@@ -39,6 +39,7 @@
#include <dla.h>
#include "mpa.h"
#include "MathLib.h"
+#include "mydefs.h"
#include "uatan.tbl"
#include "atnat2.h"
#include <fenv.h>
@@ -28,7 +28,7 @@
#define MY_H
typedef int int4;
-typedef union { int4 i[2]; double x; } mynumber;
+typedef union { int4 i[2]; double x; double d; } mynumber;
#define max(x, y) (((y) > (x)) ? (y) : (x))
#define min(x, y) (((y) < (x)) ? (y) : (x))
@@ -20,40 +20,29 @@
/* MODULE_NAME: utan.c */
/* */
/* FUNCTIONS: utan */
-/* tanMp */
/* */
-/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */
-/* branred.c sincos32.c mptan.c */
+/* FILES NEEDED:dla.h endian.h mydefs.h utan.h */
+/* branred.c */
/* utan.tbl */
/* */
-/* An ultimate tan routine. Given an IEEE double machine number x */
-/* it computes the correctly rounded (to nearest) value of tan(x). */
-/* Assumption: Machine arithmetic operations are performed in */
-/* round to nearest mode of IEEE 754 standard. */
-/* */
/*********************************************************************/
#include <errno.h>
#include <float.h>
#include "endian.h"
#include <dla.h>
-#include "mpa.h"
-#include "MathLib.h"
+#include "mydefs.h"
#include <math.h>
#include <math_private.h>
#include <fenv_private.h>
#include <math-underflow.h>
#include <libm-alias-double.h>
#include <fenv.h>
-#include <stap-probe.h>
#ifndef SECTION
# define SECTION
#endif
-static double tanMp (double);
-void __mptan (double, mp_no *, int);
-
double
SECTION
__tan (double x)
@@ -62,17 +51,14 @@ __tan (double x)
#include "utan.tbl"
int ux, i, n;
- double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz,
- s, sy, t, t1, t2, t3, t4, w, x2, xn, xx2, y, ya,
- yya, z0, z, zz, z2, zz2;
- int p;
- number num, v;
- mp_no mpa, mpt1, mpt2;
+ double a, da, a2, b, db, c, dc, fi, gi, pz,
+ s, sy, t, t1, t2, t3, t4, w, x2, xn, y, ya,
+ yya, z0, z, z2;
+ mynumber num, v;
double retval;
int __branred (double, double *, double *);
- int __mpranred (double, mp_no *, int);
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
@@ -100,7 +86,6 @@ __tan (double x)
/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
if (w <= g2.d)
{
- /* First stage */
x2 = x * x;
t2 = d9.d + x2 * d11.d;
@@ -109,50 +94,16 @@ __tan (double x)
t2 = d3.d + x2 * t2;
t2 *= x * x2;
- if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
- {
- retval = y;
- goto ret;
- }
-
- /* Second stage */
- 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;
-
- EMULV (x, x, x2, xx2);
- 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 (x, 0.0, c1, cc1, c2, cc2, t1, t2);
- ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
- if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
- {
- retval = y;
- goto ret;
- }
- retval = tanMp (x);
+ y = x + t2;
+ retval = y;
+ /* Max ULP is 0.504. */
goto ret;
}
/* (III) The case 0.0608 < abs(x) <= 0.787 */
if (w <= g3.d)
{
- /* First stage */
- i = ((int) (mfftnhf.d + TWO8 * w));
+ i = ((int) (mfftnhf.d + 256 * w));
z = w - xfg[i][0].d;
z2 = z * z;
s = (x < 0.0) ? -1 : 1;
@@ -160,41 +111,9 @@ __tan (double x)
fi = xfg[i][1].d;
gi = xfg[i][2].d;
t2 = pz * (gi + fi) / (gi - pz);
- if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d))
- {
- retval = (s * y);
- goto ret;
- }
- t3 = (t2 < 0.0) ? -t2 : t2;
- t4 = fi * ua3.d + t3 * ub3.d;
- if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
- {
- retval = (s * y);
- goto ret;
- }
-
- /* Second stage */
- ffi = xfg[i][3].d;
- c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
- EMULV (z, z, z2, zz2);
- 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, 0.0, c1, cc1, c2, cc2, t1, t2);
- ADD2 (z, 0.0, 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);
- DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
-
- if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
- {
- retval = (s * y);
- goto ret;
- }
- retval = tanMp (x);
+ y = fi + t2;
+ retval = (s * y);
+ /* Max ULP is 0.60. */
goto ret;
}
@@ -223,14 +142,7 @@ __tan (double x)
sy = 1;
}
- /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
- if (ya <= gy1.d)
- {
- retval = tanMp (x);
- goto ret;
- }
-
- /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
+ /* (VI) The case 0.787 < abs(x) <= 25, 0 < abs(y) <= 0.0608 */
if (ya <= gy2.d)
{
a2 = a * a;
@@ -242,94 +154,27 @@ __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 - u6.d * c)) == c + (dc + u6.d * c))
- {
- retval = (-y);
- goto ret;
- }
- }
- else
- {
- /* First stage tan */
- if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a))
- {
- retval = y;
- goto ret;
- }
- }
- /* Second stage */
- /* Range reduction by algorithm ii */
- t = (x * hpinv.d + toint.d);
- xn = t - toint.d;
- v.d = t;
- t1 = (x - xn * mp1.d) - xn * mp2.d;
- n = v.i[LOW_HALF] & 0x00000001;
- da = xn * pp3.d;
- t = t1 - da;
- da = (t1 - t) - da;
- t1 = xn * pp4.d;
- a = t - t1;
- da = ((t - a) - t1) + da;
-
- /* Second stage */
- EADD (a, da, t1, t2);
- a = t1;
- da = t2;
- 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 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
- {
- retval = (-y);
- goto ret;
- }
+ y = c + dc;
+ retval = (-y);
+ /* Max ULP is 0.506. */
+ goto ret;
}
else
{
- /* Second stage tan */
- if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1))
- {
- retval = y;
- goto ret;
- }
+ /* tan */
+ y = a + t2;
+ retval = y;
+ /* Max ULP is 0.506. */
+ goto ret;
}
- retval = tanMp (x);
- goto ret;
}
/* (VII) The case 0.787 < abs(x) <= 25, 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);
@@ -340,76 +185,20 @@ __tan (double x)
{
/* -cot */
t2 = pz * (fi + gi) / (fi + pz);
- if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d))
- {
- retval = (-sy * y);
- goto ret;
- }
- t3 = (t2 < 0.0) ? -t2 : t2;
- t4 = gi * ua10.d + t3 * ub10.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 * u9.d)) == fi + (t2 + fi * u9.d))
- {
- retval = (sy * y);
- goto ret;
- }
- t3 = (t2 < 0.0) ? -t2 : t2;
- t4 = fi * ua9.d + t3 * ub9.d;
- if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
- {
- retval = (sy * y);
- 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 - u12.d * c3)) == c3 + (cc3 + u12.d * c3))
- {
- retval = (-sy * y);
- goto ret;
- }
- }
- else
- {
- /* tan */
- DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
- if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3))
- {
- retval = (sy * y);
- goto ret;
- }
+ y = fi + t2;
+ retval = (sy * y);
+ /* Max ULP is 0.62. */
+ goto ret;
}
-
- retval = tanMp (x);
- goto ret;
}
/* (---) The case 25 < abs(x) <= 1e8 */
@@ -443,14 +232,7 @@ __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 +244,26 @@ __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;
- }
- }
- else
- {
- /* First stage tan */
- if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a))
- {
- retval = y;
- 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;
- }
+ y = c + dc;
+ retval = (-y);
+ /* Max ULP is 0.506. */
+ goto ret;
}
else
{
- /* Second stage tan */
- if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1))
- {
- retval = (y);
- goto ret;
- }
+ /* tan */
+ y = a + t2;
+ retval = y;
+ /* Max ULP is 0.506. */
+ 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 +274,20 @@ __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;
- }
- }
-
- /* 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;
- }
+ y = fi + t2;
+ retval = (sy * y);
+ /* Max ULP is 0.62. */
+ goto ret;
}
- retval = tanMp (x);
- goto ret;
}
/* (---) The case 1e8 < abs(x) < 2**1024 */
@@ -632,14 +309,7 @@ __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 +320,26 @@ __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;
- }
- }
- else
- {
- /* First stage tan */
- if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a))
- {
- retval = y;
- 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;
- }
+ y = c + dc;
+ retval = (-y);
+ /* Max ULP is 0.506. */
+ goto ret;
}
else
{
- /* Second stage tan */
- if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1))
- {
- retval = y;
- goto ret;
- }
+ /* tan */
+ y = a + t2;
+ retval = y;
+ /* Max ULP is 0.507. */
+ 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 +350,25 @@ __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;
- }
- }
-
- /* 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;
- }
+ y = fi + t2;
+ retval = (sy * y);
+ /* Max ULP is 0.62. */
+ 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} },