return atan(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__invtrigl.h"
-#define ATAN_CONST (BIAS + 65) /* 2**65 */
-#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
-static const long double huge = 1.0e300;
+#if LDBL_MANT_DIG == 64
+#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff))
static const long double atanhi[] = {
4.63647609000806116202e-01L,
return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
x * (aT[9] + x * aT[11]))));
}
+#elif LDBL_MANT_DIG == 113
+#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8)
+
+static const long double atanhi[] = {
+ 4.63647609000806116214256231461214397e-01L,
+ 7.85398163397448309615660845819875699e-01L,
+ 9.82793723247329067985710611014666038e-01L,
+ 1.57079632679489661923132169163975140e+00L,
+};
+
+static const long double atanlo[] = {
+ 4.89509642257333492668618435220297706e-36L,
+ 2.16795253253094525619926100651083806e-35L,
+ -2.31288434538183565909319952098066272e-35L,
+ 4.33590506506189051239852201302167613e-35L,
+};
+
+static const long double aT[] = {
+ 3.33333333333333333333333333333333125e-01L,
+ -1.99999999999999999999999999999180430e-01L,
+ 1.42857142857142857142857142125269827e-01L,
+ -1.11111111111111111111110834490810169e-01L,
+ 9.09090909090909090908522355708623681e-02L,
+ -7.69230769230769230696553844935357021e-02L,
+ 6.66666666666666660390096773046256096e-02L,
+ -5.88235294117646671706582985209643694e-02L,
+ 5.26315789473666478515847092020327506e-02L,
+ -4.76190476189855517021024424991436144e-02L,
+ 4.34782608678695085948531993458097026e-02L,
+ -3.99999999632663469330634215991142368e-02L,
+ 3.70370363987423702891250829918659723e-02L,
+ -3.44827496515048090726669907612335954e-02L,
+ 3.22579620681420149871973710852268528e-02L,
+ -3.03020767654269261041647570626778067e-02L,
+ 2.85641979882534783223403715930946138e-02L,
+ -2.69824879726738568189929461383741323e-02L,
+ 2.54194698498808542954187110873675769e-02L,
+ -2.35083879708189059926183138130183215e-02L,
+ 2.04832358998165364349957325067131428e-02L,
+ -1.54489555488544397858507248612362957e-02L,
+ 8.64492360989278761493037861575248038e-03L,
+ -2.58521121597609872727919154569765469e-03L,
+};
+
+static long double T_even(long double x)
+{
+ return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] +
+ x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] +
+ x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
+}
+
+static long double T_odd(long double x)
+{
+ return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] +
+ x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] +
+ x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
+}
+#endif
long double atanl(long double x)
{
- union IEEEl2bits u;
- long double w,s1,s2,z;
+ union ldshape u = {x};
+ long double w, s1, s2, z;
int id;
- int16_t expsign, expt;
- int32_t expman;
+ unsigned e = u.i.se & 0x7fff;
+ unsigned sign = u.i.se >> 15;
+ unsigned expman;
- u.e = x;
- expsign = u.xbits.expsign;
- expt = expsign & 0x7fff;
- if (expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
- if (expt == BIAS + LDBL_MAX_EXP &&
- ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) /* NaN */
- return x+x;
- if (expsign > 0)
- return atanhi[3]+atanlo[3];
- else
- return -atanhi[3]-atanlo[3];
+ if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */
+ if (isnan(x))
+ return x;
+ return sign ? -atanhi[3] : atanhi[3];
}
/* Extract the exponent and the first few bits of the mantissa. */
- /* XXX There should be a more convenient way to do this. */
- expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
- if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
- if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
- /* raise inexact */
- if (huge+x > 1.0)
- return x;
+ expman = EXPMAN(u);
+ if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
+ if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */
+ /* raise underflow if subnormal */
+ if (e == 0)
+ FORCE_EVAL((float)x);
+ return x;
}
id = -1;
} else {
x = fabsl(x);
- if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
- if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
+ if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */
+ if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
id = 0;
x = (2.0*x-1.0)/(2.0+x);
} else { /* 11/16 <= |x| < 19/16 */
x = (x-1.0)/(x+1.0);
}
} else {
- if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
+ if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
id = 2;
x = (x-1.5)/(1.0+1.5*x);
- } else { /* 2.4375 <= |x| < 2^ATAN_CONST */
+ } else { /* 2.4375 <= |x| */
id = 3;
x = -1.0/x;
}
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
- return expsign < 0 ? -z : z;
+ return sign ? -z : z;
}
#endif
projects / musl / blobdiff