Modular C
C◼F257◼Z—151: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—151: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
 
C◼F257◼𝔽—151 C◼F257◼generator—151 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot (C◼F257◼𝔽—151 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—add (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—sub (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—prod (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—div (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—mod (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—151◼_Operator—eq (C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—notnot (C◼F257◼𝔽—151 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—151 C◼F257◼order—151 (C◼F257◼𝔽—151 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—151
C◼snippet◼modulo◼contextC◼F257◼𝔽—151
C◼snippet◼modulo◼typeC◼F257◼𝔽—151
C◼snippet◼modulo◼orderC◼F257◼order—151
C◼snippet◼modulo◼generatorC◼F257◼generator—151
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—151

typedef _Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151

Definition at line 6126 of file C-F257.c.

Function Documentation

§ C◼F257◼order—151()

C◼F257◼𝔽—151 C◼F257◼order—151 ( C◼F257◼𝔽—151  x)

Compute the order of element .

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

Definition at line 6205 of file C-F257.c.

References C◼F257◼𝔽—151◼_Operator—add(), C◼F257◼𝔽—151◼_Operator—eq(), C◼F257◼𝔽—151◼_Operator—notnot(), and C◼F257◼𝔽—151◼_Operator—prod().

6205  {
6206 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6207  if (¬(C◼F257◼𝔽—151◼_Operator—notnot(x ))) return 0;
6208  C◼F257◼𝔽—151 y = x;
6209  for (C◼F257◼𝔽—151 i = 1; i; ((i )=(C◼F257◼𝔽—151◼_Operator—add(i , 1)))) {
6210 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6211  if (C◼F257◼𝔽—151◼_Operator—eq(y , 1 )) return i;
6213  }
6214  // should not be reached
6215  return 0;
6216 }
_Bool C◼F257◼𝔽—151◼_Operator—eq(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Equality in the ring ℤn.
Definition: C-F257.c:6184
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—add(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Operation in the ring ℤn.
Definition: C-F257.c:6155
_Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
Definition: C-F257.c:6126
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—prod(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Operation in the ring ℤn.
Definition: C-F257.c:6167
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—notnot(C◼F257◼𝔽—151 a)
Test if non-zero in ℤn.
Definition: C-F257.c:6189
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§ C◼F257◼𝔽—151◼_Operator—add()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—add ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Operation in the ring ℤn.

Definition at line 6155 of file C-F257.c.

References C◼F257◼𝔽—151◼_Operator—bnotbnot().

Referenced by C◼F257◼order—151().

6155  {
6156 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6157  C◼F257◼𝔽—151 ret = a + b;
6159 }
_Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
Definition: C-F257.c:6126
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot(C◼F257◼𝔽—151 a)
Map a into ℤn.
Definition: C-F257.c:6150
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§ C◼F257◼𝔽—151◼_Operator—bnotbnot()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot ( C◼F257◼𝔽—151  a)
inline

Map a into ℤn.

Definition at line 6150 of file C-F257.c.

Referenced by C◼F257◼𝔽—151◼_Operator—add(), C◼F257◼𝔽—151◼_Operator—eq(), and C◼F257◼𝔽—151◼_Operator—prod().

6150  {
6151 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6152  return a % _Intern◼_I584Rsma◼C◼F257◼Z—151◼mod₀;
6153 }
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§ C◼F257◼𝔽—151◼_Operator—div()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—div ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Operation in the ring ℤn.

Definition at line 6173 of file C-F257.c.

Referenced by C◼F257◼𝔽—151◼_Operator—mod().

6173  {
6174 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6175  C◼F257◼𝔽—151 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—151◼inverse(b);
6177 }
_Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
Definition: C-F257.c:6126
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot(C◼F257◼𝔽—151 a)
Map a into ℤn.
Definition: C-F257.c:6150
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§ C◼F257◼𝔽—151◼_Operator—eq()

_Bool C◼F257◼𝔽—151◼_Operator—eq ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Equality in the ring ℤn.

Definition at line 6184 of file C-F257.c.

References C◼F257◼𝔽—151◼_Operator—bnotbnot().

Referenced by C◼F257◼order—151().

6184  {
6185 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6187 }
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot(C◼F257◼𝔽—151 a)
Map a into ℤn.
Definition: C-F257.c:6150
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§ C◼F257◼𝔽—151◼_Operator—mod()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—mod ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Operation in the ring ℤn.

Definition at line 6179 of file C-F257.c.

References C◼F257◼𝔽—151◼_Operator—div(), C◼F257◼𝔽—151◼_Operator—prod(), and C◼F257◼𝔽—151◼_Operator—sub().

6179  {
6180 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6182 }
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—div(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Operation in the ring ℤn.
Definition: C-F257.c:6173
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—prod(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Operation in the ring ℤn.
Definition: C-F257.c:6167
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—sub(C◼F257◼𝔽—151 a, C◼F257◼𝔽—151 b)
Operation in the ring ℤn.
Definition: C-F257.c:6161
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§ C◼F257◼𝔽—151◼_Operator—notnot()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—notnot ( C◼F257◼𝔽—151  a)
inline

Test if non-zero in ℤn.

Definition at line 6189 of file C-F257.c.

Referenced by C◼F257◼order—151().

6189  {
6190 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6191  return ‼C◼F257◼𝔽—151◼_Operator—bnotbnot(a);
6192 }
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§ C◼F257◼𝔽—151◼_Operator—prod()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—prod ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Operation in the ring ℤn.

Definition at line 6167 of file C-F257.c.

References C◼F257◼𝔽—151◼_Operator—bnotbnot().

Referenced by C◼F257◼order—151(), and C◼F257◼𝔽—151◼_Operator—mod().

6167  {
6168 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6169  C◼F257◼𝔽—151 ret = a * b;
6171 }
_Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
Definition: C-F257.c:6126
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot(C◼F257◼𝔽—151 a)
Map a into ℤn.
Definition: C-F257.c:6150
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§ C◼F257◼𝔽—151◼_Operator—sub()

C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—sub ( C◼F257◼𝔽—151  a,
C◼F257◼𝔽—151  b 
)
inline

Operation in the ring ℤn.

Definition at line 6161 of file C-F257.c.

Referenced by C◼F257◼𝔽—151◼_Operator—mod().

6161  {
6162 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
6163  C◼F257◼𝔽—151 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—151◼mod₀ - b);
6165 }
_Intern◼_I584Rsma◼C◼F257◼Z—151◼type₀ C◼F257◼𝔽—151
Definition: C-F257.c:6126
C◼F257◼𝔽—151 C◼F257◼𝔽—151◼_Operator—bnotbnot(C◼F257◼𝔽—151 a)
Map a into ℤn.
Definition: C-F257.c:6150
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Variable Documentation

§ C◼F257◼generator—151

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 6225 of file C-F257.c.