X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb-python/blobdiff_plain/e91150b266bbd768905258166601fdf333d3d987..553d59fec08fd9102b21fd0dc83ba708862a6090:/t/t-mp.py

diff --git a/t/t-mp.py b/t/t-mp.py
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+### -*-python-*-
+###
+### Testing multiprecision integer (and related) functionality
+###
+### (c) 2019 Straylight/Edgeware
+###
+
+###----- Licensing notice ---------------------------------------------------
+###
+### This file is part of the Python interface to Catacomb.
+###
+### Catacomb/Python is free software: you can redistribute it and/or
+### modify it under the terms of the GNU General Public License as
+### published by the Free Software Foundation; either version 2 of the
+### License, or (at your option) any later version.
+###
+### Catacomb/Python is distributed in the hope that it will be useful, but
+### WITHOUT ANY WARRANTY; without even the implied warranty of
+### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+### General Public License for more details.
+###
+### You should have received a copy of the GNU General Public License
+### along with Catacomb/Python.  If not, write to the Free Software
+### Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
+### USA.
+
+###--------------------------------------------------------------------------
+### Imported modules.
+
+import catacomb as C
+import unittest as U
+import testutils as T
+
+###--------------------------------------------------------------------------
+class TestMP (U.TestCase):
+
+  def test_make(me):
+    x = C.MP(5)
+    k = C.PrimeField(17)
+    kk = C.BinPolyField(C.GF(0x13))
+    E = k.ec(-3, 1)
+    me.assertEqual(x, 5)
+    me.assertTrue(C.MP(x) is x)
+    me.assertEqual(C.MP(k(8)), 8)
+    me.assertEqual(C.MP(kk(8)), 8)
+    me.assertEqual(C.MP(E(1, 4)), 1)
+    me.assertRaises(TypeError, C.MP, E())
+
+    me.assertEqual(int(x), 5)
+    big = 6556380541834372447694561492436749633
+    me.assertEqual(type(big), T.long)
+    y = C.MP(big)
+    me.assertEqual(y, big)
+    me.assertEqual(int(y), big)
+
+    me.assertEqual(C.MP(str(big)), big)
+    me.assertEqual(C.MP('0x4eeb684a0954ec4ceb255e3e9778d41'), big)
+    me.assertEqual(C.MP('4eeb684a0954ec4ceb255e3e9778d41', 16), big)
+    me.assertEqual(C.MP('0b0', 16), 176) # not 0
+
+    me.assertEqual(C.MP('047353320450112516611472622536175135706501'), big)
+    me.assertEqual(C.MP('0o47353320450112516611472622536175135706501'), big)
+    me.assertEqual(C.MP('047353320450112516611472622536175135706501', 8), big)
+    me.assertEqual(C.MP('47353320450112516611472622536175135706501', 8), big)
+
+    me.assertEqual(C.MP('0b100111011011001100000010001011'), 661438603)
+    me.assertEqual(C.MP('100111011011001100000010001011', 2), 661438603)
+
+  def test_string(me):
+    y = C.MP(6556380541834372447694561492436749633)
+    me.assertEqual(str(y), '6556380541834372447694561492436749633')
+    me.assertEqual(repr(y), 'MP(6556380541834372447694561492436749633L)')
+    me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
+    me.assertEqual(oct(y), '047353320450112516611472622536175135706501')
+
+  def test_number(me):
+    x, y, m, zero = C.MP(169), C.MP(24), C.MP(205), C.MP(0)
+
+    me.assertEqual(-x, -169)
+    me.assertEqual(~x, -170)
+    me.assertEqual(abs(x), 169)
+    me.assertEqual(abs(-x), 169)
+
+    me.assertEqual(x + y, 193)
+    me.assertEqual(x - y, 145)
+    me.assertEqual(x*y, 4056)
+    me.assertEqual(x&y, 8)
+    me.assertEqual(x&-y, 168)
+    me.assertEqual(x | y, 185)
+    me.assertEqual(x | -y, -23)
+    me.assertEqual(x ^ y, 177)
+    me.assertEqual(x ^ -y, -191)
+
+    me.assertEqual(x << 3, 1352)
+    me.assertEqual(x << -2, 42)
+    me.assertEqual(x >> 2, 42)
+    me.assertEqual(x >> -3, 1352)
+    me.assertEqual(-x << 3, -1352)
+    me.assertEqual(-x >> 2, -43)
+
+    u = x/y; me.assertEqual((u.numer, u.denom), (169, 24))
+    me.assertEqual(x//y, 7)
+    me.assertEqual(x%y, 1)
+    me.assertEqual(divmod(x, y), (7, 1))
+    me.assertRaises(ZeroDivisionError, lambda: x/zero)
+    me.assertRaises(ZeroDivisionError, lambda: x//zero)
+    me.assertRaises(ZeroDivisionError, lambda: x%zero)
+    me.assertRaises(ZeroDivisionError, divmod, x, zero)
+
+    me.assertEqual(pow(x, y), 294632676319010105335586872991323185304149065116720321)
+    me.assertEqual(pow(x, y, m), 51)
+    me.assertRaises(ValueError, pow, x, -y)
+    me.assertEqual(pow(x, -y, m), 201)
+    me.assertRaises(ZeroDivisionError, pow, x, -y, 208)
+
+    me.assertTrue(x)
+    me.assertFalse(zero)
+
+  def test_order(me):
+    x, y = C.MP(169), C.MP(24)
+    me.assertTrue(x == x)
+    me.assertFalse(x != x)
+    me.assertFalse(x == y)
+    me.assertTrue(x != y)
+    me.assertTrue(x > y)
+    me.assertFalse(y > x)
+    me.assertFalse(x > x)
+    me.assertTrue(x >= y)
+    me.assertFalse(y >= x)
+    me.assertTrue(x >= x)
+    me.assertFalse(x <= y)
+    me.assertTrue(y <= x)
+    me.assertTrue(x <= x)
+    me.assertFalse(x < y)
+    me.assertTrue(y < x)
+    me.assertFalse(x < x)
+
+  def test_bits(me):
+    x, y, zero = C.MP(169), C.MP(-24), C.MP(0)
+    me.assertTrue(x.testbit(0))
+    me.assertFalse(x.testbit(1))
+    me.assertFalse(x.testbit(1000))
+    me.assertFalse(y.testbit(0))
+    me.assertTrue(y.testbit(3))
+    me.assertTrue(y.testbit(1000))
+
+    me.assertEqual(x.setbit(0), x)
+    me.assertEqual(x.clearbit(0), 168)
+    me.assertEqual(x.setbit(1), 171)
+    me.assertEqual(x.clearbit(1), x)
+    me.assertEqual(y.setbit(0), -23)
+    me.assertEqual(y.clearbit(0), y)
+    me.assertEqual(y.setbit(3), y)
+    me.assertEqual(y.clearbit(3), -32)
+    me.assertEqual(y.setbit(1000), y)
+
+    me.assertEqual(x.nbits, 8)
+    me.assertEqual(y.nbits, 5)
+    me.assertEqual(zero.nbits, 0)
+
+  def test_loadstore(me):
+    x = C.MP(0x0123456789ab)
+    y = -x
+    u = C.MP(0xfedcba9876)
+
+    me.assertEqual(x.noctets, 6)
+    me.assertEqual(x.noctets2c, 6)
+    me.assertEqual(y.noctets, 6)
+    me.assertEqual(y.noctets2c, 6)
+    me.assertEqual(u.noctets, 5)
+    me.assertEqual(u.noctets2c, 6)
+
+    me.assertEqual(x, C.MP.loadb(C.bytes("0123456789ab")))
+    me.assertEqual(x, C.MP.loadb2c(C.bytes("0123456789ab")))
+    me.assertEqual(y, C.MP.loadb2c(C.bytes("fedcba987655")))
+
+    me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
+    me.assertEqual(x.storeb(3), C.bytes("6789ab"))
+    me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
+    me.assertEqual(x.storeb2c(), C.bytes("0123456789ab"))
+    me.assertEqual(x.storeb2c(3), C.bytes("6789ab"))
+    me.assertEqual(x.storeb2c(8), C.bytes("00000123456789ab"))
+    me.assertEqual(u.storeb2c(), C.bytes("00fedcba9876"))
+    me.assertEqual(y.storeb2c(), C.bytes("fedcba987655"))
+    me.assertEqual(y.storeb2c(3), C.bytes("987655"))
+    me.assertEqual(y.storeb2c(8), C.bytes("fffffedcba987655"))
+
+    me.assertEqual(x, C.MP.loadl(C.bytes("ab8967452301")))
+    me.assertEqual(x, C.MP.loadl2c(C.bytes("ab8967452301")))
+    me.assertEqual(y, C.MP.loadl2c(C.bytes("557698badcfe")))
+
+    me.assertEqual(x.storel(), C.bytes("ab8967452301"))
+    me.assertEqual(x.storel(3), C.bytes("ab8967"))
+    me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
+    me.assertEqual(x.storel2c(), C.bytes("ab8967452301"))
+    me.assertEqual(x.storel2c(3), C.bytes("ab8967"))
+    me.assertEqual(x.storel2c(8), C.bytes("ab89674523010000"))
+    me.assertEqual(u.storel2c(), C.bytes("7698badcfe00"))
+    me.assertEqual(y.storel2c(), C.bytes("557698badcfe"))
+    me.assertEqual(y.storel2c(3), C.bytes("557698"))
+    me.assertEqual(y.storel2c(8), C.bytes("557698badcfeffff"))
+
+    me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
+    me.assertEqual((x, T.bin("abcd")),
+                   C.MP.frombuf(C.bytes("00060123456789ab61626364")))
+
+  def test_numbertheory(me):
+    p, x, y, z = C.MP(173), C.MP(169), C.MP(24), C.MP(20)
+
+    me.assertEqual(x.odd(), (0, x))
+    me.assertEqual(y.odd(), (3, 3))
+
+    me.assertEqual(x.sqr(), 28561)
+    me.assertEqual(x.sqrt(), 13)
+    me.assertEqual(y.sqrt(), 4)
+
+    me.assertEqual(x.gcd(y), 1)
+    me.assertEqual(x.gcdx(y), (1, -23, 162))
+    me.assertEqual(y.gcdx(x), (1, -7, 1))
+    me.assertEqual(x.modinv(y), 162)
+    me.assertEqual(y.modinv(x), 1)
+
+    me.assertEqual(x.jacobi(y), 1)
+    me.assertEqual(x.jacobi(13), 0)
+    me.assertEqual(y.jacobi(x), 1)
+    me.assertEqual(p.jacobi(y), 1)
+    me.assertEqual(p.jacobi(z), -1)
+    me.assertEqual(p.modsqrt(y), 71)
+    me.assertRaises(ValueError, p.modsqrt, z)
+
+    me.assertEqual(y.leastcongruent(x, 32), 184)
+
+    me.assertTrue(p.primep())
+    me.assertFalse(x.primep())
+
+  def test_bang(me):
+    me.assertEqual(C.MP.factorial(0), 1)
+    me.assertEqual \
+      (C.MP.factorial(50),
+       30414093201713378043612608166064768844377641568960512000000000000)
+    me.assertRaises((ValueError, OverflowError), C.MP.factorial, -1)
+
+  def test_fib(me):
+    me.assertEqual(C.MP.fibonacci(-2), -1)
+    me.assertEqual(C.MP.fibonacci(-1), +1)
+    me.assertEqual(C.MP.fibonacci( 0),  0)
+    me.assertEqual(C.MP.fibonacci(+1), +1)
+    me.assertEqual(C.MP.fibonacci(+2), +1)
+    me.assertEqual(C.MP.fibonacci(50), 12586269025)
+
+###--------------------------------------------------------------------------
+class TestMPMul (U.TestCase):
+
+  def test(me):
+    m = C.MPMul()
+    me.assertTrue(m.livep)
+    m.factor(1, 2, 3)
+    m.factor([4, 5, 6])
+    me.assertEqual(m.done(), 720)
+    me.assertFalse(m.livep)
+
+    me.assertEqual(C.MPMul(T.range(1, 7)).done(), 720)
+    me.assertEqual(C.MP.factorial(6), 720)
+
+###--------------------------------------------------------------------------
+class TestMPMont (U.TestCase):
+
+  def test(me):
+
+    me.assertRaises(ValueError,
+                    C.MPMont, 35315021952044908656941308411353985942)
+    me.assertRaises(ValueError, C.MPMont, -9)
+
+    p = C.MP(269464705320809171350781605680038324101)
+    g = C.MP(2) # lucky chance
+    x = C.MP(211184293914316080585277908844600399612)
+    y = C.MP(154454671298730680774195646814344206562)
+    xy = C.MP(209444562478584646216087606217820187655)
+    me.assertTrue(p.primep())
+    m = C.MPMont(p)
+    me.assertEqual(m.m, p)
+
+    ## The precise values of m.r and m.r2 are dependent on the internal
+    ## bignum representation.  But we expect m.r to be congruent to some
+    ## power of two.  (It should be 2^128.)
+    t = p.modinv(m.r)
+    for i in T.range(1025):
+      if t == 1: break
+      t *= 2
+      if t >= p: t -= p
+    else:
+      me.fail("m.r is not a small-ish power of 2")
+    me.assertEqual(m.r2, pow(2, 2*i, p))
+    me.assertEqual(m.ext(m.r), 1)
+    me.assertEqual(m.reduce(m.r), 1)
+
+    me.assertEqual(m.ext(m.int(x)), x)
+    me.assertEqual(m.int(x), m.mul(x, m.r2))
+    me.assertEqual(m.mul(m.int(x), y), xy)
+    me.assertEqual(m.ext(m.mul(m.int(x), m.int(y))), xy)
+
+    me.assertEqual(m.exp(2, p - 1), 1)
+    me.assertEqual(m.expr(m.int(2), p - 1), m.r)
+
+    q, r, s, z = 32, 128, 2048, pow(g, 156, p)
+    me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
+    me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
+
+    q, r, s, z = T.imap(m.int, [32, 128, 2048, pow(g, 156, p)])
+    me.assertEqual(m.mexpr([(q, 9), (r, 8), (s, 5)]), z)
+    me.assertEqual(m.mexpr(q, 9, r, 8, s, 5), z)
+
+###--------------------------------------------------------------------------
+class TestMPBarrett (U.TestCase):
+
+  def test(me):
+
+    p = C.MP(269464705320809171350781605680038324101)
+    g = C.MP(2) # lucky chance
+    x = C.MP(211184293914316080585277908844600399612)
+    y = C.MP(154454671298730680774195646814344206562)
+    xy = C.MP(209444562478584646216087606217820187655)
+    me.assertTrue(p.primep())
+    m = C.MPBarrett(p)
+    me.assertEqual(m.m, p)
+
+    me.assertEqual(m.reduce(x*y), xy)
+
+    me.assertEqual(m.exp(2, p - 1), 1)
+
+    q, r, s, z = 32, 128, 2048, pow(g, 156, p)
+    me.assertEqual(m.mexp([(q, 9), (r, 8), (s, 5)]), z)
+    me.assertEqual(m.mexp(q, 9, r, 8, s, 5), z)
+
+###--------------------------------------------------------------------------
+class TestMPReduce (U.TestCase):
+
+  def test(me):
+
+    p = C.MP(2)**127 - 1
+    g = C.MP(2) # lucky chance
+    x = C.MP(94827182170881245766374991987593163418)
+    y = C.MP(106025009945795266831396608563402138277)
+    xy = C.MP(80027041045616838298103413933629021123)
+    me.assertTrue(p.primep())
+    m = C.MPReduce(p)
+    me.assertEqual(m.m, p)
+
+    me.assertEqual(m.reduce(x*y), xy)
+
+    me.assertEqual(m.exp(2, 127), 1)
+
+###--------------------------------------------------------------------------
+class TestMPCRT (U.TestCase):
+
+  def test(me):
+
+    c = C.MPCRT(5, 7, 11)
+    me.assertEqual(c.moduli, [5, 7, 11])
+    me.assertEqual(c.product, 385)
+    me.assertEqual(c.solve([2, 3, 4]), 367)
+    me.assertEqual(c.solve([2, -4, -7]), 367)
+
+    me.assertRaises(ValueError, C.MPCRT, [6, 15, 35])
+
+###--------------------------------------------------------------------------
+class TestGF (U.TestCase):
+
+  def test_make(me):
+    x = C.GF(5)
+    k = C.PrimeField(17)
+    kk = C.BinPolyField(C.GF(0x13))
+    E = k.ec(-3, 1)
+    me.assertTrue(C.GF(x) is x)
+    me.assertEqual(C.GF(k(8)), C.GF(8))
+    me.assertEqual(C.GF(kk(8)), C.GF(8))
+    me.assertEqual(C.GF(E(1, 4)), C.GF(1))
+    me.assertRaises(TypeError, C.GF, E())
+
+    me.assertEqual(int(x), 5)
+    y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
+    me.assertEqual(type(int(y)), T.long)
+
+    me.assertEqual(C.GF('0x4eeb684a0954ec4ceb255e3e9778d41'), y)
+    me.assertEqual(C.GF('4eeb684a0954ec4ceb255e3e9778d41', 16), y)
+    me.assertEqual(C.GF('0b0', 16), C.GF(176)) # not 0
+
+    me.assertEqual(C.GF('047353320450112516611472622536175135706501'), y)
+    me.assertEqual(C.GF('0o47353320450112516611472622536175135706501'), y)
+    me.assertEqual(C.GF('047353320450112516611472622536175135706501', 8), y)
+    me.assertEqual(C.GF('47353320450112516611472622536175135706501', 8), y)
+
+    t = C.GF(661438603)
+    me.assertEqual(C.GF('0b100111011011001100000010001011'), t)
+    me.assertEqual(C.GF('100111011011001100000010001011', 2), t)
+
+  def test_string(me):
+    y = C.GF(0x4eeb684a0954ec4ceb255e3e9778d41)
+    me.assertEqual(str(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
+    me.assertEqual(repr(y), 'GF(0x4eeb684a0954ec4ceb255e3e9778d41L)')
+    me.assertEqual(hex(y), '0x4eeb684a0954ec4ceb255e3e9778d41')
+    me.assertEqual(oct(y), '047353320450112516611472622536175135706501')
+
+  def test_number(me):
+    x, y, m, zero = C.GF(0xa9), C.GF(0x18), C.GF(0x11b), C.GF(0)
+
+    me.assertEqual(x, -x)
+    me.assertEqual(abs(x), x)
+
+    me.assertEqual(x + y, C.GF(0xb1))
+    me.assertEqual(x - y, C.GF(0xb1))
+    me.assertEqual(x*y, C.GF(0xfd8))
+    me.assertEqual(x&y, C.GF(0x8))
+    me.assertEqual(x | y, C.GF(0xb9))
+    me.assertEqual(x ^ y, C.GF(0xb1))
+
+    me.assertEqual(x << 3, C.GF(0x548))
+    me.assertEqual(x << -2, C.GF(0x2a))
+    me.assertEqual(x >> 2, C.GF(0x2a))
+    me.assertEqual(x >> -3, C.GF(0x548))
+
+    u = x/y; me.assertEqual((u.numer, u.denom), (C.GF(0x67), C.GF(0x8)))
+    me.assertEqual(x//y, C.GF(0xc))
+    me.assertEqual(x%y, C.GF(0x9))
+    me.assertEqual(divmod(x, y), (C.GF(0xc), C.GF(0x9)))
+    me.assertRaises(ZeroDivisionError, lambda: x/zero)
+    me.assertRaises(ZeroDivisionError, lambda: x//zero)
+    me.assertRaises(ZeroDivisionError, lambda: x%zero)
+    me.assertRaises(ZeroDivisionError, divmod, x, zero)
+
+    me.assertEqual(pow(x, 24),
+                   C.GF(0x1000100000001010000010101000101010001000001))
+    me.assertEqual(pow(x, 24, m), C.GF(0x78))
+    me.assertEqual(pow(x, -24, m), C.GF(0xb6))
+    me.assertRaises(ZeroDivisionError, pow, x, -24, C.GF(0x18))
+
+    me.assertTrue(x)
+    me.assertFalse(zero)
+
+  def test_order(me):
+    x, y, z = C.GF(0xa9), C.GF(0x18), C.GF(0xb3)
+    me.assertTrue(x == x)
+    me.assertFalse(x != x)
+    me.assertFalse(x == y)
+    me.assertTrue(x != y)
+    me.assertTrue(x > y)
+    me.assertFalse(y > x)
+    me.assertFalse(x > x)
+    me.assertFalse(x > z)
+    me.assertFalse(z > x)
+    me.assertTrue(x >= y)
+    me.assertFalse(y >= x)
+    me.assertTrue(x >= x)
+    me.assertTrue(x >= z)
+    me.assertTrue(z >= x)
+    me.assertFalse(x <= y)
+    me.assertTrue(y <= x)
+    me.assertTrue(x <= x)
+    me.assertTrue(x <= z)
+    me.assertTrue(z <= x)
+    me.assertFalse(x < y)
+    me.assertTrue(y < x)
+    me.assertFalse(x < x)
+    me.assertFalse(x < z)
+    me.assertFalse(z < x)
+
+  def test_bits(me):
+    x, zero = C.GF(0xa9), C.GF(0)
+    me.assertTrue(x.testbit(0))
+    me.assertFalse(x.testbit(1))
+    me.assertFalse(x.testbit(1000))
+
+    me.assertEqual(x.setbit(0), x)
+    me.assertEqual(x.clearbit(0), C.GF(0xa8))
+    me.assertEqual(x.setbit(1), C.GF(0xab))
+    me.assertEqual(x.clearbit(1), x)
+
+    me.assertEqual(x.nbits, 8)
+    me.assertEqual(x.degree, 7)
+    me.assertEqual(zero.nbits, 0)
+    me.assertEqual(zero.degree, -1)
+
+  def test_loadstore(me):
+    x = C.GF(0x0123456789ab)
+
+    me.assertEqual(x.noctets, 6)
+
+    me.assertEqual(x, C.GF.loadb(C.bytes("0123456789ab")))
+
+    me.assertEqual(x.storeb(), C.bytes("0123456789ab"))
+    me.assertEqual(x.storeb(3), C.bytes("6789ab"))
+    me.assertEqual(x.storeb(8), C.bytes("00000123456789ab"))
+
+    me.assertEqual(x, C.GF.loadl(C.bytes("ab8967452301")))
+
+    me.assertEqual(x.storel(), C.bytes("ab8967452301"))
+    me.assertEqual(x.storel(3), C.bytes("ab8967"))
+    me.assertEqual(x.storel(8), C.bytes("ab89674523010000"))
+
+    me.assertEqual(x.tobuf(), C.bytes("00060123456789ab"))
+    me.assertEqual((x, T.bin("abcd")),
+                   C.GF.frombuf(C.bytes("00060123456789ab61626364")))
+
+  def test_numbertheory(me):
+    p, x, y = C.GF(0x11b), C.GF(0xa9), C.GF(0x18)
+
+    me.assertEqual(x.sqr(), C.GF(0x4441))
+
+    me.assertEqual(x.gcd(y), C.GF(0x3))
+    me.assertEqual(x.gcdx(y), (C.GF(0x3), C.GF(0x3), C.GF(0x15)))
+    me.assertEqual(p.modinv(x), C.GF(0xc8))
+
+    me.assertTrue(p.irreduciblep())
+    me.assertFalse(x.irreduciblep())
+
+###--------------------------------------------------------------------------
+class TestGFReduce (U.TestCase):
+
+  def test(me):
+    p = C.GF(0x87).setbit(128)
+    me.assertTrue(p.irreduciblep())
+    m = C.GFReduce(p)
+
+    x = C.GF(0xce46b4c1d3a1523520b1bb6eb5c61883)
+    y = C.GF(0xb5b0b3566b8e03f4b4a2b1ac413f8566)
+    xy = C.GF(0x28e5b895c11b08edc2fe7e1be5694c64)
+
+    me.assertEqual(m.reduce(x*y), xy)
+    me.assertEqual(m.trace(x), 0)
+    me.assertEqual(m.trace(y), 1)
+    me.assertEqual(m.sqrt(x), C.GF(0xa277ee4bf770e5974cf1e31b1ccb54a1))
+    me.assertEqual(m.halftrace(y), C.GF(0x9cea73e79ffd190dd3c81d33e58d8e6f))
+    me.assertEqual(m.quadsolve(x), C.GF(0x9664c09d23d168147a438de6a813c784))
+
+###--------------------------------------------------------------------------
+class TestGFN (U.TestCase):
+
+  def test(me):
+    p = C.GF(0x87).setbit(128)
+    beta = C.GF(0xc50f387e37194d4a4b41e157a3e2b5e1)
+    y = C.GF(0xdaca76dc2578a63c788a2ce0fc7878f6)
+    yy = C.GF(0x298a98f955100f054fcee3433f96b00e)
+    zero, one, fff = C.GF(0), C.GF(1), C.GF(T.long(2)**128 - 1)
+    me.assertTrue(p.irreduciblep())
+
+    gfn = C.GFN(p, beta)
+    me.assertEqual(gfn.p, p)
+    me.assertEqual(gfn.beta, beta)
+    me.assertEqual(gfn.pton(zero), zero)
+    me.assertEqual(gfn.ntop(zero), zero)
+    me.assertEqual(gfn.pton(one), fff)
+    me.assertEqual(gfn.ntop(fff), one)
+    me.assertEqual(gfn.pton(y), yy)
+    me.assertEqual(gfn.ntop(yy), y)
+
+    ## Doesn't generate a normal basis.
+    me.assertRaises(ValueError, C.GFN, p, y)
+
+###----- That's all, folks --------------------------------------------------
+
+if __name__ == "__main__": U.main()