@@ -29,7 +29,7 @@
#define M 4
#ifdef BIG_ENDI
- static const number
+ static const mynumber
/* polynomial I */
/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */
/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */
@@ -79,7 +79,7 @@
#else
#ifdef LITTLE_ENDI
- static const number
+ static const mynumber
/* polynomial I */
/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */
/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */
@@ -20,25 +20,15 @@
/* MODULE_NAME: atnat.c */
/* */
/* FUNCTIONS: uatan */
-/* atanMp */
/* signArctan */
/* */
-/* */
-/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
-/* mpatan.c mpatan2.c mpsqrt.c */
+/* FILES NEEDED: dla.h endian.h mydefs.h atnat.h */
/* uatan.tbl */
/* */
-/* An ultimate atan() routine. Given an IEEE double machine number x */
-/* it computes the correctly rounded (to nearest) value of atan(x). */
-/* */
-/* Assumption: Machine arithmetic operations are performed in */
-/* round to nearest mode of IEEE 754 standard. */
-/* */
/************************************************************************/
#include <dla.h>
-#include "mpa.h"
-#include "MathLib.h"
+#include "mydefs.h"
#include "uatan.tbl"
#include "atnat.h"
#include <fenv.h>
@@ -47,10 +37,8 @@
#include <math.h>
#include <fenv_private.h>
#include <math-underflow.h>
-#include <stap-probe.h>
-void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */
-static double atanMp (double, const int[]);
+#define TWO52 0x1.0p52
/* Fix the sign of y and return */
static double
@@ -60,16 +48,13 @@ __signArctan (double x, double y)
}
-/* An ultimate atan() routine. Given an IEEE double machine number x, */
-/* routine computes the correctly rounded (to nearest) value of atan(x). */
double
__atan (double x)
{
- double cor, s1, ss1, s2, ss2, t1, t2, t3, t4, u, u2, u3,
- v, vv, w, ww, y, yy, z, zz;
+ double cor, t1, t2, t3, u,
+ v, w, ww, y, yy, z;
int i, ux, dx;
- static const int pr[M] = { 6, 8, 10, 32 };
- number num;
+ mynumber num;
num.d = x;
ux = num.i[HIGH_HALF];
@@ -102,36 +87,14 @@ __atan (double x)
yy = d3.d + v * yy;
yy *= x * v;
- if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
- return y;
-
- EMULV (x, x, v, vv); /* v+vv=x^2 */
-
- s1 = f17.d + v * f19.d;
- s1 = f15.d + v * s1;
- s1 = f13.d + v * s1;
- s1 = f11.d + v * s1;
- s1 *= v;
-
- ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2);
- ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
- if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
- return y;
-
- return atanMp (x, pr);
+ y = x + yy;
+ /* Max ULP is 0.511. */
+ return y;
}
}
else
{ /* B <= u < C */
- i = (TWO52 + TWO8 * u) - TWO52;
+ i = (TWO52 + 256 * u) - TWO52;
i -= 16;
z = u - cij[i][0].d;
yy = cij[i][5].d + z * cij[i][6].d;
@@ -141,44 +104,9 @@ __atan (double x)
yy *= z;
t1 = cij[i][1].d;
- if (i < 112)
- {
- if (i < 48)
- u2 = U21; /* u < 1/4 */
- else
- u2 = U22;
- } /* 1/4 <= u < 1/2 */
- else
- {
- if (i < 176)
- u2 = U23; /* 1/2 <= u < 3/4 */
- else
- u2 = U24;
- } /* 3/4 <= u <= 1 */
- if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
- return __signArctan (x, y);
-
- z = u - hij[i][0].d;
-
- s1 = hij[i][14].d + z * hij[i][15].d;
- s1 = hij[i][13].d + z * s1;
- s1 = hij[i][12].d + z * s1;
- s1 = hij[i][11].d + z * s1;
- s1 *= z;
-
- ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
- MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
- if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
- return __signArctan (x, y);
-
- return atanMp (x, pr);
+ y = t1 + yy;
+ /* Max ULP is 0.56. */
+ return __signArctan (x, y);
}
}
else
@@ -188,7 +116,7 @@ __atan (double x)
w = 1 / u;
EMULV (w, u, t1, t2);
ww = w * ((1 - t1) - t2);
- i = (TWO52 + TWO8 * w) - TWO52;
+ i = (TWO52 + 256 * w) - TWO52;
i -= 16;
z = (w - cij[i][0].d) + ww;
@@ -199,37 +127,9 @@ __atan (double x)
yy = HPI1 - z * yy;
t1 = HPI - cij[i][1].d;
- if (i < 112)
- u3 = U31; /* w < 1/2 */
- else
- u3 = U32; /* w >= 1/2 */
- if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
- return __signArctan (x, y);
-
- DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
- t1 = w - hij[i][0].d;
- EADD (t1, ww, z, zz);
-
- s1 = hij[i][14].d + z * hij[i][15].d;
- s1 = hij[i][13].d + z * s1;
- s1 = hij[i][12].d + z * s1;
- s1 = hij[i][11].d + z * s1;
- s1 *= z;
-
- ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
- MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
- ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
- SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
- if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
- return __signArctan (x, y);
-
- return atanMp (x, pr);
+ y = t1 + yy;
+ /* Max ULP is 0.503. */
+ return __signArctan (x, y);
}
else
{
@@ -249,34 +149,9 @@ __atan (double x)
ww = w * ((1 - t1) - t2);
ESUB (HPI, w, t3, cor);
yy = ((HPI1 + cor) - ww) - yy;
- if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
- return __signArctan (x, y);
-
- DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
- MUL2 (w, ww, w, ww, v, vv, t1, t2);
-
- s1 = f17.d + v * f19.d;
- s1 = f15.d + v * s1;
- s1 = f13.d + v * s1;
- s1 = f11.d + v * s1;
- s1 *= v;
-
- ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
- MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
- MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2);
- ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
- SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);
-
- if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
- return __signArctan (x, y);
-
- return atanMp (x, pr);
+ y = t3 + yy;
+ /* Max ULP is 0.5003. */
+ return __signArctan (x, y);
}
else
{
@@ -290,35 +165,6 @@ __atan (double x)
}
}
- /* Final stages. Compute atan(x) by multiple precision arithmetic */
-static double
-atanMp (double x, const int pr[])
-{
- mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
- double y1, y2;
- int i, p;
-
- for (i = 0; i < M; i++)
- {
- p = pr[i];
- __dbl_mp (x, &mpx, p);
- __mpatan (&mpx, &mpy, p);
- __dbl_mp (u9[i].d, &mpt1, p);
- __mul (&mpy, &mpt1, &mperr, p);
- __add (&mpy, &mperr, &mpy1, p);
- __sub (&mpy, &mperr, &mpy2, p);
- __mp_dbl (&mpy1, &y1, p);
- __mp_dbl (&mpy2, &y2, p);
- if (y1 == y2)
- {
- LIBC_PROBE (slowatan, 3, &p, &x, &y1);
- return y1;
- }
- }
- LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
- return y1; /*if impossible to do exact computing */
-}
-
#ifndef __atan
libm_alias_double (__atan, atan)
#endif
@@ -25,7 +25,7 @@
#ifdef BIG_ENDI
- static const number
+ static const mynumber
cij[241][7] = { /* x0,cij for (1/16,1) */
/**/ {{{0X3FB04006, 0X65E0244E} },
/**/ {{0X3FB03A73, 0X7B53DD20} },
@@ -1716,7 +1716,7 @@
/**/ {{0XBF99B9A7, 0X18A3BA58} } },
};
- static const number
+ static const mynumber
hij[241][16] = { /* x0,hij for (1/16,1) */
/**/ {{{0x3fb04000, 0x00000000} },
/**/ {{0x3fb03a6d, 0x1c06693d} },
@@ -5579,7 +5579,7 @@
#else
#ifdef LITTLE_ENDI
- static const number
+ static const mynumber
cij[241][7] = { /* x0,cij for (1/16,1) */
/**/ {{{0X65E0244E, 0X3FB04006} },
/**/ {{0X7B53DD20, 0X3FB03A73} },
@@ -7270,7 +7270,7 @@
/**/ {{0X18A3BA58, 0XBF99B9A7} } },
};
- static const number
+ static const mynumber
hij[241][16] = { /* x0,hij for (1/16,1) */
/**/ {{{0x00000000, 0x3fb04000} },
/**/ {{0x1c06693d, 0x3fb03a6d} },