁ = l₂ :=
(emb_domain_injective f).eq_iff
@[simp] lemma emb_domain_eq_zero {f : α ↪ β} {l : α →₀ M} :
emb_domain f l = 0 ↔ l = 0 :=
(emb_domain_injective f).eq_iff' $ emb_domain_zero f
lemma emb_domain_map_range
(f : α ↪ β) (g : M → N) (p : α →₀ M) (hg : g 0 = 0) :
emb_domain f (map_range g hg p) = map_range g hg (emb_domain f p) :=
begin
ext a,
by_cases a ∈ set.range f,
{ rcases h with ⟨a', rfl⟩,
rw [map_range_apply, emb_domain_apply, emb_domain_apply, map_range_apply] },
{ rw [map_range_apply, emb_domain_notin_range, emb_domain_notin_range, ← hg]; assumption }
end
lemma single_of_emb_domain_single
(l : α →₀ M) (f : α ↪ β) (a : β) (b : M) (hb : b ≠ 0)
(h : l.emb_domain f = single a b) :
∃ x, l = single x b ∧ f x = a :=
begin
have h_map_support : finset.map f (l.support) = {a},
by rw [←support_emb_domain, h, support_single_ne_zero hb]; refl,
have ha : a ∈ finset.map f (l.support),
by simp only [h_map_support, finset.mem_singleton],
rcases finset.mem_map.1 ha with ⟨c, hc₁, hc₂⟩,
use c,
split,
{ ext d,
rw [← emb_domain_apply f l, h],
by_cases h_cases : c = d,
{ simp only [eq.symm h_cases, hc₂, single_eq_same] },
{ rw [single_apply, single_apply, if_neg, if_neg h_cases],
by_contra hfd,
exact h_cases (f.injective (hc₂.trans hfd)) } },
{ exact hc₂ }
end
end emb_domain
/-! ### Declarations about `zip_with` -/
section zip_with
variables [has_zero M] [has_zero N] [has_zero P]
/-- `zip_with f hf g₁ g₂` is the finitely supported function satisfying
`zip_with f hf g₁ g₂ a = f (g₁ a) (g₂ a)`, and it is well-defined when `f 0 0 = 0`. -/
def zip_with (f : M → N → P) (hf : f 0 0 = 0) (g₁ : α →₀ M) (g₂ : α →₀ N) : (α →₀ P) :=
on_finset (g₁.support ∪ g₂.support) (λa, f (g₁ a) (g₂ a)) $ λ a H,
begin
simp only [mem_union, mem_support_iff, ne], rw [← not_and_distrib],
rintro ⟨h₁, h₂⟩, rw [h₁, h₂] at H, exact H hf
end
@[simp] lemma zip_with_apply
{f : M → N → P} {hf : f 0 0 = 0} {g₁ : α →₀ M} {g₂ : α →₀ N} {a : α} :
zip_with f hf g₁ g₂ a = f (g₁ a) (g₂ a) :=
rfl
lemma support_zip_with [D : decidable_eq α] {f : M → N → P} {hf : f 0 0 = 0}
{g₁ : α →₀ M} {g₂ : α →₀ N} : (zip_with f hf g₁ g₂).support ⊆ g₁.support ∪ g₂.support :=
by rw subsingleton.elim D; exact support_on_finset_subset
end zip_with
/-! ### Declarations about `erase` -/
section erase
variables [has_zero M]
/-- `erase a f` is the finitely supported function equal to `f` except at `a` where it is equal to
`0`. -/
def erase (a : α) (f : α →₀ M) : α →₀ M :=
⟨f.support.erase a, (λa', if a' = a then 0 else f a'),
assume a', by rw [mem_erase, mem_support_iff]; split_ifs;
[exact ⟨λ H _, H.1 h, λ H, (H rfl).elim⟩,
exact and_iff_right h]⟩
@[simp] lemma support_erase {a : α} {f : α →₀ M} :
(f.erase a).support = f.support.erase a :=
rfl
@[simp] lemma erase_same {a : α} {f : α →₀ M} : (f.erase a) a = 0 :=
if_pos rfl
@[simp] lemma erase_ne {a a' : α} {f : α →₀ M} (h : a' ≠ a) : (f.erase a) a' = f a' :=
if_neg h
@[simp] lemma erase_single {a : α} {b : M} : (erase a (single a b)) = 0 :=
begin
ext s, by_cases hs : s = a,
{ rw [hs, erase_same], refl },
{ rw [erase_ne hs], exact single_eq_of_ne (ne.symm hs) }
end
lemma erase_single_ne {a a' : α} {b : M} (h : a ≠ a') : (erase a (single a' b)) = single a' b :=
begin
ext s, by_cases hs : s = a,
{ rw [hs, erase_same, single_eq_of_ne (h.symm)] },
{ rw [erase_ne hs] }
end
@[simp] lemma erase_zero (a : α) : erase a (0 : α →₀ M) = 0 :=
by rw [← support_eq_empty, support_erase, support_zero, erase_empty]
end erase
/-!
### Declarations about `sum` and `prod`
In most of this section, the domain `β` is assumed to be an `add_monoid`.
-/
section sum_prod
-- [to_additive sum] for finsupp.prod doesn't work, the equation lemmas are not generated
/-- `sum f g` is the sum of `g a (f a)` over the support of `f`. -/
def sum [has_zero M] [add_comm_monoid N] (f : α →₀ M) (g : α → M → N) : N :=
∑ a in f.support, g a (f a)
/-- `prod f g` is the product of `g a (f a)` over the support of `f`. -/
@[to_additive]
def prod [has_zero M] [comm_monoid N] (f : α →₀ M) (g : α → M → N) : N :=
∏ a in f.support, g a (f a)
variables [has_zero M] [has_zero M'] [comm_monoid N]
@[to_additive]
lemma prod_of_support_subset (f : α →₀ M) {s : finset α}
(hs : f.support ⊆ s) (g : α → M → N) (h : ∀ i ∈ s, g i 0 = 1) :
f.prod g = ∏ x in s, g x (f x) :=
finset.prod_subset hs $ λ x hxs hx, h x hxs ▸ congr_arg (g x) $ not_mem_support_iff.1 hx
@[to_additive]
lemma prod_fintype [fintype α] (f : α →₀ M) (g : α → M → N) (h : ∀ i, g i 0 = 1) :
f.prod g = ∏ i, g i (f i) :=
f.prod_of_support_subset (subset_univ _) g (λ x _, h x)
@[simp, to_additive]
lemma prod_single_index {a : α} {b : M} {h : α → M → N} (h_zero : h a 0 = 1) :
(single a b).prod h = h a b :=
calc (single a b).prod h = ∏ x in {a}, h x (single a b x) :
prod_of_support_subset _ support_single_subset h $ λ x hx, (mem_singleton.1 hx).symm ▸ h_zero
... = h a b : by simp
@[to_additive]
lemma prod_map_range_index {f : M → M'} {hf : f 0 = 0} {g : α →₀ M} {h : α → M' → N}
(h0 : ∀a, h a 0 = 1) : (map_range f hf g).prod h = g.prod (λa b, h a (f b)) :=
finset.prod_subset support_map_range $ λ _ _ H,
by rw [not_mem_support_iff.1 H, h0]
@[simp, to_additive]
lemma prod_zero_index {h : α → M → N} : (0 : α →₀ M).prod h = 1 := rfl
@[to_additive]
lemma prod_comm (f : α →₀ M) (g : β →₀ M') (h : α → M → β → M' → N) :
f.prod (λ x v, g.prod (λ x' v', h x v x' v')) = g.prod (λ x' v', f.prod (λ x v, h x v x' v')) :=
finset.prod_comm
@[simp, to_additive]
lemma prod_ite_eq [decidable_eq α] (f : α →₀ M) (a : α) (b : α → M → N) :
f.prod (λ x v, ite (a = x) (b x v) 1) = ite (a ∈ f.support) (b a (f a)) 1 :=
by { dsimp [finsupp.prod], rw f.support.prod_ite_eq, }
@[simp] lemma sum_ite_self_eq
[decidable_eq α] {N : Type*} [add_comm_monoid N] (f : α →₀ N) (a : α) :
f.sum (λ x v, ite (a = x) v 0) = f a :=
by { convert f.sum_ite_eq a (λ x, id), simp [ite_eq_right_iff.2 eq.symm] }
/-- A restatement of `prod_ite_eq` with the equality test reversed. -/
@[simp, to_additive "A restatement of `sum_ite_eq` with the equality test reversed."]
lemma prod_ite_eq' [decidable_eq α] (f : α →₀ M) (a : α) (b : α → M → N) :
f.prod (λ x v, ite (x = a) (b x v) 1) = ite (a ∈ f.support) (b a (f a)) 1 :=
by { dsimp [finsupp.prod], rw f.support.prod_ite_eq', }
@[simp] lemma sum_ite_self_eq'
[decidable_eq α] {N : Type*} [add_comm_monoid N] (f : α →₀ N) (a : α) :
f.sum (λ x v, ite (x = a) v 0) = f a :=
by { convert f.sum_ite_eq' a (λ x, id), simp [ite_eq_right_iff.2 eq.symm] }
@[simp] lemma prod_pow [fintype α] (f : α →₀ ℕ) (g : α → N) :
f.prod (λ a b, g a ^ b) = ∏ a, g a ^ (f a) :=
f.prod_fintype _ $ λ a, pow_zero _
/-- If `g` maps a second argument of 0 to 1, then multiplying it over the
result of `on_finset` is the same as multiplying it over the original
`finset`. -/
@[to_additive "If `g` maps a second argument of 0 to 0, summing it over the
result of `on_finset` is the same as summing it over the original
`finset`."]
lemma on_finset_prod {s : finset α} {f : α → M} {g : α → M → N}
(hf : ∀a, f a ≠ 0 → a ∈ s) (hg : ∀ a, g a 0 = 1) :
(on_finset s f hf).prod g = ∏ a in s, g a (f a) :=
finset.prod_subset support_on_finset_subset $ by simp [*] { contextual := tt }
end sum_prod
/-!
### Additive monoid structure on `α →₀ M`
-/
section add_monoid
variables [add_monoid M]
instance : has_add (α →₀ M) := ⟨zip_with (+) (add_zero 0)⟩
@[simp] lemma coe_add (f g : α →₀ M) : ⇑(f + g) = f + g := rfl
lemma add_apply (g₁ g₂ : α →₀ M) (a : α) : (g₁ + g₂) a = g₁ a + g₂ a := rfl
lemma support_add [decidable_eq α] {g₁ g₂ : α →₀ M} :
(g₁ + g₂).support ⊆ g₁.support ∪ g₂.support :=
support_zip_with
lemma support_add_eq [decidable_eq α] {g₁ g₂ : α →₀ M} (h : disjoint g₁.support g₂.support) :
(g₁ + g₂).support = g₁.support ∪ g₂.support :=
le_antisymm support_zip_with $ assume a ha,
(finset.mem_union.1 ha).elim
(assume ha, have a ∉ g₂.support, from disjoint_left.1 h ha,
by simp only [mem_support_iff, not_not] at *;
simpa only [add_apply, this, add_zero])
(assume ha, have a ∉ g₁.support, from disjoint_right.1 h ha,
by simp only [mem_support_iff, not_not] at *;
simpa only [add_apply, this, zero_add])
@[simp] lemma single_add {a : α} {b₁ b₂ : M} : single a (b₁ + b₂) = single a b₁ + single a b₂ :=
ext $ assume a',
begin
by_cases h : a = a',
{ rw [h, add_apply, single_eq_same, single_eq_same, single_eq_same] },
{ rw [add_apply, single_eq_of_ne h, single_eq_of_ne h, single_eq_of_ne h, zero_add] }
end
instance : add_monoid (α →₀ M) :=
{ add_monoid .
zero := 0,
add := (+),
add_assoc := assume ⟨s, f, hf⟩ ⟨t, g, hg⟩ ⟨u, h, hh⟩, ext $ assume a, add_assoc _ _ _,
zero_add := assume ⟨s, f, hf⟩, ext $ assume a, zero_add _,
add_zero := assume ⟨s, f, hf⟩, ext $ assume a, add_zero _ }
/-- `finsupp.single` as an `add_monoid_hom`.
See `finsupp.lsingle` for the stronger version as a linear map.
-/
@[simps] def single_add_hom (a : α) : M →+ α →₀ M :=
⟨single a, single_zero, λ _ _, single_add⟩
/-- Evaluation of a function `f : α →₀ M` at a point as an additive monoid homomorphism.
See `finsupp.lapply` for the stronger version as a linear map. -/
@[simps apply]
def apply_add_hom (a : α) : (α →₀ M) →+ M := ⟨λ g, g a, zero_apply, λ _ _, add_apply _ _ _⟩
lemma single_add_erase (a : α) (f : α →₀ M) : single a (f a) + f.erase a = f :=
ext $ λ a',
if h : a = a' then by subst h; simp only [add_apply, single_eq_same, erase_same, add_zero]
else by simp only [add_apply, single_eq_of_ne h, zero_add, erase_ne (ne.symm h)]
lemma erase_add_single (a : α) (f : α →₀ M) : f.erase a + single a (f a) = f :=
ext $ λ a',
if h : a = a' then by subst h; simp only [add_apply, single_eq_same, erase_same, zero_add]
else by simp only [add_apply, single_eq_of_ne h, add_zero, erase_ne (ne.symm h)]
@[simp] lemma erase_add (a : α) (f f' : α →₀ M) : erase a (f + f') = erase a f + erase a f' :=
begin
ext s, by_cases hs : s = a,
{ rw [hs, add_apply, erase_same, erase_same, erase_same, add_zero] },
rw [add_apply, erase_ne hs, erase_ne hs, erase_ne hs, add_apply],
end
@[elab_as_eliminator]
protected theorem induction {p : (α →₀ M) → Prop} (f : α →₀ M)
(h0 : p 0) (ha : ∀a b (f : α →₀ M), a ∉ f.support → b ≠ 0 → p f → p (single a b + f)) :
p f :=
suffices ∀s (f : α →₀ M), f.support = s → p f, from this _ _ rfl,
assume s, finset.induction_on s (λ f hf, by rwa [support_eq_empty.1 hf]) $
assume a s has ih f hf,
suffices p (single a (f a) + f.erase a), by rwa [single_add_erase] at this,
begin
apply ha,
{ rw [support_erase, mem_erase], exact λ H, H.1 rfl },
{ rw [← mem_support_iff, hf], exact mem_insert_self _ _ },
{ apply ih _ _,
rw [support_erase, hf, finset.erase_insert has] }
end
lemma induction₂ {p : (α →₀ M) → Prop} (f : α →₀ M)
(h0 : p 0) (ha : ∀a b (f : α →₀ M), a ∉ f.support → b ≠ 0 → p f → p (f + single a b)) :
p f :=
suffices ∀s (f : α →₀ M), f.support = s → p f, from this _ _ rfl,
assume s, finset.induction_on s (λ f hf, by rwa [support_eq_empty.1 hf]) $
assume a s has ih f hf,
suffices p (f.erase a + single a (f a)), by rwa [erase_add_single] at this,
begin
apply ha,
{ rw [support_erase, mem_erase], exact λ H, H.1 rfl },
{ rw [← mem_support_iff, hf], exact mem_insert_self _ _ },
{ apply ih _ _,
rw [support_erase, hf, finset.erase_insert has] }
end
lemma induction_linear {p : (α →₀ M) → Prop} (f : α →₀ M)
(h0 : p 0) (hadd : ∀ f g : α →₀ M, p f → p g → p (f + g)) (hsingle : ∀ a b, p (single a b)) :
p f :=
induction₂ f h0 (λ a b f _ _ w, hadd _ _ w (hsingle _ _))
@[simp] lemma add_closure_Union_range_single :
add_submonoid.closure (⋃ a : α, set.range (single a : M → α →₀ M)) = ⊤ :=
top_unique $ λ x hx, finsupp.induction x (add_submonoid.zero_mem _) $
λ a b f ha hb hf, add_submonoid.add_mem _
(add_submonoid.subset_closure $ set.mem_Union.2 ⟨a, set.mem_range_self _⟩) hf
/-- If two additive homomorphisms from `α →₀ M` are equal on each `single a b`, then
they are equal. -/
lemma add_hom_ext [add_monoid N] ⦃f g : (α →₀ M) →+ N⦄
(H : ∀ x y, f (single x y) = g (single x y)) :
f = g :=
begin
refine add_monoid_hom.eq_of_eq_on_mdense add_closure_Union_range_single (λ f hf, _),
simp only [set.mem_Union, set.mem_range] at hf,
rcases hf with ⟨x, y, rfl⟩,
apply H
end
/-- If two additive homomorphisms from `α →₀ M` are equal on each `single a b`, then
they are equal.
We formulate this using equality of `add_monoid_hom`s so that `ext` tactic can apply a type-specific
extensionality lemma after this one. E.g., if the fiber `M` is `ℕ` or `ℤ`, then it suffices to
verify `f (single a 1) = g (single a 1)`. -/
@[ext] lemma add_hom_ext' [add_monoid N] ⦃f g : (α →₀ M) →+ N⦄
(H : ∀ x, f.comp (single_add_hom x) = g.comp (single_add_hom x)) :
f = g :=
add_hom_ext $ λ x, add_monoid_hom.congr_fun (H x)
lemma mul_hom_ext [monoid N] ⦃f g : multiplicative (α →₀ M) →* N⦄
(H : ∀ x y, f (multiplicative.of_add $ single x y) = g (multiplicative.of_add $ single x y)) :
f = g :=
monoid_hom.ext $ add_monoid_hom.congr_fun $
@add_hom_ext α M (additive N) _ _ f.to_additive'' g.to_additive'' H
@[ext] lemma mul_hom_ext' [monoid N] {f g : multiplicative (α →₀ M) →* N}
(H : ∀ x, f.comp (single_add_hom x).to_multiplicative =
g.comp (single_add_hom x).to_multiplicative) :
f = g :=
mul_hom_ext $ λ x, monoid_hom.congr_fun (H x)
lemma map_range_add [add_monoid N]
{f : M → N} {hf : f 0 = 0} (hf' : ∀ x y, f (x + y) = f x + f y) (v₁ v₂ : α →₀ M) :
map_range f hf (v₁ + v₂) = map_range f hf v₁ + map_range f hf v₂ :=
ext $ λ a, by simp only [hf', add_apply, map_range_apply]
end add_monoid
end finsupp
@[to_additive]
lemma mul_equiv.map_finsupp_prod [has_zero M] [comm_monoid N] [comm_monoid P]
(h : N ≃* P) (f : α →₀ M) (g : α → M → N) : h (f.prod g) = f.prod (λ a b, h (g a b)) :=
h.map_prod _ _
@[to_additive]
lemma monoid_hom.map_finsupp_prod [has_zero M] [comm_monoid N] [comm_monoid P]
(h : N →* P) (f : α →₀ M) (g : α → M → N) : h (f.prod g) = f.prod (λ a b, h (g a b)) :=
h.map_prod _ _
lemma ring_hom.map_finsupp_sum [has_zero M] [semiring R] [semiring S]
(h : R →+* S) (f : α →₀ M) (g : α → M → R) : h (f.sum g) = f.sum (λ a b, h (g a b)) :=
h.map_sum _ _
lemma ring_hom.map_finsupp_prod [has_zero M] [comm_semiring R] [comm_semiring S]
(h : R →+* S) (f : α →₀ M) (g : α → M → R) : h (f.prod g) = f.prod (λ a b, h (g a b)) :=
h.map_prod _ _
@[to_additive]
lemma monoid_hom.coe_finsupp_prod [has_zero β] [monoid N] [comm_monoid P]
(f : α →₀ β) (g : α → β → N →* P) :
⇑(f.prod g) = f.prod (λ i fi, g i fi) :=
monoid_hom.coe_prod _ _
@[simp, to_additive]
lemma monoid_hom.finsupp_prod_apply [has_zero β] [monoid N] [comm_monoid P]
(f : α →₀ β) (g : α → β → N →* P) (x : N) :
f.prod g x = f.prod (λ i fi, g i fi x) :=
monoid_hom.finset_prod_apply _ _ _
namespace finsupp
section nat_sub
instance nat_sub : has_sub (α →₀ ℕ) := ⟨zip_with (λ m n, m - n) (nat.sub_zero 0)⟩
@[simp] lemma coe_nat_sub (g₁ g₂ : α →₀ ℕ) : ⇑(g₁ - g₂) = g₁ - g₂ := rfl
lemma nat_sub_apply (g₁ g₂ : α →₀ ℕ) (a : α) : (g₁ - g₂) a = g₁ a - g₂ a := rfl
@[simp] lemma single_sub {a : α} {n₁ n₂ : ℕ} : single a (n₁ - n₂) = single a n₁ - single a n₂ :=
begin
ext f,
by_cases h : (a = f),
{ rw [h, nat_sub_apply, single_eq_same, single_eq_same, single_eq_same] },
rw [nat_sub_apply, single_eq_of_ne h, single_eq_of_ne h, single_eq_of_ne h]
end
-- These next two lemmas are used in developing
-- the partial derivative on `mv_polynomial`.
lemma sub_single_one_add {a : α} {u u' : α →₀ ℕ} (h : u a ≠ 0) :
u - single a 1 + u' = u + u' - single a 1 :=
begin
ext b,
rw [add_apply, nat_sub_apply, nat_sub_apply, add_apply],
by_cases h : a = b,
{ rw [←h, single_eq_same], cases (u a), { contradiction }, { simp }, },
{ simp [h], }
end
lemma add_sub_single_one {a : α} {u u' : α →₀ ℕ} (h : u' a ≠ 0) :
u + (u' - single a 1) = u + u' - single a 1 :=
begin
ext b,
rw [add_apply, nat_sub_apply, nat_sub_apply, add_apply],
by_cases h : a = b,
{ rw [←h, single_eq_same], cases (u' a), { contradiction }, { simp }, },
{ simp [h], }
end
@[simp] lemma nat_zero_sub (f : α →₀ ℕ) : 0 - f = 0 := ext $ λ x, nat.zero_sub _
end nat_sub
instance [add_comm_monoid M] : add_comm_monoid (α →₀ M) :=
{ add_comm := assume ⟨s, f, _⟩ ⟨t, g, _⟩, ext $ assume a, add_comm _ _,
.. finsupp.add_monoid }
instance [add_group G] : has_sub (α →₀ G) := ⟨zip_with has_sub.sub (sub_zero _)⟩
instance [add_group G] : add_group (α →₀ G) :=
{ neg := map_range (has_neg.neg) neg_zero,
sub := has_sub.sub,
sub_eq_add_neg := λ x y, ext (λ i, sub_eq_add_neg _ _),
add_left_neg := assume ⟨s, f, _⟩, ext $ assume x, add_left_neg _,
.. finsupp.add_monoid }
instance [add_comm_group G] : add_comm_group (α →₀ G) :=
{ add_comm := add_comm, ..finsupp.add_group }
lemma single_multiset_sum [add_comm_monoid M] (s : multiset M) (a : α) :
single a s.sum = (s.map (single a)).sum :=
multiset.induction_on s single_zero $ λ a s ih,
by rw [multiset.sum_cons, single_add, ih, multiset.map_cons, multiset.sum_cons]
lemma single_finset_sum [add_comm_monoid M] (s : finset ι) (f : ι → M) (a : α) :
single a (∑ b in s, f b) = ∑ b in s, single a (f b) :=
begin
transitivity,
apply single_multiset_sum,
rw [multiset.map_map],
refl
end
lemma single_sum [has_zero M] [add_comm_monoid N] (s : ι →₀ M) (f : ι → M → N) (a : α) :
single a (s.sum f) = s.sum (λd c, single a (f d c)) :=
single_finset_sum _ _ _
@[to_additive]
lemma prod_neg_index [add_group G] [comm_monoid M] {g : α →₀ G} {h : α → G → M}
(h0 : ∀a, h a 0 = 1) :
(-g).prod h = g.prod (λa b, h a (- b)) :=
prod_map_range_index h0
@[simp] lemma coe_neg [add_group G] (g : α →₀ G) : ⇑(-g) = -g := rfl
lemma neg_apply [add_group G] (g : α →₀ G) (a : α) : (- g) a = - g a := rfl
@[simp] lemma coe_sub [add_group G] (g₁ g₂ : α →₀ G) : ⇑(g₁ - g₂) = g₁ - g₂ := rfl
lemma sub_apply [add_group G] (g₁ g₂ : α →₀ G) (a : α) : (g₁ - g₂) a = g₁ a - g₂ a := rfl
@[simp] lemma support_neg [add_group G] {f : α →₀ G} : support (-f) = support f :=
finset.subset.antisymm
support_map_range
(calc support f = support (- (- f)) : congr_arg support (neg_neg _).symm
... ⊆ support (- f) : support_map_range)
@[simp] lemma sum_apply [has_zero M] [add_comm_monoid N]
{f : α →₀ M} {g : α → M → β →₀ N} {a₂ : β} :
(f.sum g) a₂ = f.sum (λa₁ b, g a₁ b a₂) :=
(apply_add_hom a₂ : (β →₀ N) →+ _).map_sum _ _
lemma support_sum [decidable_eq β] [has_zero M] [add_comm_monoid N]
{f : α →₀ M} {g : α → M → (β →₀ N)} :
(f.sum g).support ⊆ f.support.bUnion (λa, (g a (f a)).support) :=
have ∀ c, f.sum (λ a b, g a b c) ≠ 0 → (∃ a, f a ≠ 0 ∧ ¬ (g a (f a)) c = 0),
from assume a₁ h,
let ⟨a, ha, ne⟩ := finset.exists_ne_zero_of_sum_ne_zero h in
⟨a, mem_support_iff.mp ha, ne⟩,
by simpa only [finset.subset_iff, mem_support_iff, finset.mem_bUnion, sum_apply, exists_prop]
@[simp] lemma sum_zero [has_zero M] [add_comm_monoid N] {f : α →₀ M} :
f.sum (λa b, (0 : N)) = 0 :=
finset.sum_const_zero
@[simp, to_additive]
lemma prod_mul [has_zero M] [comm_monoid N] {f : α →₀ M} {h₁ h₂ : α → M → N} :
f.prod (λa b, h₁ a b * h₂ a b) = f.prod h₁ * f.prod h₂ :=
finset.prod_mul_distrib
@[simp, to_additive]
lemma prod_inv [has_zero M] [comm_group G] {f : α →₀ M}
{h : α → M → G} : f.prod (λa b, (h a b)⁻¹) = (f.prod h)⁻¹ :=
(((monoid_hom.id G)⁻¹).map_prod _ _).symm
@[simp] lemma sum_sub [has_zero M] [add_comm_group G] {f : α →₀ M}
{h₁ h₂ : α → M → G} :
f.sum (λa b, h₁ a b - h₂ a b) = f.sum h₁ - f.sum h₂ :=
finset.sum_sub_distrib
@[to_additive]
lemma prod_add_index [add_comm_monoid M] [comm_monoid N] {f g : α →₀ M}
{h : α → M → N} (h_zero : ∀a, h a 0 = 1) (h_add : ∀a b₁ b₂, h a (b₁ + b₂) = h a b₁ * h a b₂) :
(f + g).prod h = f.prod h * g.prod h :=
have hf : f.prod h = ∏ a in f.support ∪ g.support, h a (f a),
from f.prod_of_support_subset (subset_union_left _ _) _ $ λ a ha, h_zero a,
have hg : g.prod h = ∏ a in f.support ∪ g.support, h a (g a),
from g.prod_of_support_subset (subset_union_right _ _) _ $ λ a ha, h_zero a,
have hfg : (f + g).prod h = ∏ a in f.support ∪ g.support, h a ((f + g) a),
from (f + g).prod_of_support_subset support_add _ $ λ a ha, h_zero a,
by simp only [*, add_apply, prod_mul_distrib]
@[simp]
lemma sum_add_index' [add_comm_monoid M] [add_comm_monoid N] {f g : α →₀ M} (h : α → M →+ N) :
(f + g).sum (λ x, h x) = f.sum (λ x, h x) + g.sum (λ x, h x) :=
sum_add_index (λ a, (h a).map_zero) (λ a, (h a).map_add)
@[simp]
lemma prod_add_index' [add_comm_monoid M] [comm_monoid N] {f g : α →₀ M}
(h : α → multiplicative M →* N) :
(f + g).prod (λ a b, h a (multiplicative.of_add b)) =
f.prod (λ a b, h a (multiplicative.of_add b)) * g.prod (λ a b, h a (multiplicative.of_add b)) :=
prod_add_index (λ a, (h a).map_one) (λ a, (h a).map_mul)
/-- The canonical isomorphism between families of additive monoid homomorphisms `α → (M →+ N)`
and monoid homomorphisms `(α →₀ M) →+ N`. -/
def lift_add_hom [add_comm_monoid M] [add_comm_monoid N] : (α → M →+ N) ≃+ ((α →₀ M) →+ N) :=
{ to_fun := λ F,
{ to_fun := λ f, f.sum (λ x, F x),
map_zero' := finset.sum_empty,
map_add' := λ _ _, sum_add_index (λ x, (F x).map_zero) (λ x, (F x).map_add) },
inv_fun := λ F x, F.comp $ single_add_hom x,
left_inv := λ F, by { ext, simp },
right_inv := λ F, by { ext, simp },
map_add' := λ F G, by { ext, simp } }
@[simp] lemma lift_add_hom_apply [add_comm_monoid M] [add_comm_monoid N]
(F : α → M →+ N) (f : α →₀ M) :
lift_add_hom F f = f.sum (λ x, F x) :=
rfl
@[simp] lemma lift_add_hom_symm_apply [add_comm_monoid M] [add_comm_monoid N]
(F : (α →₀ M) →+ N) (x : α) :
lift_add_hom.symm F x = F.comp (single_add_hom x) :=
rfl
lemma lift_add_hom_symm_apply_apply [add_comm_monoid M] [add_comm_monoid N]
(F : (α →₀ M) →+ N) (x : α) (y : M) :
lift_add_hom.symm F x y = F (single x y) :=
rfl
@[simp] lemma lift_add_hom_single_add_hom [add_comm_monoid M] :
lift_add_hom (single_add_hom : α → M →+ α →₀ M) = add_monoid_hom.id _ :=
lift_add_hom.to_equiv.apply_eq_iff_eq_symm_apply.2 rfl
@[simp] lemma sum_single [add_comm_monoid M] (f : α →₀ M) :
f.sum single = f :=
add_monoid_hom.congr_fun lift_add_hom_single_add_hom f
@[simp] lemma lift_add_hom_apply_single [add_comm_monoid M] [add_comm_monoid N]
(f : α → M →+ N) (a : α) (b : M) :
lift_add_hom f (single a b) = f a b :=
sum_single_index (f a).map_zero
@[simp] lemma lift_add_hom_comp_single [add_comm_monoid M] [add_comm_monoid N] (f : α → M →+ N)
(a : α) :
(lift_add_hom f).comp (single_add_hom a) = f a :=
add_monoid_hom.ext $ λ b, lift_add_hom_apply_single f a b
lemma comp_lift_add_hom [add_comm_monoid M] [add_comm_monoid N] [add_comm_monoid P]
(g : N →+ P) (f : α → M →+ N) :
g.comp (lift_add_hom f) = lift_add_hom (λ a, g.comp (f a)) :=
lift_add_hom.symm_apply_eq.1 $ funext $ λ a,
by rw [lift_add_hom_symm_apply, add_monoid_hom.comp_assoc, lift_add_hom_comp_single]
lemma sum_sub_index [add_comm_group β] [add_comm_group γ] {f g : α →₀ β}
{h : α → β → γ} (h_sub : ∀a b₁ b₂, h a (b₁ - b₂) = h a b₁ - h a b₂) :
(f - g).sum h = f.sum h - g.sum h :=
(lift_add_hom (λ a, add_monoid_hom.of_map_sub (h a) (h_sub a))).map_sub f g
@[to_additive]
lemma prod_emb_domain [has_zero M] [comm_monoid N] {v : α →₀ M} {f : α ↪ β} {g : β → M → N} :
(v.emb_domain f).prod g = v.prod (λ a b, g (f a) b) :=
begin
rw [prod, prod, support_emb_domain, finset.prod_map],
simp_rw emb_domain_apply,
end
@[to_additive]
lemma prod_finset_sum_index [add_comm_monoid M] [comm_monoid N]
{s : finset ι} {g : ι → α →₀ M}
{h : α → M → N} (h_zero : ∀a, h a 0 = 1) (h_add : ∀a b₁ b₂, h a (b₁ + b₂) = h a b₁ * h a b₂) :
∏ i in s, (g i).prod h = (∑ i in s, g i).prod h :=
finset.induction_on s rfl $ λ a s has ih,
by rw [prod_insert has, ih, sum_insert has, prod_add_index h_zero h_add]
@[to_additive]
lemma prod_sum_index
[add_comm_monoid M] [add_comm_monoid N] [comm_monoid P]
{f : α →₀ M} {g : α → M → β →₀ N}
{h : β → N → P} (h_zero : ∀a, h a 0 = 1) (h_add : ∀a b₁ b₂, h a (b₁ + b₂) = h a b₁ * h a b₂) :
(f.sum g).prod h = f.prod (λa b, (g a b).prod h) :=
(prod_finset_sum_index h_zero h_add).symm
lemma multiset_sum_sum_index
[add_comm_monoid M] [add_comm_monoid N]
(f : multiset (α →₀ M)) (h : α → M → N)
(h₀ : ∀a, h a 0 = 0) (h₁ : ∀ (a : α) (b₁ b₂ : M), h a (b₁ + b₂) = h a b₁ + h a b₂) :
(f.sum.sum h) = (f.map $ λg:α →₀ M, g.sum h).sum :=
multiset.induction_on f rfl $ assume a s ih,
by rw [multiset.sum_cons, multiset.map_cons, multiset.sum_cons, sum_add_index h₀ h₁, ih]
lemma support_sum_eq_bUnion {α : Type*} {ι : Type*} {M : Type*} [add_comm_monoid M]
{g : ι → α →₀ M} (s : finset ι) (h : ∀ i₁ i₂, i₁ ≠ i₂ → disjoint (g i₁).support (g i₂).support) :
(∑ i in s, g i).support = s.bUnion (λ i, (g i).support) :=
begin
apply finset.induction_on s,
{ simp },
{ intros i s hi,
simp only [hi, sum_insert, not_false_iff, bUnion_insert],
intro hs,
rw [finsupp.support_add_eq, hs],
rw [hs],
intros x hx,
simp only [mem_bUnion, exists_prop, inf_eq_inter, ne.def, mem_inter] at hx,
obtain ⟨hxi, j, hj, hxj⟩ := hx,
have hn : i ≠ j := λ H, hi (H.symm ▸ hj),
apply h _ _ hn,
simp [hxi, hxj] }
end
lemma multiset_map_sum [has_zero M] {f : α →₀ M} {m : β → γ} {h : α → M → multiset β} :
multiset.map m (f.sum h) = f.sum (λa b, (h a b).map m) :=
(f.support.sum_hom _).symm
lemma multiset_sum_sum [has_zero M] [add_comm_monoid N] {f : α →₀ M} {h : α → M → multiset N} :
multiset.sum (f.sum h) = f.sum (λa b, multiset.sum (h a b)) :=
(f.support.sum_hom multiset.sum).symm
section map_range
variables
[add_comm_monoid M] [add_comm_monoid N] (f : M →+ N)
/--
Composition with a fixed additive homomorphism is itself an additive homomorphism on functions.
-/
def map_range.add_monoid_hom : (α →₀ M) →+ (α →₀ N) :=
{ to_fun := (map_range f f.map_zero : (α →₀ M) → (α →₀ N)),
map_zero' := map_range_zero,
map_add' := λ a b, map_range_add f.map_add _ _ }
lemma map_range_multiset_sum (m : multiset (α →₀ M)) :
map_range f f.map_zero m.sum = (m.map $ λx, map_range f f.map_zero x).sum :=
(m.sum_hom (map_range.add_monoid_hom f)).symm
lemma map_range_finset_sum (s : finset ι) (g : ι → (α →₀ M)) :
map_range f f.map_zero (∑ x in s, g x) = ∑ x in s, map_range f f.map_zero (g x) :=
by rw [finset.sum.equations._eqn_1, map_range_multiset_sum, multiset.map_map]; refl
end map_range
/-! ### Declarations about `map_domain` -/
section map_domain
variables [add_comm_monoid M] {v v₁ v₂ : α →₀ M}
/-- Given `f : α → β` and `v : α →₀ M`, `map_domain f v : β →₀ M`
is the finitely supported function whose value at `a : β` is the sum
of `v x` over all `x` such that `f x = a`. -/
def map_domain (f : α → β) (v : α →₀ M) : β →₀ M :=
v.sum $ λa, single (f a)
lemma map_domain_apply {f : α → β} (hf : function.injective f) (x : α →₀ M) (a : α) :
map_domain f x (f a) = x a :=
begin
rw [map_domain, sum_apply, sum, finset.sum_eq_single a, single_eq_same],
{ assume b _ hba, exact single_eq_of_ne (hf.ne hba) },
{ assume h, rw [not_mem_support_iff.1 h, single_zero, zero_apply] }
end
lemma map_domain_notin_range {f : α → β} (x : α →₀ M) (a : β) (h : a ∉ set.range f) :
map_domain f x a = 0 :=
begin
rw [map_domain, sum_apply, sum],
exact finset.sum_eq_zero
(assume a' h', single_eq_of_ne $ assume eq, h $ eq ▸ set.mem_range_self _)
end
lemma map_domain_id : map_domain id v = v :=
sum_single _
lemma map_domain_comp {f : α → β} {g : β → γ} :
map_domain (g ∘ f) v = map_domain g (map_domain f v) :=
begin
refine ((sum_sum_index _ _).trans _).symm,
{ intros, exact single_zero },
{ intros, exact single_add },
refine sum_congr rfl (λ _ _, sum_single_index _),
{ exact single_zero }
end
lemma map_domain_single {f : α → β} {a : α} {b : M} : map_domain f (single a b) = single (f a) b :=
sum_single_index single_zero
@[simp] lemma map_domain_zero {f : α → β} : map_domain f (0 : α →₀ M) = (0 : β →₀ M) :=
sum_zero_index
lemma map_domain_congr {f g : α → β} (h : ∀x∈v.support, f x = g x) :
v.map_domain f = v.map_domain g :=
finset.sum_congr rfl $ λ _ H, by simp only [h _ H]
lemma map_domain_add {f : α → β} : map_domain f (v₁ + v₂) = map_domain f v₁ + map_domain f v₂ :=
sum_add_index (λ _, single_zero) (λ _ _ _, single_add)
lemma map_domain_finset_sum {f : α → β} {s : finset ι} {v : ι → α →₀ M} :
map_domain f (∑ i in s, v i) = ∑ i in s, map_domain f (v i) :=
eq.symm $ sum_finset_sum_index (λ _, single_zero) (λ _ _ _, single_add)
lemma map_domain_sum [has_zero N] {f : α → β} {s : α →₀ N} {v : α → N → α →₀ M} :
map_domain f (s.sum v) = s.sum (λa b, map_domain f (v a b)) :=
eq.symm $ sum_finset_sum_index (λ _, single_zero) (λ _ _ _, single_add)
lemma map_domain_support [decidable_eq β] {f : α → β} {s : α →₀ M} :
(s.map_domain f).support ⊆ s.support.image f :=
finset.subset.trans support_sum $
finset.subset.trans (finset.bUnion_mono $ assume a ha, support_single_subset) $
by rw [finset.bUnion_singleton]; exact subset.refl _
@[to_additive]
lemma prod_map_domain_index [comm_monoid N] {f : α → β} {s : α →₀ M}
{h : β → M → N} (h_zero : ∀b, h b 0 = 1) (h_add : ∀b m₁ m₂, h b (m₁ + m₂) = h b m₁ * h b m₂) :
(map_domain f s).prod h = s.prod (λa m, h (f a) m) :=
(prod_sum_index h_zero h_add).trans $ prod_congr rfl $ λ _ _, prod_single_index (h_zero _)
/--
A version of `sum_map_domain_index` that takes a bundled `add_monoid_hom`,
rather than separate linearity hypotheses.
-/
-- Note that in `prod_map_domain_index`, `M` is still an additive monoid,
-- so there is no analogous version in terms of `monoid_hom`.
@[simp]
lemma sum_map_domain_index_add_monoid_hom [add_comm_monoid N] {f : α → β}
{s : α →₀ M} (h : β → M →+ N) :
(map_domain f s).sum (λ b m, h b m) = s.sum (λ a m, h (f a) m) :=
@sum_map_domain_index _ _ _ _ _ _ _ _
(λ b m, h b m)
(λ b, (h b).map_zero)
(λ b m₁ m₂, (h b).map_add _ _)
lemma emb_domain_eq_map_domain (f : α ↪ β) (v : α →₀ M) :
emb_domain f v = map_domain f v :=
begin
ext a,
by_cases a ∈ set.range f,
{ rcases h with ⟨a, rfl⟩,
rw [map_domain_apply f.injective, emb_domain_apply] },
{ rw [map_domain_notin_range, emb_domain_notin_range]; assumption }
end
@[to_additive]
lemma prod_map_domain_index_inj [comm_monoid N] {f : α → β} {s : α →₀ M}
{h : β → M → N} (hf : function.injective f) :
(s.map_domain f).prod h = s.prod (λa b, h (f a) b) :=
by rw [←function.embedding.coe_fn_mk f hf, ←emb_domain_eq_map_domain, prod_emb_domain]
lemma map_domain_injective {f : α → β} (hf : function.injective f) :
function.injective (map_domain f : (α →₀ M) → (β →₀ M)) :=
begin
assume v₁ v₂ eq, ext a,
have : map_domain f v₁ (f a) = map_domain f v₂ (f a), { rw eq },
rwa [map_domain_apply hf, map_domain_apply hf] at this,
end
end map_domain
/-! ### Declarations about `comap_domain` -/
section comap_domain
/-- Given `f : α → β`, `l : β →₀ M` and a proof `hf` that `f` is injective on
the preimage of `l.support`, `comap_domain f l hf` is the finitely supported function
from `α` to `M` given by composing `l` with `f`. -/
def comap_domain [has_zero M] (f : α → β) (l : β →₀ M) (hf : set.inj_on f (f ⁻¹' ↑l.support)) :
α →₀ M :=
{ support := l.support.preimage f hf,
to_fun := (λ a, l (f a)),
mem_support_to_fun :=
begin
intros a,
simp only [finset.mem_def.symm, finset.mem_preimage],
exact l.mem_support_to_fun (f a),
end }
@[simp]
lemma comap_domain_apply [has_zero M] (f : α → β) (l : β →₀ M)
(hf : set.inj_on f (f ⁻¹' ↑l.support)) (a : α) :
comap_domain f l hf a = l (f a) :=
rfl
lemma sum_comap_domain [has_zero M] [add_comm_monoid N]
(f : α → β) (l : β →₀ M) (g : β → M → N)
(hf : set.bij_on f (f ⁻¹' ↑l.support) ↑l.support) :
(comap_domain f l hf.inj_on).sum (g ∘ f) = l.sum g :=
begin
simp only [sum, comap_domain_apply, (∘)],
simp [comap_domain, finset.sum_preimage_of_bij f _ _ (λ x, g x (l x))],
end
lemma eq_zero_of_comap_domain_eq_zero [add_comm_monoid M]
(f : α → β) (l : β →₀ M) (hf : set.bij_on f (f ⁻¹' ↑l.support) ↑l.support) :
comap_domain f l hf.inj_on = 0 → l = 0 :=
begin
rw [← support_eq_empty, ← support_eq_empty, comap_domain],
simp only [finset.ext_iff, finset.not_mem_empty, iff_false, mem_preimage],
assume h a ha,
cases hf.2.2 ha with b hb,
exact h b (hb.2.symm ▸ ha)
end
lemma map_domain_comap_domain [add_comm_monoid M] (f : α → β) (l : β →₀ M)
(hf : function.injective f) (hl : ↑l.support ⊆ set.range f):
map_domain f (comap_domain f l (hf.inj_on _)) = l :=
begin
ext a,
by_cases h_cases: a ∈ set.range f,
{ rcases set.mem_range.1 h_cases with ⟨b, hb⟩,
rw [hb.symm, map_domain_apply hf, comap_domain_apply] },
{ rw map_domain_notin_range _ _ h_cases,
by_contra h_contr,
apply h_cases (hl $ finset.mem_coe.2 $ mem_support_iff.2 $ λ h, h_contr h.symm) }
end
end comap_domain
/-! ### Declarations about `filter` -/
section filter
section has_zero
variables [has_zero M] (p : α → Prop) (f : α →₀ M)
/-- `filter p f` is the function which is `f a` if `p a` is true and 0 otherwise. -/
def filter (p : α → Prop) (f : α →₀ M) : α →₀ M :=
{ to_fun := λ a, if p a then f a else 0,
support := f.support.filter (λ a, p a),
mem_support_to_fun := λ a, by split_ifs; { simp only [h, mem_filter, mem_support_iff], tauto } }
lemma filter_apply (a : α) [D : decidable (p a)] : f.filter p a = if p a then f a else 0 :=
by rw subsingleton.elim D; refl
lemma filter_eq_indicator : ⇑(f.filter p) = set.indicator {x | p x} f := rfl
@[simp] lemma filter_apply_pos {a : α} (h : p a) : f.filter p a = f a :=
if_pos h
@[simp] lemma filter_apply_neg {a : α} (h : ¬ p a) : f.filter p a = 0 :=
if_neg h
@[simp] lemma support_filter [D : decidable_pred p] : (f.filter p).support = f.support.filter p :=
by rw subsingleton.elim D; refl
lemma filter_zero : (0 : α →₀ M).filter p = 0 :=
by rw [← support_eq_empty, support_filter, support_zero, finset.filter_empty]
@[simp] lemma filter_single_of_pos
{a : α} {b : M} (h : p a) : (single a b).filter p = single a b :=
coe_fn_injective $ by simp [filter_eq_indicator, set.subset_def, mem_support_single, h]
@[simp] lemma filter_single_of_neg
{a : α} {b : M} (h : ¬ p a) : (single a b).filter p = 0 :=
ext $ by simp [filter_eq_indicator, single_apply_eq_zero, @imp.swap (p _), h]
end has_zero
lemma filter_pos_add_filter_neg [add_monoid M] (f : α →₀ M) (p : α → Prop) :
f.filter p + f.filter (λa, ¬ p a) = f :=
coe_fn_injective $ set.indicator_self_add_compl {x | p x} f
end filter
/-! ### Declarations about `frange` -/
section frange
variables [has_zero M]
/-- `frange f` is the image of `f` on the support of `f`. -/
def frange (f : α →₀ M) : finset M := finset.image f f.support
theorem mem_frange {f : α →₀ M} {y : M} :
y ∈ f.frange ↔ y ≠ 0 ∧ ∃ x, f x = y :=
finset.mem_image.trans
⟨λ ⟨x, hx1, hx2⟩, ⟨hx2 ▸ mem_support_iff.1 hx1, x, hx2⟩,
λ ⟨hy, x, hx⟩, ⟨x, mem_support_iff.2 (hx.symm ▸ hy), hx⟩⟩
theorem zero_not_mem_frange {f : α →₀ M} : (0:M) ∉ f.frange :=
λ H, (mem_frange.1 H).1 rfl
theorem frange_single {x : α} {y : M} : frange (single x y) ⊆ {y} :=
λ r hr, let ⟨t, ht1, ht2⟩ := mem_frange.1 hr in ht2 ▸
(by rw single_apply at ht2 ⊢; split_ifs at ht2 ⊢; [exact finset.mem_singleton_self _, cc])
end frange
/-! ### Declarations about `subtype_domain` -/
section subtype_domain
section zero
variables [has_zero M] {p : α → Prop}
/-- `subtype_domain p f` is the restriction of the finitely supported function
`f` to the subtype `p`. -/
def subtype_domain (p : α → Prop) (f : α →₀ M) : (subtype p →₀ M) :=
⟨f.support.subtype p, f ∘ coe, λ a, by simp only [mem_subtype, mem_support_iff]⟩
@[simp] lemma support_subtype_domain [D : decidable_pred p] {f : α →₀ M} :
(subtype_domain p f).support = f.support.subtype p :=
by rw subsingleton.elim D; refl
@[simp] lemma subtype_domain_apply {a : subtype p} {v : α →₀ M} :
(subtype_domain p v) a = v (a.val) :=
rfl
@[simp] lemma subtype_domain_zero : subtype_domain p (0 : α →₀ M) = 0 :=
rfl
lemma subtype_domain_eq_zero_iff' {f : α →₀ M} :
f.subtype_domain p = 0 ↔ ∀ x, p x → f x = 0 :=
by simp_rw [← support_eq_empty, support_subtype_domain, subtype_eq_empty, not_mem_support_iff]
lemma subtype_domain_eq_zero_iff {f : α →₀ M} (hf : ∀ x ∈ f.support , p x) :
f.subtype_domain p = 0 ↔ f = 0 :=
subtype_domain_eq_zero_iff'.trans ⟨λ H, ext $ λ x,
if hx : p x then H x hx else not_mem_support_iff.1 $ mt (hf x) hx, λ H x _, by simp [H]⟩
@[to_additive]
lemma prod_subtype_domain_index [comm_monoid N] {v : α →₀ M}
{h : α → M → N} (hp : ∀x∈v.support, p x) :
(v.subtype_domain p).prod (λa b, h a b) = v.prod h :=
prod_bij (λp _, p.val)
(λ _, mem_subtype.1)
(λ _ _, rfl)
(λ _ _ _ _, subtype.eq)
(λ b hb, ⟨⟨b, hp b hb⟩, mem_subtype.2 hb, rfl⟩)
end zero
section monoid
variables [add_monoid M] {p : α → Prop} {v v' : α →₀ M}
@[simp] lemma subtype_domain_add {v v' : α →₀ M} :
(v + v').subtype_domain p = v.subtype_domain p + v'.subtype_domain p :=
ext $ λ _, rfl
instance subtype_domain.is_add_monoid_hom :
is_add_monoid_hom (subtype_domain p : (α →₀ M) → subtype p →₀ M) :=
{ map_add := λ _ _, subtype_domain_add, map_zero := subtype_domain_zero }
/-- `finsupp.filter` as an `add_monoid_hom`. -/
def filter_add_hom (p : α → Prop) : (α →₀ M) →+ (α →₀ M) :=
{ to_fun := filter p,
map_zero' := filter_zero p,
map_add' := λ f g, coe_fn_injective $ set.indicator_add {x | p x} f g }
@[simp] lemma filter_add {v v' : α →₀ M} : (v + v').filter p = v.filter p + v'.filter p :=
(filter_add_hom p).map_add v v'
end monoid
section comm_monoid
variables [add_comm_monoid M] {p : α → Prop}
lemma subtype_domain_sum {s : finset ι} {h : ι → α →₀ M} :
(∑ c in s, h c).subtype_domain p = ∑ c in s, (h c).subtype_domain p :=
eq.symm (s.sum_hom _)
lemma subtype_domain_finsupp_sum [has_zero N] {s : β →₀ N} {h : β → N → α →₀ M} :
(s.sum h).subtype_domain p = s.sum (λc d, (h c d).subtype_domain p) :=
subtype_domain_sum
lemma filter_sum (s : finset ι) (f : ι → α →₀ M) :
(∑ a in s, f a).filter p = ∑ a in s, filter p (f a) :=
(filter_add_hom p : (α →₀ M) →+ _).map_sum f s
lemma filter_eq_sum (p : α → Prop) [D : decidable_pred p] (f : α →₀ M) :
f.filter p = ∑ i in f.support.filter p, single i (f i) :=
(f.filter p).sum_single.symm.trans $ finset.sum_congr (by rw subsingleton.elim D; refl) $
λ x hx, by rw [filter_apply_pos _ _ (mem_filter.1 hx).2]
end comm_monoid
section group
variables [add_group G] {p : α → Prop} {v v' : α →₀ G}
@[simp] lemma subtype_domain_neg : (- v).subtype_domain p = - v.subtype_domain p :=
ext $ λ _, rfl
@[simp] lemma subtype_domain_sub :
(v - v').subtype_domain p = v.subtype_domain p - v'.subtype_domain p :=
ext $ λ _, rfl
end group
end subtype_domain
/-! ### Declarations relating `finsupp` to `multiset` -/
section multiset
/-- Given `f : α →₀ ℕ`, `f.to_multiset` is the multiset with multiplicities given by the values of
`f` on the elements of `α`. We define this function as an `add_equiv`. -/
def to_multiset : (α →₀ ℕ) ≃+ multiset α :=
{ to_fun := λ f, f.sum (λa n, n •ℕ {a}),
inv_fun := λ s, ⟨s.to_finset, λ a, s.count a, λ a, by simp⟩,
left_inv := λ f, ext $ λ a,
suffices (if f a = 0 then 0 else f a) = f a,
by simpa [finsupp.sum, multiset.count_sum', multiset.count_cons],
by split_ifs with h; [rw h, refl],
right_inv := λ s, by simp [finsupp.sum],
map_add' := λ f g, sum_add_index (λ a, zero_nsmul _) (λ a, add_nsmul _) }
lemma to_multiset_zero : (0 : α →₀ ℕ).to_multiset = 0 :=
rfl
lemma to_multiset_add (m n : α →₀ ℕ) :
(m + n).to_multiset = m.to_multiset + n.to_multiset :=
to_multiset.map_add m n
lemma to_multiset_apply (f : α →₀ ℕ) : f.to_multiset = f.sum (λ a n, n •ℕ {a}) := rfl
@[simp] lemma to_multiset_single (a : α) (n : ℕ) : to_multiset (single a n) = n •ℕ {a} :=
by rw [to_multiset_apply, sum_single_index]; apply zero_nsmul
lemma to_multiset_sum {ι : Type*} {f : ι → α →₀ ℕ} (s : finset ι) :
finsupp.to_multiset (∑ i in s, f i) = ∑ i in s, finsupp.to_multiset (f i) :=
begin
apply finset.induction_on s,
{ simp },
{ intros i s hi,
simp [hi] }
end
lemma to_multiset_sum_single {ι : Type*} (s : finset ι) (n : ℕ) :
finsupp.to_multiset (∑ i in s, single i n) = n •ℕ s.val :=
by simp_rw [to_multiset_sum, finsupp.to_multiset_single, multiset.singleton_eq_singleton,
sum_nsmul, sum_multiset_singleton]
lemma card_to_multiset (f : α →₀ ℕ) : f.to_multiset.card = f.sum (λa, id) :=
by simp [to_multiset_apply, add_monoid_hom.map_finsupp_sum, function.id_def]
lemma to_multiset_map (f : α →₀ ℕ) (g : α → β) :
f.to_multiset.map g = (f.map_domain g).to_multiset :=
begin
refine f.induction _ _,
{ rw [to_multiset_zero, multiset.map_zero, map_domain_zero, to_multiset_zero] },
{ assume a n f _ _ ih,
rw [to_multiset_add, multiset.map_add, ih, map_domain_add, map_domain_single,
to_multiset_single, to_multiset_add, to_multiset_single,
is_add_monoid_hom.map_nsmul (multiset.map g)],
refl }
end
@[simp] lemma prod_to_multiset [comm_monoid M] (f : M →₀ ℕ) :
f.to_multiset.prod = f.prod (λa n, a ^ n) :=
begin
refine f.induction _ _,
{ rw [to_multiset_zero, multiset.prod_zero, finsupp.prod_zero_index] },
{ assume a n f _ _ ih,
rw [to_multiset_add, multiset.prod_add, ih, to_multiset_single, finsupp.prod_add_index,
finsupp.prod_single_index, multiset.prod_nsmul, multiset.singleton_eq_singleton,
multiset.prod_singleton],
{ exact pow_zero a },
{ exact pow_zero },
{ exact pow_add } }
end
@[simp] lemma to_finset_to_multiset [decidable_eq α] (f : α →₀ ℕ) :
f.to_multiset.to_finset = f.support :=
begin
refine f.induction _ _,
{ rw [to_multiset_zero, multiset.to_finset_zero, support_zero] },
{ assume a n f ha hn ih,
rw [to_multiset_add, multiset.to_finset_add, ih, to_multiset_single, support_add_eq,
support_single_ne_zero hn, multiset.to_finset_nsmul _ _ hn,
multiset.singleton_eq_singleton, multiset.to_finset_cons, multiset.to_finset_zero],
refl,
refine disjoint.mono_left support_single_subset _,
rwa [finset.singleton_disjoint] }
end
@[simp] lemma count_to_multiset [decidable_eq α] (f : α →₀ ℕ) (a : α) :
f.to_multiset.count a = f a :=
calc f.to_multiset.count a = f.sum (λx n, (n •ℕ {x} : multiset α).count a) :
(f.support.sum_hom $ multiset.count a).symm
... = f.sum (λx n, n * ({x} : multiset α).count a) : by simp only [multiset.count_nsmul]
... = f.sum (λx n, n * (x ::ₘ 0 : multiset α).count a) : rfl
... = f a * (a ::ₘ 0 : multiset α).count a : sum_eq_single _
(λ a' _ H, by simp only [multiset.count_cons_of_ne (ne.symm H), multiset.count_zero, mul_zero])
(λ H, by simp only [not_mem_support_iff.1 H, zero_mul])
... = f a : by simp only [multiset.count_singleton, mul_one]
lemma mem_support_multiset_sum [add_comm_monoid M]
{s : multiset (α →₀ M)} (a : α) :
a ∈ s.sum.support → ∃f∈s, a ∈ (f : α →₀ M).support :=
multiset.induction_on s false.elim
begin
assume f s ih ha,
by_cases a ∈ f.support,
{ exact ⟨f, multiset.mem_cons_self _ _, h⟩ },
{ simp only [multiset.sum_cons, mem_support_iff, add_apply,
not_mem_support_iff.1 h, zero_add] at ha,
rcases ih (mem_support_iff.2 ha) with ⟨f', h₀, h₁⟩,
exact ⟨f', multiset.mem_cons_of_mem h₀, h₁⟩ }
end
lemma mem_support_finset_sum [add_comm_monoid M]
{s : finset ι} {h : ι → α →₀ M} (a : α) (ha : a ∈ (∑ c in s, h c).support) :
∃ c ∈ s, a ∈ (h c).support :=
let ⟨f, hf, hfa⟩ := mem_support_multiset_sum a ha in
let ⟨c, hc, eq⟩ := multiset.mem_map.1 hf in
⟨c, hc, eq.symm ▸ hfa⟩
@[simp] lemma mem_to_multiset (f : α →₀ ℕ) (i : α) :
i ∈ f.to_multiset ↔ i ∈ f.support :=
by rw [← multiset.count_ne_zero, finsupp.count_to_multiset, finsupp.mem_support_iff]
end multiset
/-! ### Declarations about `curry` and `uncurry` -/
section curry_uncurry
variables [add_comm_monoid M] [add_comm_monoid N]
/-- Given a finitely supported function `f` from a product type `α × β` to `γ`,
`curry f` is the "curried" finitely supported function from `α` to the type of
finitely supported functions from `β` to `γ`. -/
protected def curry (f : (α × β) →₀ M) : α →₀ (β →₀ M) :=
f.sum $ λp c, single p.1 (single p.2 c)
lemma sum_curry_index (f : (α × β) →₀ M) (g : α → β → M → N)
(hg₀ : ∀ a b, g a b 0 = 0) (hg₁ : ∀a b c₀ c₁, g a b (c₀ + c₁) = g a b c₀ + g a b c₁) :
f.curry.sum (λa f, f.sum (g a)) = f.sum (λp c, g p.1 p.2 c) :=
begin
rw [finsupp.curry],
transitivity,
{ exact sum_sum_index (assume a, sum_zero_index)
(assume a b₀ b₁, sum_add_index (assume a, hg₀ _ _) (assume c d₀ d₁, hg₁ _ _ _ _)) },
congr, funext p c,
transitivity,
{ exact sum_single_index sum_zero_index },
exact sum_single_index (hg₀ _ _)
end
/-- Given a finitely supported function `f` from `α` to the type of
finitely supported functions from `β` to `M`,
`uncurry f` is the "uncurried" finitely supported function from `α × β` to `M`. -/
protected def uncurry (f : α →₀ (β →₀ M)) : (α × β) →₀ M :=
f.sum $ λa g, g.sum $ λb c, single (a, b) c
/-- `finsupp_prod_equiv` defines the `equiv` between `((α × β) →₀ M)` and `(α →₀ (β →₀ M))` given by
currying and uncurrying. -/
def finsupp_prod_equiv : ((α × β) →₀ M) ≃ (α →₀ (β →₀ M)) :=
by refine ⟨finsupp.curry, finsupp.uncurry, λ f, _, λ f, _⟩; simp only [
finsupp.curry, finsupp.uncurry, sum_sum_index, sum_zero_index, sum_add_index,
sum_single_index, single_zero, single_add, eq_self_iff_true, forall_true_iff,
forall_3_true_iff, prod.mk.eta, (single_sum _ _ _).symm, sum_single]
lemma filter_curry (f : α × β →₀ M) (p : α → Prop) :
(f.filter (λa:α×β, p a.1)).curry = f.curry.filter p :=
begin
rw [finsupp.curry, finsupp.curry, finsupp.sum, finsupp.sum, filter_sum, support_filter,
sum_filter],
refine finset.sum_congr rfl _,
rintros ⟨a₁, a₂⟩ ha,
dsimp only,
split_ifs,
{ rw [filter_apply_pos, filter_single_of_pos]; exact h },
{ rwa [filter_single_of_neg] }
end
lemma support_curry [decidable_eq α] (f : α × β →₀ M) :
f.curry.support ⊆ f.support.image prod.fst :=
begin
rw ← finset.bUnion_singleton,
refine finset.subset.trans support_sum _,
refine finset.bUnion_mono (assume a _, support_single_subset)
end
end curry_uncurry
section
variables [group G] [mul_action G α] [add_comm_monoid M]
/--
Scalar multiplication by a group element g,
given by precomposition with the action of g⁻¹ on the domain.
-/
def comap_has_scalar : has_scalar G (α →₀ M) :=
{ smul := λ g f, f.comap_domain (λ a, g⁻¹ • a)
(λ a a' m m' h, by simpa [←mul_smul] using (congr_arg (λ a, g • a) h)) }
local attribute [instance] comap_has_scalar
/--
Scalar multiplication by a group element,
given by precomposition with the action of g⁻¹ on the domain,
is multiplicative in g.
-/
def comap_mul_action : mul_action G (α →₀ M) :=
{ one_smul := λ f, by { ext, dsimp [(•)], simp, },
mul_smul := λ g g' f, by { ext, dsimp [(•)], simp [mul_smul], }, }
local attribute [instance] comap_mul_action
/--
Scalar multiplication by a group element,
given by precomposition with the action of g⁻¹ on the domain,
is additive in the second argument.
-/
def comap_distrib_mul_action :
distrib_mul_action G (α →₀ M) :=
{ smul_zero := λ g, by { ext, dsimp [(•)], simp, },
smul_add := λ g f f', by { ext, dsimp [(•)], simp, }, }
/--
Scalar multiplication by a group element on finitely supported functions on a group,
given by precomposition with the action of g⁻¹. -/
def comap_distrib_mul_action_self :
distrib_mul_action G (G →₀ M) :=
@finsupp.comap_distrib_mul_action G M G _ (monoid.to_mul_action G) _
@[simp]
lemma comap_smul_single (g : G) (a : α) (b : M) :
g • single a b = single (g • a) b :=
begin
ext a',
dsimp [(•)],
by_cases h : g • a = a',
{ subst h, simp [←mul_smul], },
{ simp [single_eq_of_ne h], rw [single_eq_of_ne],
rintro rfl, simpa [←mul_smul] using h, }
end
@[simp]
lemma comap_smul_apply (g : G) (f : α →₀ M) (a : α) :
(g • f) a = f (g⁻¹ • a) := rfl
end
section
instance [semiring R] [add_comm_monoid M] [semimodule R M] : has_scalar R (α →₀ M) :=
⟨λa v, v.map_range ((•) a) (smul_zero _)⟩
/-!
Throughout this section, some `semiring` arguments are specified with `{}` instead of `[]`.
See note [implicit instance arguments].
-/
@[simp] lemma coe_smul {_ : semiring R} [add_comm_monoid M] [semimodule R M]
(b : R) (v : α →₀ M) : ⇑(b • v) = b • v := rfl
lemma smul_apply {_ : semiring R} [add_comm_monoid M] [semimodule R M]
(b : R) (v : α →₀ M) (a : α) : (b • v) a = b • (v a) := rfl
variables (α M)
instance [semiring R] [add_comm_monoid M] [semimodule R M] : semimodule R (α →₀ M) :=
{ smul := (•),
smul_add := λ a x y, ext $ λ _, smul_add _ _ _,
add_smul := λ a x y, ext $ λ _, add_smul _ _ _,
one_smul := λ x, ext $ λ _, one_smul _ _,
mul_smul := λ r s x, ext $ λ _, mul_smul _ _ _,
zero_smul := λ x, ext $ λ _, zero_smul _ _,
smul_zero := λ x, ext $ λ _, smul_zero _ }
instance [semiring R] [semiring S] [add_comm_monoid M] [semimodule R M] [semimodule S M]
[has_scalar R S] [is_scalar_tower R S M] :
is_scalar_tower R S (α →₀ M) :=
{ smul_assoc := λ r s a, ext $ λ _, smul_assoc _ _ _ }
instance [semiring R] [semiring S] [add_comm_monoid M] [semimodule R M] [semimodule S M]
[smul_comm_class R S M] :
smul_comm_class R S (α →₀ M) :=
{ smul_comm := λ r s a, ext $ λ _, smul_comm _ _ _ }
variables {α M} {R}
lemma support_smul {_ : semiring R} [add_comm_monoid M] [semimodule R M] {b : R} {g : α →₀ M} :
(b • g).support ⊆ g.support :=
λ a, by simp only [smul_apply, mem_support_iff, ne.def]; exact mt (λ h, h.symm ▸ smul_zero _)
section
variables {p : α → Prop}
@[simp] lemma filter_smul {_ : semiring R} [add_comm_monoid M] [semimodule R M]
{b : R} {v : α →₀ M} : (b • v).filter p = b • v.filter p :=
coe_fn_injective $ set.indicator_smul {x | p x} b v
end
lemma map_domain_smul {_ : semiring R} [add_comm_monoid M] [semimodule R M]
{f : α → β} (b : R) (v : α →₀ M) : map_domain f (b • v) = b • map_domain f v :=
begin
change map_domain f (map_range _ _ _) = map_range _ _ _,
apply finsupp.induction v, { simp only [map_domain_zero, map_range_zero] },
intros a b v' hv₁ hv₂ IH,
rw [map_range_add, map_domain_add, IH, map_domain_add, map_range_add,
map_range_single, map_domain_single, map_domain_single, map_range_single];
apply smul_add
end
@[simp] lemma smul_single {_ : semiring R} [add_comm_monoid M] [semimodule R M]
(c : R) (a : α) (b : M) : c • finsupp.single a b = finsupp.single a (c • b) :=
map_range_single
@[simp] lemma smul_single' {_ : semiring R}
(c : R) (a : α) (b : R) : c • finsupp.single a b = finsupp.single a (c * b) :=
smul_single _ _ _
lemma smul_single_one [semiring R] (a : α) (b : R) : b • single a 1 = single a b :=
by rw [smul_single, smul_eq_mul, mul_one]
end
lemma sum_smul_index [semiring R] [add_comm_monoid M] {g : α →₀ R} {b : R} {h : α → R → M}
(h0 : ∀i, h i 0 = 0) : (b • g).sum h = g.sum (λi a, h i (b * a)) :=
finsupp.sum_map_range_index h0
lemma sum_smul_index' [semiring R] [add_comm_monoid M] [semimodule R M] [add_comm_monoid N]
{g : α →₀ M} {b : R} {h : α → M → N} (h0 : ∀i, h i 0 = 0) :
(b • g).sum h = g.sum (λi c, h i (b • c)) :=
finsupp.sum_map_range_index h0
/-- A version of `finsupp.sum_smul_index'` for bundled additive maps. -/
lemma sum_smul_index_add_monoid_hom
[semiring R] [add_comm_monoid M] [add_comm_monoid N] [semimodule R M]
{g : α →₀ M} {b : R} {h : α → M →+ N} :
(b • g).sum (λ a, h a) = g.sum (λ i c, h i (b • c)) :=
sum_map_range_index (λ i, (h i).map_zero)
instance [semiring R] [add_comm_monoid M] [semimodule R M] {ι : Type*}
[no_zero_smul_divisors R M] : no_zero_smul_divisors R (ι →₀ M) :=
⟨λ c f h, or_iff_not_imp_left.mpr (λ hc, finsupp.ext
(λ i, (smul_eq_zero.mp (finsupp.ext_iff.mp h i)).resolve_left hc))⟩
section
variables [semiring R] [semiring S]
lemma sum_mul (b : S) (s : α →₀ R) {f : α → R → S} :
(s.sum f) * b = s.sum (λ a c, (f a c) * b) :=
by simp only [finsupp.sum, finset.sum_mul]
lemma mul_sum (b : S) (s : α →₀ R) {f : α → R → S} :
b * (s.sum f) = s.sum (λ a c, b * (f a c)) :=
by simp only [finsupp.sum, finset.mul_sum]
instance unique_of_right [subsingleton R] : unique (α →₀ R) :=
{ uniq := λ l, ext $ λ i, subsingleton.elim _ _,
.. finsupp.inhabited }
end
/-- Given an `add_comm_monoid M` and `s : set α`, `restrict_support_equiv s M` is the `equiv`
between the subtype of finitely supported functions with support contained in `s` and
the type of finitely supported functions from `s`. -/
def restrict_support_equiv (s : set α) (M : Type*) [add_comm_monoid M] :
{f : α →₀ M // ↑f.support ⊆ s } ≃ (s →₀ M) :=
begin
refine ⟨λf, subtype_domain (λx, x ∈ s) f.1, λ f, ⟨f.map_domain subtype.val, _⟩, _, _⟩,
{ refine set.subset.trans (finset.coe_subset.2 map_domain_support) _,
rw [finset.coe_image, set.image_subset_iff],
exact assume x hx, x.2 },
{ rintros ⟨f, hf⟩,
apply subtype.eq,
ext a,
dsimp only,
refine classical.by_cases (assume h : a ∈ set.range (subtype.val : s → α), _) (assume h, _),
{ rcases h with ⟨x, rfl⟩,
rw [map_domain_apply subtype.val_injective, subtype_domain_apply] },
{ convert map_domain_notin_range _ _ h,
rw [← not_mem_support_iff],
refine mt _ h,
exact assume ha, ⟨⟨a, hf ha⟩, rfl⟩ } },
{ assume f,
ext ⟨a, ha⟩,
dsimp only,
rw [subtype_domain_apply, map_domain_apply subtype.val_injective] }
end
/-- Given `add_comm_monoid M` and `e : α ≃ β`, `dom_congr e` is the corresponding `equiv` between
`α →₀ M` and `β →₀ M`. -/
protected def dom_congr [add_comm_monoid M] (e : α ≃ β) : (α →₀ M) ≃+ (β →₀ M) :=
{ to_fun := map_domain e,
inv_fun := map_domain e.symm,
left_inv := begin
assume v,
simp only [map_domain_comp.symm, (∘), equiv.symm_apply_apply],
exact map_domain_id
end,
right_inv := begin
assume v,
simp only [map_domain_comp.symm, (∘), equiv.apply_symm_apply],
exact map_domain_id
end,
map_add' := λ a b, map_domain_add, }
end finsupp
namespace finsupp
/-! ### Declarations about sigma types -/
section sigma
variables {αs : ι → Type*} [has_zero M] (l : (Σ i, αs i) →₀ M)
/-- Given `l`, a finitely supported function from the sigma type `Σ (i : ι), αs i` to `M` and
an index element `i : ι`, `split l i` is the `i`th component of `l`,
a finitely supported function from `as i` to `M`. -/
def split (i : ι) : αs i →₀ M :=
l.comap_domain (sigma.mk i) (λ x1 x2 _ _ hx, heq_iff_eq.1 (sigma.mk.inj hx).2)
lemma split_apply (i : ι) (x : αs i) : split l i x = l ⟨i, x⟩ :=
begin
dunfold split,
rw comap_domain_apply
end
/-- Given `l`, a finitely supported function from the sigma type `Σ (i : ι), αs i` to `β`,
`split_support l` is the finset of indices in `ι` that appear in the support of `l`. -/
def split_support : finset ι := l.support.image sigma.fst
lemma mem_split_support_iff_nonzero (i : ι) :
i ∈ split_support l ↔ split l i ≠ 0 :=
begin
rw [split_support, mem_image, ne.def, ← support_eq_empty, ← ne.def,
← finset.nonempty_iff_ne_empty, split, comap_domain, finset.nonempty],
simp only [exists_prop, finset.mem_preimage, exists_and_distrib_right, exists_eq_right,
mem_support_iff, sigma.exists, ne.def]
end
/-- Given `l`, a finitely supported function from the sigma type `Σ i, αs i` to `β` and
an `ι`-indexed family `g` of functions from `(αs i →₀ β)` to `γ`, `split_comp` defines a
finitely supported function from the index type `ι` to `γ` given by composing `g i` with
`split l i`. -/
def split_comp [has_zero N] (g : Π i, (αs i →₀ M) → N)
(hg : ∀ i x, x = 0 ↔ g i x = 0) : ι →₀ N :=
{ support := split_support l,
to_fun := λ i, g i (split l i),
mem_support_to_fun :=
begin
intros i,
rw [mem_split_support_iff_nonzero, not_iff_not, hg],
end }
lemma sigma_support : l.support = l.split_support.sigma (λ i, (l.split i).support) :=
by simp only [finset.ext_iff, split_support, split, comap_domain, mem_image,
mem_preimage, sigma.forall, mem_sigma]; tauto
lemma sigma_sum [add_comm_monoid N] (f : (Σ (i : ι), αs i) → M → N) :
l.sum f = ∑ i in split_support l, (split l i).sum (λ (a : αs i) b, f ⟨i, a⟩ b) :=
by simp only [sum, sigma_support, sum_sigma, split_apply]
end sigma
end finsupp
/-! ### Declarations relating `multiset` to `finsupp` -/
namespace multiset
/-- Given a multiset `s`, `s.to_finsupp` returns the finitely supported function on `ℕ` given by
the multiplicities of the elements of `s`. -/
def to_finsupp : multiset α ≃+ (α →₀ ℕ) := finsupp.to_multiset.symm
@[simp] lemma to_finsupp_support [D : decidable_eq α] (s : multiset α) :
s.to_finsupp.support = s.to_finset :=
by rw subsingleton.elim D; refl
@[simp] lemma to_finsupp_apply [D : decidable_eq α] (s : multiset α) (a : α) :
to_finsupp s a = s.count a :=
by rw subsingleton.elim D; refl
lemma to_finsupp_zero : to_finsupp (0 : multiset α) = 0 := add_equiv.map_zero _
lemma to_finsupp_add (s t : multiset α) :
to_finsupp (s + t) = to_finsupp s + to_finsupp t :=
to_finsupp.map_add s t
@[simp] lemma to_finsupp_singleton (a : α) : to_finsupp (a ::ₘ 0) = finsupp.single a 1 :=
finsupp.to_multiset.symm_apply_eq.2 $ by simp
@[simp] lemma to_finsupp_to_multiset (s : multiset α) :
s.to_finsupp.to_multiset = s :=
finsupp.to_multiset.apply_symm_apply s
lemma to_finsupp_eq_iff {s : multiset α} {f : α →₀ ℕ} : s.to_finsupp = f ↔ s = f.to_multiset :=
finsupp.to_multiset.symm_apply_eq
end multiset
@[simp] lemma finsupp.to_multiset_to_finsupp (f : α →₀ ℕ) :
f.to_multiset.to_finsupp = f :=
finsupp.to_multiset.symm_apply_apply f
/-! ### Declarations about order(ed) instances on `finsupp` -/
namespace finsupp
instance [preorder M] [has_zero M] : preorder (α →₀ M) :=
{ le := λ f g, ∀ s, f s ≤ g s,
le_refl := λ f s, le_refl _,
le_trans := λ f g h Hfg Hgh s, le_trans (Hfg s) (Hgh s) }
instance [partial_order M] [has_zero M] : partial_order (α →₀ M) :=
{ le_antisymm := λ f g hfg hgf, ext $ λ s, le_antisymm (hfg s) (hgf s),
.. finsupp.preorder }
instance [ordered_cancel_add_comm_monoid M] : add_left_cancel_semigroup (α →₀ M) :=
{ add_left_cancel := λ a b c h, ext $ λ s,
by { rw ext_iff at h, exact add_left_cancel (h s) },
.. finsupp.add_monoid }
instance [ordered_cancel_add_comm_monoid M] : add_right_cancel_semigroup (α →₀ M) :=
{ add_right_cancel := λ a b c h, ext $ λ s,
by { rw ext_iff at h, exact add_right_cancel (h s) },
.. finsupp.add_monoid }
instance [ordered_cancel_add_comm_monoid M] : ordered_cancel_add_comm_monoid (α →₀ M) :=
{ add_le_add_left := λ a b h c s, add_le_add_left (h s) (c s),
le_of_add_le_add_left := λ a b c h s, le_of_add_le_add_left (h s),
.. finsupp.add_comm_monoid, .. finsupp.partial_order,
.. finsupp.add_left_cancel_semigroup, .. finsupp.add_right_cancel_semigroup }
lemma le_def [preorder M] [has_zero M] {f g : α →₀ M} : f ≤ g ↔ ∀ x, f x ≤ g x := iff.rfl
lemma le_iff [canonically_ordered_add_monoid M] (f g : α →₀ M) :
f ≤ g ↔ ∀ s ∈ f.support, f s ≤ g s :=
⟨λ h s hs, h s,
λ h s, if H : s ∈ f.support then h s H else (not_mem_support_iff.1 H).symm ▸ zero_le (g s)⟩
@[simp] lemma add_eq_zero_iff [canonically_ordered_add_monoid M] (f g : α →₀ M) :
f + g = 0 ↔ f = 0 ∧ g = 0 :=
by simp [ext_iff, forall_and_distrib]
/-- `finsupp.to_multiset` as an order isomorphism. -/
def order_iso_multiset : (α →₀ ℕ) ≃o multiset α :=
{ to_equiv := to_multiset.to_equiv,
map_rel_iff' := λ f g, by simp [multiset.le_iff_count, le_def] }
@[simp] lemma coe_order_iso_multiset : ⇑(@order_iso_multiset α) = to_multiset := rfl
@[simp] lemma coe_order_iso_multiset_symm :
⇑(@order_iso_multiset α).symm = multiset.to_finsupp := rfl
lemma to_multiset_strict_mono : strict_mono (@to_multiset α) :=
order_iso_multiset.strict_mono
lemma sum_id_lt_of_lt (m n : α →₀ ℕ) (h : m < n) :
m.sum (λ _, id) < n.sum (λ _, id) :=
begin
rw [← card_to_multiset, ← card_to_multiset],
apply multiset.card_lt_of_lt,
exact to_multiset_strict_mono h
end
variable (α)
/-- The order on `σ →₀ ℕ` is well-founded.-/
lemma lt_wf : well_founded (@has_lt.lt (α →₀ ℕ) _) :=
subrelation.wf (sum_id_lt_of_lt) $ inv_image.wf _ nat.lt_wf
instance decidable_le : decidable_rel (@has_le.le (α →₀ ℕ) _) :=
λ m n, by rw le_iff; apply_instance
variable {α}
@[simp] lemma nat_add_sub_cancel (f g : α →₀ ℕ) : f + g - g = f :=
ext $ λ a, nat.add_sub_cancel _ _
@[simp] lemma nat_add_sub_cancel_left (f g : α →₀ ℕ) : f + g - f = g :=
ext $ λ a, nat.add_sub_cancel_left _ _
lemma nat_add_sub_of_le {f g : α →₀ ℕ} (h : f ≤ g) : f + (g - f) = g :=
ext $ λ a, nat.add_sub_of_le (h a)
lemma nat_sub_add_cancel {f g : α →₀ ℕ} (h : f ≤ g) : g - f + f = g :=
ext $ λ a, nat.sub_add_cancel (h a)
instance : canonically_ordered_add_monoid (α →₀ ℕ) :=
{ bot := 0,
bot_le := λ f s, zero_le (f s),
le_iff_exists_add := λ f g, ⟨λ H, ⟨g - f, (nat_add_sub_of_le H).symm⟩,
λ ⟨c, hc⟩, hc.symm ▸ λ x, by simp⟩,
.. (infer_instance : ordered_add_comm_monoid (α →₀ ℕ)) }
/-- The `finsupp` counterpart of `multiset.antidiagonal`: the antidiagonal of
`s : α →₀ ℕ` consists of all pairs `(t₁, t₂) : (α →₀ ℕ) × (α →₀ ℕ)` such that `t₁ + t₂ = s`.
The finitely supported function `antidiagonal s` is equal to the multiplicities of these pairs. -/
def antidiagonal (f : α →₀ ℕ) : ((α →₀ ℕ) × (α →₀ ℕ)) →₀ ℕ :=
(f.to_multiset.antidiagonal.map (prod.map multiset.to_finsupp multiset.to_finsupp)).to_finsupp
@[simp] lemma mem_antidiagonal_support {f : α →₀ ℕ} {p : (α →₀ ℕ) × (α →₀ ℕ)} :
p ∈ (antidiagonal f).support ↔ p.1 + p.2 = f :=
begin
rcases p with ⟨p₁, p₂⟩,
simp [antidiagonal, ← and.assoc, ← finsupp.to_multiset.apply_eq_iff_eq]
end
lemma swap_mem_antidiagonal_support {n : α →₀ ℕ} {f : (α →₀ ℕ) × (α →₀ ℕ)} :
f.swap ∈ (antidiagonal n).support ↔ f ∈ (antidiagonal n).support :=
by simp only [mem_antidiagonal_support, add_comm, prod.swap]
lemma antidiagonal_support_filter_fst_eq (f g : α →₀ ℕ)
[D : Π (p : (α →₀ ℕ) × (α →₀ ℕ)), decidable (p.1 = g)] :
(antidiagonal f).support.filter (λ p, p.1 = g) = if g ≤ f then {(g, f - g)} else ∅ :=
begin
ext ⟨a, b⟩,
suffices : a = g → (a + b = f ↔ g ≤ f ∧ b = f - g),
{ simpa [apply_ite ((∈) (a, b)), ← and.assoc, @and.right_comm _ (a = _), and.congr_left_iff] },
unfreezingI {rintro rfl}, split,
{ rintro rfl, exact ⟨le_add_right le_rfl, (nat_add_sub_cancel_left _ _).symm⟩ },
{ rintro ⟨h, rfl⟩, exact nat_add_sub_of_le h }
end
lemma antidiagonal_support_filter_snd_eq (f g : α →₀ ℕ)
[D : Π (p : (α →₀ ℕ) × (α →₀ ℕ)), decidable (p.2 = g)] :
(antidiagonal f).support.filter (λ p, p.2 = g) = if g ≤ f then {(f - g, g)} else ∅ :=
begin
ext ⟨a, b⟩,
suffices : b = g → (a + b = f ↔ g ≤ f ∧ a = f - g),
{ simpa [apply_ite ((∈) (a, b)), ← and.assoc, and.congr_left_iff] },
unfreezingI {rintro rfl}, split,
{ rintro rfl, exact ⟨le_add_left le_rfl, (nat_add_sub_cancel _ _).symm⟩ },
{ rintro ⟨h, rfl⟩, exact nat_sub_add_cancel h }
end
@[simp] lemma antidiagonal_zero : antidiagonal (0 : α →₀ ℕ) = single (0,0) 1 :=
by rw [← multiset.to_finsupp_singleton]; refl
@[to_additive]
lemma prod_antidiagonal_support_swap {M : Type*} [comm_monoid M] (n : α →₀ ℕ)
(f : (α →₀ ℕ) → (α →₀ ℕ) → M) :
∏ p in (antidiagonal n).support, f p.1 p.2 = ∏ p in (antidiagonal n).support, f p.2 p.1 :=
finset.prod_bij (λ p hp, p.swap) (λ p, swap_mem_antidiagonal_support.2) (λ p hp, rfl)
(λ p₁ p₂ _ _ h, prod.swap_injective h)
(λ p hp, ⟨p.swap, swap_mem_antidiagonal_support.2 hp, p.swap_swap.symm⟩)
/-- The set `{m : α →₀ ℕ | m ≤ n}` as a `finset`. -/
def Iic_finset (n : α →₀ ℕ) : finset (α →₀ ℕ) :=
(antidiagonal n).support.image prod.fst
@[simp] lemma mem_Iic_finset {m n : α →₀ ℕ} : m ∈ Iic_finset n ↔ m ≤ n :=
by simp [Iic_finset, le_iff_exists_add, eq_comm]
@[simp] lemma coe_Iic_finset (n : α →₀ ℕ) : ↑(Iic_finset n) = set.Iic n :=
by { ext, simp }
/-- Let `n : α →₀ ℕ` be a finitely supported function.
The set of `m : α →₀ ℕ` that are coordinatewise less than or equal to `n`,
is a finite set. -/
lemma finite_le_nat (n : α →₀ ℕ) : set.finite {m | m ≤ n} :=
by simpa using (Iic_finset n).finite_to_set
/-- Let `n : α →₀ ℕ` be a finitely supported function.
The set of `m : α →₀ ℕ` that are coordinatewise less than or equal to `n`,
but not equal to `n` everywhere, is a finite set. -/
lemma finite_lt_nat (n : α →₀ ℕ) : set.finite {m | m < n} :=
(finite_le_nat n).subset $ λ m, le_of_lt
end finsupp
namespace multiset
lemma to_finsuppstrict_mono : strict_mono (@to_finsupp α) :=
finsupp.order_iso_multiset.symm.strict_mono
end multiset
| Lean | 81,233 | lean | 1 | 37.331342 | 100 | 0.635788 |
%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2005-2012. All Rights Reserved.
%%
%% Licensed under the Apache License, Version 2.0 (the "License");
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%% http://www.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%% %CopyrightEnd%
%%
%%
%%----------------------------------------------------------------------
%% Purpose: Verify the application specifics of the asn1 application
%%----------------------------------------------------------------------
-module(asn1_app_test).
-compile(export_all).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
all() ->
[fields, modules, exportall, app_depend].
groups() ->
[].
init_per_group(_GroupName, Config) ->
Config.
end_per_group(_GroupName, Config) ->
Config.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
init_per_suite(suite) -> [];
init_per_suite(doc) -> [];
init_per_suite(Config) when is_list(Config) ->
case is_app(asn1) of
{ok, AppFile} ->
io:format("AppFile: ~n~p~n", [AppFile]),
[{app_file, AppFile}|Config];
{error, Reason} ->
fail(Reason)
end.
is_app(App) ->
LibDir = code:lib_dir(App),
File = filename:join([LibDir, "ebin", atom_to_list(App) ++ ".app"]),
case file:consult(File) of
{ok, [{application, App, AppFile}]} ->
{ok, AppFile};
Error ->
{error, {invalid_format, Error}}
end.
end_per_suite(suite) -> [];
end_per_suite(doc) -> [];
end_per_suite(Config) when is_list(Config) ->
Config.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fields(suite) ->
[];
fields(doc) ->
[];
fields(Config) when is_list(Config) ->
AppFile = key1search(app_file, Config),
Fields = [vsn, description, modules, registered, applications],
case check_fields(Fields, AppFile, []) of
[] ->
ok;
Missing ->
fail({missing_fields, Missing})
end.
check_fields([], _AppFile, Missing) ->
Missing;
check_fields([Field|Fields], AppFile, Missing) ->
check_fields(Fields, AppFile, check_field(Field, AppFile, Missing)).
check_field(Name, AppFile, Missing) ->
io:format("checking field: ~p~n", [Name]),
case lists:keymember(Name, 1, AppFile) of
true ->
Missing;
false ->
[Name|Missing]
end.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
modules(suite) ->
[];
modules(doc) ->
[];
modules(Config) when is_list(Config) ->
AppFile = key1search(app_file, Config),
Mods = key1search(modules, AppFile),
EbinList = get_ebin_mods(asn1),
case missing_modules(Mods, EbinList, []) of
[] ->
ok;
Missing ->
throw({error, {missing_modules, Missing}})
end,
case extra_modules(Mods, EbinList, []) of
[] ->
ok;
Extra ->
check_asn1ct_modules(Extra)
% throw({error, {extra_modules, Extra}})
end,
{ok, Mods}.
get_ebin_mods(App) ->
LibDir = code:lib_dir(App),
EbinDir = filename:join([LibDir,"ebin"]),
{ok, Files0} = file:list_dir(EbinDir),
Files1 = [lists:reverse(File) || File <- Files0],
[list_to_atom(lists:reverse(Name)) || [$m,$a,$e,$b,$.|Name] <- Files1].
check_asn1ct_modules(Extra) ->
ASN1CTMods = [asn1ct,asn1ct_check,asn1_db,asn1ct_pretty_format,
asn1ct_gen,asn1ct_gen_check,asn1ct_gen_per,
asn1ct_name,asn1ct_constructed_per,asn1ct_constructed_ber,
asn1ct_gen_ber,asn1ct_constructed_ber_bin_v2,
asn1ct_gen_ber_bin_v2,asn1ct_value,
asn1ct_tok,asn1ct_parser2,asn1ct_table,
asn1ct_imm,asn1ct_func,asn1ct_rtt,
asn1ct_eval_ext],
case Extra -- ASN1CTMods of
[] ->
ok;
Extra2 ->
throw({error, {extra_modules, Extra2}})
end.
missing_modules([], _Ebins, Missing) ->
Missing;
missing_modules([Mod|Mods], Ebins, Missing) ->
case lists:member(Mod, Ebins) of
true ->
missing_modules(Mods, Ebins, Missing);
false ->
io:format("missing module: ~p~n", [Mod]),
missing_modules(Mods, Ebins, [Mod|Missing])
end.
extra_modules(_Mods, [], Extra) ->
Extra;
extra_modules(Mods, [Mod|Ebins], Extra) ->
case lists:member(Mod, Mods) of
true ->
extra_modules(Mods, Ebins, Extra);
false ->
io:format("supefluous module: ~p~n", [Mod]),
extra_modules(Mods, Ebins, [Mod|Extra])
end.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
exportall(suite) ->
[];
exportall(doc) ->
[];
exportall(Config) when is_list(Config) ->
AppFile = key1search(app_file, Config),
Mods = key1search(modules, AppFile),
check_export_all(Mods).
check_export_all([]) ->
ok;
check_export_all([Mod|Mods]) ->
case (catch apply(Mod, module_info, [compile])) of
{'EXIT', {undef, _}} ->
check_export_all(Mods);
O ->
case lists:keysearch(options, 1, O) of
false ->
check_export_all(Mods);
{value, {options, List}} ->
case lists:member(export_all, List) of
true ->
throw({error, {export_all, Mod}});
false ->
check_export_all(Mods)
end
end
end.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
app_depend(suite) ->
[];
app_depend(doc) ->
[];
app_depend(Config) when is_list(Config) ->
AppFile = key1search(app_file, Config),
Apps = key1search(applications, AppFile),
check_apps(Apps).
check_apps([]) ->
ok;
check_apps([App|Apps]) ->
case is_app(App) of
{ok, _} ->
check_apps(Apps);
Error ->
throw({error, {missing_app, {App, Error}}})
end.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fail(Reason) ->
exit({suite_failed, Reason}).
key1search(Key, L) ->
case lists:keysearch(Key, 1, L) of
undefined ->
fail({not_found, Key, L});
{value, {Key, Value}} ->
Value
end.
| Erlang | 6,294 | erl | 1 | 25.585366 | 75 | 0.563394 |
#lang scribble/doc
@(require scribble/manual scribble/eval "guide-utils.rkt"
(for-label racket/undefined
racket/shared))
@; @title[#:tag "void+undefined"]{Void and Undefined}
@title[#:tag "void+undefined"]{void 与 undefined}
@; Some procedures or expression forms have no need for a result
@; value. For example, the @racket[display] procedure is called only for
@; the side-effect of writing output. In such cases the result value is
@; normally a special constant that prints as @|void-const|. When the
@; result of an expression is simply @|void-const|, the @tech{REPL} does not
@; print anything.
有些过程或表达式形式无需产生结果值。例如，调用过程 @racket[display]
只是为了其写入到输出的副作用。此时的结果值一般为打印作 @|void-const|
的特殊常量当表达式的结果只是简单的 @|void-const| 时，@tech{REPL}
不会打印任何东西。
@; The @racket[void] procedure takes any number of arguments and returns
@; @|void-const|. (That is, the identifier @racketidfont{void} is bound
@; to a procedure that returns @|void-const|, instead of being bound
@; directly to @|void-const|.)
过程 @racket[void] 接受任意数量的参数并返回 @|void-const|。
（也就是说，标识符 @racketidfont{void} 被绑定到了一个返回 @|void-const|
的过程上，而非直接绑定到 @|void-const|。）
@examples[
(void)
(void 1 2 3)
(list (void))
]
@; The @racket[undefined] constant, which prints as @|undefined-const|, is
@; sometimes used as the result of a reference whose value is not yet
@; available. In previous versions of Racket (before version 6.1),
@; referencing a local binding too early produced @|undefined-const|;
@; too-early references now raise an exception, instead.
@; @margin-note{The @racket[undefined] result can still be produced
@; in some cases by the @racket[shared] form.}
常量 @racket[undefined] 打印为 @|undefined-const|，当某个引用的值不可用时，
它通常作为其结果来使用。在 6.1 版之前的 Racket 中，过早地引用局部绑定会产生
@|undefined-const|；而现在过早的引用则会触发一个异常。
@margin-note{@racket[undefined] 的结果也可以在某些使用 @racket[shared]
形式的情况下产生。}
@def+int[
(define (fails)
(define x x)
x)
(fails)
]
| Racket | 1,926 | scrbl | 4 | 32.644068 | 76 | 0.727934 |
End of preview. Expand
in Dataset Viewer.
bigcode/the-stack-smol-xs - all configs
All configs from bigcode/the-stack-smol-xs concatenated and shuffled. 100 examples each of:
['ada', 'agda', 'alloy', 'antlr', 'applescript', 'assembly', 'augeas', 'awk',
'batchfile', 'bison', 'bluespec', 'c', 'c++', 'c-sharp', 'clojure', 'cmake',
'coffeescript', 'common-lisp', 'css', 'cuda', 'dart', 'dockerfile', 'elixir',
'elm', 'emacs-lisp', 'erlang', 'f-sharp', 'fortran', 'glsl', 'go', 'groovy',
'haskell', 'html', 'idris', 'isabelle', 'java', 'java-server-pages',
'javascript', 'julia', 'kotlin', 'lean', 'literate-agda',
'literate-coffeescript', 'literate-haskell', 'lua', 'makefile', 'maple',
'markdown', 'mathematica', 'matlab', 'ocaml', 'pascal', 'perl', 'php',
'powershell', 'prolog', 'protocol-buffer', 'python', 'r', 'racket',
'restructuredtext', 'rmarkdown', 'ruby', 'rust', 'sas', 'scala', 'scheme',
'shell', 'smalltalk', 'solidity', 'sparql', 'sql', 'stan', 'standard-ml',
'stata', 'systemverilog', 'tcl', 'tcsh', 'tex', 'thrift', 'typescript',
'verilog', 'vhdl', 'visual-basic', 'xslt', 'yacc', 'zig']
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