to answer the original question, here is how we can decompose in Sage a 35-digit constant into three 53-bit floating-point values:
sage: R120 = RealField(120) sage: R53 = RealField(53) sage: x = R120(pi) sage: x 3.1415926535897932384626433832795029 sage: a = R53(x) # extracts the 53 most significant bits of x sage: a.exact_rational() 884279719003555/281474976710656 sage: r = x - R120(a) sage: r 1.2246467991473531772315719253130892e-16 sage: b = R53(r) sage: b.exact_rational() 4967757600021511/40564819207303340847894502572032 sage: r = r - R120(b) sage: r -2.9942192104145307402979657076125042e-33 sage: c = R53(r) sage: c.exact_rational() -995/332306998946228968225951765070086144 thus we have decomposed x into a + b + c. We can check it is correct: sage: x.exact_rational() == a.exact_rational() + b.exact_rational() + c.exact_rational() True Paul Zimmermann -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
