Modular C
C◼F257◼Z—89: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—89: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
 
C◼F257◼𝔽—89 C◼F257◼generator—89 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot (C◼F257◼𝔽—89 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—add (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—sub (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—prod (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—div (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—mod (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—89◼_Operator—eq (C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—notnot (C◼F257◼𝔽—89 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—89 C◼F257◼order—89 (C◼F257◼𝔽—89 x)
 Compute the order of element . More...
 

Detailed Description

See also
C◼snippet◼modulo snippet: identifiers inserted directly to an importer for details
This import uses the following slot(s)
slotreplacement
C◼snippet◼modulo◼modC◼F257◼MOD—89
C◼snippet◼modulo◼contextC◼F257◼𝔽—89
C◼snippet◼modulo◼typeC◼F257◼𝔽—89
C◼snippet◼modulo◼orderC◼F257◼order—89
C◼snippet◼modulo◼generatorC◼F257◼generator—89
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—89

typedef _Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89

Definition at line 8934 of file C-F257.c.

Function Documentation

§ C◼F257◼order—89()

C◼F257◼𝔽—89 C◼F257◼order—89 ( C◼F257◼𝔽—89  x)

Compute the order of element .

The order is the smallest number r such that $x^{r} \mod n$.

Definition at line 9013 of file C-F257.c.

References C◼F257◼𝔽—89◼_Operator—add(), C◼F257◼𝔽—89◼_Operator—eq(), C◼F257◼𝔽—89◼_Operator—notnot(), and C◼F257◼𝔽—89◼_Operator—prod().

9013  {
9014 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9015  if (¬(C◼F257◼𝔽—89◼_Operator—notnot(x ))) return 0;
9016  C◼F257◼𝔽—89 y = x;
9017  for (C◼F257◼𝔽—89 i = 1; i; ((i )=(C◼F257◼𝔽—89◼_Operator—add(i , 1)))) {
9018 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9019  if (C◼F257◼𝔽—89◼_Operator—eq(y , 1 )) return i;
9020  ((y )=(C◼F257◼𝔽—89◼_Operator—prod(y , x )));
9021  }
9022  // should not be reached
9023  return 0;
9024 }
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—add(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Operation in the ring ℤn.
Definition: C-F257.c:8963
_Bool C◼F257◼𝔽—89◼_Operator—eq(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Equality in the ring ℤn.
Definition: C-F257.c:8992
_Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
Definition: C-F257.c:8934
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—prod(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Operation in the ring ℤn.
Definition: C-F257.c:8975
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—notnot(C◼F257◼𝔽—89 a)
Test if non-zero in ℤn.
Definition: C-F257.c:8997
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§ C◼F257◼𝔽—89◼_Operator—add()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—add ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Operation in the ring ℤn.

Definition at line 8963 of file C-F257.c.

References C◼F257◼𝔽—89◼_Operator—bnotbnot().

Referenced by C◼F257◼order—89().

8963  {
8964 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8965  C◼F257◼𝔽—89 ret = a + b;
8967 }
_Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
Definition: C-F257.c:8934
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot(C◼F257◼𝔽—89 a)
Map a into ℤn.
Definition: C-F257.c:8958
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§ C◼F257◼𝔽—89◼_Operator—bnotbnot()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot ( C◼F257◼𝔽—89  a)
inline

Map a into ℤn.

Definition at line 8958 of file C-F257.c.

Referenced by C◼F257◼𝔽—89◼_Operator—add(), C◼F257◼𝔽—89◼_Operator—eq(), and C◼F257◼𝔽—89◼_Operator—prod().

8958  {
8959 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8960  return a % _Intern◼_I584Rsma◼C◼F257◼Z—89◼mod₀;
8961 }
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§ C◼F257◼𝔽—89◼_Operator—div()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—div ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Operation in the ring ℤn.

Definition at line 8981 of file C-F257.c.

Referenced by C◼F257◼𝔽—89◼_Operator—mod().

8981  {
8982 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8983  C◼F257◼𝔽—89 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—89◼inverse(b);
8985 }
_Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
Definition: C-F257.c:8934
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot(C◼F257◼𝔽—89 a)
Map a into ℤn.
Definition: C-F257.c:8958
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§ C◼F257◼𝔽—89◼_Operator—eq()

_Bool C◼F257◼𝔽—89◼_Operator—eq ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Equality in the ring ℤn.

Definition at line 8992 of file C-F257.c.

References C◼F257◼𝔽—89◼_Operator—bnotbnot().

Referenced by C◼F257◼order—89().

8992  {
8993 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8995 }
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot(C◼F257◼𝔽—89 a)
Map a into ℤn.
Definition: C-F257.c:8958
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§ C◼F257◼𝔽—89◼_Operator—mod()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—mod ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Operation in the ring ℤn.

Definition at line 8987 of file C-F257.c.

References C◼F257◼𝔽—89◼_Operator—div(), C◼F257◼𝔽—89◼_Operator—prod(), and C◼F257◼𝔽—89◼_Operator—sub().

8987  {
8988 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8990 }
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—prod(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Operation in the ring ℤn.
Definition: C-F257.c:8975
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—sub(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Operation in the ring ℤn.
Definition: C-F257.c:8969
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—div(C◼F257◼𝔽—89 a, C◼F257◼𝔽—89 b)
Operation in the ring ℤn.
Definition: C-F257.c:8981
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§ C◼F257◼𝔽—89◼_Operator—notnot()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—notnot ( C◼F257◼𝔽—89  a)
inline

Test if non-zero in ℤn.

Definition at line 8997 of file C-F257.c.

Referenced by C◼F257◼order—89().

8997  {
8998 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8999  return ‼C◼F257◼𝔽—89◼_Operator—bnotbnot(a);
9000 }
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§ C◼F257◼𝔽—89◼_Operator—prod()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—prod ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Operation in the ring ℤn.

Definition at line 8975 of file C-F257.c.

References C◼F257◼𝔽—89◼_Operator—bnotbnot().

Referenced by C◼F257◼order—89(), and C◼F257◼𝔽—89◼_Operator—mod().

8975  {
8976 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8977  C◼F257◼𝔽—89 ret = a * b;
8979 }
_Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
Definition: C-F257.c:8934
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot(C◼F257◼𝔽—89 a)
Map a into ℤn.
Definition: C-F257.c:8958
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§ C◼F257◼𝔽—89◼_Operator—sub()

C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—sub ( C◼F257◼𝔽—89  a,
C◼F257◼𝔽—89  b 
)
inline

Operation in the ring ℤn.

Definition at line 8969 of file C-F257.c.

Referenced by C◼F257◼𝔽—89◼_Operator—mod().

8969  {
8970 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8971  C◼F257◼𝔽—89 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—89◼mod₀ - b);
8973 }
_Intern◼_I584Rsma◼C◼F257◼Z—89◼type₀ C◼F257◼𝔽—89
Definition: C-F257.c:8934
C◼F257◼𝔽—89 C◼F257◼𝔽—89◼_Operator—bnotbnot(C◼F257◼𝔽—89 a)
Map a into ℤn.
Definition: C-F257.c:8958
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Variable Documentation

§ C◼F257◼generator—89

A generator of the multiplicative group.

Remarks
This will only be computed automatically at program startup, if ◼C◼snippet◼modulo◼max_find is set to a high enough value.

Definition at line 9033 of file C-F257.c.