Modular C
C◼F257◼Z—83: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—83: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
 
C◼F257◼𝔽—83 C◼F257◼generator—83 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot (C◼F257◼𝔽—83 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—add (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—sub (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—prod (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—div (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—mod (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—83◼_Operator—eq (C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—notnot (C◼F257◼𝔽—83 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—83 C◼F257◼order—83 (C◼F257◼𝔽—83 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—83
C◼snippet◼modulo◼contextC◼F257◼𝔽—83
C◼snippet◼modulo◼typeC◼F257◼𝔽—83
C◼snippet◼modulo◼orderC◼F257◼order—83
C◼snippet◼modulo◼generatorC◼F257◼generator—83
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—83

typedef _Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83

Definition at line 9168 of file C-F257.c.

Function Documentation

§ C◼F257◼order—83()

C◼F257◼𝔽—83 C◼F257◼order—83 ( C◼F257◼𝔽—83  x)

Compute the order of element .

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

Definition at line 9247 of file C-F257.c.

References C◼F257◼𝔽—83◼_Operator—add(), C◼F257◼𝔽—83◼_Operator—eq(), C◼F257◼𝔽—83◼_Operator—notnot(), and C◼F257◼𝔽—83◼_Operator—prod().

9247  {
9248 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9249  if (¬(C◼F257◼𝔽—83◼_Operator—notnot(x ))) return 0;
9250  C◼F257◼𝔽—83 y = x;
9251  for (C◼F257◼𝔽—83 i = 1; i; ((i )=(C◼F257◼𝔽—83◼_Operator—add(i , 1)))) {
9252 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9253  if (C◼F257◼𝔽—83◼_Operator—eq(y , 1 )) return i;
9254  ((y )=(C◼F257◼𝔽—83◼_Operator—prod(y , x )));
9255  }
9256  // should not be reached
9257  return 0;
9258 }
_Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
Definition: C-F257.c:9168
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—notnot(C◼F257◼𝔽—83 a)
Test if non-zero in ℤn.
Definition: C-F257.c:9231
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—prod(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Operation in the ring ℤn.
Definition: C-F257.c:9209
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—add(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Operation in the ring ℤn.
Definition: C-F257.c:9197
_Bool C◼F257◼𝔽—83◼_Operator—eq(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Equality in the ring ℤn.
Definition: C-F257.c:9226
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§ C◼F257◼𝔽—83◼_Operator—add()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—add ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Operation in the ring ℤn.

Definition at line 9197 of file C-F257.c.

References C◼F257◼𝔽—83◼_Operator—bnotbnot().

Referenced by C◼F257◼order—83().

9197  {
9198 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9199  C◼F257◼𝔽—83 ret = a + b;
9201 }
_Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
Definition: C-F257.c:9168
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot(C◼F257◼𝔽—83 a)
Map a into ℤn.
Definition: C-F257.c:9192
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§ C◼F257◼𝔽—83◼_Operator—bnotbnot()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot ( C◼F257◼𝔽—83  a)
inline

Map a into ℤn.

Definition at line 9192 of file C-F257.c.

Referenced by C◼F257◼𝔽—83◼_Operator—add(), C◼F257◼𝔽—83◼_Operator—eq(), and C◼F257◼𝔽—83◼_Operator—prod().

9192  {
9193 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9194  return a % _Intern◼_I584Rsma◼C◼F257◼Z—83◼mod₀;
9195 }
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§ C◼F257◼𝔽—83◼_Operator—div()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—div ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Operation in the ring ℤn.

Definition at line 9215 of file C-F257.c.

Referenced by C◼F257◼𝔽—83◼_Operator—mod().

9215  {
9216 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9217  C◼F257◼𝔽—83 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—83◼inverse(b);
9219 }
_Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
Definition: C-F257.c:9168
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot(C◼F257◼𝔽—83 a)
Map a into ℤn.
Definition: C-F257.c:9192
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§ C◼F257◼𝔽—83◼_Operator—eq()

_Bool C◼F257◼𝔽—83◼_Operator—eq ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Equality in the ring ℤn.

Definition at line 9226 of file C-F257.c.

References C◼F257◼𝔽—83◼_Operator—bnotbnot().

Referenced by C◼F257◼order—83().

9226  {
9227 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9229 }
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot(C◼F257◼𝔽—83 a)
Map a into ℤn.
Definition: C-F257.c:9192
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§ C◼F257◼𝔽—83◼_Operator—mod()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—mod ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Operation in the ring ℤn.

Definition at line 9221 of file C-F257.c.

References C◼F257◼𝔽—83◼_Operator—div(), C◼F257◼𝔽—83◼_Operator—prod(), and C◼F257◼𝔽—83◼_Operator—sub().

9221  {
9222 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9224 }
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—div(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Operation in the ring ℤn.
Definition: C-F257.c:9215
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—prod(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Operation in the ring ℤn.
Definition: C-F257.c:9209
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—sub(C◼F257◼𝔽—83 a, C◼F257◼𝔽—83 b)
Operation in the ring ℤn.
Definition: C-F257.c:9203
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§ C◼F257◼𝔽—83◼_Operator—notnot()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—notnot ( C◼F257◼𝔽—83  a)
inline

Test if non-zero in ℤn.

Definition at line 9231 of file C-F257.c.

Referenced by C◼F257◼order—83().

9231  {
9232 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9233  return ‼C◼F257◼𝔽—83◼_Operator—bnotbnot(a);
9234 }
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§ C◼F257◼𝔽—83◼_Operator—prod()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—prod ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Operation in the ring ℤn.

Definition at line 9209 of file C-F257.c.

References C◼F257◼𝔽—83◼_Operator—bnotbnot().

Referenced by C◼F257◼order—83(), and C◼F257◼𝔽—83◼_Operator—mod().

9209  {
9210 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9211  C◼F257◼𝔽—83 ret = a * b;
9213 }
_Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
Definition: C-F257.c:9168
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot(C◼F257◼𝔽—83 a)
Map a into ℤn.
Definition: C-F257.c:9192
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§ C◼F257◼𝔽—83◼_Operator—sub()

C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—sub ( C◼F257◼𝔽—83  a,
C◼F257◼𝔽—83  b 
)
inline

Operation in the ring ℤn.

Definition at line 9203 of file C-F257.c.

Referenced by C◼F257◼𝔽—83◼_Operator—mod().

9203  {
9204 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
9205  C◼F257◼𝔽—83 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—83◼mod₀ - b);
9207 }
_Intern◼_I584Rsma◼C◼F257◼Z—83◼type₀ C◼F257◼𝔽—83
Definition: C-F257.c:9168
C◼F257◼𝔽—83 C◼F257◼𝔽—83◼_Operator—bnotbnot(C◼F257◼𝔽—83 a)
Map a into ℤn.
Definition: C-F257.c:9192
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Variable Documentation

§ C◼F257◼generator—83

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 9267 of file C-F257.c.