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-rw-r--r--sysdeps/ieee754/dbl-64/e_log.c228
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..f9300f9cef 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 / 0.0; /* return -INF */
+ if (__builtin_expect (ux < 0, 0))
+ return (x - x) / 0.0; /* 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 - 1;
+ 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, 0, 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, 0, 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, 0, 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, 0, 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, 0, 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, 0, 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, 0, 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, 0, 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, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
+ MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (w, 0, 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 = (1 + (i - 75) * DEL_U) * (1 + (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 * ((1 - 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, 0, 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
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