Modular C
C◼F257◼Z—97: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—97: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
 
C◼F257◼𝔽—97 C◼F257◼generator—97 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot (C◼F257◼𝔽—97 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—add (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—sub (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—prod (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—div (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—mod (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—97◼_Operator—eq (C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—notnot (C◼F257◼𝔽—97 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—97 C◼F257◼order—97 (C◼F257◼𝔽—97 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—97
C◼snippet◼modulo◼contextC◼F257◼𝔽—97
C◼snippet◼modulo◼typeC◼F257◼𝔽—97
C◼snippet◼modulo◼orderC◼F257◼order—97
C◼snippet◼modulo◼generatorC◼F257◼generator—97
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—97

typedef _Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97

Definition at line 8700 of file C-F257.c.

Function Documentation

§ C◼F257◼order—97()

C◼F257◼𝔽—97 C◼F257◼order—97 ( C◼F257◼𝔽—97  x)

Compute the order of element .

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

Definition at line 8779 of file C-F257.c.

References C◼F257◼𝔽—97◼_Operator—add(), C◼F257◼𝔽—97◼_Operator—eq(), C◼F257◼𝔽—97◼_Operator—notnot(), and C◼F257◼𝔽—97◼_Operator—prod().

8779  {
8780 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8781  if (¬(C◼F257◼𝔽—97◼_Operator—notnot(x ))) return 0;
8782  C◼F257◼𝔽—97 y = x;
8783  for (C◼F257◼𝔽—97 i = 1; i; ((i )=(C◼F257◼𝔽—97◼_Operator—add(i , 1)))) {
8784 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8785  if (C◼F257◼𝔽—97◼_Operator—eq(y , 1 )) return i;
8786  ((y )=(C◼F257◼𝔽—97◼_Operator—prod(y , x )));
8787  }
8788  // should not be reached
8789  return 0;
8790 }
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—prod(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Operation in the ring ℤn.
Definition: C-F257.c:8741
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—notnot(C◼F257◼𝔽—97 a)
Test if non-zero in ℤn.
Definition: C-F257.c:8763
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—add(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Operation in the ring ℤn.
Definition: C-F257.c:8729
_Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
Definition: C-F257.c:8700
_Bool C◼F257◼𝔽—97◼_Operator—eq(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Equality in the ring ℤn.
Definition: C-F257.c:8758
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§ C◼F257◼𝔽—97◼_Operator—add()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—add ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Operation in the ring ℤn.

Definition at line 8729 of file C-F257.c.

References C◼F257◼𝔽—97◼_Operator—bnotbnot().

Referenced by C◼F257◼order—97().

8729  {
8730 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8731  C◼F257◼𝔽—97 ret = a + b;
8733 }
_Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
Definition: C-F257.c:8700
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot(C◼F257◼𝔽—97 a)
Map a into ℤn.
Definition: C-F257.c:8724
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§ C◼F257◼𝔽—97◼_Operator—bnotbnot()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot ( C◼F257◼𝔽—97  a)
inline

Map a into ℤn.

Definition at line 8724 of file C-F257.c.

Referenced by C◼F257◼𝔽—97◼_Operator—add(), C◼F257◼𝔽—97◼_Operator—eq(), and C◼F257◼𝔽—97◼_Operator—prod().

8724  {
8725 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8726  return a % _Intern◼_I584Rsma◼C◼F257◼Z—97◼mod₀;
8727 }
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§ C◼F257◼𝔽—97◼_Operator—div()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—div ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Operation in the ring ℤn.

Definition at line 8747 of file C-F257.c.

Referenced by C◼F257◼𝔽—97◼_Operator—mod().

8747  {
8748 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8749  C◼F257◼𝔽—97 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—97◼inverse(b);
8751 }
_Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
Definition: C-F257.c:8700
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot(C◼F257◼𝔽—97 a)
Map a into ℤn.
Definition: C-F257.c:8724
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§ C◼F257◼𝔽—97◼_Operator—eq()

_Bool C◼F257◼𝔽—97◼_Operator—eq ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Equality in the ring ℤn.

Definition at line 8758 of file C-F257.c.

References C◼F257◼𝔽—97◼_Operator—bnotbnot().

Referenced by C◼F257◼order—97().

8758  {
8759 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8761 }
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot(C◼F257◼𝔽—97 a)
Map a into ℤn.
Definition: C-F257.c:8724
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§ C◼F257◼𝔽—97◼_Operator—mod()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—mod ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Operation in the ring ℤn.

Definition at line 8753 of file C-F257.c.

References C◼F257◼𝔽—97◼_Operator—div(), C◼F257◼𝔽—97◼_Operator—prod(), and C◼F257◼𝔽—97◼_Operator—sub().

8753  {
8754 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8756 }
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—prod(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Operation in the ring ℤn.
Definition: C-F257.c:8741
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—div(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Operation in the ring ℤn.
Definition: C-F257.c:8747
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—sub(C◼F257◼𝔽—97 a, C◼F257◼𝔽—97 b)
Operation in the ring ℤn.
Definition: C-F257.c:8735
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§ C◼F257◼𝔽—97◼_Operator—notnot()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—notnot ( C◼F257◼𝔽—97  a)
inline

Test if non-zero in ℤn.

Definition at line 8763 of file C-F257.c.

Referenced by C◼F257◼order—97().

8763  {
8764 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8765  return ‼C◼F257◼𝔽—97◼_Operator—bnotbnot(a);
8766 }
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§ C◼F257◼𝔽—97◼_Operator—prod()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—prod ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Operation in the ring ℤn.

Definition at line 8741 of file C-F257.c.

References C◼F257◼𝔽—97◼_Operator—bnotbnot().

Referenced by C◼F257◼order—97(), and C◼F257◼𝔽—97◼_Operator—mod().

8741  {
8742 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8743  C◼F257◼𝔽—97 ret = a * b;
8745 }
_Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
Definition: C-F257.c:8700
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot(C◼F257◼𝔽—97 a)
Map a into ℤn.
Definition: C-F257.c:8724
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§ C◼F257◼𝔽—97◼_Operator—sub()

C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—sub ( C◼F257◼𝔽—97  a,
C◼F257◼𝔽—97  b 
)
inline

Operation in the ring ℤn.

Definition at line 8735 of file C-F257.c.

Referenced by C◼F257◼𝔽—97◼_Operator—mod().

8735  {
8736 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
8737  C◼F257◼𝔽—97 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—97◼mod₀ - b);
8739 }
_Intern◼_I584Rsma◼C◼F257◼Z—97◼type₀ C◼F257◼𝔽—97
Definition: C-F257.c:8700
C◼F257◼𝔽—97 C◼F257◼𝔽—97◼_Operator—bnotbnot(C◼F257◼𝔽—97 a)
Map a into ℤn.
Definition: C-F257.c:8724
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Variable Documentation

§ C◼F257◼generator—97

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 8799 of file C-F257.c.