Fixed and Arbitrary Precision Numerical Fields - Sage

Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.21sage: RR(-infinity).fp_rank()-9671406552413433770278913 # 32-bit-41538374868278621023740371006390273 # 64-bitsage: RR(-infinity).fp_rank() - RR(-infinity).nextabove().fp_rank()-1fp_rank_delta(other)Return the floating-point rank delta between self and other. That is, if the return value is positive, thisis the number of times you have to call .nextabove() to get from self to other.EXAMPLES:sage: [x.fp_rank_delta(x.nextabove()) for x in... (RR(-infinity), -1.0, 0.0, 1.0, RR(pi), RR(infinity))][1, 1, 1, 1, 1, 0]In the 2-bit floating-point field, one subsegment of the floating-point numbers is: 1, 1.5, 2, 3, 4, 6, 8, 12,16, 24, 32sage: R2 = RealField(2)sage: R2(1).fp_rank_delta(R2(2))2sage: R2(2).fp_rank_delta(R2(1))-2sage: R2(1).fp_rank_delta(R2(1048576))40sage: R2(24).fp_rank_delta(R2(4))-5sage: R2(-4).fp_rank_delta(R2(-24))-5There are lots of floating-point numbers around 0:sage: R2(-1).fp_rank_delta(R2(1))4294967298 # 32-bit18446744073709551618 # 64-bitfrac()Return a real number such that self = self.trunc() + self.frac(). The return value willalso satisfy -1 < self.frac() < 1.EXAMPLES:sage: (2.99).frac()0.990000000000000sage: (2.50).frac()0.500000000000000sage: (-2.79).frac()-0.790000000000000sage: (-2.79).trunc() + (-2.79).frac()-2.79000000000000gamma()Return the value of the Euler gamma function on self.EXAMPLES:sage: R = RealField()sage: R(6).gamma()120.00000000000042 Chapter 2. Arbitrary Precision Real Numbers