Modular C
C◼F257◼Z—221: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—221: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
 
C◼F257◼𝔽—221 C◼F257◼generator—221 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot (C◼F257◼𝔽—221 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—add (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—sub (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—prod (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—div (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—mod (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—221◼_Operator—eq (C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—notnot (C◼F257◼𝔽—221 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—221 C◼F257◼order—221 (C◼F257◼𝔽—221 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—221
C◼snippet◼modulo◼contextC◼F257◼𝔽—221
C◼snippet◼modulo◼typeC◼F257◼𝔽—221
C◼snippet◼modulo◼orderC◼F257◼order—221
C◼snippet◼modulo◼generatorC◼F257◼generator—221
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—221

typedef _Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221

Definition at line 3318 of file C-F257.c.

Function Documentation

§ C◼F257◼order—221()

C◼F257◼𝔽—221 C◼F257◼order—221 ( C◼F257◼𝔽—221  x)

Compute the order of element .

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

Definition at line 3397 of file C-F257.c.

References C◼F257◼𝔽—221◼_Operator—add(), C◼F257◼𝔽—221◼_Operator—eq(), C◼F257◼𝔽—221◼_Operator—notnot(), and C◼F257◼𝔽—221◼_Operator—prod().

3397  {
3398 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3399  if (¬(C◼F257◼𝔽—221◼_Operator—notnot(x ))) return 0;
3400  C◼F257◼𝔽—221 y = x;
3401  for (C◼F257◼𝔽—221 i = 1; i; ((i )=(C◼F257◼𝔽—221◼_Operator—add(i , 1)))) {
3402 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3403  if (C◼F257◼𝔽—221◼_Operator—eq(y , 1 )) return i;
3405  }
3406  // should not be reached
3407  return 0;
3408 }
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—notnot(C◼F257◼𝔽—221 a)
Test if non-zero in ℤn.
Definition: C-F257.c:3381
_Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
Definition: C-F257.c:3318
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—add(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Operation in the ring ℤn.
Definition: C-F257.c:3347
_Bool C◼F257◼𝔽—221◼_Operator—eq(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Equality in the ring ℤn.
Definition: C-F257.c:3376
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—prod(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Operation in the ring ℤn.
Definition: C-F257.c:3359
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§ C◼F257◼𝔽—221◼_Operator—add()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—add ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Operation in the ring ℤn.

Definition at line 3347 of file C-F257.c.

References C◼F257◼𝔽—221◼_Operator—bnotbnot().

Referenced by C◼F257◼order—221().

3347  {
3348 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3349  C◼F257◼𝔽—221 ret = a + b;
3351 }
_Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
Definition: C-F257.c:3318
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot(C◼F257◼𝔽—221 a)
Map a into ℤn.
Definition: C-F257.c:3342
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§ C◼F257◼𝔽—221◼_Operator—bnotbnot()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot ( C◼F257◼𝔽—221  a)
inline

Map a into ℤn.

Definition at line 3342 of file C-F257.c.

Referenced by C◼F257◼𝔽—221◼_Operator—add(), C◼F257◼𝔽—221◼_Operator—eq(), and C◼F257◼𝔽—221◼_Operator—prod().

3342  {
3343 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3344  return a % _Intern◼_I584Rsma◼C◼F257◼Z—221◼mod₀;
3345 }
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§ C◼F257◼𝔽—221◼_Operator—div()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—div ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Operation in the ring ℤn.

Definition at line 3365 of file C-F257.c.

Referenced by C◼F257◼𝔽—221◼_Operator—mod().

3365  {
3366 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3367  C◼F257◼𝔽—221 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—221◼inverse(b);
3369 }
_Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
Definition: C-F257.c:3318
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot(C◼F257◼𝔽—221 a)
Map a into ℤn.
Definition: C-F257.c:3342
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§ C◼F257◼𝔽—221◼_Operator—eq()

_Bool C◼F257◼𝔽—221◼_Operator—eq ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Equality in the ring ℤn.

Definition at line 3376 of file C-F257.c.

References C◼F257◼𝔽—221◼_Operator—bnotbnot().

Referenced by C◼F257◼order—221().

3376  {
3377 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3379 }
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot(C◼F257◼𝔽—221 a)
Map a into ℤn.
Definition: C-F257.c:3342
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§ C◼F257◼𝔽—221◼_Operator—mod()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—mod ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Operation in the ring ℤn.

Definition at line 3371 of file C-F257.c.

References C◼F257◼𝔽—221◼_Operator—div(), C◼F257◼𝔽—221◼_Operator—prod(), and C◼F257◼𝔽—221◼_Operator—sub().

3371  {
3372 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3374 }
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—div(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Operation in the ring ℤn.
Definition: C-F257.c:3365
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—prod(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Operation in the ring ℤn.
Definition: C-F257.c:3359
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—sub(C◼F257◼𝔽—221 a, C◼F257◼𝔽—221 b)
Operation in the ring ℤn.
Definition: C-F257.c:3353
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§ C◼F257◼𝔽—221◼_Operator—notnot()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—notnot ( C◼F257◼𝔽—221  a)
inline

Test if non-zero in ℤn.

Definition at line 3381 of file C-F257.c.

Referenced by C◼F257◼order—221().

3381  {
3382 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3383  return ‼C◼F257◼𝔽—221◼_Operator—bnotbnot(a);
3384 }
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§ C◼F257◼𝔽—221◼_Operator—prod()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—prod ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Operation in the ring ℤn.

Definition at line 3359 of file C-F257.c.

References C◼F257◼𝔽—221◼_Operator—bnotbnot().

Referenced by C◼F257◼order—221(), and C◼F257◼𝔽—221◼_Operator—mod().

3359  {
3360 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3361  C◼F257◼𝔽—221 ret = a * b;
3363 }
_Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
Definition: C-F257.c:3318
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot(C◼F257◼𝔽—221 a)
Map a into ℤn.
Definition: C-F257.c:3342
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§ C◼F257◼𝔽—221◼_Operator—sub()

C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—sub ( C◼F257◼𝔽—221  a,
C◼F257◼𝔽—221  b 
)
inline

Operation in the ring ℤn.

Definition at line 3353 of file C-F257.c.

Referenced by C◼F257◼𝔽—221◼_Operator—mod().

3353  {
3354 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3355  C◼F257◼𝔽—221 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—221◼mod₀ - b);
3357 }
_Intern◼_I584Rsma◼C◼F257◼Z—221◼type₀ C◼F257◼𝔽—221
Definition: C-F257.c:3318
C◼F257◼𝔽—221 C◼F257◼𝔽—221◼_Operator—bnotbnot(C◼F257◼𝔽—221 a)
Map a into ℤn.
Definition: C-F257.c:3342
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Variable Documentation

§ C◼F257◼generator—221

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 3417 of file C-F257.c.