Modular C
C◼F257◼Z—227: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—227: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
 
C◼F257◼𝔽—227 C◼F257◼generator—227 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot (C◼F257◼𝔽—227 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—add (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—sub (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—prod (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—div (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—mod (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—227◼_Operator—eq (C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—notnot (C◼F257◼𝔽—227 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—227 C◼F257◼order—227 (C◼F257◼𝔽—227 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—227
C◼snippet◼modulo◼contextC◼F257◼𝔽—227
C◼snippet◼modulo◼typeC◼F257◼𝔽—227
C◼snippet◼modulo◼orderC◼F257◼order—227
C◼snippet◼modulo◼generatorC◼F257◼generator—227
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—227

typedef _Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227

Definition at line 2850 of file C-F257.c.

Function Documentation

§ C◼F257◼order—227()

C◼F257◼𝔽—227 C◼F257◼order—227 ( C◼F257◼𝔽—227  x)

Compute the order of element .

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

Definition at line 2929 of file C-F257.c.

References C◼F257◼𝔽—227◼_Operator—add(), C◼F257◼𝔽—227◼_Operator—eq(), C◼F257◼𝔽—227◼_Operator—notnot(), and C◼F257◼𝔽—227◼_Operator—prod().

2929  {
2930 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2931  if (¬(C◼F257◼𝔽—227◼_Operator—notnot(x ))) return 0;
2932  C◼F257◼𝔽—227 y = x;
2933  for (C◼F257◼𝔽—227 i = 1; i; ((i )=(C◼F257◼𝔽—227◼_Operator—add(i , 1)))) {
2934 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2935  if (C◼F257◼𝔽—227◼_Operator—eq(y , 1 )) return i;
2937  }
2938  // should not be reached
2939  return 0;
2940 }
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—notnot(C◼F257◼𝔽—227 a)
Test if non-zero in ℤn.
Definition: C-F257.c:2913
_Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
Definition: C-F257.c:2850
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—prod(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Operation in the ring ℤn.
Definition: C-F257.c:2891
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—add(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Operation in the ring ℤn.
Definition: C-F257.c:2879
_Bool C◼F257◼𝔽—227◼_Operator—eq(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Equality in the ring ℤn.
Definition: C-F257.c:2908
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§ C◼F257◼𝔽—227◼_Operator—add()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—add ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Operation in the ring ℤn.

Definition at line 2879 of file C-F257.c.

References C◼F257◼𝔽—227◼_Operator—bnotbnot().

Referenced by C◼F257◼order—227().

2879  {
2880 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2881  C◼F257◼𝔽—227 ret = a + b;
2883 }
_Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
Definition: C-F257.c:2850
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot(C◼F257◼𝔽—227 a)
Map a into ℤn.
Definition: C-F257.c:2874
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§ C◼F257◼𝔽—227◼_Operator—bnotbnot()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot ( C◼F257◼𝔽—227  a)
inline

Map a into ℤn.

Definition at line 2874 of file C-F257.c.

Referenced by C◼F257◼𝔽—227◼_Operator—add(), C◼F257◼𝔽—227◼_Operator—eq(), and C◼F257◼𝔽—227◼_Operator—prod().

2874  {
2875 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2876  return a % _Intern◼_I584Rsma◼C◼F257◼Z—227◼mod₀;
2877 }
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§ C◼F257◼𝔽—227◼_Operator—div()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—div ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Operation in the ring ℤn.

Definition at line 2897 of file C-F257.c.

Referenced by C◼F257◼𝔽—227◼_Operator—mod().

2897  {
2898 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2899  C◼F257◼𝔽—227 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—227◼inverse(b);
2901 }
_Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
Definition: C-F257.c:2850
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot(C◼F257◼𝔽—227 a)
Map a into ℤn.
Definition: C-F257.c:2874
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§ C◼F257◼𝔽—227◼_Operator—eq()

_Bool C◼F257◼𝔽—227◼_Operator—eq ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Equality in the ring ℤn.

Definition at line 2908 of file C-F257.c.

References C◼F257◼𝔽—227◼_Operator—bnotbnot().

Referenced by C◼F257◼order—227().

2908  {
2909 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2911 }
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot(C◼F257◼𝔽—227 a)
Map a into ℤn.
Definition: C-F257.c:2874
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§ C◼F257◼𝔽—227◼_Operator—mod()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—mod ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Operation in the ring ℤn.

Definition at line 2903 of file C-F257.c.

References C◼F257◼𝔽—227◼_Operator—div(), C◼F257◼𝔽—227◼_Operator—prod(), and C◼F257◼𝔽—227◼_Operator—sub().

2903  {
2904 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2906 }
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—sub(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Operation in the ring ℤn.
Definition: C-F257.c:2885
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—div(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Operation in the ring ℤn.
Definition: C-F257.c:2897
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—prod(C◼F257◼𝔽—227 a, C◼F257◼𝔽—227 b)
Operation in the ring ℤn.
Definition: C-F257.c:2891
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§ C◼F257◼𝔽—227◼_Operator—notnot()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—notnot ( C◼F257◼𝔽—227  a)
inline

Test if non-zero in ℤn.

Definition at line 2913 of file C-F257.c.

Referenced by C◼F257◼order—227().

2913  {
2914 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2915  return ‼C◼F257◼𝔽—227◼_Operator—bnotbnot(a);
2916 }
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§ C◼F257◼𝔽—227◼_Operator—prod()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—prod ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Operation in the ring ℤn.

Definition at line 2891 of file C-F257.c.

References C◼F257◼𝔽—227◼_Operator—bnotbnot().

Referenced by C◼F257◼order—227(), and C◼F257◼𝔽—227◼_Operator—mod().

2891  {
2892 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2893  C◼F257◼𝔽—227 ret = a * b;
2895 }
_Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
Definition: C-F257.c:2850
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot(C◼F257◼𝔽—227 a)
Map a into ℤn.
Definition: C-F257.c:2874
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§ C◼F257◼𝔽—227◼_Operator—sub()

C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—sub ( C◼F257◼𝔽—227  a,
C◼F257◼𝔽—227  b 
)
inline

Operation in the ring ℤn.

Definition at line 2885 of file C-F257.c.

Referenced by C◼F257◼𝔽—227◼_Operator—mod().

2885  {
2886 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
2887  C◼F257◼𝔽—227 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—227◼mod₀ - b);
2889 }
_Intern◼_I584Rsma◼C◼F257◼Z—227◼type₀ C◼F257◼𝔽—227
Definition: C-F257.c:2850
C◼F257◼𝔽—227 C◼F257◼𝔽—227◼_Operator—bnotbnot(C◼F257◼𝔽—227 a)
Map a into ℤn.
Definition: C-F257.c:2874
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Variable Documentation

§ C◼F257◼generator—227

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 2949 of file C-F257.c.