JP4915454B2 - 演算回路及び方法 - Google Patents
演算回路及び方法 Download PDFInfo
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- JP4915454B2 JP4915454B2 JP2010038703A JP2010038703A JP4915454B2 JP 4915454 B2 JP4915454 B2 JP 4915454B2 JP 2010038703 A JP2010038703 A JP 2010038703A JP 2010038703 A JP2010038703 A JP 2010038703A JP 4915454 B2 JP4915454 B2 JP 4915454B2
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y=ROUNDUP[ROUNDUP(x×5/54,0)×62/5,0] (数式1)
ここで、ROUNDUP(A,K)は数値Aを指定した桁数Kで切り上げる演算関数である。
q=INT[(x×75245+2304)÷216] (数式2)
ここで、qは正整数を表す。INT(B)は数値Bを超えない最大の整数であり、小数点以下を切り捨てるINT演算を行う演算関数である。
r=MOD[INT[(x×9709+2560)÷212],27] (数式3)
ここで、rは正整数を表す。MOD(C,D)は数値Cを数値Dで割った場合の余りを求める演算関数である。即ち、rは、所定のxの関数[INT[(x×9709+2560)÷212]を所定値27で除算した余りである。2のn乗(この場合n=12)の除算で近似しており、nが大きい値ほど近似精度がよくなる。この除算は除数が2のn乗であるためビットシフトで実現することができる。
INT(r×54/27+1/2) (数式4)
f(r)=INT{INT[INT(r×54/27+1/2)×5/54+63/64]×62/5+7/8}−INT[INT(r×54/27+1/2)×62/54] (数式5)
ここで、f(r)は正整数となる。
y=q+f(r) (数式6)
ここで、0≦x≦(216−1)であれば誤差は生じない。
11,13 INT回路
14 MOD回路
15 テーブル
16 加算回路
Claims (2)
- 切り上げ演算を含むxの関数である数式の近似計算を行う演算回路であって、
所定のxの関数を所定値で除算した余りをrとし、前記数式のxをrの関数で置き換えかつ前記切り上げ演算の代わりに1に近い1未満の値を加算してから小数点以下を切り捨てる演算を行う第1の式から、前記数式のxを前記rの関数で置き換えかつ前記切り上げ演算を行わない第2の式を引いた関数をf(r)とし、rに対するf(r)の計算結果を予めまとめたテーブルと、
与えられたxの値に対して前記切り上げ演算を行わないで前記数式を計算して近似値qを計算する回路と、
与えられたxの値に対してrを計算する回路と、
計算したrの値に対するf(r)の値を前記テーブルから取り出し、このf(r)の値と前記近似値qを足し合わせる回路とを備えることを特徴とする演算回路。 - 所定のxの関数を所定値で除算した余りをrとし、前記数式のxをrの関数で置き換えかつ前記切り上げ演算の代わりに1に近い1未満の値を加算してから小数点以下を切り捨てる演算を行う第1の式から、前記数式のxを前記rの関数で置き換えかつ前記切り上げ演算を行わない第2の式を引いた関数をf(r)とし、rに対するf(r)の計算結果を予めまとめたテーブルを用いて、切り上げ演算を含むxの関数である数式の近似計算を行う演算方法であって、
第1の計算回路が、与えられたxの値に対して前記切り上げ演算を行わないで前記数式を計算して近似値qを計算する工程と、
第2の計算回路が、与えられたxの値に対してrを計算する工程と、
加算回路が、計算したrの値に対するf(r)の値を前記テーブルから取り出し、このf(r)の値と前記近似値qを足し合わせる工程とを備えることを特徴とする演算方法。
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JP4915454B2 true JP4915454B2 (ja) | 2012-04-11 |
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US5212661A (en) * | 1989-10-16 | 1993-05-18 | Matsushita Electric Industrial Co., Ltd. | Apparatus for performing floating point arithmetic operation and rounding the result thereof |
JP2000081968A (ja) * | 1998-09-04 | 2000-03-21 | Sharp Corp | 逆数演算装置 |
JP3845636B2 (ja) * | 2004-01-21 | 2006-11-15 | 株式会社東芝 | 関数近似値の演算器 |
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