Modular C
C◼F257◼Z—73: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—73: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
 
C◼F257◼𝔽—73 C◼F257◼generator—73 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot (C◼F257◼𝔽—73 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—add (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—sub (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—prod (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—div (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—mod (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—73◼_Operator—eq (C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—notnot (C◼F257◼𝔽—73 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—73 C◼F257◼order—73 (C◼F257◼𝔽—73 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—73
C◼snippet◼modulo◼contextC◼F257◼𝔽—73
C◼snippet◼modulo◼typeC◼F257◼𝔽—73
C◼snippet◼modulo◼orderC◼F257◼order—73
C◼snippet◼modulo◼generatorC◼F257◼generator—73
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—73

typedef _Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73

Definition at line 9636 of file C-F257.c.

Function Documentation

§ C◼F257◼order—73()

C◼F257◼𝔽—73 C◼F257◼order—73 ( C◼F257◼𝔽—73  x)

Compute the order of element .

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

Definition at line 9715 of file C-F257.c.

References C◼F257◼𝔽—73◼_Operator—add(), C◼F257◼𝔽—73◼_Operator—eq(), C◼F257◼𝔽—73◼_Operator—notnot(), and C◼F257◼𝔽—73◼_Operator—prod().

9715  {
9716 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9717  if (¬(C◼F257◼𝔽—73◼_Operator—notnot(x ))) return 0;
9718  C◼F257◼𝔽—73 y = x;
9719  for (C◼F257◼𝔽—73 i = 1; i; ((i )=(C◼F257◼𝔽—73◼_Operator—add(i , 1)))) {
9720 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9721  if (C◼F257◼𝔽—73◼_Operator—eq(y , 1 )) return i;
9722  ((y )=(C◼F257◼𝔽—73◼_Operator—prod(y , x )));
9723  }
9724  // should not be reached
9725  return 0;
9726 }
_Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
Definition: C-F257.c:9636
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—notnot(C◼F257◼𝔽—73 a)
Test if non-zero in ℤn.
Definition: C-F257.c:9699
_Bool C◼F257◼𝔽—73◼_Operator—eq(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Equality in the ring ℤn.
Definition: C-F257.c:9694
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—add(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Operation in the ring ℤn.
Definition: C-F257.c:9665
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—prod(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Operation in the ring ℤn.
Definition: C-F257.c:9677
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§ C◼F257◼𝔽—73◼_Operator—add()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—add ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Operation in the ring ℤn.

Definition at line 9665 of file C-F257.c.

References C◼F257◼𝔽—73◼_Operator—bnotbnot().

Referenced by C◼F257◼order—73().

9665  {
9666 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9667  C◼F257◼𝔽—73 ret = a + b;
9669 }
_Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
Definition: C-F257.c:9636
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot(C◼F257◼𝔽—73 a)
Map a into ℤn.
Definition: C-F257.c:9660
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§ C◼F257◼𝔽—73◼_Operator—bnotbnot()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot ( C◼F257◼𝔽—73  a)
inline

Map a into ℤn.

Definition at line 9660 of file C-F257.c.

Referenced by C◼F257◼𝔽—73◼_Operator—add(), C◼F257◼𝔽—73◼_Operator—eq(), and C◼F257◼𝔽—73◼_Operator—prod().

9660  {
9661 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9662  return a % _Intern◼_I584Rsma◼C◼F257◼Z—73◼mod₀;
9663 }
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§ C◼F257◼𝔽—73◼_Operator—div()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—div ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Operation in the ring ℤn.

Definition at line 9683 of file C-F257.c.

Referenced by C◼F257◼𝔽—73◼_Operator—mod().

9683  {
9684 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9685  C◼F257◼𝔽—73 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—73◼inverse(b);
9687 }
_Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
Definition: C-F257.c:9636
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot(C◼F257◼𝔽—73 a)
Map a into ℤn.
Definition: C-F257.c:9660
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§ C◼F257◼𝔽—73◼_Operator—eq()

_Bool C◼F257◼𝔽—73◼_Operator—eq ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Equality in the ring ℤn.

Definition at line 9694 of file C-F257.c.

References C◼F257◼𝔽—73◼_Operator—bnotbnot().

Referenced by C◼F257◼order—73().

9694  {
9695 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9697 }
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot(C◼F257◼𝔽—73 a)
Map a into ℤn.
Definition: C-F257.c:9660
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§ C◼F257◼𝔽—73◼_Operator—mod()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—mod ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Operation in the ring ℤn.

Definition at line 9689 of file C-F257.c.

References C◼F257◼𝔽—73◼_Operator—div(), C◼F257◼𝔽—73◼_Operator—prod(), and C◼F257◼𝔽—73◼_Operator—sub().

9689  {
9690 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9692 }
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—sub(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Operation in the ring ℤn.
Definition: C-F257.c:9671
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—div(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Operation in the ring ℤn.
Definition: C-F257.c:9683
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—prod(C◼F257◼𝔽—73 a, C◼F257◼𝔽—73 b)
Operation in the ring ℤn.
Definition: C-F257.c:9677
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§ C◼F257◼𝔽—73◼_Operator—notnot()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—notnot ( C◼F257◼𝔽—73  a)
inline

Test if non-zero in ℤn.

Definition at line 9699 of file C-F257.c.

Referenced by C◼F257◼order—73().

9699  {
9700 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9701  return ‼C◼F257◼𝔽—73◼_Operator—bnotbnot(a);
9702 }
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§ C◼F257◼𝔽—73◼_Operator—prod()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—prod ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Operation in the ring ℤn.

Definition at line 9677 of file C-F257.c.

References C◼F257◼𝔽—73◼_Operator—bnotbnot().

Referenced by C◼F257◼order—73(), and C◼F257◼𝔽—73◼_Operator—mod().

9677  {
9678 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9679  C◼F257◼𝔽—73 ret = a * b;
9681 }
_Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
Definition: C-F257.c:9636
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot(C◼F257◼𝔽—73 a)
Map a into ℤn.
Definition: C-F257.c:9660
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§ C◼F257◼𝔽—73◼_Operator—sub()

C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—sub ( C◼F257◼𝔽—73  a,
C◼F257◼𝔽—73  b 
)
inline

Operation in the ring ℤn.

Definition at line 9671 of file C-F257.c.

Referenced by C◼F257◼𝔽—73◼_Operator—mod().

9671  {
9672 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9673  C◼F257◼𝔽—73 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—73◼mod₀ - b);
9675 }
_Intern◼_I584Rsma◼C◼F257◼Z—73◼type₀ C◼F257◼𝔽—73
Definition: C-F257.c:9636
C◼F257◼𝔽—73 C◼F257◼𝔽—73◼_Operator—bnotbnot(C◼F257◼𝔽—73 a)
Map a into ℤn.
Definition: C-F257.c:9660
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Variable Documentation

§ C◼F257◼generator—73

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 9735 of file C-F257.c.