Modular C
C◼F257◼Z—2: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—2: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
 
C◼F257◼𝔽—2 C◼F257◼generator—2 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot (C◼F257◼𝔽—2 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—add (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—sub (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—prod (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—div (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—mod (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—2◼_Operator—eq (C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—notnot (C◼F257◼𝔽—2 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—2 C◼F257◼order—2 (C◼F257◼𝔽—2 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—2
C◼snippet◼modulo◼contextC◼F257◼𝔽—2
C◼snippet◼modulo◼typeC◼F257◼𝔽—2
C◼snippet◼modulo◼orderC◼F257◼order—2
C◼snippet◼modulo◼generatorC◼F257◼generator—2
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—2

typedef _Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2

Definition at line 14316 of file C-F257.c.

Function Documentation

§ C◼F257◼order—2()

C◼F257◼𝔽—2 C◼F257◼order—2 ( C◼F257◼𝔽—2  x)

Compute the order of element .

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

Definition at line 14395 of file C-F257.c.

References C◼F257◼𝔽—2◼_Operator—add(), C◼F257◼𝔽—2◼_Operator—eq(), C◼F257◼𝔽—2◼_Operator—notnot(), and C◼F257◼𝔽—2◼_Operator—prod().

14395  {
14396 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14397  if (¬(C◼F257◼𝔽—2◼_Operator—notnot(x ))) return 0;
14398  C◼F257◼𝔽—2 y = x;
14399  for (C◼F257◼𝔽—2 i = 1; i; ((i )=(C◼F257◼𝔽—2◼_Operator—add(i , 1)))) {
14400 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14401  if (C◼F257◼𝔽—2◼_Operator—eq(y , 1 )) return i;
14402  ((y )=(C◼F257◼𝔽—2◼_Operator—prod(y , x )));
14403  }
14404  // should not be reached
14405  return 0;
14406 }
_Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
Definition: C-F257.c:14316
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—add(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Operation in the ring ℤn.
Definition: C-F257.c:14345
_Bool C◼F257◼𝔽—2◼_Operator—eq(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Equality in the ring ℤn.
Definition: C-F257.c:14374
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—notnot(C◼F257◼𝔽—2 a)
Test if non-zero in ℤn.
Definition: C-F257.c:14379
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—prod(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Operation in the ring ℤn.
Definition: C-F257.c:14357
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§ C◼F257◼𝔽—2◼_Operator—add()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—add ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Operation in the ring ℤn.

Definition at line 14345 of file C-F257.c.

References C◼F257◼𝔽—2◼_Operator—bnotbnot().

Referenced by C◼F257◼order—2().

14345  {
14346 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14347  C◼F257◼𝔽—2 ret = a + b;
14349 }
_Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
Definition: C-F257.c:14316
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot(C◼F257◼𝔽—2 a)
Map a into ℤn.
Definition: C-F257.c:14340
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§ C◼F257◼𝔽—2◼_Operator—bnotbnot()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot ( C◼F257◼𝔽—2  a)
inline

Map a into ℤn.

Definition at line 14340 of file C-F257.c.

Referenced by C◼F257◼𝔽—2◼_Operator—add(), C◼F257◼𝔽—2◼_Operator—eq(), and C◼F257◼𝔽—2◼_Operator—prod().

14340  {
14341 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14342  return a % _Intern◼_I584Rsma◼C◼F257◼Z—2◼mod₀;
14343 }
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§ C◼F257◼𝔽—2◼_Operator—div()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—div ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Operation in the ring ℤn.

Definition at line 14363 of file C-F257.c.

Referenced by C◼F257◼𝔽—2◼_Operator—mod().

14363  {
14364 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14365  C◼F257◼𝔽—2 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—2◼inverse(b);
14367 }
_Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
Definition: C-F257.c:14316
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot(C◼F257◼𝔽—2 a)
Map a into ℤn.
Definition: C-F257.c:14340
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§ C◼F257◼𝔽—2◼_Operator—eq()

_Bool C◼F257◼𝔽—2◼_Operator—eq ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Equality in the ring ℤn.

Definition at line 14374 of file C-F257.c.

References C◼F257◼𝔽—2◼_Operator—bnotbnot().

Referenced by C◼F257◼order—2().

14374  {
14375 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14377 }
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot(C◼F257◼𝔽—2 a)
Map a into ℤn.
Definition: C-F257.c:14340
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§ C◼F257◼𝔽—2◼_Operator—mod()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—mod ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Operation in the ring ℤn.

Definition at line 14369 of file C-F257.c.

References C◼F257◼𝔽—2◼_Operator—div(), C◼F257◼𝔽—2◼_Operator—prod(), and C◼F257◼𝔽—2◼_Operator—sub().

14369  {
14370 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14372 }
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—sub(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Operation in the ring ℤn.
Definition: C-F257.c:14351
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—div(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Operation in the ring ℤn.
Definition: C-F257.c:14363
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—prod(C◼F257◼𝔽—2 a, C◼F257◼𝔽—2 b)
Operation in the ring ℤn.
Definition: C-F257.c:14357
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§ C◼F257◼𝔽—2◼_Operator—notnot()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—notnot ( C◼F257◼𝔽—2  a)
inline

Test if non-zero in ℤn.

Definition at line 14379 of file C-F257.c.

Referenced by C◼F257◼order—2().

14379  {
14380 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14381  return ‼C◼F257◼𝔽—2◼_Operator—bnotbnot(a);
14382 }
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§ C◼F257◼𝔽—2◼_Operator—prod()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—prod ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Operation in the ring ℤn.

Definition at line 14357 of file C-F257.c.

References C◼F257◼𝔽—2◼_Operator—bnotbnot().

Referenced by C◼F257◼order—2(), and C◼F257◼𝔽—2◼_Operator—mod().

14357  {
14358 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14359  C◼F257◼𝔽—2 ret = a * b;
14361 }
_Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
Definition: C-F257.c:14316
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot(C◼F257◼𝔽—2 a)
Map a into ℤn.
Definition: C-F257.c:14340
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§ C◼F257◼𝔽—2◼_Operator—sub()

C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—sub ( C◼F257◼𝔽—2  a,
C◼F257◼𝔽—2  b 
)
inline

Operation in the ring ℤn.

Definition at line 14351 of file C-F257.c.

Referenced by C◼F257◼𝔽—2◼_Operator—mod().

14351  {
14352 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
14353  C◼F257◼𝔽—2 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—2◼mod₀ - b);
14355 }
_Intern◼_I584Rsma◼C◼F257◼Z—2◼type₀ C◼F257◼𝔽—2
Definition: C-F257.c:14316
C◼F257◼𝔽—2 C◼F257◼𝔽—2◼_Operator—bnotbnot(C◼F257◼𝔽—2 a)
Map a into ℤn.
Definition: C-F257.c:14340
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Variable Documentation

§ C◼F257◼generator—2

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 14415 of file C-F257.c.