Modular C
C◼F257◼Z—109: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—109: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
 
C◼F257◼𝔽—109 C◼F257◼generator—109 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot (C◼F257◼𝔽—109 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—add (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—sub (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—prod (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—div (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—mod (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—109◼_Operator—eq (C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—notnot (C◼F257◼𝔽—109 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—109 C◼F257◼order—109 (C◼F257◼𝔽—109 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—109
C◼snippet◼modulo◼contextC◼F257◼𝔽—109
C◼snippet◼modulo◼typeC◼F257◼𝔽—109
C◼snippet◼modulo◼orderC◼F257◼order—109
C◼snippet◼modulo◼generatorC◼F257◼generator—109
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—109

typedef _Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109

Definition at line 7764 of file C-F257.c.

Function Documentation

§ C◼F257◼order—109()

C◼F257◼𝔽—109 C◼F257◼order—109 ( C◼F257◼𝔽—109  x)

Compute the order of element .

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

Definition at line 7843 of file C-F257.c.

References C◼F257◼𝔽—109◼_Operator—add(), C◼F257◼𝔽—109◼_Operator—eq(), C◼F257◼𝔽—109◼_Operator—notnot(), and C◼F257◼𝔽—109◼_Operator—prod().

7843  {
7844 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7845  if (¬(C◼F257◼𝔽—109◼_Operator—notnot(x ))) return 0;
7846  C◼F257◼𝔽—109 y = x;
7847  for (C◼F257◼𝔽—109 i = 1; i; ((i )=(C◼F257◼𝔽—109◼_Operator—add(i , 1)))) {
7848 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7849  if (C◼F257◼𝔽—109◼_Operator—eq(y , 1 )) return i;
7851  }
7852  // should not be reached
7853  return 0;
7854 }
_Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
Definition: C-F257.c:7764
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—prod(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Operation in the ring ℤn.
Definition: C-F257.c:7805
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—add(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Operation in the ring ℤn.
Definition: C-F257.c:7793
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—notnot(C◼F257◼𝔽—109 a)
Test if non-zero in ℤn.
Definition: C-F257.c:7827
_Bool C◼F257◼𝔽—109◼_Operator—eq(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Equality in the ring ℤn.
Definition: C-F257.c:7822
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§ C◼F257◼𝔽—109◼_Operator—add()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—add ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Operation in the ring ℤn.

Definition at line 7793 of file C-F257.c.

References C◼F257◼𝔽—109◼_Operator—bnotbnot().

Referenced by C◼F257◼order—109().

7793  {
7794 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7795  C◼F257◼𝔽—109 ret = a + b;
7797 }
_Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
Definition: C-F257.c:7764
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot(C◼F257◼𝔽—109 a)
Map a into ℤn.
Definition: C-F257.c:7788
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§ C◼F257◼𝔽—109◼_Operator—bnotbnot()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot ( C◼F257◼𝔽—109  a)
inline

Map a into ℤn.

Definition at line 7788 of file C-F257.c.

Referenced by C◼F257◼𝔽—109◼_Operator—add(), C◼F257◼𝔽—109◼_Operator—eq(), and C◼F257◼𝔽—109◼_Operator—prod().

7788  {
7789 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7790  return a % _Intern◼_I584Rsma◼C◼F257◼Z—109◼mod₀;
7791 }
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§ C◼F257◼𝔽—109◼_Operator—div()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—div ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Operation in the ring ℤn.

Definition at line 7811 of file C-F257.c.

Referenced by C◼F257◼𝔽—109◼_Operator—mod().

7811  {
7812 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7813  C◼F257◼𝔽—109 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—109◼inverse(b);
7815 }
_Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
Definition: C-F257.c:7764
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot(C◼F257◼𝔽—109 a)
Map a into ℤn.
Definition: C-F257.c:7788
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§ C◼F257◼𝔽—109◼_Operator—eq()

_Bool C◼F257◼𝔽—109◼_Operator—eq ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Equality in the ring ℤn.

Definition at line 7822 of file C-F257.c.

References C◼F257◼𝔽—109◼_Operator—bnotbnot().

Referenced by C◼F257◼order—109().

7822  {
7823 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7825 }
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot(C◼F257◼𝔽—109 a)
Map a into ℤn.
Definition: C-F257.c:7788
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§ C◼F257◼𝔽—109◼_Operator—mod()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—mod ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Operation in the ring ℤn.

Definition at line 7817 of file C-F257.c.

References C◼F257◼𝔽—109◼_Operator—div(), C◼F257◼𝔽—109◼_Operator—prod(), and C◼F257◼𝔽—109◼_Operator—sub().

7817  {
7818 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7820 }
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—sub(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Operation in the ring ℤn.
Definition: C-F257.c:7799
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—prod(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Operation in the ring ℤn.
Definition: C-F257.c:7805
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—div(C◼F257◼𝔽—109 a, C◼F257◼𝔽—109 b)
Operation in the ring ℤn.
Definition: C-F257.c:7811
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§ C◼F257◼𝔽—109◼_Operator—notnot()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—notnot ( C◼F257◼𝔽—109  a)
inline

Test if non-zero in ℤn.

Definition at line 7827 of file C-F257.c.

Referenced by C◼F257◼order—109().

7827  {
7828 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7829  return ‼C◼F257◼𝔽—109◼_Operator—bnotbnot(a);
7830 }
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§ C◼F257◼𝔽—109◼_Operator—prod()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—prod ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Operation in the ring ℤn.

Definition at line 7805 of file C-F257.c.

References C◼F257◼𝔽—109◼_Operator—bnotbnot().

Referenced by C◼F257◼order—109(), and C◼F257◼𝔽—109◼_Operator—mod().

7805  {
7806 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7807  C◼F257◼𝔽—109 ret = a * b;
7809 }
_Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
Definition: C-F257.c:7764
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot(C◼F257◼𝔽—109 a)
Map a into ℤn.
Definition: C-F257.c:7788
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§ C◼F257◼𝔽—109◼_Operator—sub()

C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—sub ( C◼F257◼𝔽—109  a,
C◼F257◼𝔽—109  b 
)
inline

Operation in the ring ℤn.

Definition at line 7799 of file C-F257.c.

Referenced by C◼F257◼𝔽—109◼_Operator—mod().

7799  {
7800 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
7801  C◼F257◼𝔽—109 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—109◼mod₀ - b);
7803 }
_Intern◼_I584Rsma◼C◼F257◼Z—109◼type₀ C◼F257◼𝔽—109
Definition: C-F257.c:7764
C◼F257◼𝔽—109 C◼F257◼𝔽—109◼_Operator—bnotbnot(C◼F257◼𝔽—109 a)
Map a into ℤn.
Definition: C-F257.c:7788
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Variable Documentation

§ C◼F257◼generator—109

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 7863 of file C-F257.c.