Subject: [Boost-commit] svn:boost r82120 - sandbox/e_float/libs/e_float/src/functions/constants
From: e_float_at_[hidden]
Date: 2012-12-20 12:32:11
Author: christopher_kormanyos
Date: 2012-12-20 12:32:10 EST (Thu, 20 Dec 2012)
New Revision: 82120
URL: http://svn.boost.org/trac/boost/changeset/82120
Log:
The value of pi is now computed with an AGM.
Text files modified:
sandbox/e_float/libs/e_float/src/functions/constants/constants.cpp | 57 +++++++++++++++++++++++++++++++++++++++
1 files changed, 56 insertions(+), 1 deletions(-)
Modified: sandbox/e_float/libs/e_float/src/functions/constants/constants.cpp
==============================================================================
--- sandbox/e_float/libs/e_float/src/functions/constants/constants.cpp (original)
+++ sandbox/e_float/libs/e_float/src/functions/constants/constants.cpp 2012-12-20 12:32:10 EST (Thu, 20 Dec 2012)
@@ -113,6 +113,7 @@
const e_float& ef::pi(void)
{
+/*
// 1100 digits of pi
static const std::string str =
std::string("3.")
@@ -128,9 +129,63 @@
+ std::string("5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989")
+ std::string("3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913152")
;
-
+
static const e_float val(str.c_str());
return val;
+*/
+
+ static bool is_initialized = false;
+ static e_float val_pi;
+
+ if(!is_initialized)
+ {
+ is_initialized = true;
+
+ e_float a(1U);
+ e_float bB(ef::half());
+ e_float s (ef::half());
+ e_float t ("0.375");
+
+ // This loop is designed for a maximum of several million
+ // decimal digits of pi. The index k should reach no higher
+ // than about 25. The decimal precision after 18 iterations
+ // is more than one million digits.
+
+ for(INT32 k = static_cast<INT32>(1); k < static_cast<INT32>(64); k++)
+ {
+ bB = ef::sqrt(bB);
+ a += bB;
+ a /= static_cast<INT32>(2);
+ val_pi = a;
+ val_pi *= a;
+ bB = val_pi;
+ bB -= t;
+ bB *= static_cast<INT32>(2);
+
+ e_float iterate_term(bB);
+ iterate_term -= val_pi;
+ iterate_term *= static_cast<INT32>(1UL << k);
+ s += iterate_term;
+
+ // Test the significant digits of the current iteration change.
+ // If the amount of the iteration is within the desired precision,
+ // then the calculation is finished.
+ if(ef::fabs(iterate_term) < std::numeric_limits<e_float>::epsilon())
+ {
+ break;
+ }
+
+ t = val_pi;
+ t += bB;
+ t /= static_cast<INT32>(4);
+ }
+
+ val_pi += bB;
+ val_pi *= s.calculate_inv();
+ }
+
+ static const e_float val(val_pi);
+ return val;
}
const e_float& ef::pi_half (void) { static const e_float val = ef::pi() / static_cast<INT32>(2); return val; }