// output of ./demo/mod/modinfo-demo.cc:
// Description:
//% Demo of mod_init(): properties of (Z/mZ)*

arg 1: 0 == m  [Modulus,  0==>use all moduli from list]  default=0
-------- start MOD_INIT():  m=4 --------
modulus= 4 == 0x4
modulus is cyclic
modulus is composite   == 2^2
bits(modulus)= 3
euler_phi(modulus)= 2 == 0x2 == 2
maxorder= 2 == 0x2
maxordelem= 3 == 0x3
order(2)= 0
max2pow= 1   (max FFT length = 2**1 == 2)
2\modulus, cannot divide by 2 (or 2**n)
 =--> no length 2**n inverse FFT !
root2pow(max2pow)=3   root2pow(-max2pow)=3
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=17 --------
modulus= 17 == 0x11
modulus is cyclic
modulus is prime 
bits(modulus)= 4.0874628  == 5 - 0.91253716
euler_phi(modulus)= 16 == 0x10 == 2^4
maxorder= 16 == 0x10
maxordelem= 3 == 0x3
order(2)= 8 == 2^3
order(2^2)=2^2
order(2^3)=2^3
order(2^4)=2^1
max2pow= 4   (max FFT length = 2**4 == 16)
root2pow(max2pow)=3   root2pow(-max2pow)=6
sqrt(-1) =: i = 13
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=18 --------
modulus= 18 == 0x12
modulus is cyclic
modulus is composite   == 2 * 3^2
bits(modulus)= 4.169925  == 5 - 0.830075
euler_phi(modulus)= 6 == 0x6 == 2 * 3
maxorder= 6 == 0x6
maxordelem= 5 == 0x5
order(2)= 0
max2pow= 1   (max FFT length = 2**1 == 2)
2\modulus, cannot divide by 2 (or 2**n)
 =--> no length 2**n inverse FFT !
root2pow(max2pow)=17   root2pow(-max2pow)=17
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=31 --------
modulus= 31 == 0x1f
modulus is cyclic
modulus is prime 
bits(modulus)= 4.9541963  == 5 - 0.04580369
euler_phi(modulus)= 30 == 0x1e == 2 * 3 * 5
maxorder= 30 == 0x1e
maxordelem= 3 == 0x3
order(2)= 5 == 5
max2pow= 1   (max FFT length = 2**1 == 2)
root2pow(max2pow)=30   root2pow(-max2pow)=30
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=32 --------
modulus= 32 == 0x20
modulus is NOT cyclic
modulus is composite   == 2^5
bits(modulus)= 6
euler_phi(modulus)= 16 == 0x10 == 2^4
maxorder= 8 == 0x8
maxordelem= 3 == 0x3
order(2)= 0
max2pow= 3   (max FFT length = 2**3 == 8)
2\modulus, cannot divide by 2 (or 2**n)
 =--> no length 2**n inverse FFT !
root2pow(max2pow)=3   root2pow(-max2pow)=11
sqrt(-1) =: i = 9
root2pow(1)=17 != -1  (!)
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=121 --------
modulus= 121 == 0x79
modulus is cyclic
modulus is composite   == 11^2
bits(modulus)= 6.9188632  == 7 - 0.081136763
euler_phi(modulus)= 110 == 0x6e == 2 * 5 * 11
maxorder= 110 == 0x6e
maxordelem= 2 == 0x2
order(2)= 110 == 2 * 5 * 11
max2pow= 1   (max FFT length = 2**1 == 2)
root2pow(max2pow)=120   root2pow(-max2pow)=120
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=2047 --------
modulus= 2047 == 0x7ff
modulus is NOT cyclic
modulus is composite   == 23 * 89
bits(modulus)= 10.999295  == 11 - 0.00070461298
euler_phi(modulus)= 1936 == 0x790 == 2^4 * 11^2
maxorder= 88 == 0x58
maxordelem= 3 == 0x3
order(2)= 11 == 11
max2pow= 3   (max FFT length = 2**3 == 8)
root2pow(max2pow)=1105   root2pow(-max2pow)=967
sqrt(-1) =: i = 1013
root2pow(1)=622 != -1  (!)
-------- end MOD_INIT(). --------

-------- start MOD_INIT():  m=65537 --------
modulus= 65537 == 0x10001
modulus is cyclic
modulus is prime 
bits(modulus)= 16.000022  == 17 - 0.99997799
euler_phi(modulus)= 65536 == 0x10000 == 2^16
maxorder= 65536 == 0x10000
maxordelem= 3 == 0x3
order(2)= 32 == 2^5
order(2^2)=2^4
order(2^3)=2^5
order(2^4)=2^3
order(2^8)=2^2
order(2^16)=2^1
max2pow= 16   (max FFT length = 2**16 == 65536)
root2pow(max2pow)=3   root2pow(-max2pow)=21846
sqrt(-1) =: i = 65281
-------- end MOD_INIT(). --------