Modular C
C◼F257◼Z—13: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—13: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
 
C◼F257◼𝔽—13 C◼F257◼generator—13 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot (C◼F257◼𝔽—13 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—add (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—sub (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—prod (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—div (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—mod (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—13◼_Operator—eq (C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—notnot (C◼F257◼𝔽—13 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—13 C◼F257◼order—13 (C◼F257◼𝔽—13 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—13
C◼snippet◼modulo◼contextC◼F257◼𝔽—13
C◼snippet◼modulo◼typeC◼F257◼𝔽—13
C◼snippet◼modulo◼orderC◼F257◼order—13
C◼snippet◼modulo◼generatorC◼F257◼generator—13
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—13

typedef _Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13

Definition at line 13146 of file C-F257.c.

Function Documentation

§ C◼F257◼order—13()

C◼F257◼𝔽—13 C◼F257◼order—13 ( C◼F257◼𝔽—13  x)

Compute the order of element .

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

Definition at line 13225 of file C-F257.c.

References C◼F257◼𝔽—13◼_Operator—add(), C◼F257◼𝔽—13◼_Operator—eq(), C◼F257◼𝔽—13◼_Operator—notnot(), and C◼F257◼𝔽—13◼_Operator—prod().

13225  {
13226 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13227  if (¬(C◼F257◼𝔽—13◼_Operator—notnot(x ))) return 0;
13228  C◼F257◼𝔽—13 y = x;
13229  for (C◼F257◼𝔽—13 i = 1; i; ((i )=(C◼F257◼𝔽—13◼_Operator—add(i , 1)))) {
13230 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13231  if (C◼F257◼𝔽—13◼_Operator—eq(y , 1 )) return i;
13232  ((y )=(C◼F257◼𝔽—13◼_Operator—prod(y , x )));
13233  }
13234  // should not be reached
13235  return 0;
13236 }
_Bool C◼F257◼𝔽—13◼_Operator—eq(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Equality in the ring ℤn.
Definition: C-F257.c:13204
_Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
Definition: C-F257.c:13146
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—prod(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Operation in the ring ℤn.
Definition: C-F257.c:13187
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—notnot(C◼F257◼𝔽—13 a)
Test if non-zero in ℤn.
Definition: C-F257.c:13209
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—add(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Operation in the ring ℤn.
Definition: C-F257.c:13175
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§ C◼F257◼𝔽—13◼_Operator—add()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—add ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Operation in the ring ℤn.

Definition at line 13175 of file C-F257.c.

References C◼F257◼𝔽—13◼_Operator—bnotbnot().

Referenced by C◼F257◼order—13().

13175  {
13176 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13177  C◼F257◼𝔽—13 ret = a + b;
13179 }
_Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
Definition: C-F257.c:13146
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot(C◼F257◼𝔽—13 a)
Map a into ℤn.
Definition: C-F257.c:13170
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§ C◼F257◼𝔽—13◼_Operator—bnotbnot()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot ( C◼F257◼𝔽—13  a)
inline

Map a into ℤn.

Definition at line 13170 of file C-F257.c.

Referenced by C◼F257◼𝔽—13◼_Operator—add(), C◼F257◼𝔽—13◼_Operator—eq(), and C◼F257◼𝔽—13◼_Operator—prod().

13170  {
13171 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13172  return a % _Intern◼_I584Rsma◼C◼F257◼Z—13◼mod₀;
13173 }
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§ C◼F257◼𝔽—13◼_Operator—div()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—div ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Operation in the ring ℤn.

Definition at line 13193 of file C-F257.c.

Referenced by C◼F257◼𝔽—13◼_Operator—mod().

13193  {
13194 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13195  C◼F257◼𝔽—13 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—13◼inverse(b);
13197 }
_Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
Definition: C-F257.c:13146
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot(C◼F257◼𝔽—13 a)
Map a into ℤn.
Definition: C-F257.c:13170
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§ C◼F257◼𝔽—13◼_Operator—eq()

_Bool C◼F257◼𝔽—13◼_Operator—eq ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Equality in the ring ℤn.

Definition at line 13204 of file C-F257.c.

References C◼F257◼𝔽—13◼_Operator—bnotbnot().

Referenced by C◼F257◼order—13().

13204  {
13205 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13207 }
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot(C◼F257◼𝔽—13 a)
Map a into ℤn.
Definition: C-F257.c:13170
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§ C◼F257◼𝔽—13◼_Operator—mod()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—mod ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Operation in the ring ℤn.

Definition at line 13199 of file C-F257.c.

References C◼F257◼𝔽—13◼_Operator—div(), C◼F257◼𝔽—13◼_Operator—prod(), and C◼F257◼𝔽—13◼_Operator—sub().

13199  {
13200 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13202 }
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—sub(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Operation in the ring ℤn.
Definition: C-F257.c:13181
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—prod(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Operation in the ring ℤn.
Definition: C-F257.c:13187
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—div(C◼F257◼𝔽—13 a, C◼F257◼𝔽—13 b)
Operation in the ring ℤn.
Definition: C-F257.c:13193
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§ C◼F257◼𝔽—13◼_Operator—notnot()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—notnot ( C◼F257◼𝔽—13  a)
inline

Test if non-zero in ℤn.

Definition at line 13209 of file C-F257.c.

Referenced by C◼F257◼order—13().

13209  {
13210 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13211  return ‼C◼F257◼𝔽—13◼_Operator—bnotbnot(a);
13212 }
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§ C◼F257◼𝔽—13◼_Operator—prod()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—prod ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Operation in the ring ℤn.

Definition at line 13187 of file C-F257.c.

References C◼F257◼𝔽—13◼_Operator—bnotbnot().

Referenced by C◼F257◼order—13(), and C◼F257◼𝔽—13◼_Operator—mod().

13187  {
13188 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13189  C◼F257◼𝔽—13 ret = a * b;
13191 }
_Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
Definition: C-F257.c:13146
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot(C◼F257◼𝔽—13 a)
Map a into ℤn.
Definition: C-F257.c:13170
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§ C◼F257◼𝔽—13◼_Operator—sub()

C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—sub ( C◼F257◼𝔽—13  a,
C◼F257◼𝔽—13  b 
)
inline

Operation in the ring ℤn.

Definition at line 13181 of file C-F257.c.

Referenced by C◼F257◼𝔽—13◼_Operator—mod().

13181  {
13182 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
13183  C◼F257◼𝔽—13 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—13◼mod₀ - b);
13185 }
_Intern◼_I584Rsma◼C◼F257◼Z—13◼type₀ C◼F257◼𝔽—13
Definition: C-F257.c:13146
C◼F257◼𝔽—13 C◼F257◼𝔽—13◼_Operator—bnotbnot(C◼F257◼𝔽—13 a)
Map a into ℤn.
Definition: C-F257.c:13170
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Variable Documentation

§ C◼F257◼generator—13

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 13245 of file C-F257.c.