Commit 4fe3b9d0 authored by Michael Hamburg's avatar Michael Hamburg

begin groundwork for sage testing

parent 6947f380
......@@ -55,13 +55,17 @@ ifeq ($(CC),clang)
WARNFLAGS += -Wgcc-compat
endif
SAGE ?= sage
SAGES= $(shell ls test/*.sage)
BUILDPYS= $(SAGES:test/%.sage=build/%.py)
ARCHFLAGS += $(XARCHFLAGS)
CFLAGS = $(LANGFLAGS) $(WARNFLAGS) $(INCFLAGS) $(OFLAGS) $(ARCHFLAGS) $(GENFLAGS) $(XCFLAGS)
CXXFLAGS = $(LANGXXFLAGS) $(WARNFLAGS) $(INCFLAGS) $(OFLAGS) $(ARCHFLAGS) $(GENFLAGS) $(XCXXFLAGS)
LDFLAGS = $(ARCHFLAGS) $(XLDFLAGS)
ASFLAGS = $(ARCHFLAGS) $(XASFLAGS)
.PHONY: clean all test bench todo doc lib bat
.PHONY: clean all test bench todo doc lib bat sage sagetest
.PRECIOUS: build/%.s
HEADERS= Makefile $(shell find src include test -name "*.h") $(shell find . -name "*.hxx") build/timestamp
......@@ -149,6 +153,21 @@ build/%.s: src/$(FIELD)/$(ARCH)/%.c $(HEADERS)
build/%.s: src/$(FIELD)/%.c $(HEADERS)
$(CC) $(CFLAGS) -S -c -o $@ $<
sage: $(BUILDPYS)
sagetest: sage lib
LD_LIBRARY_PATH=build sage build/test_decaf.sage
$(BUILDPYS): $(SAGES) build/timestamp
cp -f $(SAGES) build/
$(SAGE) --preparse $(SAGES:test/%.sage=build/%.sage)
# some sage versions compile to .sage.py
for f in $(SAGES:test/%.sage=build/%); do \
if [ -e $$f.sage.py ]; then \
mv $$f.sage.py $$f.py; \
fi; \
done
doc/timestamp:
mkdir -p doc
......
from idealized import Idealized
from collections import namedtuple
debugging = True
def debug_print(foo):
if debugging: print foo
checkGroupLaws = True
checkTorsion = True
checkIsogenies = True
def memoize(f):
# list cache because my __hash__ hack doesn't seem to work
cache = []
def ff(*args, **kwargs):
key = (tuple(args),tuple(sorted(kwargs.iteritems())))
for key_,value in cache:
if key == key_: return value
out = f(*args,**kwargs)
cache.append((key,out))
return out
try:
ff.__name__ = f.__name__
except AttributeError: pass
return ff
def EcBase(curvename,varnames,ad=()):
if isinstance(ad,str) or isinstance(ad[0],str):
ad = Idealized.vars(ad)
class Inner(namedtuple(curvename,(v for v in varnames))):
params = ad
torsion_points = {}
def __new__(cls,*xy):
def apply_invariants(xy,x):
for inv in cls.invariants(*(ad+xy)):
x = x.assuming(inv)
return x
xy = tuple(xy)
if len(xy) == 0:
xy = Idealized.uvars(varnames)
xy = [apply_invariants(xy,x) for x in xy]
else:
for i,inv in enumerate(cls.invariants(*(ad + xy))):
if inv != 0:
raise Exception("Invariant inv[%d] not satisfied for %s: got \n%s" %
(i,curvename,str(inv)))
return super(Inner,cls).__new__(cls,*xy)
varnames = "xy"
@classmethod
def invariants(self,*args): return []
@classmethod
@memoize
def check_group(cls):
if checkGroupLaws:
debug_print("Checking group law for %s..." % cls.__name__)
a,b,c,z = cls(),cls(),cls(),cls.basepoint
if a+z != a:
raise Exception("Base point is not identity!")
if a-a != z:
raise Exception("Subtraction doesn't work!")
if a+b != b+a:
raise Exception("Addition is not commutative!")
#if a+(b+c) != (a+b)+c:
# raise Exception("Addition is not associative!")
for t,n in cls.torsion():
if checkTorsion:
debug_print(" Checking %d-torsion..." % n)
cls.check_torsion(t,n)
#if n not in cls.torsion_points:
# cls.torsion_points[n] = set()
#cls.torsion_points[n].add(cls(*t(cls.basepoint)))
@classmethod
def check_torsion(cls,f,n):
P = Q = cls()
good = False
for i in xrange(1,n+1):
Q = cls(*f(Q))
if Q == P:
if i==n:
good = True
break
raise Exception("Claimed %d-torsion, but is actually %d-torsion" % (n,i))
if not good: raise Exception("Claimed %d-torsion, but isn't" % n)
if n*P+n*cls(*f(P)) == cls.basepoint:
raise Exception("Torsion operation inverts element")
@classmethod
def torsion(cls):
return []
def __sub__(self,other):
return self + (-other)
def __mul__(self,other):
if other==0: return self.basepoint
if other < 0: return -(self*-other)
if other==1: return self
if is_even(other): return (self+self)*(other//2)
return (self+self)*(other//2) + self
def __rmul__(self,other):
return self*other
Inner.__name__ = curvename + "_base"
return Inner
class Isogeny(object):
isograph = DiGraph(weighted=True)
isomap = {}
@classmethod
def generate(cls, fro, to):
path = cls.isograph.shortest_path(fro,to,by_weight=True)
if len(path):
iso = cls.isomap[(path[0], path[1])]
for i in xrange(1,len(path)-1):
iso = cls.isomap[(path[i],path[i+1])].compose(iso)
return iso
else:
return None
def __init__(self,c1,c2,deg,fw,rv,check=True,dual=None,add=True):
self.c1 = c1
self.c2 = c2
self.fw = fw
self.rv = rv
self.deg = deg
if add:
Isogeny.isomap[(c1,c2)] = self
Isogeny.isograph.add_edge(c1,c2,log(deg)/log(2) + 0.1)
if dual is not None:
self.dual = dual
else:
self.dual = Isogeny(c2,c1,deg,rv,fw,False,self,add)
if not check: return
if not checkIsogenies: return
debug_print("Checking isogeny %s <-%d-> %s..." % (c1.__name__,deg,c2.__name__))
if c2(*fw(*c1.basepoint)) != c2.basepoint:
raise Exception("Isogeny doesn't preserve basepoints")
if c1(*fw(*c2.basepoint)) != c1.basepoint:
raise Exception("Isogeny dual doesn't preserve basepoints")
foo = c1()
bar = c2()
c2(*fw(*foo))
c1(*rv(*bar))
if c1(*rv(*c2(*fw(*foo)))) != deg*foo:
raise Exception("Isogeny degree is wrong")
if c2(*fw(*c1(*rv(*bar)))) != deg*bar:
raise Exception("Isogeny degree is wrong")
if -c2(*fw(*foo)) != c2(*fw(*(-foo))):
raise Exception("Isogeny uses wrong negmap")
if -c1(*rv(*bar)) != c1(*rv(*(-bar))):
raise Exception("Isogeny uses wrong negmap")
def __call__(self,ipt,**kwargs):
return self.c2(*self.fw(*ipt,**kwargs))
def __repr__(self): return str(self)
def __str__(self):
out = "Isogeny %s%s <-%d-> %s%s..." %\
(self.c1.__name__,str(self.c1.params),self.deg,
self.c2.__name__,self.c2.params)
out += "\n fw: %s" % str(self(self.c1()))
out += "\n rv: %s" % str(self.dual(self.c2()))
return out
def compose(self,other):
def fw(*args): return self.fw(*other.fw(*args))
def rv(*args): return other.rv(*self.rv(*args))
return Isogeny(other.c1,self.c2,self.deg*other.deg,fw,rv,False,None,False)
def ec_family(defs,vars):
def inner1(CLS):
@memoize
def inner2(*args,**kwargs):
if len(args)==0 and len(kwargs)==0:
args = tuple(defs)
chk = True
else:
chk = False
class ret(CLS,EcBase(CLS.__name__,vars,args)):
def __new__(cls,*args,**kwargs):
return super(ret,cls).__new__(cls,*args,**kwargs)
ret.__name__ = CLS.__name__
ret.basepoint = ret(*ret.get_basepoint())
if chk: ret.check_group()
return ret
inner2.__name__ = CLS.__name__ + "_family"
inner2()
return inner2
return inner1
#checkGroupLaws = checkTorsion = False
@ec_family("ad","xy")
class Edwards:
@classmethod
def invariants(cls,a,d,x,y):
return [y^2 + a*x^2 - 1 - d*x^2*y^2]
def __neg__(self):
return self.__class__(-self.x,self.y)
def __add__(self,other):
(x,y) = self
(X,Y) = other
a,d = self.params
dd = d*x*X*y*Y
return self.__class__((x*Y+X*y)/(1+dd),(y*Y-a*x*X)/(1-dd))
@classmethod
def get_basepoint(cls): return (0,1)
@classmethod
@memoize
def torsion(cls):
a,d = cls.params
sa = a.sqrt()
sd = d.sqrt()
sad = (a*d).sqrt()
def tor2_1((x,y)): return (-x,-y)
def tor4_1((x,y)): return (y/sa,-x*sa)
def tor4_2((x,y)): return (1/(sd*y),-1/(sd*x))
def tor2_2((x,y)): return (-1/(sad*x),-a/(sad*y))
return [(tor2_1,2),(tor2_2,2),(tor4_1,4),(tor4_2,4)]
@ec_family("eA","st")
class JacobiQuartic:
@classmethod
def invariants(cls,e,A,s,t):
return [-t^2 + e*s^4 + 2*A*s^2 + 1]
def __neg__(self):
return self.__class__(-self.s,self.t)
def __add__(self,other):
(x,y) = self
(X,Y) = other
e,A = self.params
dd = e*(x*X)^2
YY = (1+dd)*(y*Y+2*A*x*X) + 2*e*x*X*(x^2+X^2)
return self.__class__((x*Y+X*y)/(1-dd),YY/(1-dd)^2)
@classmethod
def get_basepoint(cls): return (0,1)
@classmethod
@memoize
def torsion(cls):
e,A = cls.params
se = e.sqrt()
def tor2_1((s,t)): return (-s,-t)
def tor2_2((s,t)): return (1/(se*s),-t/(se*s^2))
return [(tor2_1,2),(tor2_2,2)]
a,d = Idealized.vars("ad")
def phi_iso(a,d):
return Isogeny(Edwards(a,d),JacobiQuartic(a^2,a-2*d),
2,
lambda x,y: (x/y, (2-y^2-a*x^2)/y^2),
lambda s,t: (2*s/(1+a*s^2), (1-a*s^2)/t)
)
print phi_iso(a,d)
print phi_iso(-a,d-a)
print Isogeny.generate(Edwards(a,d),Edwards(-a,d-a))
\ No newline at end of file
class Unique(object):
def __init__(self,name):
self.name = name
def __str__(self):
return self.name
def __repr__(self):
return "Unique(\"%s\")" % self.name
class Idealized(object):
UNION = ["UNION"]
def __init__(self, R, idealMap = 0, vars = {}):
self.varnames = vars
if not isinstance(idealMap,dict):
idealMap = {()*R:idealMap}
self.idealMap = idealMap
self.R = R
self._sqrt = None
self._isqrt = None
@staticmethod
def uvar(x):
return Idealized.var(Unique(x))
@staticmethod
def var(x):
name = str(x)
R = PolynomialRing(QQ,[name])
rx = R.gens()[0]
return Idealized(R,rx,{x:(name,rx)})
@staticmethod
def vars(xs):
return tuple((Idealized.var(x) for x in xs))
@staticmethod
def uvars(xs):
return tuple((Idealized.uvar(x) for x in xs))
def __str__(self):
def rep(I,x):
x = str(x)
gs = I.gens()
gs = [g for g in gs if g != 0]
if len(gs) == 0: return x
else:
g = ", ".join(["(%s)" % str(gen) for gen in gs])
return g + ": " + x
return "\n".join([rep(I,self.idealMap[I]) for I in self.idealMap])
def __repr__(self):
# HACK!
if len(self.idealMap) == 0:
return "undef"
if len(self.idealMap) > 1:
return str(self)
for _,v in self.idealMap.iteritems():
return str(v)
def prune(self):
self.idealMap = {I:v for I,v in self.idealMap.iteritems() if not (I*self.R).is_one()}
return self
def __add__(self,other):
def f(x,y): return x+y
return self.op(other,f)
def __radd__(self,other):
def f(x,y): return y+x
return self.op(other,f)
def __rsub__(self,other):
def f(x,y): return y-x
return self.op(other,f)
def __neg__(self):
def f(x,y): return y-x
return self.op(0,f)
def __sub__(self,other):
def f(x,y): return x-y
return self.op(other,f)
def is_square(self):
for _,v in self.idealMap.iteritems():
if not is_square(v): return False
return True
def sqrt(self):
if self._sqrt is None:
s = Idealized.uvar("s")
self._sqrt = s.assuming(s^2 - self)
return self._sqrt
def isqrt(self):
if self._isqrt is None:
s = Idealized.uvar("s")
z = Idealized(0).assuming(Self)
self._isqrt = s.assuming(s^2*self-1).union(z)
return self._isqrt
def __mul__(self,other):
def f(x,y): return x*y
return self.op(other,f)
def __rmul__(self,other):
def f(x,y): return y*x
return self.op(other,f)
def __pow__(self,n):
if n < 0: return 1/self^(-n)
if n == 0: return 1
if n == 1: return self
if is_even(n): return (self*self)^(n//2)
if is_odd(n): return (self*self)^(n//2) * self
def __div__(self,other):
def f(x,y): return x/y
return self.op(other,f)
def __rdiv__(self,other):
def f(x,y): return y/x
return self.op(other,f)
def union(self,other):
return self.op(other,Idealized.UNION)
def __eq__(self,other):
return (self - other).is_zero()
def __ne__(self,other):
return not (self==other)
def __hash__(self):
return 0
def assume_zero(self):
out = {}
for I,J in self.idealMap.iteritems():
IJ = I+J.numerator()
if IJ.is_one(): continue
out[IJ] = self.R(0)
if len(out) == 0:
raise Exception("Inconsistent assumption")
return Idealized(self.R,out,self.varnames)
def assuming(self,other):
return self + other.assume_zero()
def is_zero(self):
for I,v in self.idealMap.iteritems():
if v.denominator() in I: return False
if v.numerator() not in I: return False
return True
def op(self,other,f):
if not isinstance(other,Idealized):
other = Idealized(self.R,other,self.varnames)
bad = False
for v in self.varnames:
if v not in other.varnames or self.varnames[v] != other.varnames[v]:
bad = True
break
for v in other.varnames:
if v not in self.varnames or self.varnames[v] != other.varnames[v]:
bad = True
break
if bad:
def incrVar(v):
if v[-1] not in "0123456789": return v + "1"
elif v[-1] == 9: return incrVar(v[:-1]) + "0"
else: return v[:-1] + str(int(v[-1])+1)
vars = {}
names = set()
for v,(name,_) in self.varnames.iteritems():
assert(name not in names)
names.add(name)
vars[v] = name
subMe = {n:n for n in names}
subThem = {}
for v,(name,_) in other.varnames.iteritems():
if v in self.varnames:
subThem[name] = self.varnames[v][0]
else:
oname = name
while name in names:
name = incrVar(name)
names.add(name)
subThem[oname] = name
vars[v] = name
R = PolynomialRing(QQ,sorted(list(names)),order="degrevlex")
gd = R.gens_dict()
subMe = {m:gd[n] for m,n in subMe.iteritems()}
subThem = {m:gd[n] for m,n in subThem.iteritems()}
vars = {v:(n,gd[n]) for v,n in vars.iteritems()}
def subIdeal(I,sub):
return [g(**sub) for g in I.gens()]*R
idealMe = {subIdeal(I,subMe):v(**subMe) for I,v in self.idealMap.iteritems()}
idealThem = {subIdeal(I,subThem):v(**subThem) for I,v in other.idealMap.iteritems()}
else:
R = self.R
idealMe = self.idealMap
idealThem = other.idealMap
vars = self.varnames
def consist(I,x,y):
if (x-y).numerator() not in I:
raise Exception("Inconsistent: %s != %s in ideal %s" %
(str(x),str(y),str(I)))
out = {}
if f is Idealized.UNION:
for I,v in idealMe.iteritems():
if I in idealThem:
consist(I,v,idealThem[I])
out[I] = v
for I,v in idealThem.iteritems():
if I in idealMe:
consist(I,v,idealMe[I])
out[I] = v
else:
for I,v in idealMe.iteritems():
if I in idealThem:
x = f(v,idealThem[I])
if I in out:
consist(I,x,out[I])
else: out[I] = x
else:
for J,w in idealThem.iteritems():
IJ = I+J
if not IJ.is_one():
x = f(v,w)
if IJ in out:
consist(IJ,x,out[IJ])
else:
out[IJ] = x
def gb(I):
II = [0]*R
for g in I.gens():
if g not in II: II = II+[g]*R
return II
def red(I,v):
if I.is_zero(): return v
return I.reduce(R(v.numerator())) / I.reduce(R(v.denominator()))
out = {gb(I):v for I,v in out.iteritems()}
out = {I:red(I,v) for I,v in out.iteritems()}
return Idealized(R,out,vars)
def reduce(self):
def red(I,v):
if I.is_zero(): return v
return I.reduce(R(v.numerator())) / I.reduce(R(v.denominator()))
out = {I:red(I,v) for I,v in self.idealMap.iteritems()}
return Idealized(self.R,out,self.vars)
Idealized.INF = Idealized.uvar("inf")
Idealized.ZOZ = Idealized.uvar("zoz")
\ No newline at end of file
from ctypes import *
decaf = CDLL("libdecaf.so")
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