diff options
| -rw-r--r-- | ChangeLog | 2 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_atan.c | 397 |
2 files changed, 248 insertions, 151 deletions
diff --git a/ChangeLog b/ChangeLog index a6d5d02f2c..cf2cb41654 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,5 +1,7 @@ 2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com> + * sysdeps/ieee754/dbl-64/s_atan.c: Fix formatting. + * sysdeps/ieee754/dbl-64/e_log.c: Fix formatting. 2013-03-28 Roland McGrath <roland@hack.frob.com> diff --git a/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c index aa3564d560..dc1716f93a 100644 --- a/sysdeps/ieee754/dbl-64/s_atan.c +++ b/sysdeps/ieee754/dbl-64/s_atan.c @@ -43,177 +43,272 @@ #include "atnat.h" #include <math.h> -void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */ -static double atanMp(double,const int[]); +void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */ +static double atanMp (double, const int[]); /* Fix the sign of y and return */ -static double __signArctan(double x,double y){ - return __copysign(y, x); +static double +__signArctan (double x, double y) +{ + return __copysign (y, x); } /* An ultimate atan() routine. Given an IEEE double machine number x, */ /* routine computes the correctly rounded (to nearest) value of atan(x). */ -double atan(double x) { - - - double cor,s1,ss1,s2,ss2,t1,t2,t3,t7,t8,t9,t10,u,u2,u3, - v,vv,w,ww,y,yy,z,zz; +double +atan (double x) +{ + double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3, + v, vv, w, ww, y, yy, z, zz; #ifndef DLA_FMS - double t4,t5,t6; + double t4, t5, t6; #endif - int i,ux,dx; - static const int pr[M]={6,8,10,32}; + int i, ux, dx; + static const int pr[M] = { 6, 8, 10, 32 }; number num; - num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF]; + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; /* x=NaN */ - if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000)) - return x+x; + if (((ux & 0x7ff00000) == 0x7ff00000) + && (((ux & 0x000fffff) | dx) != 0x00000000)) + return x + x; /* Regular values of x, including denormals +-0 and +-INF */ - u = (x<ZERO) ? -x : x; - if (u<C) { - if (u<B) { - if (u<A) { /* u < A */ - return x; } - else { /* A <= u < B */ - v=x*x; yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d))))); - if ((y=x+(yy-U1*x)) == x+(yy+U1*x)) return y; - - EMULV(x,x,v,vv,t1,t2,t3,t4,t5) /* v+vv=x^2 */ - s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d)))); - ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - MUL2(x,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(x,ZERO,s2,ss2,s1,ss1,t1,t2) - if ((y=s1+(ss1-U5*s1)) == s1+(ss1+U5*s1)) return y; - - return atanMp(x,pr); - } } - else { /* B <= u < C */ - i=(TWO52+TWO8*u)-TWO52; i-=16; - z=u-cij[i][0].d; - yy=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+ - z*(cij[i][5].d+z* cij[i][6].d)))); - t1=cij[i][1].d; - if (i<112) { - if (i<48) u2=U21; /* u < 1/4 */ - else u2=U22; } /* 1/4 <= u < 1/2 */ - else { - if (i<176) u2=U23; /* 1/2 <= u < 3/4 */ - else u2=U24; } /* 3/4 <= u <= 1 */ - if ((y=t1+(yy-u2*t1)) == t1+(yy+u2*t1)) return __signArctan(x,y); - - z=u-hij[i][0].d; - s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+ - z*(hij[i][14].d+z* hij[i][15].d)))); - ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2) - MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2) - if ((y=s2+(ss2-U6*s2)) == s2+(ss2+U6*s2)) return __signArctan(x,y); - - return atanMp(x,pr); - } - } - else { - if (u<D) { /* C <= u < D */ - w=ONE/u; - EMULV(w,u,t1,t2,t3,t4,t5,t6,t7) - ww=w*((ONE-t1)-t2); - i=(TWO52+TWO8*w)-TWO52; i-=16; - z=(w-cij[i][0].d)+ww; - yy=HPI1-z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+ - z*(cij[i][5].d+z* cij[i][6].d)))); - t1=HPI-cij[i][1].d; - if (i<112) u3=U31; /* w < 1/2 */ - else u3=U32; /* w >= 1/2 */ - if ((y=t1+(yy-u3)) == t1+(yy+u3)) return __signArctan(x,y); - - DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) - t1=w-hij[i][0].d; - EADD(t1,ww,z,zz) - s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+ - z*(hij[i][14].d+z* hij[i][15].d)))); - ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2) - MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2) - MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2) - SUB2(HPI,HPI1,s2,ss2,s1,ss1,t1,t2) - if ((y=s1+(ss1-U7)) == s1+(ss1+U7)) return __signArctan(x,y); - - return atanMp(x,pr); - } - else { - if (u<E) { /* D <= u < E */ - w=ONE/u; v=w*w; - EMULV(w,u,t1,t2,t3,t4,t5,t6,t7) - yy=w*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d))))); - ww=w*((ONE-t1)-t2); - ESUB(HPI,w,t3,cor) - yy=((HPI1+cor)-ww)-yy; - if ((y=t3+(yy-U4)) == t3+(yy+U4)) return __signArctan(x,y); - - DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) - MUL2(w,ww,w,ww,v,vv,t1,t2,t3,t4,t5,t6,t7,t8) - s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d)))); - ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2) - MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8) - MUL2(w,ww,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(w,ww,s2,ss2,s1,ss1,t1,t2) - SUB2(HPI,HPI1,s1,ss1,s2,ss2,t1,t2) - if ((y=s2+(ss2-U8)) == s2+(ss2+U8)) return __signArctan(x,y); - - return atanMp(x,pr); - } - else { - /* u >= E */ - if (x>0) return HPI; - else return MHPI; } + u = (x < ZERO) ? -x : x; + if (u < C) + { + if (u < B) + { + if (u < A) + return x; + else + { /* A <= u < B */ + v = x * x; + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= x * v; + + if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x)) + return y; + + EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */ + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, ZERO, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (x, ZERO, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, + t8); + ADD2 (x, ZERO, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1)) + return y; + + return atanMp (x, pr); + } + } + else + { /* B <= u < C */ + i = (TWO52 + TWO8 * u) - TWO52; + i -= 16; + z = u - cij[i][0].d; + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy *= z; + + t1 = cij[i][1].d; + if (i < 112) + { + if (i < 48) + u2 = U21; /* u < 1/4 */ + else + u2 = U22; + } /* 1/4 <= u < 1/2 */ + else + { + if (i < 176) + u2 = U23; /* 1/2 <= u < 3/4 */ + else + u2 = U24; + } /* 3/4 <= u <= 1 */ + if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1)) + return __signArctan (x, y); + + z = u - hij[i][0].d; + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, ZERO, s2, ss2, t1, t2); + MUL2 (z, ZERO, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, ZERO, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, ZERO, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, ZERO, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2)) + return __signArctan (x, y); + + return atanMp (x, pr); + } } - } + else + { + if (u < D) + { /* C <= u < D */ + w = ONE / u; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + ww = w * ((ONE - t1) - t2); + i = (TWO52 + TWO8 * w) - TWO52; + i -= 16; + z = (w - cij[i][0].d) + ww; + + yy = cij[i][5].d + z * cij[i][6].d; + yy = cij[i][4].d + z * yy; + yy = cij[i][3].d + z * yy; + yy = cij[i][2].d + z * yy; + yy = HPI1 - z * yy; + t1 = HPI - cij[i][1].d; + if (i < 112) + u3 = U31; /* w < 1/2 */ + else + u3 = U32; /* w >= 1/2 */ + if ((y = t1 + (yy - u3)) == t1 + (yy + u3)) + return __signArctan (x, y); + + DIV2 (ONE, ZERO, u, ZERO, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9, + t10); + t1 = w - hij[i][0].d; + EADD (t1, ww, z, zz); + + s1 = hij[i][14].d + z * hij[i][15].d; + s1 = hij[i][13].d + z * s1; + s1 = hij[i][12].d + z * s1; + s1 = hij[i][11].d + z * s1; + s1 *= z; + + ADD2 (hij[i][9].d, hij[i][10].d, s1, ZERO, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); + MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); + SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2); + if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + if (u < E) + { /* D <= u < E */ + w = ONE / u; + v = w * w; + EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); + + yy = d11.d + v * d13.d; + yy = d9.d + v * yy; + yy = d7.d + v * yy; + yy = d5.d + v * yy; + yy = d3.d + v * yy; + yy *= w * v; + + ww = w * ((ONE - t1) - t2); + ESUB (HPI, w, t3, cor); + yy = ((HPI1 + cor) - ww) - yy; + if ((y = t3 + (yy - U4)) == t3 + (yy + U4)) + return __signArctan (x, y); + + DIV2 (ONE, ZERO, u, ZERO, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, + t9, t10); + MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); + + s1 = f17.d + v * f19.d; + s1 = f15.d + v * s1; + s1 = f13.d + v * s1; + s1 = f11.d + v * s1; + s1 *= v; + + ADD2 (f9.d, ff9.d, s1, ZERO, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); + MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2); + SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2); + + if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8)) + return __signArctan (x, y); + + return atanMp (x, pr); + } + else + { + /* u >= E */ + if (x > 0) + return HPI; + else + return MHPI; + } + } + } } /* Final stages. Compute atan(x) by multiple precision arithmetic */ -static double atanMp(double x,const int pr[]){ - mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1; - double y1,y2; - int i,p; - -for (i=0; i<M; i++) { - p = pr[i]; - __dbl_mp(x,&mpx,p); __mpatan(&mpx,&mpy,p); - __dbl_mp(u9[i].d,&mpt1,p); __mul(&mpy,&mpt1,&mperr,p); - __add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p); - __mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p); - if (y1==y2) return y1; - } - return y1; /*if unpossible to do exact computing */ +static double +atanMp (double x, const int pr[]) +{ + mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1; + double y1, y2; + int i, p; + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __mpatan (&mpx, &mpy, p); + __dbl_mp (u9[i].d, &mpt1, p); + __mul (&mpy, &mpt1, &mperr, p); + __add (&mpy, &mperr, &mpy1, p); + __sub (&mpy, &mperr, &mpy2, p); + __mp_dbl (&mpy1, &y1, p); + __mp_dbl (&mpy2, &y2, p); + if (y1 == y2) + return y1; + } + return y1; /*if impossible to do exact computing */ } #ifdef NO_LONG_DOUBLE |