Modular C
C◼F257◼Z—71: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—71: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
 
C◼F257◼𝔽—71 C◼F257◼generator—71 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot (C◼F257◼𝔽—71 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—add (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—sub (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—prod (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—div (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—mod (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—71◼_Operator—eq (C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—notnot (C◼F257◼𝔽—71 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—71 C◼F257◼order—71 (C◼F257◼𝔽—71 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—71
C◼snippet◼modulo◼contextC◼F257◼𝔽—71
C◼snippet◼modulo◼typeC◼F257◼𝔽—71
C◼snippet◼modulo◼orderC◼F257◼order—71
C◼snippet◼modulo◼generatorC◼F257◼generator—71
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—71

typedef _Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71

Definition at line 9870 of file C-F257.c.

Function Documentation

§ C◼F257◼order—71()

C◼F257◼𝔽—71 C◼F257◼order—71 ( C◼F257◼𝔽—71  x)

Compute the order of element .

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

Definition at line 9949 of file C-F257.c.

References C◼F257◼𝔽—71◼_Operator—add(), C◼F257◼𝔽—71◼_Operator—eq(), C◼F257◼𝔽—71◼_Operator—notnot(), and C◼F257◼𝔽—71◼_Operator—prod().

9949  {
9950 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9951  if (¬(C◼F257◼𝔽—71◼_Operator—notnot(x ))) return 0;
9952  C◼F257◼𝔽—71 y = x;
9953  for (C◼F257◼𝔽—71 i = 1; i; ((i )=(C◼F257◼𝔽—71◼_Operator—add(i , 1)))) {
9954 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9955  if (C◼F257◼𝔽—71◼_Operator—eq(y , 1 )) return i;
9956  ((y )=(C◼F257◼𝔽—71◼_Operator—prod(y , x )));
9957  }
9958  // should not be reached
9959  return 0;
9960 }
_Bool C◼F257◼𝔽—71◼_Operator—eq(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Equality in the ring ℤn.
Definition: C-F257.c:9928
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—prod(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Operation in the ring ℤn.
Definition: C-F257.c:9911
_Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
Definition: C-F257.c:9870
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—add(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Operation in the ring ℤn.
Definition: C-F257.c:9899
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—notnot(C◼F257◼𝔽—71 a)
Test if non-zero in ℤn.
Definition: C-F257.c:9933
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§ C◼F257◼𝔽—71◼_Operator—add()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—add ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Operation in the ring ℤn.

Definition at line 9899 of file C-F257.c.

References C◼F257◼𝔽—71◼_Operator—bnotbnot().

Referenced by C◼F257◼order—71().

9899  {
9900 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9901  C◼F257◼𝔽—71 ret = a + b;
9903 }
_Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
Definition: C-F257.c:9870
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot(C◼F257◼𝔽—71 a)
Map a into ℤn.
Definition: C-F257.c:9894
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§ C◼F257◼𝔽—71◼_Operator—bnotbnot()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot ( C◼F257◼𝔽—71  a)
inline

Map a into ℤn.

Definition at line 9894 of file C-F257.c.

Referenced by C◼F257◼𝔽—71◼_Operator—add(), C◼F257◼𝔽—71◼_Operator—eq(), and C◼F257◼𝔽—71◼_Operator—prod().

9894  {
9895 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9896  return a % _Intern◼_I584Rsma◼C◼F257◼Z—71◼mod₀;
9897 }
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§ C◼F257◼𝔽—71◼_Operator—div()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—div ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Operation in the ring ℤn.

Definition at line 9917 of file C-F257.c.

Referenced by C◼F257◼𝔽—71◼_Operator—mod().

9917  {
9918 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9919  C◼F257◼𝔽—71 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—71◼inverse(b);
9921 }
_Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
Definition: C-F257.c:9870
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot(C◼F257◼𝔽—71 a)
Map a into ℤn.
Definition: C-F257.c:9894
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§ C◼F257◼𝔽—71◼_Operator—eq()

_Bool C◼F257◼𝔽—71◼_Operator—eq ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Equality in the ring ℤn.

Definition at line 9928 of file C-F257.c.

References C◼F257◼𝔽—71◼_Operator—bnotbnot().

Referenced by C◼F257◼order—71().

9928  {
9929 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9931 }
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot(C◼F257◼𝔽—71 a)
Map a into ℤn.
Definition: C-F257.c:9894
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§ C◼F257◼𝔽—71◼_Operator—mod()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—mod ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Operation in the ring ℤn.

Definition at line 9923 of file C-F257.c.

References C◼F257◼𝔽—71◼_Operator—div(), C◼F257◼𝔽—71◼_Operator—prod(), and C◼F257◼𝔽—71◼_Operator—sub().

9923  {
9924 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9926 }
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—prod(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Operation in the ring ℤn.
Definition: C-F257.c:9911
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—div(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Operation in the ring ℤn.
Definition: C-F257.c:9917
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—sub(C◼F257◼𝔽—71 a, C◼F257◼𝔽—71 b)
Operation in the ring ℤn.
Definition: C-F257.c:9905
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§ C◼F257◼𝔽—71◼_Operator—notnot()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—notnot ( C◼F257◼𝔽—71  a)
inline

Test if non-zero in ℤn.

Definition at line 9933 of file C-F257.c.

Referenced by C◼F257◼order—71().

9933  {
9934 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9935  return ‼C◼F257◼𝔽—71◼_Operator—bnotbnot(a);
9936 }
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§ C◼F257◼𝔽—71◼_Operator—prod()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—prod ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Operation in the ring ℤn.

Definition at line 9911 of file C-F257.c.

References C◼F257◼𝔽—71◼_Operator—bnotbnot().

Referenced by C◼F257◼order—71(), and C◼F257◼𝔽—71◼_Operator—mod().

9911  {
9912 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9913  C◼F257◼𝔽—71 ret = a * b;
9915 }
_Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
Definition: C-F257.c:9870
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot(C◼F257◼𝔽—71 a)
Map a into ℤn.
Definition: C-F257.c:9894
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§ C◼F257◼𝔽—71◼_Operator—sub()

C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—sub ( C◼F257◼𝔽—71  a,
C◼F257◼𝔽—71  b 
)
inline

Operation in the ring ℤn.

Definition at line 9905 of file C-F257.c.

Referenced by C◼F257◼𝔽—71◼_Operator—mod().

9905  {
9906 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9907  C◼F257◼𝔽—71 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—71◼mod₀ - b);
9909 }
_Intern◼_I584Rsma◼C◼F257◼Z—71◼type₀ C◼F257◼𝔽—71
Definition: C-F257.c:9870
C◼F257◼𝔽—71 C◼F257◼𝔽—71◼_Operator—bnotbnot(C◼F257◼𝔽—71 a)
Map a into ℤn.
Definition: C-F257.c:9894
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Variable Documentation

§ C◼F257◼generator—71

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 9969 of file C-F257.c.