diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_log.c | 228 |
1 files changed, 133 insertions, 95 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_log.c b/sysdeps/ieee754/dbl-64/e_log.c index 58c9a8e76b..d3b5e6ea82 100644 --- a/sysdeps/ieee754/dbl-64/e_log.c +++ b/sysdeps/ieee754/dbl-64/e_log.c @@ -44,7 +44,7 @@ # define SECTION #endif -void __mplog(mp_no *, mp_no *, int); +void __mplog (mp_no *, mp_no *, int); /*********************************************************************/ /* An ultimate log routine. Given an IEEE double machine number x */ @@ -52,163 +52,201 @@ void __mplog(mp_no *, mp_no *, int); /*********************************************************************/ double SECTION -__ieee754_log(double x) { +__ieee754_log (double x) +{ #define M 4 - static const int pr[M]={8,10,18,32}; - int i,j,n,ux,dx,p; - double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj, - sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb, - t1,t2,t7,t8,t,ra,rb,ww, - a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c; + static const int pr[M] = {8, 10, 18, 32}; + int i, j, n, ux, dx, p; + double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj, + sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb, + t1, t2, t7, t8, t, ra, rb, ww, + a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c; #ifndef DLA_FMS - double t3,t4,t5,t6; + double t3, t4, t5, t6; #endif number num; - mp_no mpx,mpy,mpy1,mpy2,mperr; + mp_no mpx, mpy, mpy1, mpy2, mperr; #include "ulog.tbl" #include "ulog.h" /* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */ - num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF]; - n=0; - if (__builtin_expect(ux < 0x00100000, 0)) { - if (__builtin_expect(((ux & 0x7fffffff) | dx) == 0, 0)) - return MHALF/ZERO; /* return -INF */ - if (__builtin_expect(ux < 0, 0)) - return (x-x)/ZERO; /* return NaN */ - n -= 54; x *= two54.d; /* scale x */ - num.d = x; - } - if (__builtin_expect(ux >= 0x7ff00000, 0)) - return x+x; /* INF or NaN */ + num.d = x; + ux = num.i[HIGH_HALF]; + dx = num.i[LOW_HALF]; + n = 0; + if (__builtin_expect (ux < 0x00100000, 0)) + { + if (__builtin_expect (((ux & 0x7fffffff) | dx) == 0, 0)) + return MHALF / ZERO; /* return -INF */ + if (__builtin_expect (ux < 0, 0)) + return (x - x) / ZERO; /* return NaN */ + n -= 54; + x *= two54.d; /* scale x */ + num.d = x; + } + if (__builtin_expect (ux >= 0x7ff00000, 0)) + return x + x; /* INF or NaN */ /* Regular values of x */ - w = x-ONE; - if (__builtin_expect(ABS(w) > U03, 1)) { goto case_03; } - + w = x - ONE; + if (__builtin_expect (ABS (w) > U03, 1)) + goto case_03; /*--- Stage I, the case abs(x-1) < 0.03 */ - t8 = MHALF*w; - EMULV(t8,w,a,aa,t1,t2,t3,t4,t5) - EADD(w,a,b,bb) - + t8 = MHALF * w; + EMULV (t8, w, a, aa, t1, t2, t3, t4, t5); + EADD (w, a, b, bb); /* Evaluate polynomial II */ - polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+ - w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w; - c = (aa+bb)+polII; + polII = b7.d + w * b8.d; + polII = b6.d + w * polII; + polII = b5.d + w * polII; + polII = b4.d + w * polII; + polII = b3.d + w * polII; + polII = b2.d + w * polII; + polII = b1.d + w * polII; + polII = b0.d + w * polII; + polII *= w * w * w; + c = (aa + bb) + polII; /* End stage I, case abs(x-1) < 0.03 */ - if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y; + if ((y = b + (c + b * E2)) == b + (c - b * E2)) + return y; /*--- Stage II, the case abs(x-1) < 0.03 */ - a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+ - w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d)))))))); - EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5) - ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2) - MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(w,ZERO, s3,ss3, b, bb,t1,t2) + a = d19.d + w * d20.d; + a = d18.d + w * a; + a = d17.d + w * a; + a = d16.d + w * a; + a = d15.d + w * a; + a = d14.d + w * a; + a = d13.d + w * a; + a = d12.d + w * a; + a = d11.d + w * a; + + EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5); + ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2); + MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (w, ZERO, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (w, ZERO, s3, ss3, b, bb, t1, t2); /* End stage II, case abs(x-1) < 0.03 */ - if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y; + if ((y = b + (bb + b * E4)) == b + (bb - b * E4)) + return y; goto stage_n; /*--- Stage I, the case abs(x-1) > 0.03 */ - case_03: +case_03: /* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */ n += (num.i[HIGH_HALF] >> 20) - 1023; num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000; - if (num.d > SQRT_2) { num.d *= HALF; n++; } - u = num.d; dbl_n = (double) n; + if (num.d > SQRT_2) + { + num.d *= HALF; + n++; + } + u = num.d; + dbl_n = (double) n; /* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */ num.d += h1.d; i = (num.i[HIGH_HALF] & 0x000fffff) >> 12; /* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */ - num.d = u*Iu[i].d + h2.d; + num.d = u * Iu[i].d + h2.d; j = (num.i[HIGH_HALF] & 0x000fffff) >> 4; /* Compute w=(u-ui*vj)/(ui*vj) */ - p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V); - q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0; + p0 = (ONE + (i - 75) * DEL_U) * (ONE + (j - 180) * DEL_V); + q = u - p0; + r0 = Iu[i].d * Iv[j].d; + w = q * r0; /* Evaluate polynomial I */ - polI = w+(a2.d+a3.d*w)*w*w; + polI = w + (a2.d + a3.d * w) * w * w; /* Add up everything */ - nln2a = dbl_n*LN2A; - luai = Lu[i][0].d; lubi = Lu[i][1].d; - lvaj = Lv[j][0].d; lvbj = Lv[j][1].d; - EADD(luai,lvaj,sij,ssij) - EADD(nln2a,sij,A ,ttij) - B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B; - B = polI+B0; + nln2a = dbl_n * LN2A; + luai = Lu[i][0].d; + lubi = Lu[i][1].d; + lvaj = Lv[j][0].d; + lvbj = Lv[j][1].d; + EADD (luai, lvaj, sij, ssij); + EADD (nln2a, sij, A, ttij); + B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B; + B = polI + B0; /* End stage I, case abs(x-1) >= 0.03 */ - if ((y=A+(B+E1)) == A+(B-E1)) return y; + if ((y = A + (B + E1)) == A + (B - E1)) + return y; /*--- Stage II, the case abs(x-1) > 0.03 */ /* Improve the accuracy of r0 */ - EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5) - t=r0*((ONE-sa)-sb); - EADD(r0,t,ra,rb) + EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5); + t = r0 * ((ONE - sa) - sb); + EADD (r0, t, ra, rb); /* Compute w */ - MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8) + MUL2 (q, ZERO, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8); - EADD(A,B0,a0,aa0) + EADD (A, B0, a0, aa0); /* Evaluate polynomial III */ - s1 = (c3.d+(c4.d+c5.d*w)*w)*w; - EADD(c2.d,s1,s2,ss2) - MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8) - MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8) - ADD2(s2,ss2,w,ww,s3,ss3,t1,t2) - ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2) + s1 = (c3.d + (c4.d + c5.d * w) * w) * w; + EADD (c2.d, s1, s2, ss2); + MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8); + MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); + ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2); + ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2); /* End stage II, case abs(x-1) >= 0.03 */ - if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y; + if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3)) + return y; /* Final stages. Use multi-precision arithmetic. */ - stage_n: - - for (i=0; i<M; i++) { - p = pr[i]; - __dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p); - __mplog(&mpx,&mpy,p); - __dbl_mp(e[i].d,&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; - } +stage_n: + + for (i = 0; i < M; i++) + { + p = pr[i]; + __dbl_mp (x, &mpx, p); + __dbl_mp (y, &mpy, p); + __mplog (&mpx, &mpy, p); + __dbl_mp (e[i].d, &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; } + #ifndef __ieee754_log strong_alias (__ieee754_log, __log_finite) #endif |