Double Precision Real Numbers

Double Precision Real Numbers

EXAMPLES:

We create the real double vector space of dimension \(3\):

sage: V = RDF^3; V
Vector space of dimension 3 over Real Double Field

Notice that this space is unique:

sage: V is RDF^3
True
sage: V is FreeModule(RDF, 3)
True
sage: V is VectorSpace(RDF, 3)
True

Also, you can instantly create a space of large dimension:

sage: V = RDF^10000

TESTS:

Test NumPy conversions:

sage: RDF(1).__array_interface__
{'typestr': '=f8'}
sage: import numpy
sage: numpy.array([RDF.pi()]).dtype
dtype('float64')
class sage.rings.real_double.RealDoubleElement

Bases: sage.structure.element.FieldElement

An approximation to a real number using double precision floating point numbers. Answers derived from calculations with such approximations may differ from what they would be if those calculations were performed with true real numbers. This is due to the rounding errors inherent to finite precision calculations.

NaN()

Return Not-a-Number NaN.

EXAMPLES:

sage: RDF.NaN()
NaN
abs()

Returns the absolute value of self.

EXAMPLES:

sage: RDF(1e10).abs()
10000000000.0
sage: RDF(-1e10).abs()
10000000000.0
acosh()

Return the hyperbolic inverse cosine of self.

EXAMPLES:

sage: q = RDF.pi()/2
sage: i = q.cosh() ; i
2.50917847866
sage: abs(i.acosh()-q) < 1e-15
True
agm(other)

Return the arithmetic-geometric mean of self and other. The arithmetic-geometric mean is the common limit of the sequences \(u_n\) and \(v_n\), where \(u_0\) is self, \(v_0\) is other, \(u_{n+1}\) is the arithmetic mean of \(u_n\) and \(v_n\), and \(v_{n+1}\) is the geometric mean of \(u_n\) and \(v_n\). If any operand is negative, the return value is NaN.

EXAMPLES:

sage: a = RDF(1.5)
sage: b = RDF(2.3)
sage: a.agm(b)
1.87864845581

The arithmetic-geometric mean always lies between the geometric and arithmetic mean:

sage: sqrt(a*b) < a.agm(b) < (a+b)/2
True
algdep(n)

Return a polynomial of degree at most \(n\) which is approximately satisfied by this number.

Note

The resulting polynomial need not be irreducible, and indeed usually won’t be if this number is a good approximation to an algebraic number of degree less than \(n\).

ALGORITHM:

Uses the PARI C-library algdep command.

EXAMPLE:

sage: r = sqrt(RDF(2)); r
1.41421356237
sage: r.algebraic_dependency(5)
x^2 - 2
algebraic_dependency(n)

Return a polynomial of degree at most \(n\) which is approximately satisfied by this number.

Note

The resulting polynomial need not be irreducible, and indeed usually won’t be if this number is a good approximation to an algebraic number of degree less than \(n\).

ALGORITHM:

Uses the PARI C-library algdep command.

EXAMPLE:

sage: r = sqrt(RDF(2)); r
1.41421356237
sage: r.algebraic_dependency(5)
x^2 - 2
arccos()

Return the inverse cosine of self.

EXAMPLES:

sage: q = RDF.pi()/3
sage: i = q.cos()
sage: i.arccos() == q
True
arcsin()

Return the inverse sine of self.

EXAMPLES:

sage: q = RDF.pi()/5
sage: i = q.sin()
sage: i.arcsin() == q
True
arcsinh()

Return the hyperbolic inverse sine of self.

EXAMPLES:

sage: q = RDF.pi()/2
sage: i = q.sinh() ; i
2.30129890231
sage: abs(i.arcsinh()-q) < 1e-15
True
arctan()

Return the inverse tangent of self.

EXAMPLES:

sage: q = RDF.pi()/5
sage: i = q.tan()
sage: i.arctan() == q
True
arctanh()

Return the hyperbolic inverse tangent of self.

EXAMPLES:

sage: q = RDF.pi()/2
sage: i = q.tanh() ; i
0.917152335667
sage: i.arctanh() - q      # output is random, depending on arch.
-4.4408920985e-16
ceil()

Return the ceiling of self.

EXAMPLES:

sage: RDF(2.99).ceil()
3
sage: RDF(2.00).ceil()
2
sage: RDF(-5/2).ceil()
-2
ceiling()

Return the ceiling of self.

EXAMPLES:

sage: RDF(2.99).ceil()
3
sage: RDF(2.00).ceil()
2
sage: RDF(-5/2).ceil()
-2
conjugate()

Returns the complex conjugate of this real number, which is the real number itself.

EXAMPLES:

sage: RDF(4).conjugate()
4.0
cos()

Return the cosine of self.

EXAMPLES:

sage: t=RDF.pi()/2
sage: t.cos()
6.12323399574e-17
cosh()

Return the hyperbolic cosine of self.

EXAMPLES:

sage: q = RDF.pi()/12
sage: q.cosh()
1.0344656401
coth()

Return the hyperbolic cotangent of self.

EXAMPLES:

sage: RDF(pi).coth()
1.0037418732
sage: CDF(pi).coth()
1.0037418732
csch()

Return the hyperbolic cosecant of self.

EXAMPLES:

sage: RDF(pi).csch()
0.08658953753
sage: CDF(pi).csch()
0.08658953753
cube_root()

Return the cubic root (defined over the real numbers) of self.

EXAMPLES:

sage: r = RDF(125.0); r.cube_root()
5.0
sage: r = RDF(-119.0)
sage: r.cube_root()^3 - r         # output is random, depending on arch.
0.0
erf()

Return the value of the error function on self.

EXAMPLES:

sage: RDF(6).erf()
1.0
exp()

Return \(e^\mathtt{self}\).

EXAMPLES:

sage: r = RDF(0.0)
sage: r.exp()
1.0
sage: r = RDF('32.3')
sage: a = r.exp(); a
1.06588847275e+14
sage: a.log()
32.3
sage: r = RDF('-32.3')
sage: r.exp()
9.3818445885e-15
sage: RDF(1000).exp()
+infinity
exp10()

Return \(10^\mathtt{self}\).

EXAMPLES:

sage: r = RDF(0.0)
sage: r.exp10()
1.0
sage: r = RDF(32.0)
sage: r.exp10()
1e+32
sage: r = RDF(-32.3)
sage: r.exp10()
5.01187233627e-33
exp2()

Return \(2^\mathtt{self}\).

EXAMPLES:

sage: r = RDF(0.0)
sage: r.exp2()
1.0
sage: r = RDF(32.0)
sage: r.exp2()
4294967296.0
sage: r = RDF(-32.3)
sage: r.exp2()
1.89117248253e-10
floor()

Return the floor of self.

EXAMPLES:

sage: RDF(2.99).floor()
2
sage: RDF(2.00).floor()
2
sage: RDF(-5/2).floor()
-3
frac()

Return a real number in \((-1, 1)\). It satisfies the relation: x = x.trunc() + x.frac()

EXAMPLES:

sage: RDF(2.99).frac()
0.99
sage: RDF(2.50).frac()
0.5
sage: RDF(-2.79).frac()
-0.79
gamma()

Return the value of the Euler gamma function on self.

EXAMPLES:

sage: RDF(6).gamma()
120.0
sage: RDF(1.5).gamma()
0.886226925453
hypot(other)

Computes the value \(\sqrt{s^2 + o^2}\) where \(s\) is self and \(o\) is other in such a way as to avoid overflow.

EXAMPLES:

sage: x = RDF(4e300); y = RDF(3e300);
sage: x.hypot(y)
5e+300
sage: sqrt(x^2+y^2) # overflow
+infinity
imag()

Return the imaginary part of this number, which is zero.

EXAMPLES:

sage: a = RDF(3)
sage: a.imag()
0.0
integer_part()

If in decimal this number is written n.defg, returns n.

EXAMPLES:

sage: r = RDF('-1.6')
sage: a = r.integer_part(); a
-1
sage: type(a)
<type 'sage.rings.integer.Integer'>
sage: r = RDF(0.0/0.0)
sage: a = r.integer_part()
Traceback (most recent call last):
...
TypeError: Attempt to get integer part of NaN
is_NaN()

Check if self is NaN.

EXAMPLES:

sage: RDF(1).is_NaN()
False
sage: a = RDF(0)/RDF(0)
sage: a.is_NaN()
True
is_infinity()

Check if self is \(\infty\).

EXAMPLES:

sage: a = RDF(2); b = RDF(0)
sage: (a/b).is_infinity()
True
sage: (b/a).is_infinity()
False
is_negative_infinity()

Check if self is \(-\infty\).

EXAMPLES:

sage: a = RDF(2)/RDF(0)
sage: a.is_negative_infinity()
False
sage: a = RDF(-3)/RDF(0)
sage: a.is_negative_infinity()
True
is_positive_infinity()

Check if self is \(+\infty\).

EXAMPLES:

sage: a = RDF(1)/RDF(0)
sage: a.is_positive_infinity()
True
sage: a = RDF(-1)/RDF(0)
sage: a.is_positive_infinity()
False
is_square()

Return whether or not this number is a square in this field. For the real numbers, this is True if and only if self is non-negative.

EXAMPLES:

sage: RDF(3.5).is_square()
True
sage: RDF(0).is_square()
True
sage: RDF(-4).is_square()
False
log(base=None)

Return the logarithm.

INPUT:

  • base – integer or None (default). The base of the logarithm. If None is specified, the base is \(e\) (the so-called natural logarithm).

OUTPUT:

The logarithm of self. If self is positive, a double floating point number. Infinity if self is zero. A imaginary complex floating point number if self is negative.

EXAMPLES:

sage: RDF(2).log()
0.69314718056
sage: RDF(2).log(2)
1.0
sage: RDF(2).log(pi)
0.605511561398
sage: RDF(2).log(10)
0.301029995664
sage: RDF(2).log(1.5)
1.70951129135
sage: RDF(0).log()
-infinity
sage: RDF(-1).log()
3.14159265359*I
sage: RDF(-1).log(2)
4.53236014183*I

TESTS:

Make sure that we can take the log of small numbers accurately and the fix doesn’t break preexisting values (trac ticket #12557):

sage: R = RealField(128)
sage: def check_error(x):
....:   x = RDF(x)
....:   log_RDF = x.log()
....:   log_RR = R(x).log()
....:   diff = R(log_RDF) - log_RR
....:   if abs(diff) < log_RDF.ulp():
....:       return True
....:   print "logarithm check failed for %s (diff = %s ulp)"%             ....:       (x, diff/log_RDF.ulp())
....:   return False
sage: all( check_error(2^x) for x in range(-100,100) )
True
sage: all( check_error(x) for x in sxrange(0.01, 2.00, 0.01) )
True
sage: all( check_error(x) for x in sxrange(0.99, 1.01, 0.001) )
True
sage: RDF(1.000000001).log()
1.00000008224e-09
sage: RDF(1e-17).log()
-39.1439465809
sage: RDF(1e-50).log()
-115.12925465
log10()

Return log to the base 10 of self.

EXAMPLES:

sage: r = RDF('16.0'); r.log10()
1.20411998266
sage: r.log() / RDF(log(10))
1.20411998266
sage: r = RDF('39.9'); r.log10()
1.60097289569
log2()

Return log to the base 2 of self.

EXAMPLES:

sage: r = RDF(16.0)
sage: r.log2()
4.0
sage: r = RDF(31.9); r.log2()
4.99548451888
logpi()

Return log to the base \(\pi\) of self.

EXAMPLES:

sage: r = RDF(16); r.logpi()
2.42204624559
sage: r.log() / RDF(log(pi))
2.42204624559
sage: r = RDF('39.9'); r.logpi()
3.22030233461
multiplicative_order()

Returns \(n\) such that self^n == 1.

Only \(\pm 1\) have finite multiplicative order.

EXAMPLES:

sage: RDF(1).multiplicative_order()
1
sage: RDF(-1).multiplicative_order()
2
sage: RDF(3).multiplicative_order()
+Infinity
nan()

Return Not-a-Number NaN.

EXAMPLES:

sage: RDF.NaN()
NaN
nth_root(n)

Return the \(n^{th}\) root of self.

INPUT:

  • n – an integer

OUTPUT:

The output is a complex double if self is negative and \(n\) is even, otherwise it is a real double.

EXAMPLES:

sage: r = RDF(-125.0); r.nth_root(3)
-5.0
sage: r.nth_root(5)
-2.6265278044
sage: RDF(-2).nth_root(5)^5
-2.0
sage: RDF(-1).nth_root(5)^5
-1.0
sage: RDF(3).nth_root(10)^10
3.0
sage: RDF(-1).nth_root(2)
6.12323399574e-17 + 1.0*I
sage: RDF(-1).nth_root(4)
0.707106781187 + 0.707106781187*I
parent()

Return the real double field, which is the parent of self.

EXAMPLES:

sage: a = RDF(2.3)
sage: a.parent()
Real Double Field
sage: parent(a)
Real Double Field
prec()

Return the precision of this number in bits.

Always returns 53.

EXAMPLES:

sage: RDF(0).prec()
53
real()

Return self - we are already real.

EXAMPLES:

sage: a = RDF(3)
sage: a.real()
3.0
restrict_angle()

Return a number congruent to self mod \(2\pi\) that lies in the interval \((-\pi, \pi]\).

Specifically, it is the unique \(x \in (-\pi, \pi]\) such that `self \(= x + 2\pi n\) for some \(n \in \ZZ\).

EXAMPLES:

sage: RDF(pi).restrict_angle()
3.14159265359
sage: RDF(pi + 1e-10).restrict_angle()
-3.14159265349
sage: RDF(1+10^10*pi).restrict_angle()
0.9999977606...
round()

Given real number \(x\), rounds up if fractional part is greater than \(0.5\), rounds down if fractional part is less than \(0.5\).

EXAMPLES:

sage: RDF(0.49).round()
0
sage: a=RDF(0.51).round(); a
1
sech()

Return the hyperbolic secant of self.

EXAMPLES:

sage: RDF(pi).sech()
0.0862667383341
sage: CDF(pi).sech()
0.0862667383341
sign()

Returns -1,0, or 1 if self is negative, zero, or positive; respectively.

EXAMPLES:

sage: RDF(-1.5).sign()
-1
sage: RDF(0).sign()
0
sage: RDF(2.5).sign()
1
sign_mantissa_exponent()

Return the sign, mantissa, and exponent of self.

In Sage (as in MPFR), floating-point numbers of precision \(p\) are of the form \(s m 2^{e-p}\), where \(s \in \{-1, 1\}\), \(2^{p-1} \leq m < 2^p\), and \(-2^{30} + 1 \leq e \leq 2^{30} - 1\); plus the special values +0, -0, +infinity, -infinity, and NaN (which stands for Not-a-Number).

This function returns \(s\), \(m\), and \(e-p\). For the special values:

  • +0 returns (1, 0, 0)
  • -0 returns (-1, 0, 0)
  • the return values for +infinity, -infinity, and NaN are not specified.

EXAMPLES:

sage: a = RDF(exp(1.0)); a
2.71828182846
sage: sign,mantissa,exponent = RDF(exp(1.0)).sign_mantissa_exponent()
sage: sign,mantissa,exponent
(1, 6121026514868073, -51)
sage: sign*mantissa*(2**exponent) == a
True

The mantissa is always a nonnegative number:

sage: RDF(-1).sign_mantissa_exponent()
(-1, 4503599627370496, -52)

TESTS:

sage: RDF('+0').sign_mantissa_exponent()
(1, 0, 0)
sage: RDF('-0').sign_mantissa_exponent()
(-1, 0, 0)
sin()

Return the sine of self.

EXAMPLES:

sage: RDF(2).sin()
0.909297426826
sincos()

Return a pair consisting of the sine and cosine of self.

EXAMPLES:

sage: t = RDF.pi()/6
sage: t.sincos()
(0.5, 0.866025403784)
sinh()

Return the hyperbolic sine of self.

EXAMPLES:

sage: q = RDF.pi()/12
sage: q.sinh()
0.264800227602
sqrt(extend=True, all=False)

The square root function.

INPUT:

  • extend – bool (default: True); if True, return a square root in a complex field if necessary if self is negative; otherwise raise a ValueError.
  • all – bool (default: False); if True, return a list of all square roots.

EXAMPLES:

sage: r = RDF(4.0)
sage: r.sqrt()
2.0
sage: r.sqrt()^2 == r
True
sage: r = RDF(4344)
sage: r.sqrt()
65.9090282131
sage: r.sqrt()^2 - r
0.0
sage: r = RDF(-2.0)
sage: r.sqrt()
1.41421356237*I
sage: RDF(2).sqrt(all=True)
[1.41421356237, -1.41421356237]
sage: RDF(0).sqrt(all=True)
[0.0]
sage: RDF(-2).sqrt(all=True)
[1.41421356237*I, -1.41421356237*I]
str()

Return string representation of self.

EXAMPLES:

sage: a = RDF('4.5'); a.str()
'4.5'
sage: a = RDF('49203480923840.2923904823048'); a.str()
'4.92034809238e+13'
sage: a = RDF(1)/RDF(0); a.str()
'+infinity'
sage: a = -RDF(1)/RDF(0); a.str()
'-infinity'
sage: a = RDF(0)/RDF(0); a.str()
'NaN'

We verify consistency with RR (mpfr reals):

sage: str(RR(RDF(1)/RDF(0))) == str(RDF(1)/RDF(0))
True
sage: str(RR(-RDF(1)/RDF(0))) == str(-RDF(1)/RDF(0))
True
sage: str(RR(RDF(0)/RDF(0))) == str(RDF(0)/RDF(0))
True
tan()

Return the tangent of self.

EXAMPLES:

sage: q = RDF.pi()/3
sage: q.tan()
1.73205080757
sage: q = RDF.pi()/6
sage: q.tan()
0.57735026919
tanh()

Return the hyperbolic tangent of self.

EXAMPLES:

sage: q = RDF.pi()/12
sage: q.tanh()
0.255977789246
trunc()

Truncates this number (returns integer part).

EXAMPLES:

sage: RDF(2.99).trunc()
2
sage: RDF(-2.00).trunc()
-2
sage: RDF(0.00).trunc()
0
ulp()

Returns the unit of least precision of self, which is the weight of the least significant bit of self. This is always a strictly positive number. It is also the gap between this number and the closest number with larger absolute value that can be represented.

EXAMPLES:

sage: a = RDF(pi)
sage: a.ulp()
4.4408920985e-16
sage: b = a + a.ulp()

Adding or subtracting an ulp always gives a different number:

sage: a + a.ulp() == a
False
sage: a - a.ulp() == a
False
sage: b + b.ulp() == b
False
sage: b - b.ulp() == b
False

Since the default rounding mode is round-to-nearest, adding or subtracting something less than half an ulp always gives the same number, unless the result has a smaller ulp. The latter can only happen if the input number is (up to sign) exactly a power of 2:

sage: a - a.ulp()/3 == a
True
sage: a + a.ulp()/3 == a
True
sage: b - b.ulp()/3 == b
True
sage: b + b.ulp()/3 == b
True
sage: c = RDF(1)
sage: c - c.ulp()/3 == c
False
sage: c.ulp()
2.22044604925e-16
sage: (c - c.ulp()).ulp()
1.11022302463e-16

The ulp is always positive:

sage: RDF(-1).ulp()
2.22044604925e-16

The ulp of zero is the smallest positive number in RDF:

sage: RDF(0).ulp()
4.94065645841e-324
sage: RDF(0).ulp()/2
0.0

Some special values:

sage: a = RDF(1)/RDF(0); a
+infinity
sage: a.ulp()
+infinity
sage: (-a).ulp()
+infinity
sage: a = RDF('nan')
sage: a.ulp() is a
True

The ulp method works correctly with small numbers:

sage: u = RDF(0).ulp()
sage: u.ulp() == u
True
sage: x = u * (2^52-1)  # largest denormal number
sage: x.ulp() == u
True
sage: x = u * 2^52  # smallest normal number
sage: x.ulp() == u
True
zeta()

Return the Riemann zeta function evaluated at this real number.

Note

PARI is vastly more efficient at computing the Riemann zeta function. See the example below for how to use it.

EXAMPLES:

sage: RDF(2).zeta()
1.64493406685
sage: RDF.pi()^2/6
1.64493406685
sage: RDF(-2).zeta()       # slightly random-ish arch dependent output
-2.37378795339e-18
sage: RDF(1).zeta()
+infinity
sage.rings.real_double.RealDoubleField()

Return the unique instance of the real double field.

EXAMPLES:

sage: RealDoubleField() is RealDoubleField()
True
class sage.rings.real_double.RealDoubleField_class

Bases: sage.rings.ring.Field

An approximation to the field of real numbers using double precision floating point numbers. Answers derived from calculations in this approximation may differ from what they would be if those calculations were performed in the true field of real numbers. This is due to the rounding errors inherent to finite precision calculations.

EXAMPLES:

sage: RR == RDF
False
sage: RDF == RealDoubleField()    # RDF is the shorthand
True
sage: RDF(1)
1.0
sage: RDF(2/3)
0.666666666667

A TypeError is raised if the coercion doesn’t make sense:

sage: RDF(QQ['x'].0)
Traceback (most recent call last):
...
TypeError: cannot coerce nonconstant polynomial to float
sage: RDF(QQ['x'](3))
3.0

One can convert back and forth between double precision real numbers and higher-precision ones, though of course there may be loss of precision:

sage: a = RealField(200)(2).sqrt(); a
1.4142135623730950488016887242096980785696718753769480731767
sage: b = RDF(a); b
1.41421356237
sage: a.parent()(b)
1.4142135623730951454746218587388284504413604736328125000000
sage: a.parent()(b) == b
True
sage: b == RR(a)
True
NaN()

Return Not-a-Number NaN.

EXAMPLES:

sage: RDF.NaN()
NaN
algebraic_closure()

Return the algebraic closure of self, i.e., the complex double field.

EXAMPLES:

sage: RDF.algebraic_closure()
Complex Double Field
characteristic()

Returns 0, since the field of real numbers has characteristic 0.

EXAMPLES:

sage: RDF.characteristic()
0
complex_field()

Return the complex field with the same precision as self, i.e., the complex double field.

EXAMPLES:

sage: RDF.complex_field()
Complex Double Field
construction()

Returns the functorial construction of self, namely, completion of the rational numbers with respect to the prime at \(\infty\).

Also preserves other information that makes this field unique (i.e. the Real Double Field).

EXAMPLES:

sage: c, S = RDF.construction(); S
Rational Field
sage: RDF == c(S)
True
euler_constant()

Return Euler’s gamma constant to double precision.

EXAMPLES:

sage: RDF.euler_constant()
0.577215664902
factorial(n)

Return the factorial of the integer \(n\) as a real number.

EXAMPLES:

sage: RDF.factorial(100)
9.33262154439e+157
gen(n=0)

Return the generator of the real double field.

EXAMPLES:

sage: RDF.0
1.0
sage: RDF.gens()
(1.0,)
is_exact()

Returns False, because doubles are not exact.

EXAMPLE:

sage: RDF.is_exact()
False
is_finite()

Return False, since the field of real numbers is not finite.

Technical note: There exists an upper bound on the double representation.

EXAMPLES:

sage: RDF.is_finite()
False
log2()

Return \(\log(2)\) to the precision of this field.

EXAMPLES:

sage: RDF.log2()
0.69314718056
sage: RDF(2).log()
0.69314718056
name()

The name of self.

EXAMPLES:

sage: RDF.name()
'RealDoubleField'
nan()

Return Not-a-Number NaN.

EXAMPLES:

sage: RDF.NaN()
NaN
ngens()

Return the number of generators which is always 1.

EXAMPLES:

sage: RDF.ngens()
1
pi()

Returns \(\pi\) to double-precision.

EXAMPLES:

sage: RDF.pi()
3.14159265359
sage: RDF.pi().sqrt()/2
0.886226925453
prec()

Return the precision of this real double field in bits.

Always returns 53.

EXAMPLES:

sage: RDF.precision()
53
precision()

Return the precision of this real double field in bits.

Always returns 53.

EXAMPLES:

sage: RDF.precision()
53
random_element(min=-1, max=1)

Return a random element of this real double field in the interval [min, max].

EXAMPLES:

sage: RDF.random_element()
0.736945423566
sage: RDF.random_element(min=100, max=110)
102.815947352
to_prec(prec)

Return the real field to the specified precision. As doubles have fixed precision, this will only return a real double field if prec is exactly 53.

EXAMPLES:

sage: RDF.to_prec(52)
Real Field with 52 bits of precision
sage: RDF.to_prec(53)
Real Double Field
zeta(n=2)

Return an \(n\)-th root of unity in the real field, if one exists, or raise a ValueError otherwise.

EXAMPLES:

sage: RDF.zeta()
-1.0
sage: RDF.zeta(1)
1.0
sage: RDF.zeta(5)
Traceback (most recent call last):
...
ValueError: No 5th root of unity in self
class sage.rings.real_double.ToRDF

Bases: sage.categories.morphism.Morphism

Fast morphism from anything with a __float__ method to an RDF element.

EXAMPLES:

sage: f = RDF.coerce_map_from(ZZ); f
Native morphism:
  From: Integer Ring
  To:   Real Double Field
sage: f(4)
4.0
sage: f = RDF.coerce_map_from(QQ); f
Native morphism:
  From: Rational Field
  To:   Real Double Field
sage: f(1/2)
0.5
sage: f = RDF.coerce_map_from(int); f
Native morphism:
  From: Set of Python objects of type 'int'
  To:   Real Double Field
sage: f(3r)
3.0
sage: f = RDF.coerce_map_from(float); f
Native morphism:
  From: Set of Python objects of type 'float'
  To:   Real Double Field
sage: f(3.5)
3.5
sage.rings.real_double.is_RealDoubleElement(x)

Check if x is an element of the real double field.

EXAMPLE:

sage: from sage.rings.real_double import is_RealDoubleElement
sage: is_RealDoubleElement(RDF(3))
True
sage: is_RealDoubleElement(RIF(3))
False
sage.rings.real_double.is_RealDoubleField(x)

Returns True if x is the field of real double precision numbers.

EXAMPLES:

sage: from sage.rings.real_double import is_RealDoubleField
sage: is_RealDoubleField(RDF)
True
sage: is_RealDoubleField(RealField(53))
False
sage.rings.real_double.pool_stats()

Statistics for the real double pool.

EXAMPLES:

We first pull all elements from the pool (making sure it is empty to illustrate how the pool works):

sage: from sage.rings.real_double import time_alloc_list, pool_stats
sage: L = time_alloc_list(50)
sage: pool_stats()
Used pool 0 / 0 times
Pool contains 0 / 50 items

During the operation (in this example, addition), we end up with two temporary elements. After completion of the operation, they are added to the pool:

sage: RDF(2.1) + RDF(2.2)
4.3
sage: pool_stats()
Used pool 0 / 0 times
Pool contains 2 / 50 items

Next when we call time_alloc_list(), the “created” elements are actually pulled from the pool:

sage: time_alloc_list(3)
[2.2, 2.1, 0.0]

Note that the number of objects left in the pool depends on the garbage collector:

sage: pool_stats()
Used pool 0 / 0 times
Pool contains 1 / 50 items
sage.rings.real_double.time_alloc(n)

Allocate n RealDoubleElement instances.

EXAMPLES:

Since this does not store anything in a python object, the created elements will not be sent to the garbage collector. Therefore they remain in the pool:

sage: from sage.rings.real_double import time_alloc, pool_stats
sage: pool_stats()
Used pool 0 / 0 times
Pool contains 7 / 50 items
sage: time_alloc(25)
sage: pool_stats()
Used pool 0 / 0 times
Pool contains 7 / 50 items
sage.rings.real_double.time_alloc_list(n)

Allocate a list of length n of RealDoubleElement instances.

EXAMPLES:

During the operation (in this example, addition), we end up with two temporary elements. After completion of the operation, they are added to the pool:

sage: from sage.rings.real_double import time_alloc_list
sage: RDF(2.1) + RDF(2.2)
4.3

Next when we call time_alloc_list(), the “created” elements are actually pulled from the pool:

sage: time_alloc_list(2)
[2.2, 2.1]

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