Modular C
C◼F257◼Z—167: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—167: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
 
C◼F257◼𝔽—167 C◼F257◼generator—167 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot (C◼F257◼𝔽—167 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—add (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—sub (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—prod (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—div (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—mod (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—167◼_Operator—eq (C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—notnot (C◼F257◼𝔽—167 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—167 C◼F257◼order—167 (C◼F257◼𝔽—167 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—167
C◼snippet◼modulo◼contextC◼F257◼𝔽—167
C◼snippet◼modulo◼typeC◼F257◼𝔽—167
C◼snippet◼modulo◼orderC◼F257◼order—167
C◼snippet◼modulo◼generatorC◼F257◼generator—167
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—167

typedef _Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167

Definition at line 5424 of file C-F257.c.

Function Documentation

§ C◼F257◼order—167()

C◼F257◼𝔽—167 C◼F257◼order—167 ( C◼F257◼𝔽—167  x)

Compute the order of element .

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

Definition at line 5503 of file C-F257.c.

References C◼F257◼𝔽—167◼_Operator—add(), C◼F257◼𝔽—167◼_Operator—eq(), C◼F257◼𝔽—167◼_Operator—notnot(), and C◼F257◼𝔽—167◼_Operator—prod().

5503  {
5504 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5505  if (¬(C◼F257◼𝔽—167◼_Operator—notnot(x ))) return 0;
5506  C◼F257◼𝔽—167 y = x;
5507  for (C◼F257◼𝔽—167 i = 1; i; ((i )=(C◼F257◼𝔽—167◼_Operator—add(i , 1)))) {
5508 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5509  if (C◼F257◼𝔽—167◼_Operator—eq(y , 1 )) return i;
5511  }
5512  // should not be reached
5513  return 0;
5514 }
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—prod(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Operation in the ring ℤn.
Definition: C-F257.c:5465
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—notnot(C◼F257◼𝔽—167 a)
Test if non-zero in ℤn.
Definition: C-F257.c:5487
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—add(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Operation in the ring ℤn.
Definition: C-F257.c:5453
_Bool C◼F257◼𝔽—167◼_Operator—eq(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Equality in the ring ℤn.
Definition: C-F257.c:5482
_Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
Definition: C-F257.c:5424
+ Here is the call graph for this function:

§ C◼F257◼𝔽—167◼_Operator—add()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—add ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Operation in the ring ℤn.

Definition at line 5453 of file C-F257.c.

References C◼F257◼𝔽—167◼_Operator—bnotbnot().

Referenced by C◼F257◼order—167().

5453  {
5454 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5455  C◼F257◼𝔽—167 ret = a + b;
5457 }
_Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
Definition: C-F257.c:5424
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot(C◼F257◼𝔽—167 a)
Map a into ℤn.
Definition: C-F257.c:5448
+ Here is the call graph for this function:
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—bnotbnot()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot ( C◼F257◼𝔽—167  a)
inline

Map a into ℤn.

Definition at line 5448 of file C-F257.c.

Referenced by C◼F257◼𝔽—167◼_Operator—add(), C◼F257◼𝔽—167◼_Operator—eq(), and C◼F257◼𝔽—167◼_Operator—prod().

5448  {
5449 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5450  return a % _Intern◼_I584Rsma◼C◼F257◼Z—167◼mod₀;
5451 }
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—div()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—div ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Operation in the ring ℤn.

Definition at line 5471 of file C-F257.c.

Referenced by C◼F257◼𝔽—167◼_Operator—mod().

5471  {
5472 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5473  C◼F257◼𝔽—167 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—167◼inverse(b);
5475 }
_Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
Definition: C-F257.c:5424
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot(C◼F257◼𝔽—167 a)
Map a into ℤn.
Definition: C-F257.c:5448
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—eq()

_Bool C◼F257◼𝔽—167◼_Operator—eq ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Equality in the ring ℤn.

Definition at line 5482 of file C-F257.c.

References C◼F257◼𝔽—167◼_Operator—bnotbnot().

Referenced by C◼F257◼order—167().

5482  {
5483 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5485 }
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot(C◼F257◼𝔽—167 a)
Map a into ℤn.
Definition: C-F257.c:5448
+ Here is the call graph for this function:
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—mod()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—mod ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Operation in the ring ℤn.

Definition at line 5477 of file C-F257.c.

References C◼F257◼𝔽—167◼_Operator—div(), C◼F257◼𝔽—167◼_Operator—prod(), and C◼F257◼𝔽—167◼_Operator—sub().

5477  {
5478 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5480 }
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—div(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Operation in the ring ℤn.
Definition: C-F257.c:5471
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—prod(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Operation in the ring ℤn.
Definition: C-F257.c:5465
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—sub(C◼F257◼𝔽—167 a, C◼F257◼𝔽—167 b)
Operation in the ring ℤn.
Definition: C-F257.c:5459
+ Here is the call graph for this function:

§ C◼F257◼𝔽—167◼_Operator—notnot()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—notnot ( C◼F257◼𝔽—167  a)
inline

Test if non-zero in ℤn.

Definition at line 5487 of file C-F257.c.

Referenced by C◼F257◼order—167().

5487  {
5488 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5489  return ‼C◼F257◼𝔽—167◼_Operator—bnotbnot(a);
5490 }
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—prod()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—prod ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Operation in the ring ℤn.

Definition at line 5465 of file C-F257.c.

References C◼F257◼𝔽—167◼_Operator—bnotbnot().

Referenced by C◼F257◼order—167(), and C◼F257◼𝔽—167◼_Operator—mod().

5465  {
5466 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5467  C◼F257◼𝔽—167 ret = a * b;
5469 }
_Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
Definition: C-F257.c:5424
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot(C◼F257◼𝔽—167 a)
Map a into ℤn.
Definition: C-F257.c:5448
+ Here is the call graph for this function:
+ Here is the caller graph for this function:

§ C◼F257◼𝔽—167◼_Operator—sub()

C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—sub ( C◼F257◼𝔽—167  a,
C◼F257◼𝔽—167  b 
)
inline

Operation in the ring ℤn.

Definition at line 5459 of file C-F257.c.

Referenced by C◼F257◼𝔽—167◼_Operator—mod().

5459  {
5460 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
5461  C◼F257◼𝔽—167 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—167◼mod₀ - b);
5463 }
_Intern◼_I584Rsma◼C◼F257◼Z—167◼type₀ C◼F257◼𝔽—167
Definition: C-F257.c:5424
C◼F257◼𝔽—167 C◼F257◼𝔽—167◼_Operator—bnotbnot(C◼F257◼𝔽—167 a)
Map a into ℤn.
Definition: C-F257.c:5448
+ Here is the caller graph for this function:

Variable Documentation

§ C◼F257◼generator—167

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 5523 of file C-F257.c.