=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/fft/dft.c,v retrieving revision 1.4 retrieving revision 1.5 diff -u -p -r1.4 -r1.5 --- OpenXM_contrib2/asir2000/fft/dft.c 2003/02/14 22:29:10 1.4 +++ OpenXM_contrib2/asir2000/fft/dft.c 2018/03/29 01:32:53 1.5 @@ -45,15 +45,15 @@ * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. * - * $OpenXM: OpenXM_contrib2/asir2000/fft/dft.c,v 1.3 2000/08/22 05:04:12 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/fft/dft.c,v 1.4 2003/02/14 22:29:10 ohara Exp $ */ /* - * store arith modulus - * ------------------------------------------------------- - * IEEE: float (23+1) <-> double (52+1) 24 bits - * int (32) <-> double (52+1) 26 bits - * 370: float (24) <-> double (56) 24/25 bits - * int (32) <-> double (56) 28 bits + * store arith modulus + * ------------------------------------------------------- + * IEEE: float (23+1) <-> double (52+1) 24 bits + * int (32) <-> double (52+1) 26 bits + * 370: float (24) <-> double (56) 24/25 bits + * int (32) <-> double (56) 28 bits */ @@ -71,9 +71,9 @@ void C_DFT_FORE( in, nin, i1, K, powa, #ifdef POWA_STRIDE - a1, + a1, #endif - out, o1, P, Pinv, wk ) + out, o1, P, Pinv, wk ) ModNum in[], powa[], out[], wk[]; ModNum P; int nin, i1, K, o1; @@ -102,13 +102,13 @@ double Pinv; ModNum *qi, *qo, *qis, *qos, a, t0, tn; /* - * for k = K-1, ..., 0 do the following: + * for k = K-1, ..., 0 do the following: * - * Out[2^{K-k}*i + j] <= t0 + \alpha^{2^k * j} * tn; - * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{2^k * j} * tn; + * Out[2^{K-k}*i + j] <= t0 + \alpha^{2^k * j} * tn; + * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{2^k * j} * tn; * * where t0 = In[2^{K-k-1}*i + j] and - * tn = In[2^{K-k-1}*i + j + 2^{K-1}], + * tn = In[2^{K-k-1}*i + j + 2^{K-1}], * for 0 <= i < 2^k and 0 <= j < 2^{K-k-1}. * */ @@ -127,13 +127,13 @@ double Pinv; for ( i = nin; i > 0; i--, qi += i1, qo += ostep ) qo[0] = qo[odist] = qi[0]; for ( i = n - nin; i > 0; i--, qo += ostep ) qo[0] = qo[odist] = 0; } else { - idist = i1 << k; /* distance = 2^{K-1} */ + idist = i1 << k; /* distance = 2^{K-1} */ for ( j = i = nin - n; i > 0; i--, qi += i1, qo += ostep ) { t0 = qi[0], tn = qi[idist]; if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; else { - qo[0] = AplusBmodP( t0, tn, P ); - qo[odist] = A_BmodP( t0, tn, P ); + qo[0] = AplusBmodP( t0, tn, P ); + qo[odist] = A_BmodP( t0, tn, P ); } } for ( i = n - j; i > 0; i--, qi += i1, qo += ostep ) @@ -145,15 +145,15 @@ double Pinv; #ifndef OPT K_k = (K_k_1 = K_k) + 1; #endif - n >>= 1; /* == 2^k */ - Ndiv2n <<= 1; /* == 2^{K-k-1} */ + n >>= 1; /* == 2^k */ + Ndiv2n <<= 1; /* == 2^{K-k-1} */ if ( inwk ) qi = wk, qo = out, iostep = 1, oostep = o1, idist = idistwk; else qi = out, qo = wk, iostep = o1, oostep = 1, idist = idistout; qis = qi, qos = qo; /**/ - istep = ostep; /* = iostep << K_k_1; */ + istep = ostep; /* = iostep << K_k_1; */ #ifndef OPT ostep = oostep << K_k; odist = oostep << K_k_1; @@ -167,8 +167,8 @@ double Pinv; t0 = qi[0], tn = qi[idist]; if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; else { - qo[0] = AplusBmodP( t0, tn, P ); - qo[odist] = A_BmodP( t0, tn, P ); + qo[0] = AplusBmodP( t0, tn, P ); + qo[odist] = A_BmodP( t0, tn, P ); } } /**/ @@ -181,19 +181,19 @@ double Pinv; #endif qi = (qis += iostep), qo = (qos += oostep); for ( i = 0; i < n; i++, qi += istep, qo += ostep ) { - t0 = qi[0], tn = qi[idist]; - if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; - else { - AxBmodP( tn, ModNum, tn, a, P, Pinv ); - qo[0] = AplusBmodP( t0, tn, P ); - qo[odist] = A_BmodP( t0, tn, P ); - } + t0 = qi[0], tn = qi[idist]; + if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; + else { + AxBmodP( tn, ModNum, tn, a, P, Pinv ); + qo[0] = AplusBmodP( t0, tn, P ); + qo[odist] = A_BmodP( t0, tn, P ); + } } } } /* * When k = 0, for i = 0 (0 <= i < 2^0=1) and 0 <= j < 2^{K-1}, - * Out[j] <= t0 + \alpha^{j}*tn and Out[j+2^{K-1}] <= t0 - \alpha^{j}*tn, + * Out[j] <= t0 + \alpha^{j}*tn and Out[j+2^{K-1}] <= t0 - \alpha^{j}*tn, * where t0 = In[j] and tn = In[j + 2^{K-1}]. */ qi = wk, qo = out, idist = idistwk, odist = idistout; @@ -228,13 +228,13 @@ double Pinv; #ifndef OPT K_k = (K_k_1 = K_k) + 1; #endif - n >>= 1; /* == 2^k */ - Ndiv2n <<= 1; /* == 2^{K-k-1} */ + n >>= 1; /* == 2^k */ + Ndiv2n <<= 1; /* == 2^{K-k-1} */ if ( inwk ) qi = wk, qo = out, istep = 1, ostep = o1, idist = idistwk; else qi = out, qo = wk, istep = o1, ostep = 1, idist = idistout; qis = qi, qos = qo; /**/ - iostep = oostep; /* = istep << K_k_1; */ + iostep = oostep; /* = istep << K_k_1; */ #ifndef OPT oostep = ostep << K_k; odist = ostep << K_k_1; @@ -248,27 +248,27 @@ double Pinv; t0 = qis[0], tn = qis[idist]; if ( tn == (ModNum)0 ) qos[0] = qos[odist] = t0; else { - qos[0] = AplusBmodP( t0, tn, P ); - qos[odist] = A_BmodP( t0, tn, P ); + qos[0] = AplusBmodP( t0, tn, P ); + qos[odist] = A_BmodP( t0, tn, P ); } #ifdef POWA_STRIDE for ( aj = a1, j = 1, qi = qis, qo = qos; j < Ndiv2n; aj += a1, j++ ) { #else for ( j = 1, qi = qis, qo = qos; j < Ndiv2n; j++ ) { #endif - qi += istep, qo += ostep; - t0 = qi[0], tn = qi[idist]; - if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; - else { + qi += istep, qo += ostep; + t0 = qi[0], tn = qi[idist]; + if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0; + else { #ifdef POWA_STRIDE - a = powa[aj << k]; + a = powa[aj << k]; #else - a = powa[j << k]; + a = powa[j << k]; #endif - AxBmodP( tn, ModNum, tn, a, P, Pinv ); - qo[0] = AplusBmodP( t0, tn, P ); - qo[odist] = A_BmodP( t0, tn, P ); - } + AxBmodP( tn, ModNum, tn, a, P, Pinv ); + qo[0] = AplusBmodP( t0, tn, P ); + qo[odist] = A_BmodP( t0, tn, P ); + } } } } @@ -280,20 +280,20 @@ double Pinv; * NOTE: * (1) Let \alpha be a primitive N-th root of unity modulo P, * where N is even, - * and t be an integer s.t. 0 <= t < N/2. - * Then, 1/\alpha^t is given by (- \alpha^s) with s = N/2 - t. + * and t be an integer s.t. 0 <= t < N/2. + * Then, 1/\alpha^t is given by (- \alpha^s) with s = N/2 - t. * * (2) Let P be a prime s.t. P = 2^n*Q + 1, where Q is an odd integer. - * Then, for 0 < s <= n, 2^{-s} \equiv - 2^{n-s}*Q \bmod P, - * because 1 \equiv - 2^n*Q \bmod P. + * Then, for 0 < s <= n, 2^{-s} \equiv - 2^{n-s}*Q \bmod P, + * because 1 \equiv - 2^n*Q \bmod P. * **********************************************************************/ void C_DFT_BACK( in, N, i1, log2N, powa, #ifdef POWA_STRIDE - a1, + a1, #endif - out, o1, osi, nout, Ninv, P, Pinv, wk ) + out, o1, osi, nout, Ninv, P, Pinv, wk ) ModNum in[], powa[], out[], wk[]; int N, log2N, osi, nout, i1, o1; #ifdef POWA_STRIDE @@ -319,21 +319,21 @@ double Pinv; ModNum *qi, *qo, *qis, *qos, a, t0, tn, tt; /* - * for k = K-1, ..., 0 do the following: + * for k = K-1, ..., 0 do the following: * - * Out[2^{K-k}*i + j] <= t0 + \alpha^{- 2^k * j} * tn; - * = t0 - \alpha^{N/2 - 2^k * j}*tn; - * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{- 2^k * j} * tn; - * = t0 + \alpha^{N/2 - 2^k * j}*tn; + * Out[2^{K-k}*i + j] <= t0 + \alpha^{- 2^k * j} * tn; + * = t0 - \alpha^{N/2 - 2^k * j}*tn; + * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{- 2^k * j} * tn; + * = t0 + \alpha^{N/2 - 2^k * j}*tn; * * where t0 = In[2^{K-k-1}*i + j] and - * tn = In[2^{K-k-1}*i + j + 2^{K-1}], + * tn = In[2^{K-k-1}*i + j + 2^{K-1}], * for 0 <= i < 2^k and 0 <= j < 2^{K-k-1}. * */ if ( log2N == 1 ) { /* K = 1, k = 0, 0 <= i < 1, 0 <= j < 1. - * Out[0] <= t0 + tn, Out[1] <= t0 - tn, + * Out[0] <= t0 + tn, Out[1] <= t0 - tn, * where t0 = In[0] and Tn = In[1]. */ t0 = in[0], tn = in[i1]; @@ -341,7 +341,7 @@ double Pinv; /* out[0] = (t0 + tn)*Ninv; */ tt = tn == (ModNum)0 ? t0 : AplusBmodP( t0, tn, P ); if ( tt != (ModNum)0 ) { - AxBmodP( tt, ModNum, tt, Ninv, P, Pinv ); + AxBmodP( tt, ModNum, tt, Ninv, P, Pinv ); } out[0] = tt; i = 1; @@ -351,20 +351,20 @@ double Pinv; /* out[osi == 0 ? 1 : 0] = (t0 - tn)*Ninv; */ tt = tn == (ModNum)0 ? t0 : A_BmodP( t0, tn, P ); if ( tt != (ModNum)0 ) { - AxBmodP( tt, ModNum, tt, Ninv, P, Pinv ); + AxBmodP( tt, ModNum, tt, Ninv, P, Pinv ); } out[i] = tt; } return; } /****/ - halfN = n = 1 << (k = log2N - 1); /* == 2^{K-1} */ + halfN = n = 1 << (k = log2N - 1); /* == 2^{K-1} */ #ifdef POWA_STRIDE halfNa = a1 << k; #endif /* * when k = K-1, - * Out[2*i] <= t0 + tn, and Out[2*i+1] <= t0 - tn, + * Out[2*i] <= t0 + tn, and Out[2*i+1] <= t0 - tn, * where t0 = In[i] and tn = In[i+2^{K-1}], * for 0 <= i < 2^{K-1}. */ @@ -390,22 +390,22 @@ double Pinv; idist = halfN; for ( ostep = 2; --k > 0; inwk = 1 - inwk ) { n >>= 1; - istep = ostep; /* == 2^{K-k-1} */ - ostep <<= 1; /* == 2^{K-k} */ + istep = ostep; /* == 2^{K-k-1} */ + ostep <<= 1; /* == 2^{K-k} */ if ( inwk ) qi = &wk[N], qo = wk; else qi = wk, qo = &wk[N]; qis = qi, qos = qo; /* * for j = 0, - * Out[2^{K-k}*i] <= t0 + tn, and Out[2^{K-k}*i + 2^{K-k-1}] <= t0 - tn, - * where t0 = In[2^{K-k-1}*i] and tn = In[2^{K-k-1}*i + 2^{K-1}]. + * Out[2^{K-k}*i] <= t0 + tn, and Out[2^{K-k}*i + 2^{K-k-1}] <= t0 - tn, + * where t0 = In[2^{K-k-1}*i] and tn = In[2^{K-k-1}*i + 2^{K-1}]. */ for ( i = n, is = os = 0; i-- > 0; qi += istep, qo += ostep ) { t0 = qi[0], tn = qi[idist]; if ( tn == (ModNum)0 ) qo[0] = qo[istep] = t0; else { - qo[0] = AplusBmodP( t0, tn, P ); - qo[istep] = A_BmodP( t0, tn, P ); + qo[0] = AplusBmodP( t0, tn, P ); + qo[istep] = A_BmodP( t0, tn, P ); } } #ifdef POWA_STRIDE @@ -419,15 +419,15 @@ double Pinv; #endif qi = ++qis, qo = ++qos; for ( i = n; i-- > 0; qi += istep, qo += ostep ) { - t0 = qi[0], tn = qi[idist]; - if ( tn == (ModNum)0 ) qo[0] = qo[istep] = t0; - else { - AxBmodP( tn, ModNum, tn, a, P, Pinv ); -/*** qo[0] = AplusBmodP( t0, tn, P ); ***/ -/*** qo[istep] = A_BmodP( t0, tn, P ); ***/ - qo[0] = A_BmodP( t0, tn, P ); - qo[istep] = AplusBmodP( t0, tn, P ); - } + t0 = qi[0], tn = qi[idist]; + if ( tn == (ModNum)0 ) qo[0] = qo[istep] = t0; + else { + AxBmodP( tn, ModNum, tn, a, P, Pinv ); +/*** qo[0] = AplusBmodP( t0, tn, P ); ***/ +/*** qo[istep] = A_BmodP( t0, tn, P ); ***/ + qo[0] = A_BmodP( t0, tn, P ); + qo[istep] = AplusBmodP( t0, tn, P ); + } } } } @@ -437,22 +437,22 @@ double Pinv; /* * The final step of k = 0. i can take only the value 0. * - * Out[j] <= t0 + \alpha^{-j} * tn; - * Out[j + 2^{K-1}] <= t0 - \alpha^{-j} * tn; + * Out[j] <= t0 + \alpha^{-j} * tn; + * Out[j + 2^{K-1}] <= t0 - \alpha^{-j} * tn; * * where t0 = In[j] and tn = In[j + 2^{K-1}], * for 0 <= j < 2^{K-1}. * */ qo = out, qi = &wk[inwk ? N : 0]; - if ( (n = osi + nout) > N ) nout = (n = N) - osi; /* true nout */ - if ( (k = nout - halfN) <= 0 ) { /* no overlap, i.e., no +- */ + if ( (n = osi + nout) > N ) nout = (n = N) - osi; /* true nout */ + if ( (k = nout - halfN) <= 0 ) { /* no overlap, i.e., no +- */ if ( osi <= 0 ) { t0 = qi[0], tn = qi[idist]; if ( tn != (ModNum)0 ) t0 = AplusBmodP( t0, tn, P ); if ( t0 == (ModNum)0 ) qo[0] = t0; else { - AxBmodP( qo[0], ModNum, t0, Ninv, P, Pinv ); + AxBmodP( qo[0], ModNum, t0, Ninv, P, Pinv ); } #ifdef POWA_STRIDE aj = a1; @@ -463,10 +463,10 @@ double Pinv; #ifdef POWA_STRIDE aj = osi*a1; #endif - if ( n <= halfN ) i = 0, k = n; /* lower only */ - else if ( j == halfN ) goto L_halfN; /* start with j = N/2 */ - else if ( j > halfN ) goto L_upper; /* upper only */ - else i = n - halfN + 1, k = halfN; /* we have lower, and i upper */ + if ( n <= halfN ) i = 0, k = n; /* lower only */ + else if ( j == halfN ) goto L_halfN; /* start with j = N/2 */ + else if ( j > halfN ) goto L_upper; /* upper only */ + else i = n - halfN + 1, k = halfN; /* we have lower, and i upper */ } } else { os = o1*halfN; @@ -476,16 +476,16 @@ double Pinv; if ( osi <= 0 ) { t0 = qi[0], tn = qi[idist]; if ( tn == (ModNum)0 ) { - if ( t0 == (ModNum)0 ) tt = t0; - else { AxBmodP( tt, ModNum, t0, Ninv, P, Pinv ); } - qo[0] = qo[os] = tt; + if ( t0 == (ModNum)0 ) tt = t0; + else { AxBmodP( tt, ModNum, t0, Ninv, P, Pinv ); } + qo[0] = qo[os] = tt; } else { - tt = AplusBmodP( t0, tn, P ); - if ( tt == (ModNum)0 ) qo[0] = tt; - else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); } - tt = A_BmodP( t0, tn, P ); - if ( tt == (ModNum)0 ) qo[os] = tt; - else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); } + tt = AplusBmodP( t0, tn, P ); + if ( tt == (ModNum)0 ) qo[0] = tt; + else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); } + tt = A_BmodP( t0, tn, P ); + if ( tt == (ModNum)0 ) qo[os] = tt; + else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); } } #ifdef EBUG fprintf( stderr, "::::: DFT^{-1} ::: [0]=%d, [%d]=%d\n", (int)qo[0], os, (int)qo[os] ); @@ -503,27 +503,27 @@ double Pinv; #endif t0 = qi[j], tn = qi[j+idist]; if ( tn == (ModNum)0 ) { - if ( t0 != (ModNum)0 ) { - AxBmodP( t0, ModNum, t0, Ninv, P, Pinv ); - } - qo[0] = qo[os] = t0; + if ( t0 != (ModNum)0 ) { + AxBmodP( t0, ModNum, t0, Ninv, P, Pinv ); + } + qo[0] = qo[os] = t0; } else { #ifdef POWA_STRIDE -/*** a = P - powa[halfNa - aj]; ***/ - a = powa[halfNa - aj]; +/*** a = P - powa[halfNa - aj]; ***/ + a = powa[halfNa - aj]; #else -/*** a = P - powa[halfN - j]; ***/ - a = powa[halfN - j]; +/*** a = P - powa[halfN - j]; ***/ + a = powa[halfN - j]; #endif - AxBmodP( tn, ModNum, tn, a, P, Pinv ); -/*** tt = AplusBmodP( t0, tn, P ); ***/ - tt = A_BmodP( t0, tn, P ); - if ( tt == (ModNum)0 ) qo[0] = tt; - else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); } -/*** tt = A_BmodP( t0, tn, P ); ***/ - tt = AplusBmodP( t0, tn, P ); - if ( tt == (ModNum)0 ) qo[os] = tt; - else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); } + AxBmodP( tn, ModNum, tn, a, P, Pinv ); +/*** tt = AplusBmodP( t0, tn, P ); ***/ + tt = A_BmodP( t0, tn, P ); + if ( tt == (ModNum)0 ) qo[0] = tt; + else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); } +/*** tt = A_BmodP( t0, tn, P ); ***/ + tt = AplusBmodP( t0, tn, P ); + if ( tt == (ModNum)0 ) qo[os] = tt; + else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); } } } k = halfN;