def bench2():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench2()[0]
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
"""
desc = """Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001"""
t = cputime()
a = ZZ(3)**1000001 * ZZ(19)**100001
return (desc, cputime(t))
def bench3():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench3()[0]
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
"""
desc = """Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001"""
t = cputime()
a = QQ('2/3')**100001 * QQ('17/19')**100001
return (desc, cputime(t))
def bench3():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench3()[0]
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
"""
desc = """Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001"""
t = cputime()
a = QQ('2/3')**100001 * QQ('17/19')**100001
return (desc, cputime(t))
def bench2():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench2()[0]
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
"""
desc = """Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001"""
t = cputime()
a = ZZ(3)**1000001 * ZZ(19)**100001
return (desc, cputime(t))
def bench1():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench1()[0]
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
"""
desc = """Find the Mordell-Weil group of the elliptic curve 5077A using mwrank"""
E = mwrank_EllipticCurve([0, 0, 1, -7, 6])
t = cputime()
g = E.gens()
return (desc, cputime(t))
def bench7():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench7()[0]
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
"""
desc = """Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997."""
E = EllipticCurve([0,0,0,37,-997])
t = cputime()
G = E.gens()
return (desc, cputime(t))
def bench7():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench7()[0]
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
"""
desc = """Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997."""
E = EllipticCurve([0, 0, 0, 37, -997])
t = cputime()
G = E.gens()
return (desc, cputime(t))
def bench1():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench1()[0]
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
"""
desc = """Find the Mordell-Weil group of the elliptic curve 5077A using mwrank"""
E = mwrank_EllipticCurve([0, 0, 1, -7, 6])
t = cputime()
g = E.gens()
return (desc, cputime(t))
def bench6():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench6()[0]
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
"""
desc = """Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40."""
E = EllipticCurve([0, 0, 0, 37, -997])
t = cputime()
for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
f = E.division_polynomial(p)
return (desc, cputime(t))
def bench5():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench5()[0]
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
"""
desc = """Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times."""
x = PolynomialRing(QQ, 'x').gen()
t = cputime()
f = x**19 - 18 * x + 1
w = [f**50 for _ in range(100)]
return (desc, cputime(t))
def bench4():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench4()[0]
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
"""
desc = """Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200."""
x = PolynomialRing(QQ, 'x').gen()
t = cputime()
f = x**29 + 17 * x - 5
a = f**200
return (desc, cputime(t))
def bench6():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench6()[0]
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
"""
desc = """Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40."""
E = EllipticCurve([0,0,0,37,-997])
t = cputime()
for p in [2,3,5,7,11,13,17,19,23,29,31,37]:
f = E.division_polynomial(p)
return (desc, cputime(t))
def bench5():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench5()[0]
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
"""
desc = """Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times."""
x = PolynomialRing(QQ, 'x').gen()
t = cputime()
f = x**19 - 18*x + 1
w = [f**50 for _ in range(100)]
return (desc, cputime(t))
def bench4():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench4()[0]
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
"""
desc = """Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200."""
x = PolynomialRing(QQ, 'x').gen()
t = cputime()
f = x**29 + 17*x-5
a = f**200
return (desc, cputime(t))
def bench0():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench0()[0]
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
"""
desc = """Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)"""
x = polygen(QQ,"x")
f = (x**97+19*x+1)*(x**103-19*x**97+14)*(x**100-1)
t = cputime()
F = f.factor()
return (desc, cputime(t))
def bench0():
"""
Run a benchmark.
BENCHMARK:
sage: from sage.misc.benchmark import *
sage: print bench0()[0]
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
"""
desc = """Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)"""
x = polygen(QQ, "x")
f = (x**97 + 19 * x + 1) * (x**103 - 19 * x**97 + 14) * (x**100 - 1)
t = cputime()
F = f.factor()
return (desc, cputime(t))
def run(self, context):
lastCheckpoint = misc.cputime()
shouldStop = False
while not shouldStop:
if context.iteration >= self.maxIterations:
print >> context.log, 'maximum number of iterations reached.'
break
print >> context.log, 'iteration: %s' % context.iteration
try:
shouldStop = self.iterate(context)
except:
import traceback
traceback.print_exc()
print >> context.log, 'iteration failed.'
break
if ((self.checkpointInterval) and
(misc.cputime() > lastCheckpoint + self.checkpointInterval)):
self.checkpoint(context)
lastCheckpoint = misc.cputime()
context.iteration += 1
misc.reportMemoryUsage()
print >> context.log
context.log.flush()
def run(self, context):
lastCheckpoint = misc.cputime()
shouldStop = False
while not shouldStop:
if context.iteration >= self.maxIterations:
print >> context.log, 'maximum number of iterations reached.'
break
print >> context.log, 'iteration: %s' % context.iteration
try:
shouldStop = self.iterate(context)
except Exception:
import traceback
traceback.print_exc()
print >> context.log, 'iteration failed.'
break
if ((self.checkpointInterval) and
(misc.cputime() > lastCheckpoint + self.checkpointInterval)):
self.checkpoint(context)
lastCheckpoint = misc.cputime()
context.iteration += 1
misc.reportMemoryUsage()
print >> context.log
context.log.flush()
def benchmark(n=-1):
"""
Run a well-chosen range of Sage commands and record the time it
takes for each to run.
INPUT:
n -- int (default: -1) the benchmark number; the default
of -1 runs all the benchmarks.
OUTPUT:
list -- summary of timings for each benchmark.
int -- if n == -1, also return the total time
EXAMPLE:
sage: from sage.misc.benchmark import *
sage: _ = benchmark()
Running benchmark 0
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: ... seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: ... seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: ... seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: ... seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: ... seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: ... seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: ... seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: ... seconds
Running benchmark 8
"""
if isinstance(n, list):
t = cputime()
v = [benchmark(m) for m in n]
return v, cputime(t)
if n != -1:
print "Running benchmark %s"%n
try:
desc, t = eval("bench%s()"%n)
except NameError:
raise RuntimeError, "no benchmark %s"%n
print desc
print "Time: %s seconds"%t
return (n, t, desc)
t = cputime()
m = 0
v = []
while True:
try:
v.append(benchmark(m))
m += 1
except RuntimeError:
break
return v, cputime(t)
def benchmark(n=-1):
"""
Run a well-chosen range of Sage commands and record the time it
takes for each to run.
INPUT:
n -- int (default: -1) the benchmark number; the default
of -1 runs all the benchmarks.
OUTPUT:
list -- summary of timings for each benchmark.
int -- if n == -1, also return the total time
EXAMPLE:
sage: from sage.misc.benchmark import *
sage: _ = benchmark()
Running benchmark 0
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: ... seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: ... seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: ... seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: ... seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: ... seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: ... seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: ... seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: ... seconds
Running benchmark 8
"""
if isinstance(n, list):
t = cputime()
v = [benchmark(m) for m in n]
return v, cputime(t)
if n != -1:
print "Running benchmark %s" % n
try:
desc, t = eval("bench%s()" % n)
except NameError:
raise RuntimeError, "no benchmark %s" % n
print desc
print "Time: %s seconds" % t
return (n, t, desc)
t = cputime()
m = 0
v = []
while True:
try:
v.append(benchmark(m))
m += 1
except RuntimeError:
break
return v, cputime(t)
