Modular C
C◼F257◼Z—191: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—191: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
 
C◼F257◼𝔽—191 C◼F257◼generator—191 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot (C◼F257◼𝔽—191 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—add (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—sub (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—prod (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—div (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—mod (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—191◼_Operator—eq (C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—notnot (C◼F257◼𝔽—191 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—191 C◼F257◼order—191 (C◼F257◼𝔽—191 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—191
C◼snippet◼modulo◼contextC◼F257◼𝔽—191
C◼snippet◼modulo◼typeC◼F257◼𝔽—191
C◼snippet◼modulo◼orderC◼F257◼order—191
C◼snippet◼modulo◼generatorC◼F257◼generator—191
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—191

typedef _Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191

Definition at line 4488 of file C-F257.c.

Function Documentation

§ C◼F257◼order—191()

C◼F257◼𝔽—191 C◼F257◼order—191 ( C◼F257◼𝔽—191  x)

Compute the order of element .

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

Definition at line 4567 of file C-F257.c.

References C◼F257◼𝔽—191◼_Operator—add(), C◼F257◼𝔽—191◼_Operator—eq(), C◼F257◼𝔽—191◼_Operator—notnot(), and C◼F257◼𝔽—191◼_Operator—prod().

4567  {
4568 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4569  if (¬(C◼F257◼𝔽—191◼_Operator—notnot(x ))) return 0;
4570  C◼F257◼𝔽—191 y = x;
4571  for (C◼F257◼𝔽—191 i = 1; i; ((i )=(C◼F257◼𝔽—191◼_Operator—add(i , 1)))) {
4572 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4573  if (C◼F257◼𝔽—191◼_Operator—eq(y , 1 )) return i;
4575  }
4576  // should not be reached
4577  return 0;
4578 }
_Bool C◼F257◼𝔽—191◼_Operator—eq(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Equality in the ring ℤn.
Definition: C-F257.c:4546
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—notnot(C◼F257◼𝔽—191 a)
Test if non-zero in ℤn.
Definition: C-F257.c:4551
_Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
Definition: C-F257.c:4488
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—prod(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Operation in the ring ℤn.
Definition: C-F257.c:4529
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—add(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Operation in the ring ℤn.
Definition: C-F257.c:4517
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§ C◼F257◼𝔽—191◼_Operator—add()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—add ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Operation in the ring ℤn.

Definition at line 4517 of file C-F257.c.

References C◼F257◼𝔽—191◼_Operator—bnotbnot().

Referenced by C◼F257◼order—191().

4517  {
4518 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4519  C◼F257◼𝔽—191 ret = a + b;
4521 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot(C◼F257◼𝔽—191 a)
Map a into ℤn.
Definition: C-F257.c:4512
_Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
Definition: C-F257.c:4488
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§ C◼F257◼𝔽—191◼_Operator—bnotbnot()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot ( C◼F257◼𝔽—191  a)
inline

Map a into ℤn.

Definition at line 4512 of file C-F257.c.

Referenced by C◼F257◼𝔽—191◼_Operator—add(), C◼F257◼𝔽—191◼_Operator—eq(), and C◼F257◼𝔽—191◼_Operator—prod().

4512  {
4513 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4514  return a % _Intern◼_I584Rsma◼C◼F257◼Z—191◼mod₀;
4515 }
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§ C◼F257◼𝔽—191◼_Operator—div()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—div ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Operation in the ring ℤn.

Definition at line 4535 of file C-F257.c.

Referenced by C◼F257◼𝔽—191◼_Operator—mod().

4535  {
4536 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4537  C◼F257◼𝔽—191 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—191◼inverse(b);
4539 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot(C◼F257◼𝔽—191 a)
Map a into ℤn.
Definition: C-F257.c:4512
_Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
Definition: C-F257.c:4488
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§ C◼F257◼𝔽—191◼_Operator—eq()

_Bool C◼F257◼𝔽—191◼_Operator—eq ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Equality in the ring ℤn.

Definition at line 4546 of file C-F257.c.

References C◼F257◼𝔽—191◼_Operator—bnotbnot().

Referenced by C◼F257◼order—191().

4546  {
4547 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4549 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot(C◼F257◼𝔽—191 a)
Map a into ℤn.
Definition: C-F257.c:4512
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§ C◼F257◼𝔽—191◼_Operator—mod()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—mod ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Operation in the ring ℤn.

Definition at line 4541 of file C-F257.c.

References C◼F257◼𝔽—191◼_Operator—div(), C◼F257◼𝔽—191◼_Operator—prod(), and C◼F257◼𝔽—191◼_Operator—sub().

4541  {
4542 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4544 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—sub(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Operation in the ring ℤn.
Definition: C-F257.c:4523
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—div(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Operation in the ring ℤn.
Definition: C-F257.c:4535
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—prod(C◼F257◼𝔽—191 a, C◼F257◼𝔽—191 b)
Operation in the ring ℤn.
Definition: C-F257.c:4529
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§ C◼F257◼𝔽—191◼_Operator—notnot()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—notnot ( C◼F257◼𝔽—191  a)
inline

Test if non-zero in ℤn.

Definition at line 4551 of file C-F257.c.

Referenced by C◼F257◼order—191().

4551  {
4552 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4553  return ‼C◼F257◼𝔽—191◼_Operator—bnotbnot(a);
4554 }
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§ C◼F257◼𝔽—191◼_Operator—prod()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—prod ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Operation in the ring ℤn.

Definition at line 4529 of file C-F257.c.

References C◼F257◼𝔽—191◼_Operator—bnotbnot().

Referenced by C◼F257◼order—191(), and C◼F257◼𝔽—191◼_Operator—mod().

4529  {
4530 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4531  C◼F257◼𝔽—191 ret = a * b;
4533 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot(C◼F257◼𝔽—191 a)
Map a into ℤn.
Definition: C-F257.c:4512
_Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
Definition: C-F257.c:4488
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§ C◼F257◼𝔽—191◼_Operator—sub()

C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—sub ( C◼F257◼𝔽—191  a,
C◼F257◼𝔽—191  b 
)
inline

Operation in the ring ℤn.

Definition at line 4523 of file C-F257.c.

Referenced by C◼F257◼𝔽—191◼_Operator—mod().

4523  {
4524 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
4525  C◼F257◼𝔽—191 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—191◼mod₀ - b);
4527 }
C◼F257◼𝔽—191 C◼F257◼𝔽—191◼_Operator—bnotbnot(C◼F257◼𝔽—191 a)
Map a into ℤn.
Definition: C-F257.c:4512
_Intern◼_I584Rsma◼C◼F257◼Z—191◼type₀ C◼F257◼𝔽—191
Definition: C-F257.c:4488
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Variable Documentation

§ C◼F257◼generator—191

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 4587 of file C-F257.c.