Modular C
C◼F257◼Z—211: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—211: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
 
C◼F257◼𝔽—211 C◼F257◼generator—211 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot (C◼F257◼𝔽—211 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—add (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—sub (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—prod (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—div (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—mod (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—211◼_Operator—eq (C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—notnot (C◼F257◼𝔽—211 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—211 C◼F257◼order—211 (C◼F257◼𝔽—211 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—211
C◼snippet◼modulo◼contextC◼F257◼𝔽—211
C◼snippet◼modulo◼typeC◼F257◼𝔽—211
C◼snippet◼modulo◼orderC◼F257◼order—211
C◼snippet◼modulo◼generatorC◼F257◼generator—211
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—211

typedef _Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211

Definition at line 3552 of file C-F257.c.

Function Documentation

§ C◼F257◼order—211()

C◼F257◼𝔽—211 C◼F257◼order—211 ( C◼F257◼𝔽—211  x)

Compute the order of element .

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

Definition at line 3631 of file C-F257.c.

References C◼F257◼𝔽—211◼_Operator—add(), C◼F257◼𝔽—211◼_Operator—eq(), C◼F257◼𝔽—211◼_Operator—notnot(), and C◼F257◼𝔽—211◼_Operator—prod().

3631  {
3632 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3633  if (¬(C◼F257◼𝔽—211◼_Operator—notnot(x ))) return 0;
3634  C◼F257◼𝔽—211 y = x;
3635  for (C◼F257◼𝔽—211 i = 1; i; ((i )=(C◼F257◼𝔽—211◼_Operator—add(i , 1)))) {
3636 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3637  if (C◼F257◼𝔽—211◼_Operator—eq(y , 1 )) return i;
3639  }
3640  // should not be reached
3641  return 0;
3642 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—notnot(C◼F257◼𝔽—211 a)
Test if non-zero in ℤn.
Definition: C-F257.c:3615
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—prod(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Operation in the ring ℤn.
Definition: C-F257.c:3593
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—add(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Operation in the ring ℤn.
Definition: C-F257.c:3581
_Bool C◼F257◼𝔽—211◼_Operator—eq(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Equality in the ring ℤn.
Definition: C-F257.c:3610
_Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
Definition: C-F257.c:3552
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§ C◼F257◼𝔽—211◼_Operator—add()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—add ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Operation in the ring ℤn.

Definition at line 3581 of file C-F257.c.

References C◼F257◼𝔽—211◼_Operator—bnotbnot().

Referenced by C◼F257◼order—211().

3581  {
3582 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3583  C◼F257◼𝔽—211 ret = a + b;
3585 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot(C◼F257◼𝔽—211 a)
Map a into ℤn.
Definition: C-F257.c:3576
_Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
Definition: C-F257.c:3552
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§ C◼F257◼𝔽—211◼_Operator—bnotbnot()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot ( C◼F257◼𝔽—211  a)
inline

Map a into ℤn.

Definition at line 3576 of file C-F257.c.

Referenced by C◼F257◼𝔽—211◼_Operator—add(), C◼F257◼𝔽—211◼_Operator—eq(), and C◼F257◼𝔽—211◼_Operator—prod().

3576  {
3577 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3578  return a % _Intern◼_I584Rsma◼C◼F257◼Z—211◼mod₀;
3579 }
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§ C◼F257◼𝔽—211◼_Operator—div()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—div ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Operation in the ring ℤn.

Definition at line 3599 of file C-F257.c.

Referenced by C◼F257◼𝔽—211◼_Operator—mod().

3599  {
3600 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3601  C◼F257◼𝔽—211 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—211◼inverse(b);
3603 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot(C◼F257◼𝔽—211 a)
Map a into ℤn.
Definition: C-F257.c:3576
_Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
Definition: C-F257.c:3552
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§ C◼F257◼𝔽—211◼_Operator—eq()

_Bool C◼F257◼𝔽—211◼_Operator—eq ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Equality in the ring ℤn.

Definition at line 3610 of file C-F257.c.

References C◼F257◼𝔽—211◼_Operator—bnotbnot().

Referenced by C◼F257◼order—211().

3610  {
3611 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3613 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot(C◼F257◼𝔽—211 a)
Map a into ℤn.
Definition: C-F257.c:3576
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§ C◼F257◼𝔽—211◼_Operator—mod()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—mod ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Operation in the ring ℤn.

Definition at line 3605 of file C-F257.c.

References C◼F257◼𝔽—211◼_Operator—div(), C◼F257◼𝔽—211◼_Operator—prod(), and C◼F257◼𝔽—211◼_Operator—sub().

3605  {
3606 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3608 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—div(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Operation in the ring ℤn.
Definition: C-F257.c:3599
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—prod(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Operation in the ring ℤn.
Definition: C-F257.c:3593
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—sub(C◼F257◼𝔽—211 a, C◼F257◼𝔽—211 b)
Operation in the ring ℤn.
Definition: C-F257.c:3587
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§ C◼F257◼𝔽—211◼_Operator—notnot()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—notnot ( C◼F257◼𝔽—211  a)
inline

Test if non-zero in ℤn.

Definition at line 3615 of file C-F257.c.

Referenced by C◼F257◼order—211().

3615  {
3616 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3617  return ‼C◼F257◼𝔽—211◼_Operator—bnotbnot(a);
3618 }
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§ C◼F257◼𝔽—211◼_Operator—prod()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—prod ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Operation in the ring ℤn.

Definition at line 3593 of file C-F257.c.

References C◼F257◼𝔽—211◼_Operator—bnotbnot().

Referenced by C◼F257◼order—211(), and C◼F257◼𝔽—211◼_Operator—mod().

3593  {
3594 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3595  C◼F257◼𝔽—211 ret = a * b;
3597 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot(C◼F257◼𝔽—211 a)
Map a into ℤn.
Definition: C-F257.c:3576
_Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
Definition: C-F257.c:3552
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§ C◼F257◼𝔽—211◼_Operator—sub()

C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—sub ( C◼F257◼𝔽—211  a,
C◼F257◼𝔽—211  b 
)
inline

Operation in the ring ℤn.

Definition at line 3587 of file C-F257.c.

Referenced by C◼F257◼𝔽—211◼_Operator—mod().

3587  {
3588 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
3589  C◼F257◼𝔽—211 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—211◼mod₀ - b);
3591 }
C◼F257◼𝔽—211 C◼F257◼𝔽—211◼_Operator—bnotbnot(C◼F257◼𝔽—211 a)
Map a into ℤn.
Definition: C-F257.c:3576
_Intern◼_I584Rsma◼C◼F257◼Z—211◼type₀ C◼F257◼𝔽—211
Definition: C-F257.c:3552
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Variable Documentation

§ C◼F257◼generator—211

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 3651 of file C-F257.c.