| |
| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001 Free Software Foundation |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU Lesser General Public License as published by |
| * the Free Software Foundation; either version 2.1 of the License, or |
| * (at your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| * GNU Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
| */ |
| /******************************************************************/ |
| /* */ |
| /* MODULE_NAME:mpatan.c */ |
| /* */ |
| /* FUNCTIONS:mpatan */ |
| /* */ |
| /* FILES NEEDED: mpa.h endian.h mpatan.h */ |
| /* mpa.c */ |
| /* */ |
| /* Multi-Precision Atan function subroutine, for precision p >= 4.*/ |
| /* The relative error of the result is bounded by 34.32*r**(1-p), */ |
| /* where r=2**24. */ |
| /******************************************************************/ |
| |
| #include "endian.h" |
| #include "mpa.h" |
| void __mpsqrt(mp_no *, mp_no *, int); |
| |
| void __mpatan(mp_no *x, mp_no *y, int p) { |
| #include "mpatan.h" |
| |
| int i,m,n; |
| double dx; |
| mp_no |
| mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}}, |
| mptwo = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}}, |
| mptwoim1 = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, |
| 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}}; |
| |
| mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3; |
| |
| /* Choose m and initiate mpone, mptwo & mptwoim1 */ |
| if (EX>0) m=7; |
| else if (EX<0) m=0; |
| else { |
| __mp_dbl(x,&dx,p); dx=ABS(dx); |
| for (m=6; m>0; m--) |
| {if (dx>xm[m].d) break;} |
| } |
| mpone.e = mptwo.e = mptwoim1.e = 1; |
| mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE; |
| mptwo.d[1] = TWO; |
| |
| /* Reduce x m times */ |
| __mul(x,x,&mpsm,p); |
| if (m==0) __cpy(x,&mps,p); |
| else { |
| for (i=0; i<m; i++) { |
| __add(&mpone,&mpsm,&mpt1,p); |
| __mpsqrt(&mpt1,&mpt2,p); |
| __add(&mpt2,&mpt2,&mpt1,p); |
| __add(&mptwo,&mpsm,&mpt2,p); |
| __add(&mpt1,&mpt2,&mpt3,p); |
| __dvd(&mpsm,&mpt3,&mpt1,p); |
| __cpy(&mpt1,&mpsm,p); |
| } |
| __mpsqrt(&mpsm,&mps,p); mps.d[0] = X[0]; |
| } |
| |
| /* Evaluate a truncated power series for Atan(s) */ |
| n=np[p]; mptwoim1.d[1] = twonm1[p].d; |
| __dvd(&mpsm,&mptwoim1,&mpt,p); |
| for (i=n-1; i>1; i--) { |
| mptwoim1.d[1] -= TWO; |
| __dvd(&mpsm,&mptwoim1,&mpt1,p); |
| __mul(&mpsm,&mpt,&mpt2,p); |
| __sub(&mpt1,&mpt2,&mpt,p); |
| } |
| __mul(&mps,&mpt,&mpt1,p); |
| __sub(&mps,&mpt1,&mpt,p); |
| |
| /* Compute Atan(x) */ |
| mptwoim1.d[1] = twom[m].d; |
| __mul(&mptwoim1,&mpt,y,p); |
| |
| return; |
| } |