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math: Remove slow paths in tan [BZ #15267]
Remove slow paths in tan. Add ULP annotations. Merge 'number' into 'mynumber'. Remove unused entries from tan constants. Reviewed-By: Paul Zimmermann <Paul.Zimmermann@inria.fr>
This commit is contained in:
Wilco Dijkstra
Wilco Dijkstra
parent
db3f7bb558
commit
476d692e8a
@ -39,6 +39,7 @@
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include "mydefs.h"
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#include "uatan.tbl"
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#include "atnat2.h"
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#include <fenv.h>
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@ -28,7 +28,7 @@
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#define MY_H
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typedef int int4;
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typedef union { int4 i[2]; double x; } mynumber;
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typedef union { int4 i[2]; double x; double d; } mynumber;
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#define max(x, y) (((y) > (x)) ? (y) : (x))
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#define min(x, y) (((y) < (x)) ? (y) : (x))
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@ -20,40 +20,30 @@
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/* MODULE_NAME: utan.c */
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/* */
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/* FUNCTIONS: utan */
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/* tanMp */
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/* */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */
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/* branred.c sincos32.c mptan.c */
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/* FILES NEEDED:dla.h endian.h mydefs.h utan.h */
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/* branred.c */
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/* utan.tbl */
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/* */
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/* An ultimate tan routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of tan(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include <errno.h>
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#include <float.h>
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#include "endian.h"
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include "mydefs.h"
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#include <math.h>
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#include <math_private.h>
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#include <fenv_private.h>
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#include <math-underflow.h>
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#include <libm-alias-double.h>
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#include <fenv.h>
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#include <stap-probe.h>
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#ifndef SECTION
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# define SECTION
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#endif
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static double tanMp (double);
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void __mptan (double, mp_no *, int);
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/* tan with max ULP of ~0.619 based on random sampling. */
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double
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SECTION
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__tan (double x)
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@ -62,17 +52,14 @@ __tan (double x)
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#include "utan.tbl"
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int ux, i, n;
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double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz,
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s, sy, t, t1, t2, t3, t4, w, x2, xn, xx2, y, ya,
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yya, z0, z, zz, z2, zz2;
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int p;
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number num, v;
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mp_no mpa, mpt1, mpt2;
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double a, da, a2, b, db, c, dc, fi, gi, pz,
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s, sy, t, t1, t2, t3, t4, w, x2, xn, y, ya,
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yya, z0, z, z2;
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mynumber num, v;
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double retval;
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int __branred (double, double *, double *);
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int __mpranred (double, mp_no *, int);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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@ -100,7 +87,6 @@ __tan (double x)
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/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
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if (w <= g2.d)
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{
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/* First stage */
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x2 = x * x;
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t2 = d9.d + x2 * d11.d;
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@ -109,50 +95,16 @@ __tan (double x)
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t2 = d3.d + x2 * t2;
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t2 *= x * x2;
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if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
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{
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retval = y;
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goto ret;
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}
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/* Second stage */
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c1 = a25.d + x2 * a27.d;
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c1 = a23.d + x2 * c1;
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c1 = a21.d + x2 * c1;
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c1 = a19.d + x2 * c1;
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c1 = a17.d + x2 * c1;
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c1 = a15.d + x2 * c1;
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c1 *= x2;
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EMULV (x, x, x2, xx2);
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ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2);
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ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
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if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
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{
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retval = y;
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goto ret;
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}
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retval = tanMp (x);
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y = x + t2;
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retval = y;
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/* Max ULP is 0.504. */
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goto ret;
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}
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/* (III) The case 0.0608 < abs(x) <= 0.787 */
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if (w <= g3.d)
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{
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/* First stage */
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i = ((int) (mfftnhf.d + TWO8 * w));
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i = ((int) (mfftnhf.d + 256 * w));
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z = w - xfg[i][0].d;
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z2 = z * z;
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s = (x < 0.0) ? -1 : 1;
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@ -160,41 +112,9 @@ __tan (double x)
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fi = xfg[i][1].d;
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gi = xfg[i][2].d;
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t2 = pz * (gi + fi) / (gi - pz);
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if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d))
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{
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retval = (s * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = fi * ua3.d + t3 * ub3.d;
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if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
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{
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retval = (s * y);
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goto ret;
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}
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/* Second stage */
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ffi = xfg[i][3].d;
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c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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EMULV (z, z, z2, zz2);
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ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
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MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2);
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ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2);
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ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
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MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
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SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
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DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
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if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
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{
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retval = (s * y);
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goto ret;
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}
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retval = tanMp (x);
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y = fi + t2;
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retval = (s * y);
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/* Max ULP is 0.60. */
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goto ret;
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}
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@ -223,14 +143,7 @@ __tan (double x)
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sy = 1;
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}
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/* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
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if (ya <= gy1.d)
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{
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retval = tanMp (x);
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goto ret;
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}
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/* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
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/* (VI) The case 0.787 < abs(x) <= 25, 0 < abs(y) <= 0.0608 */
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if (ya <= gy2.d)
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{
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a2 = a * a;
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@ -242,94 +155,27 @@ __tan (double x)
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if (n)
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{
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/* First stage -cot */
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/* -cot */
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EADD (a, t2, b, db);
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DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
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if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c))
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{
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retval = (-y);
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goto ret;
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}
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y = c + dc;
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retval = (-y);
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/* Max ULP is 0.506. */
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goto ret;
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}
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else
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{
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/* First stage tan */
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if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a))
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{
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retval = y;
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goto ret;
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}
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/* tan */
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y = a + t2;
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retval = y;
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/* Max ULP is 0.506. */
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goto ret;
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}
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/* Second stage */
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/* Range reduction by algorithm ii */
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t = (x * hpinv.d + toint.d);
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xn = t - toint.d;
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v.d = t;
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t1 = (x - xn * mp1.d) - xn * mp2.d;
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n = v.i[LOW_HALF] & 0x00000001;
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da = xn * pp3.d;
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t = t1 - da;
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da = (t1 - t) - da;
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t1 = xn * pp4.d;
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a = t - t1;
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da = ((t - a) - t1) + da;
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/* Second stage */
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EADD (a, da, t1, t2);
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a = t1;
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da = t2;
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MUL2 (a, da, a, da, x2, xx2, t1, t2);
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c1 = a25.d + x2 * a27.d;
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c1 = a23.d + x2 * c1;
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c1 = a21.d + x2 * c1;
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c1 = a19.d + x2 * c1;
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c1 = a17.d + x2 * c1;
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c1 = a15.d + x2 * c1;
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c1 *= x2;
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ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
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ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
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if (n)
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{
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/* Second stage -cot */
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DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
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if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
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{
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retval = (-y);
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goto ret;
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}
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}
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else
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{
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/* Second stage tan */
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if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1))
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{
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retval = y;
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goto ret;
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}
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}
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retval = tanMp (x);
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goto ret;
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}
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/* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */
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/* First stage */
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i = ((int) (mfftnhf.d + TWO8 * ya));
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i = ((int) (mfftnhf.d + 256 * ya));
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z = (z0 = (ya - xfg[i][0].d)) + yya;
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z2 = z * z;
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pz = z + z * z2 * (e0.d + z2 * e1.d);
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@ -340,76 +186,20 @@ __tan (double x)
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{
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/* -cot */
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t2 = pz * (fi + gi) / (fi + pz);
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if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d))
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{
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retval = (-sy * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = gi * ua10.d + t3 * ub10.d;
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if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
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{
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retval = (-sy * y);
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goto ret;
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}
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y = gi - t2;
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retval = (-sy * y);
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/* Max ULP is 0.62. */
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goto ret;
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}
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else
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{
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/* tan */
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t2 = pz * (gi + fi) / (gi - pz);
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if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d))
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{
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retval = (sy * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = fi * ua9.d + t3 * ub9.d;
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if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
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{
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retval = (sy * y);
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goto ret;
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}
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y = fi + t2;
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retval = (sy * y);
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/* Max ULP is 0.62. */
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goto ret;
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}
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/* Second stage */
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ffi = xfg[i][3].d;
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EADD (z0, yya, z, zz)
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MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
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c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
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MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
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ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
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ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
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MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
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SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
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if (n)
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{
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/* -cot */
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DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
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if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3))
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{
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retval = (-sy * y);
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goto ret;
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}
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}
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else
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{
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/* tan */
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DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
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if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3))
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{
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retval = (sy * y);
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goto ret;
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}
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}
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retval = tanMp (x);
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goto ret;
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}
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/* (---) The case 25 < abs(x) <= 1e8 */
|
||||
@ -443,14 +233,7 @@ __tan (double x)
|
||||
sy = 1;
|
||||
}
|
||||
|
||||
/* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */
|
||||
if (ya <= gy1.d)
|
||||
{
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */
|
||||
/* (VIII) The case 25 < abs(x) <= 1e8, 0 < abs(y) <= 0.0608 */
|
||||
if (ya <= gy2.d)
|
||||
{
|
||||
a2 = a * a;
|
||||
@ -462,76 +245,26 @@ __tan (double x)
|
||||
|
||||
if (n)
|
||||
{
|
||||
/* First stage -cot */
|
||||
/* -cot */
|
||||
EADD (a, t2, b, db);
|
||||
DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
|
||||
if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c))
|
||||
{
|
||||
retval = (-y);
|
||||
goto ret;
|
||||
}
|
||||
y = c + dc;
|
||||
retval = (-y);
|
||||
/* Max ULP is 0.506. */
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* First stage tan */
|
||||
if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a))
|
||||
{
|
||||
retval = y;
|
||||
goto ret;
|
||||
}
|
||||
/* tan */
|
||||
y = a + t2;
|
||||
retval = y;
|
||||
/* Max ULP is 0.506. */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* Second stage */
|
||||
MUL2 (a, da, a, da, x2, xx2, t1, t2);
|
||||
c1 = a25.d + x2 * a27.d;
|
||||
c1 = a23.d + x2 * c1;
|
||||
c1 = a21.d + x2 * c1;
|
||||
c1 = a19.d + x2 * c1;
|
||||
c1 = a17.d + x2 * c1;
|
||||
c1 = a15.d + x2 * c1;
|
||||
c1 *= x2;
|
||||
|
||||
ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
|
||||
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
|
||||
|
||||
if (n)
|
||||
{
|
||||
/* Second stage -cot */
|
||||
DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
|
||||
if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2))
|
||||
{
|
||||
retval = (-y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* Second stage tan */
|
||||
if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1))
|
||||
{
|
||||
retval = (y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */
|
||||
/* First stage */
|
||||
i = ((int) (mfftnhf.d + TWO8 * ya));
|
||||
i = ((int) (mfftnhf.d + 256 * ya));
|
||||
z = (z0 = (ya - xfg[i][0].d)) + yya;
|
||||
z2 = z * z;
|
||||
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
||||
@ -542,75 +275,20 @@ __tan (double x)
|
||||
{
|
||||
/* -cot */
|
||||
t2 = pz * (fi + gi) / (fi + pz);
|
||||
if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||
t4 = gi * ua18.d + t3 * ub18.d;
|
||||
if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
y = gi - t2;
|
||||
retval = (-sy * y);
|
||||
/* Max ULP is 0.62. */
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* tan */
|
||||
t2 = pz * (gi + fi) / (gi - pz);
|
||||
if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||
t4 = fi * ua17.d + t3 * ub17.d;
|
||||
if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
y = fi + t2;
|
||||
retval = (sy * y);
|
||||
/* Max ULP is 0.62. */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* Second stage */
|
||||
ffi = xfg[i][3].d;
|
||||
EADD (z0, yya, z, zz);
|
||||
MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
|
||||
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
||||
ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
|
||||
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
|
||||
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
|
||||
ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
|
||||
|
||||
ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
|
||||
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
|
||||
|
||||
if (n)
|
||||
{
|
||||
/* -cot */
|
||||
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
|
||||
if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* tan */
|
||||
DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
|
||||
if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* (---) The case 1e8 < abs(x) < 2**1024 */
|
||||
@ -632,14 +310,7 @@ __tan (double x)
|
||||
sy = 1;
|
||||
}
|
||||
|
||||
/* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */
|
||||
if (ya <= gy1.d)
|
||||
{
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */
|
||||
/* (X) The case 1e8 < abs(x) < 2**1024, 0 < abs(y) <= 0.0608 */
|
||||
if (ya <= gy2.d)
|
||||
{
|
||||
a2 = a * a;
|
||||
@ -650,85 +321,26 @@ __tan (double x)
|
||||
t2 = da + a * a2 * t2;
|
||||
if (n)
|
||||
{
|
||||
/* First stage -cot */
|
||||
/* -cot */
|
||||
EADD (a, t2, b, db);
|
||||
DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
|
||||
if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c))
|
||||
{
|
||||
retval = (-y);
|
||||
goto ret;
|
||||
}
|
||||
y = c + dc;
|
||||
retval = (-y);
|
||||
/* Max ULP is 0.506. */
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* First stage tan */
|
||||
if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a))
|
||||
{
|
||||
retval = y;
|
||||
goto ret;
|
||||
}
|
||||
/* tan */
|
||||
y = a + t2;
|
||||
retval = y;
|
||||
/* Max ULP is 0.507. */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* Second stage */
|
||||
/* Reduction by algorithm iv */
|
||||
p = 10;
|
||||
n = (__mpranred (x, &mpa, p)) & 0x00000001;
|
||||
__mp_dbl (&mpa, &a, p);
|
||||
__dbl_mp (a, &mpt1, p);
|
||||
__sub (&mpa, &mpt1, &mpt2, p);
|
||||
__mp_dbl (&mpt2, &da, p);
|
||||
|
||||
MUL2 (a, da, a, da, x2, xx2, t1, t2);
|
||||
|
||||
c1 = a25.d + x2 * a27.d;
|
||||
c1 = a23.d + x2 * c1;
|
||||
c1 = a21.d + x2 * c1;
|
||||
c1 = a19.d + x2 * c1;
|
||||
c1 = a17.d + x2 * c1;
|
||||
c1 = a15.d + x2 * c1;
|
||||
c1 *= x2;
|
||||
|
||||
ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
|
||||
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
|
||||
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
|
||||
|
||||
if (n)
|
||||
{
|
||||
/* Second stage -cot */
|
||||
DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
|
||||
if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2))
|
||||
{
|
||||
retval = (-y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* Second stage tan */
|
||||
if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1))
|
||||
{
|
||||
retval = y;
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */
|
||||
/* First stage */
|
||||
i = ((int) (mfftnhf.d + TWO8 * ya));
|
||||
i = ((int) (mfftnhf.d + 256 * ya));
|
||||
z = (z0 = (ya - xfg[i][0].d)) + yya;
|
||||
z2 = z * z;
|
||||
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
||||
@ -739,97 +351,25 @@ __tan (double x)
|
||||
{
|
||||
/* -cot */
|
||||
t2 = pz * (fi + gi) / (fi + pz);
|
||||
if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||
t4 = gi * ua26.d + t3 * ub26.d;
|
||||
if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
y = gi - t2;
|
||||
retval = (-sy * y);
|
||||
/* Max ULP is 0.62. */
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* tan */
|
||||
t2 = pz * (gi + fi) / (gi - pz);
|
||||
if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||
t4 = fi * ua25.d + t3 * ub25.d;
|
||||
if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
y = fi + t2;
|
||||
retval = (sy * y);
|
||||
/* Max ULP is 0.62. */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* Second stage */
|
||||
ffi = xfg[i][3].d;
|
||||
EADD (z0, yya, z, zz);
|
||||
MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
|
||||
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
||||
ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
|
||||
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
|
||||
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
|
||||
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
|
||||
ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
|
||||
|
||||
ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
|
||||
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
|
||||
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
|
||||
|
||||
if (n)
|
||||
{
|
||||
/* -cot */
|
||||
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
|
||||
if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3))
|
||||
{
|
||||
retval = (-sy * y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* tan */
|
||||
DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
|
||||
if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3))
|
||||
{
|
||||
retval = (sy * y);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
retval = tanMp (x);
|
||||
goto ret;
|
||||
|
||||
ret:
|
||||
return retval;
|
||||
}
|
||||
|
||||
/* multiple precision stage */
|
||||
/* Convert x to multi precision number,compute tan(x) by mptan() routine */
|
||||
/* and converts result back to double */
|
||||
static double
|
||||
SECTION
|
||||
tanMp (double x)
|
||||
{
|
||||
int p;
|
||||
double y;
|
||||
mp_no mpy;
|
||||
p = 32;
|
||||
__mptan (x, &mpy, p);
|
||||
__mp_dbl (&mpy, &y, p);
|
||||
LIBC_PROBE (slowtan, 2, &x, &y);
|
||||
return y;
|
||||
}
|
||||
|
||||
#ifndef __tan
|
||||
libm_alias_double (__tan, tan)
|
||||
#endif
|
||||
|
||||
@ -28,7 +28,7 @@
|
||||
#define UTAN_H
|
||||
|
||||
#ifdef BIG_ENDI
|
||||
static const number
|
||||
static const mynumber
|
||||
/* polynomial I */
|
||||
/**/ d3 = {{0x3FD55555, 0x55555555} }, /* 0.333... */
|
||||
/**/ d5 = {{0x3FC11111, 0x111107C6} }, /* 0.133... */
|
||||
@ -36,46 +36,6 @@
|
||||
/**/ d9 = {{0x3F9664ED, 0x49CFC666} }, /* . */
|
||||
/**/ d11 = {{0x3F82385A, 0x3CF2E4EA} }, /* . */
|
||||
/* polynomial II */
|
||||
/**/ a3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */
|
||||
/**/ aa3 = {{0x3c755555, 0x55555555} }, /* 1/3-a3 */
|
||||
/**/ a5 = {{0x3fc11111, 0x11111111} }, /* 2/15 */
|
||||
/**/ aa5 = {{0x3c411111, 0x11111111} }, /* 2/15-a5 */
|
||||
/**/ a7 = {{0x3faba1ba, 0x1ba1ba1c} }, /* 17/315 */
|
||||
/**/ aa7 = {{0xbc479179, 0x17917918} }, /* ()-a7 */
|
||||
/**/ a9 = {{0x3f9664f4, 0x882c10fa} }, /* 62/2835 */
|
||||
/**/ aa9 = {{0xbc09a528, 0x8b6c44fd} }, /* ()-a9 */
|
||||
/**/ a11 = {{0x3f8226e3, 0x55e6c23d} }, /* . */
|
||||
/**/ aa11 = {{0xbc2c292b, 0x8f1a2c13} }, /* . */
|
||||
/**/ a13 = {{0x3f6d6d3d, 0x0e157de0} }, /* . */
|
||||
/**/ aa13 = {{0xbc0280cf, 0xc968d971} }, /* . */
|
||||
/**/ a15 = {{0x3f57da36, 0x452b75e3} }, /* . */
|
||||
#if 0
|
||||
/**/ aa15 = {{0xbbf25789, 0xb285d2ed} }, /* . */
|
||||
#endif
|
||||
/**/ a17 = {{0x3f435582, 0x48036744} }, /* . */
|
||||
#if 0
|
||||
/**/ aa17 = {{0x3be488d9, 0x563f1f23} }, /* . */
|
||||
#endif
|
||||
/**/ a19 = {{0x3f2f57d7, 0x734d1664} }, /* . */
|
||||
#if 0
|
||||
/**/ aa19 = {{0x3bb0d55a, 0x913ccb50} }, /* . */
|
||||
#endif
|
||||
/**/ a21 = {{0x3f1967e1, 0x8afcafad} }, /* . */
|
||||
#if 0
|
||||
/**/ aa21 = {{0xbbbd7614, 0xa42d44e6} }, /* . */
|
||||
#endif
|
||||
/**/ a23 = {{0x3f0497d8, 0xeea25259} }, /* . */
|
||||
#if 0
|
||||
/**/ aa23 = {{0x3b99f2d0, 0x2e4d2863} }, /* . */
|
||||
#endif
|
||||
/**/ a25 = {{0x3ef0b132, 0xd39a6050} }, /* . */
|
||||
#if 0
|
||||
/**/ aa25 = {{0x3b93b274, 0xc2c19614} }, /* . */
|
||||
#endif
|
||||
/**/ a27 = {{0x3edb0f72, 0xd3ee24e9} }, /* . */
|
||||
#if 0
|
||||
/**/ aa27 = {{0x3b61688d, 0xdd595609} }, /* . */
|
||||
#endif
|
||||
/* polynomial III */
|
||||
/**/ e0 = {{0x3FD55555, 0x55554DBD} }, /* . */
|
||||
/**/ e1 = {{0x3FC11112, 0xE0A6B45F} }, /* . */
|
||||
@ -88,52 +48,8 @@
|
||||
/**/ g3 = {{0x3fe92f1a, 0x00000000} }, /* 0.787 */
|
||||
/**/ g4 = {{0x40390000, 0x00000000} }, /* 25.0 */
|
||||
/**/ g5 = {{0x4197d784, 0x00000000} }, /* 1e8 */
|
||||
/**/ gy1 = {{0x3e7ad7f2, 0x9abcaf48} }, /* 1e-7 */
|
||||
/**/ gy2 = {{0x3faf212d, 0x00000000} }, /* 0.0608 */
|
||||
|
||||
/**/ u1 = {{0x3cc8c33a, 0x00000000} }, /* 6.873e-16 */
|
||||
/**/ u2 = {{0x3983dc4d, 0x00000000} }, /* 1.224e-31 */
|
||||
/**/ u3 = {{0x3c78e14b, 0x00000000} }, /* 2.158e-17 */
|
||||
/**/ ua3 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
|
||||
/**/ ub3 = {{0x3cc81898, 0x00000000} }, /* 6.688e-16 */
|
||||
/**/ u4 = {{0x399856c2, 0x00000000} }, /* 3e-31 */
|
||||
/**/ u5 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */
|
||||
/**/ u6 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */
|
||||
/**/ u7 = {{0x39903beb, 0x00000000} }, /* 2.001e-31 */
|
||||
/**/ u8 = {{0x399c56ae, 0x00000000} }, /* 3.493e-31 */
|
||||
/**/ u9 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
|
||||
/**/ ua9 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
|
||||
/**/ ub9 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
|
||||
/**/ u10 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
|
||||
/**/ ua10 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
|
||||
/**/ ub10 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
|
||||
/**/ u11 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */
|
||||
/**/ u12 = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */
|
||||
/**/ u13 = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */
|
||||
/**/ u14 = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */
|
||||
/**/ u15 = {{0x3ab5767a, 0x00000000} }, /* 6.935e-26 */
|
||||
/**/ u16 = {{0x3ab57744, 0x00000000} }, /* 6.936e-26 */
|
||||
/**/ u17 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
|
||||
/**/ ua17 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */
|
||||
/**/ ub17 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
|
||||
/**/ u18 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
|
||||
/**/ ua18 = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */
|
||||
/**/ ub18 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
|
||||
/**/ u19 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */
|
||||
/**/ u20 = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */
|
||||
/**/ u21 = {{0x3c3bb9b8, 0x00000000} }, /* 1.503e-18 */
|
||||
/**/ u22 = {{0x3c392e08, 0x00000000} }, /* 1.365e-18 */
|
||||
/**/ u23 = {{0x3a0ce706, 0x00000000} }, /* 4.560e-29 */
|
||||
/**/ u24 = {{0x3a0cff5d, 0x00000000} }, /* 4.575e-29 */
|
||||
/**/ u25 = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
|
||||
/**/ ua25 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
|
||||
/**/ ub25 = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
|
||||
/**/ u26 = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
|
||||
/**/ ua26 = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
|
||||
/**/ ub26 = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
|
||||
/**/ u27 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */
|
||||
/**/ u28 = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */
|
||||
|
||||
/**/ mp1 = {{0x3FF921FB, 0x58000000} },
|
||||
/**/ mp2 = {{0xBE4DDE97, 0x3C000000} },
|
||||
/**/ mp3 = {{0xBC8CB3B3, 0x99D747F2} },
|
||||
@ -145,7 +61,7 @@
|
||||
#else
|
||||
#ifdef LITTLE_ENDI
|
||||
|
||||
static const number
|
||||
static const mynumber
|
||||
/* polynomial I */
|
||||
/**/ d3 = {{0x55555555, 0x3FD55555} }, /* 0.333... */
|
||||
/**/ d5 = {{0x111107C6, 0x3FC11111} }, /* 0.133... */
|
||||
@ -153,46 +69,6 @@
|
||||
/**/ d9 = {{0x49CFC666, 0x3F9664ED} }, /* . */
|
||||
/**/ d11 = {{0x3CF2E4EA, 0x3F82385A} }, /* . */
|
||||
/* polynomial II */
|
||||
/**/ a3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */
|
||||
/**/ aa3 = {{0x55555555, 0x3c755555} }, /* 1/3-a3 */
|
||||
/**/ a5 = {{0x11111111, 0x3fc11111} }, /* 2/15 */
|
||||
/**/ aa5 = {{0x11111111, 0x3c411111} }, /* 2/15-a5 */
|
||||
/**/ a7 = {{0x1ba1ba1c, 0x3faba1ba} }, /* 17/315 */
|
||||
/**/ aa7 = {{0x17917918, 0xbc479179} }, /* ()-a7 */
|
||||
/**/ a9 = {{0x882c10fa, 0x3f9664f4} }, /* 62/2835 */
|
||||
/**/ aa9 = {{0x8b6c44fd, 0xbc09a528} }, /* ()-a9 */
|
||||
/**/ a11 = {{0x55e6c23d, 0x3f8226e3} }, /* . */
|
||||
/**/ aa11 = {{0x8f1a2c13, 0xbc2c292b} }, /* . */
|
||||
/**/ a13 = {{0x0e157de0, 0x3f6d6d3d} }, /* . */
|
||||
/**/ aa13 = {{0xc968d971, 0xbc0280cf} }, /* . */
|
||||
/**/ a15 = {{0x452b75e3, 0x3f57da36} }, /* . */
|
||||
#if 0
|
||||
/**/ aa15 = {{0xb285d2ed, 0xbbf25789} }, /* . */
|
||||
#endif
|
||||
/**/ a17 = {{0x48036744, 0x3f435582} }, /* . */
|
||||
#if 0
|
||||
/**/ aa17 = {{0x563f1f23, 0x3be488d9} }, /* . */
|
||||
#endif
|
||||
/**/ a19 = {{0x734d1664, 0x3f2f57d7} }, /* . */
|
||||
#if 0
|
||||
/**/ aa19 = {{0x913ccb50, 0x3bb0d55a} }, /* . */
|
||||
#endif
|
||||
/**/ a21 = {{0x8afcafad, 0x3f1967e1} }, /* . */
|
||||
#if 0
|
||||
/**/ aa21 = {{0xa42d44e6, 0xbbbd7614} }, /* . */
|
||||
#endif
|
||||
/**/ a23 = {{0xeea25259, 0x3f0497d8} }, /* . */
|
||||
#if 0
|
||||
/**/ aa23 = {{0x2e4d2863, 0x3b99f2d0} }, /* . */
|
||||
#endif
|
||||
/**/ a25 = {{0xd39a6050, 0x3ef0b132} }, /* . */
|
||||
#if 0
|
||||
/**/ aa25 = {{0xc2c19614, 0x3b93b274} }, /* . */
|
||||
#endif
|
||||
/**/ a27 = {{0xd3ee24e9, 0x3edb0f72} }, /* . */
|
||||
#if 0
|
||||
/**/ aa27 = {{0xdd595609, 0x3b61688d} }, /* . */
|
||||
#endif
|
||||
/* polynomial III */
|
||||
/**/ e0 = {{0x55554DBD, 0x3FD55555} }, /* . */
|
||||
/**/ e1 = {{0xE0A6B45F, 0x3FC11112} }, /* . */
|
||||
@ -205,52 +81,8 @@
|
||||
/**/ g3 = {{0x00000000, 0x3fe92f1a} }, /* 0.787 */
|
||||
/**/ g4 = {{0x00000000, 0x40390000} }, /* 25.0 */
|
||||
/**/ g5 = {{0x00000000, 0x4197d784} }, /* 1e8 */
|
||||
/**/ gy1 = {{0x9abcaf48, 0x3e7ad7f2} }, /* 1e-7 */
|
||||
/**/ gy2 = {{0x00000000, 0x3faf212d} }, /* 0.0608 */
|
||||
|
||||
/**/ u1 = {{0x00000000, 0x3cc8c33a} }, /* 6.873e-16 */
|
||||
/**/ u2 = {{0x00000000, 0x3983dc4d} }, /* 1.224e-31 */
|
||||
/**/ u3 = {{0x00000000, 0x3c78e14b} }, /* 2.158e-17 */
|
||||
/**/ ua3 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
|
||||
/**/ ub3 = {{0x00000000, 0x3cc81898} }, /* 6.688e-16 */
|
||||
/**/ u4 = {{0x00000000, 0x399856c2} }, /* 3e-31 */
|
||||
/**/ u5 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */
|
||||
/**/ u6 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */
|
||||
/**/ u7 = {{0x00000000, 0x39903beb} }, /* 2.001e-31 */
|
||||
/**/ u8 = {{0x00000000, 0x399c56ae} }, /* 3.493e-31 */
|
||||
/**/ u9 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
|
||||
/**/ ua9 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
|
||||
/**/ ub9 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
|
||||
/**/ u10 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
|
||||
/**/ ua10 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
|
||||
/**/ ub10 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
|
||||
/**/ u11 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */
|
||||
/**/ u12 = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */
|
||||
/**/ u13 = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */
|
||||
/**/ u14 = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */
|
||||
/**/ u15 = {{0x00000000, 0x3ab5767a} }, /* 6.935e-26 */
|
||||
/**/ u16 = {{0x00000000, 0x3ab57744} }, /* 6.936e-26 */
|
||||
/**/ u17 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
|
||||
/**/ ua17 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */
|
||||
/**/ ub17 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
|
||||
/**/ u18 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
|
||||
/**/ ua18 = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */
|
||||
/**/ ub18 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
|
||||
/**/ u19 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */
|
||||
/**/ u20 = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */
|
||||
/**/ u21 = {{0x00000000, 0x3c3bb9b8} }, /* 1.503e-18 */
|
||||
/**/ u22 = {{0x00000000, 0x3c392e08} }, /* 1.365e-18 */
|
||||
/**/ u23 = {{0x00000000, 0x3a0ce706} }, /* 4.560e-29 */
|
||||
/**/ u24 = {{0x00000000, 0x3a0cff5d} }, /* 4.575e-29 */
|
||||
/**/ u25 = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
|
||||
/**/ ua25 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
|
||||
/**/ ub25 = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
|
||||
/**/ u26 = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
|
||||
/**/ ua26 = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
|
||||
/**/ ub26 = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
|
||||
/**/ u27 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */
|
||||
/**/ u28 = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */
|
||||
|
||||
/**/ mp1 = {{0x58000000, 0x3FF921FB} },
|
||||
/**/ mp2 = {{0x3C000000, 0xBE4DDE97} },
|
||||
/**/ mp3 = {{0x99D747F2, 0xBC8CB3B3} },
|
||||
|
||||
@ -23,7 +23,7 @@
|
||||
|
||||
|
||||
#ifdef BIG_ENDI
|
||||
static const number
|
||||
static const mynumber
|
||||
xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */
|
||||
/**/ {{{0x3fb00000, 0x1e519d60} },
|
||||
/**/ {{0x3fb00557, 0x96c4e240} },
|
||||
@ -773,7 +773,7 @@ static const number
|
||||
|
||||
#else
|
||||
#ifdef LITTLE_ENDI
|
||||
static const number
|
||||
static const mynumber
|
||||
xfg[186][4] = { /* xi,Fi,Gi,FFi, i=16..201 */
|
||||
/**/ {{{0x1e519d60, 0x3fb00000} },
|
||||
/**/ {{0x96c4e240, 0x3fb00557} },
|
||||
|
||||
Loading…
Reference in New Issue
Block a user