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Format e_log.c
This commit is contained in:
Siddhesh Poyarekar
parent
e57b0c6100
commit
0f6a8d4b0b
@ -1,3 +1,7 @@
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2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/e_log.c: Fix formatting.
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2013-03-28 Roland McGrath <roland@hack.frob.com>
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* include/stdlib.h [!SHARED] (__call_tls_dtors):
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@ -44,7 +44,7 @@
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# define SECTION
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#endif
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void __mplog(mp_no *, mp_no *, int);
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void __mplog (mp_no *, mp_no *, int);
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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@ -52,163 +52,201 @@ void __mplog(mp_no *, mp_no *, int);
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/*********************************************************************/
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double
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SECTION
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__ieee754_log(double x) {
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__ieee754_log (double x)
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{
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#define M 4
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static const int pr[M]={8,10,18,32};
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int i,j,n,ux,dx,p;
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double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
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sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
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t1,t2,t7,t8,t,ra,rb,ww,
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a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
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static const int pr[M] = {8, 10, 18, 32};
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int i, j, n, ux, dx, p;
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double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
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sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb,
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t1, t2, t7, t8, t, ra, rb, ww,
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a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c;
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#ifndef DLA_FMS
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double t3,t4,t5,t6;
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double t3, t4, t5, t6;
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#endif
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number num;
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mp_no mpx,mpy,mpy1,mpy2,mperr;
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mp_no mpx, mpy, mpy1, mpy2, mperr;
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#include "ulog.tbl"
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#include "ulog.h"
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/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
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num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
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n=0;
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if (__builtin_expect(ux < 0x00100000, 0)) {
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if (__builtin_expect(((ux & 0x7fffffff) | dx) == 0, 0))
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return MHALF/ZERO; /* return -INF */
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if (__builtin_expect(ux < 0, 0))
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return (x-x)/ZERO; /* return NaN */
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n -= 54; x *= two54.d; /* scale x */
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num.d = x;
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}
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if (__builtin_expect(ux >= 0x7ff00000, 0))
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return x+x; /* INF or NaN */
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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n = 0;
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if (__builtin_expect (ux < 0x00100000, 0))
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{
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if (__builtin_expect (((ux & 0x7fffffff) | dx) == 0, 0))
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return MHALF / ZERO; /* return -INF */
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if (__builtin_expect (ux < 0, 0))
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return (x - x) / ZERO; /* return NaN */
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n -= 54;
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x *= two54.d; /* scale x */
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num.d = x;
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}
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if (__builtin_expect (ux >= 0x7ff00000, 0))
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return x + x; /* INF or NaN */
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/* Regular values of x */
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w = x-ONE;
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if (__builtin_expect(ABS(w) > U03, 1)) { goto case_03; }
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w = x - ONE;
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if (__builtin_expect (ABS (w) > U03, 1))
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goto case_03;
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/*--- Stage I, the case abs(x-1) < 0.03 */
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t8 = MHALF*w;
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EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
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EADD(w,a,b,bb)
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t8 = MHALF * w;
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EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
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EADD (w, a, b, bb);
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/* Evaluate polynomial II */
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polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
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w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
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c = (aa+bb)+polII;
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polII = b7.d + w * b8.d;
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polII = b6.d + w * polII;
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polII = b5.d + w * polII;
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polII = b4.d + w * polII;
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polII = b3.d + w * polII;
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polII = b2.d + w * polII;
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polII = b1.d + w * polII;
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polII = b0.d + w * polII;
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polII *= w * w * w;
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c = (aa + bb) + polII;
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/* End stage I, case abs(x-1) < 0.03 */
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if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y;
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if ((y = b + (c + b * E2)) == b + (c - b * E2))
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return y;
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/*--- Stage II, the case abs(x-1) < 0.03 */
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a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
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w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
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EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
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ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(w,ZERO, s3,ss3, b, bb,t1,t2)
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a = d19.d + w * d20.d;
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a = d18.d + w * a;
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a = d17.d + w * a;
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a = d16.d + w * a;
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a = d15.d + w * a;
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a = d14.d + w * a;
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a = d13.d + w * a;
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a = d12.d + w * a;
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a = d11.d + w * a;
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EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5);
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ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, ZERO, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (w, ZERO, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (w, ZERO, s3, ss3, b, bb, t1, t2);
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/* End stage II, case abs(x-1) < 0.03 */
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if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y;
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if ((y = b + (bb + b * E4)) == b + (bb - b * E4))
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return y;
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goto stage_n;
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/*--- Stage I, the case abs(x-1) > 0.03 */
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case_03:
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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n += (num.i[HIGH_HALF] >> 20) - 1023;
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num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
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if (num.d > SQRT_2) { num.d *= HALF; n++; }
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u = num.d; dbl_n = (double) n;
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if (num.d > SQRT_2)
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{
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num.d *= HALF;
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n++;
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}
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u = num.d;
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dbl_n = (double) n;
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/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
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num.d += h1.d;
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i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
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/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
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num.d = u*Iu[i].d + h2.d;
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num.d = u * Iu[i].d + h2.d;
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j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
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/* Compute w=(u-ui*vj)/(ui*vj) */
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p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
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q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0;
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p0 = (ONE + (i - 75) * DEL_U) * (ONE + (j - 180) * DEL_V);
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q = u - p0;
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r0 = Iu[i].d * Iv[j].d;
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w = q * r0;
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/* Evaluate polynomial I */
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polI = w+(a2.d+a3.d*w)*w*w;
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polI = w + (a2.d + a3.d * w) * w * w;
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/* Add up everything */
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nln2a = dbl_n*LN2A;
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luai = Lu[i][0].d; lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d; lvbj = Lv[j][1].d;
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EADD(luai,lvaj,sij,ssij)
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EADD(nln2a,sij,A ,ttij)
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B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
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B = polI+B0;
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nln2a = dbl_n * LN2A;
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luai = Lu[i][0].d;
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lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d;
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lvbj = Lv[j][1].d;
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EADD (luai, lvaj, sij, ssij);
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EADD (nln2a, sij, A, ttij);
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B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
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B = polI + B0;
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/* End stage I, case abs(x-1) >= 0.03 */
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if ((y=A+(B+E1)) == A+(B-E1)) return y;
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if ((y = A + (B + E1)) == A + (B - E1))
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return y;
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/*--- Stage II, the case abs(x-1) > 0.03 */
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/* Improve the accuracy of r0 */
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EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
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t=r0*((ONE-sa)-sb);
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EADD(r0,t,ra,rb)
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EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5);
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t = r0 * ((ONE - sa) - sb);
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EADD (r0, t, ra, rb);
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/* Compute w */
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MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (q, ZERO, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8);
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EADD(A,B0,a0,aa0)
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EADD (A, B0, a0, aa0);
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/* Evaluate polynomial III */
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s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
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EADD(c2.d,s1,s2,ss2)
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MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
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ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)
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s1 = (c3.d + (c4.d + c5.d * w) * w) * w;
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EADD (c2.d, s1, s2, ss2);
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MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2);
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ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2);
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/* End stage II, case abs(x-1) >= 0.03 */
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if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;
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if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3))
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return y;
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/* Final stages. Use multi-precision arithmetic. */
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stage_n:
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stage_n:
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for (i=0; i<M; i++) {
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p = pr[i];
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__dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
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__mplog(&mpx,&mpy,p);
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__dbl_mp(e[i].d,&mperr,p);
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__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
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__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
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if (y1==y2) return y1;
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}
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for (i = 0; i < M; i++)
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{
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p = pr[i];
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__dbl_mp (x, &mpx, p);
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__dbl_mp (y, &mpy, p);
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__mplog (&mpx, &mpy, p);
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__dbl_mp (e[i].d, &mperr, p);
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__add (&mpy, &mperr, &mpy1, p);
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__sub (&mpy, &mperr, &mpy2, p);
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__mp_dbl (&mpy1, &y1, p);
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__mp_dbl (&mpy2, &y2, p);
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if (y1 == y2)
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return y1;
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}
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return y1;
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}
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#ifndef __ieee754_log
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strong_alias (__ieee754_log, __log_finite)
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#endif
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