From 39db6fc4693a8c157d14037528e61361fcccf220 Mon Sep 17 00:00:00 2001 From: Tomasz Sowa Date: Mon, 28 Dec 2009 15:41:28 +0000 Subject: [PATCH] fixed: in Big::ToString_CreateNewMantissaAndExponent() changed the formula: new_exp_ = [log base (2^exponent)] + 1 now the part '+ 1' is only made when the logarithm is positive and with fraction if the value is negative we can only skip the fraction, previously we lost some last digits from the new mantissa Consider this binary value (32 bit mantissa): (bin)1.0000000000000000000000000000011 previously ToString() gave 1, now we have: 1.000000001 git-svn-id: svn://ttmath.org/publicrep/ttmath/trunk@274 e52654a7-88a9-db11-a3e9-0013d4bc506e --- CHANGELOG | 10 +++++++++- ttmath/ttmathbig.h | 22 +++++++++++++++++----- 2 files changed, 26 insertions(+), 6 deletions(-) diff --git a/CHANGELOG b/CHANGELOG index a689369..1f90bbb 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -1,4 +1,4 @@ -Version 0.9.1 prerelease (2009.12.25): +Version 0.9.1 prerelease (2009.12.28): * fixed: the parser didn't use characters for changing the base (# and &) those characters were skipped (this bug was introduced in 0.9.0) @@ -6,6 +6,14 @@ Version 0.9.1 prerelease (2009.12.25): operator ^ (powering) is right-associative: sample: 2^3^4 is equal 2^(3^4) and it is: 2.41e+24 previously was: 2^3^4 = (2^3)^4 = 4096 + * fixed: in Big::ToString_CreateNewMantissaAndExponent() changed the formula: + new_exp_ = [log base (2^exponent)] + 1 + now the part '+ 1' is only made when the logarithm is positive and with fraction + if the value is negative we can only skip the fraction, previously + we lost some last digits from the new mantissa + Consider this binary value (32 bit mantissa): + (bin)1.0000000000000000000000000000011 + previously ToString() gave 1, now we have: 1.000000001 * added: IEEE 754 half-to-even rounding (bankers' rounding) to the following floating point algorithms: Big::Add, Big::Sub, Big::Mul, Big::Div * added: to Big::ToString() - additional rounding when conv.base_round is used diff --git a/ttmath/ttmathbig.h b/ttmath/ttmathbig.h index 6d46ddd..0159503 100644 --- a/ttmath/ttmathbig.h +++ b/ttmath/ttmathbig.h @@ -3312,8 +3312,11 @@ private: 2^exponent <= base^new_exp new_exp >= log base (2^exponent) <- logarithm with the base 'base' from (2^exponent) - but we need 'new'exp' as integer then we take: - new_exp = [log base (2^exponent)] + 1 <- where [x] means integer value from x + but we need new_exp as integer then we test: + if new_exp is greater than zero and with fraction we add one to new_exp + new_exp = new_exp + 1 (if new_exp>0 and with fraction) + and at the end we take the integer part: + new_exp = int(new_exp) */ template uint ToString_CreateNewMantissaAndExponent( string_type & new_man, const Conv & conv, @@ -3351,12 +3354,21 @@ private: temp.mantissa.SetOne(); c += temp.Standardizing(); - // new_exp_ = [log base (2^exponent)] + 1 + // new_exp_ = log base (2^exponent) + // if new_exp_ is positive and with fraction then we add one Big new_exp_; c += new_exp_.ToString_Log(temp, conv.base); // this logarithm isn't very complicated + + if( !new_exp_.IsSign() && !new_exp_.IsInteger() ) + { + // new_exp_ > 0 and with fraction + temp.SetOne(); + c += new_exp_.Add( temp ); + } + + // new_exp_ = int(new_exp_) new_exp_.SkipFraction(); - temp.SetOne(); - c += new_exp_.Add( temp ); + // because 'base^new_exp' is >= '2^exponent' then // because base is >= 2 then we've got: