Coverage for local/lib/python2.7/site-packages/sage/misc/benchmark.py : 96%

"Benchmarks" 

from __future__ import print_function 

from __future__ import absolute_import 

from .misc import cputime 

from sage.all import * 

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 

EXAMPLES:: 

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 {}".format(n)) 

try: 

desc, t = eval("bench{}()".format(n)) 

except NameError: 

raise RuntimeError("no benchmark {}".format(n)) 

print(desc) 

print("Time: {} seconds".format(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 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 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 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 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 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 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 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))