long double
__ieee754_exp2l (long double x)
{
if (__glibc_likely (isless (x, (long double) LDBL_MAX_EXP)))
{
if (__builtin_expect (isgreaterequal (x, (long double) (LDBL_MIN_EXP
- LDBL_MANT_DIG
- 1)), 1))
{
int intx = (int) x;
long double fractx = x - intx;
long double result;
if (fabsl (fractx) < LDBL_EPSILON / 4.0L)
result = __scalbnl (1.0L + fractx, intx);
else
result = __scalbnl (__ieee754_expl (M_LN2l * fractx), intx);
math_check_force_underflow_nonneg (result);
return result;
}
else
{
/* Underflow or exact zero. */
if (isinf (x))
return 0;
else
return LDBL_MIN * LDBL_MIN;
}
}
else
/* Infinity, NaN or overflow. */
return LDBL_MAX * x;
}
double
__ieee754_hypot (double x, double y)
{
x = fabs (x);
y = fabs (y);
TEST_INF_NAN (x, y);
if (y > x)
{
double t = x;
x = y;
y = t;
}
if (y == 0.0)
return x;
/* if y is higher enough, y * 2^60 might overflow. The tests if
y >= 1.7976931348623157e+308/2^60 (two60factor) and uses the
appropriate check to avoid the overflow exception generation. */
if (y > two60factor)
{
if ((x / y) > two60)
return x + y;
}
else
{
if (x > (y * two60))
return x + y;
}
if (x > two500)
{
x *= twoM600;
y *= twoM600;
return __ieee754_sqrt (x * x + y * y) / twoM600;
}
if (y < twoM500)
{
if (y <= pdnum)
{
x *= two1022;
y *= two1022;
double ret = __ieee754_sqrt (x * x + y * y) / two1022;
math_check_force_underflow_nonneg (ret);
return ret;
}
else
{
x *= two600;
y *= two600;
return __ieee754_sqrt (x * x + y * y) / two600;
}
}
return __ieee754_sqrt (x * x + y * y);
}
__complex__ long double
__clogl (__complex__ long double x)
{
__complex__ long double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
__imag__ result = __copysignl (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsl (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
int scale = 0;
if (absx < absy)
{
long double t = absx;
absx = absy;
absy = t;
}
if (absx > LDBL_MAX / 2.0L)
{
scale = -1;
absx = __scalbnl (absx, scale);
absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
}
else if (absx < LDBL_MIN && absy < LDBL_MIN)
{
scale = LDBL_MANT_DIG;
absx = __scalbnl (absx, scale);
absy = __scalbnl (absy, scale);
}
if (absx == 1.0L && scale == 0)
{
__real__ result = __log1pl (absy * absy) / 2.0L;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
if (absy >= LDBL_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1pl (d2m1) / 2.0L;
}
else if (absx < 1.0L
&& absx >= 0.5L
&& absy < LDBL_EPSILON / 2.0L
&& scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
__real__ result = __log1pl (d2m1) / 2.0L;
}
else if (absx < 1.0L
&& absx >= 0.5L
&& scale == 0
&& absx * absx + absy * absy >= 0.5L)
{
long double d2m1 = __x2y2m1l (absx, absy);
__real__ result = __log1pl (d2m1) / 2.0L;
}
else
{
long double d = __ieee754_hypotl (absx, absy);
__real__ result = __ieee754_logl (d) - scale * M_LN2l;
}
__imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanl ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALL;
else
__real__ result = __nanl ("");
}
return result;
}
/* An ultimate power routine. Given two IEEE double machine numbers y, x it
computes the correctly rounded (to nearest) value of X^y. */
double
SECTION
__ieee754_pow (double x, double y)
{
double z, a, aa, error, t, a1, a2, y1, y2;
mynumber u, v;
int k;
int4 qx, qy;
v.x = y;
u.x = x;
if (v.i[LOW_HALF] == 0)
{ /* of y */
qx = u.i[HIGH_HALF] & 0x7fffffff;
/* Is x a NaN? */
if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
&& (y != 0 || issignaling (x)))
return x + x;
if (y == 1.0)
return x;
if (y == 2.0)
return x * x;
if (y == -1.0)
return 1.0 / x;
if (y == 0)
return 1.0;
}
/* else */
if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
(u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
{ /* if y<-1 or y>1 */
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */
if (fabs (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
t = y * CN;
y1 = t - (t - y);
y2 = y - y1;
t = z * CN;
a1 = t - (t - z);
a2 = (z - a1) + aa;
a = y1 * a1;
aa = y2 * a1 + y * a2;
a1 = a + aa;
a2 = (a - a1) + aa;
error = error * fabs (y);
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
retval = (t > 0) ? t : power1 (x, y);
}
if (isinf (retval))
retval = huge * huge;
else if (retval == 0)
retval = tiny * tiny;
else
math_check_force_underflow_nonneg (retval);
return retval;
}
if (x == 0)
{
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
return y + y;
if (fabs (y) > 1.0e20)
return (y > 0) ? 0 : 1.0 / 0.0;
k = checkint (y);
if (k == -1)
return y < 0 ? 1.0 / x : x;
else
return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
}
qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
return x + y;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
return x == 1.0 && !issignaling (y) ? 1.0 : y + y;
/* if x<0 */
if (u.i[HIGH_HALF] < 0)
{
k = checkint (y);
if (k == 0)
{
if (qy == 0x7ff00000)
{
if (x == -1.0)
return 1.0;
else if (x > -1.0)
return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
else
return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
}
else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x;
return (x - x) / (x - x); /* y not integer and x<0 */
}
else if (qx == 0x7ff00000)
{
if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
/* if y even or odd */
if (k == 1)
return __ieee754_pow (-x, y);
else
{
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
retval = -__ieee754_pow (-x, y);
}
if (isinf (retval))
retval = -huge * huge;
else if (retval == 0)
retval = -tiny * tiny;
return retval;
}
}
/* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
return y > 0 ? x : 0;
if (qy > 0x45f00000 && qy < 0x7ff00000)
{
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? huge * huge : tiny * tiny;
if (y < 0)
return (x < 1.0) ? huge * huge : tiny * tiny;
}
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? INF.x : 0;
if (y < 0)
return (x < 1.0) ? INF.x : 0;
return 0; /* unreachable, to make the compiler happy */
}
__complex__ double
__kernel_casinh (__complex__ double x, int adj)
{
__complex__ double res;
double rx, ix;
__complex__ double y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabs (__real__ x);
ix = fabs (__imag__ x);
if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
double t = __real__ y;
__real__ y = __copysign (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clog (y);
__real__ res += M_LN2;
}
else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
{
double s = __ieee754_hypot (1.0, rx);
__real__ res = __ieee754_log (rx + s);
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
{
double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
__real__ res = __ieee754_log (ix + s);
if (adj)
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
else
__imag__ res = __ieee754_atan2 (s, rx);
}
else if (ix > 1.0 && ix < 1.5 && rx < 0.5)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double s = __ieee754_sqrt (ix2m1);
__real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
else
__imag__ res = __ieee754_atan2 (s, rx);
}
else
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (ix2m1 * ix2m1 + f);
double dp = d + ix2m1;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dm + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
else if (ix == 1.0 && rx < 0.5)
{
if (rx < DBL_EPSILON / 8.0)
{
__real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx),
__copysign (1.0, __imag__ x));
else
__imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx));
}
else
{
double d = rx * __ieee754_sqrt (4.0 + rx * rx);
double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0);
double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0);
__real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1);
}
}
else if (ix < 1.0 && rx < 0.5)
{
if (ix >= DBL_EPSILON)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double s = __ieee754_sqrt (onemix2);
__real__ res = __log1p (2.0 * rx / s) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
else
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (onemix2 * onemix2 + f);
double dp = d + onemix2;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dp + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res
= __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1,
__copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
else
{
double s = __ieee754_hypot (1.0, rx);
__real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0;
__imag__ y = 2.0 * rx * ix;
y = __csqrt (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
double t = __real__ y;
__real__ y = __copysign (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clog (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysign (__real__ res, __real__ x);
__imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
return res;
}
float
__ieee754_exp2f (float x)
{
static const float himark = (float) FLT_MAX_EXP;
static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
/* Check for usual case. */
if (isless (x, himark) && isgreaterequal (x, lomark))
{
static const float THREEp14 = 49152.0;
int tval, unsafe;
float rx, x22, result;
union ieee754_float ex2_u, scale_u;
if (fabsf (x) < FLT_EPSILON / 4.0f)
return 1.0f + x;
{
SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
/* 1. Argument reduction.
Choose integers ex, -128 <= t < 128, and some real
-1/512 <= x1 <= 1/512 so that
x = ex + t/512 + x1.
First, calculate rx = ex + t/256. */
rx = x + THREEp14;
rx -= THREEp14;
x -= rx; /* Compute x=x1. */
/* Compute tval = (ex*256 + t)+128.
Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %;
and /-round-to-nearest not the usual c integer /]. */
tval = (int) (rx * 256.0f + 128.0f);
/* 2. Adjust for accurate table entry.
Find e so that
x = ex + t/256 + e + x2
where -7e-4 < e < 7e-4, and
(float)(2^(t/256+e))
is accurate to one part in 2^-64. */
/* 'tval & 255' is the same as 'tval%256' except that it's always
positive.
Compute x = x2. */
x -= __exp2f_deltatable[tval & 255];
/* 3. Compute ex2 = 2^(t/255+e+ex). */
ex2_u.f = __exp2f_atable[tval & 255];
tval >>= 8;
/* x2 is an integer multiple of 2^-30; avoid intermediate
underflow from the calculation of x22 * x. */
unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
ex2_u.ieee.exponent += tval >> unsafe;
scale_u.f = 1.0;
scale_u.ieee.exponent += tval - (tval >> unsafe);
/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
less than 1.3e-10. */
x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
}
/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
result = x22 * x + ex2_u.f;
if (!unsafe)
return result;
else
{
result *= scale_u.f;
math_check_force_underflow_nonneg (result);
return result;
}
}
/* Exceptional cases: */
else if (isless (x, himark))
long double __ieee754_hypotl(long double x, long double y)
{
long double a,b,t1,t2,y1,y2,w;
u_int32_t j,k,ea,eb;
GET_LDOUBLE_EXP(ea,x);
ea &= 0x7fff;
GET_LDOUBLE_EXP(eb,y);
eb &= 0x7fff;
if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
k=0;
if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
if(ea == 0x7fff) { /* Inf or NaN */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
w = a+b; /* for sNaN */
GET_LDOUBLE_WORDS(exp,high,low,a);
if(((high&0x7fffffff)|low)==0) w = a;
GET_LDOUBLE_WORDS(exp,high,low,b);
if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ea -= 0x2580; eb -= 0x2580; k += 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
if(eb == 0) { /* subnormal b or 0 */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
GET_LDOUBLE_WORDS(exp,high,low,b);
if((high|low)==0) return a;
SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_LDOUBLE_EXP (ea, a);
GET_LDOUBLE_EXP (eb, b);
if (eb > ea)
{
t1 = a;
a = b;
b = t1;
j = ea;
ea = eb;
eb = j;
}
} else { /* scale a and b by 2^9600 */
ea += 0x2580; /* a *= 2^9600 */
eb += 0x2580; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
u_int32_t high;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea,high,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
u_int32_t high;
GET_LDOUBLE_MSW(high,b);
a = a+a;
SET_LDOUBLE_WORDS(y1,eb,high,0);
y2 = b - y1;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea+1,high,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t exp;
t1 = 1.0;
GET_LDOUBLE_EXP(exp,t1);
SET_LDOUBLE_EXP(t1,exp+k);
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
} else return w;
}
float
__ieee754_gammaf_r (float x, int *signgamp)
{
int32_t hx;
float ret;
GET_FLOAT_WORD (hx, x);
if (__glibc_unlikely ((hx & 0x7fffffff) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__builtin_expect (hx < 0, 0)
&& (u_int32_t) hx < 0xff800000 && __rintf (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (__glibc_unlikely (hx == 0xff800000))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 36.0f)
{
/* Overflow. */
*signgamp = 0;
ret = math_narrow_eval (FLT_MAX * FLT_MAX);
return ret;
}
else
{
SET_RESTORE_ROUNDF (FE_TONEAREST);
if (x > 0.0f)
{
*signgamp = 0;
int exp2_adj;
float tret = gammaf_positive (x, &exp2_adj);
ret = __scalbnf (tret, exp2_adj);
}
else if (x >= -FLT_EPSILON / 4.0f)
{
*signgamp = 0;
ret = 1.0f / x;
}
else
{
float tx = __truncf (x);
*signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;
if (x <= -42.0f)
/* Underflow. */
ret = FLT_MIN * FLT_MIN;
else
{
float frac = tx - x;
if (frac > 0.5f)
frac = 1.0f - frac;
float sinpix = (frac <= 0.25f
? __sinf ((float) M_PI * frac)
: __cosf ((float) M_PI * (0.5f - frac)));
int exp2_adj;
float tret = (float) M_PI / (-x * sinpix
* gammaf_positive (-x, &exp2_adj));
ret = __scalbnf (tret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
}
ret = math_narrow_eval (ret);
}
if (isinf (ret) && x != 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX);
ret = -ret;
}
else
ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX);
return ret;
}
else if (ret == 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN);
ret = -ret;
}
else
ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN);
return ret;
}
else
return ret;
}
_Float128
__ieee754_expl (_Float128 x)
{
/* Check for usual case. */
if (isless (x, himark) && isgreater (x, lomark))
{
int tval1, tval2, unsafe, n_i;
_Float128 x22, n, t, result, xl;
union ieee854_long_double ex2_u, scale_u;
fenv_t oldenv;
feholdexcept (&oldenv);
#ifdef FE_TONEAREST
fesetround (FE_TONEAREST);
#endif
/* Calculate n. */
n = x * M_1_LN2 + THREEp111;
n -= THREEp111;
x = x - n * M_LN2_0;
xl = n * M_LN2_1;
/* Calculate t/256. */
t = x + THREEp103;
t -= THREEp103;
/* Compute tval1 = t. */
tval1 = (int) (t * TWO8);
x -= __expl_table[T_EXPL_ARG1+2*tval1];
xl -= __expl_table[T_EXPL_ARG1+2*tval1+1];
/* Calculate t/32768. */
t = x + THREEp96;
t -= THREEp96;
/* Compute tval2 = t. */
tval2 = (int) (t * TWO15);
x -= __expl_table[T_EXPL_ARG2+2*tval2];
xl -= __expl_table[T_EXPL_ARG2+2*tval2+1];
x = x + xl;
/* Compute ex2 = 2^n_0 e^(argtable[tval1]) e^(argtable[tval2]). */
ex2_u.d = __expl_table[T_EXPL_RES1 + tval1]
* __expl_table[T_EXPL_RES2 + tval2];
n_i = (int)n;
/* 'unsafe' is 1 iff n_1 != 0. */
unsafe = abs(n_i) >= 15000;
ex2_u.ieee.exponent += n_i >> unsafe;
/* Compute scale = 2^n_1. */
scale_u.d = 1;
scale_u.ieee.exponent += n_i - (n_i >> unsafe);
/* Approximate e^x2 - 1, using a seventh-degree polynomial,
with maximum error in [-2^-16-2^-53,2^-16+2^-53]
less than 4.8e-39. */
x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
/* Return result. */
fesetenv (&oldenv);
result = x22 * ex2_u.d + ex2_u.d;
/* Now we can test whether the result is ultimate or if we are unsure.
In the later case we should probably call a mpn based routine to give
the ultimate result.
Empirically, this routine is already ultimate in about 99.9986% of
cases, the test below for the round to nearest case will be false
in ~ 99.9963% of cases.
Without proc2 routine maximum error which has been seen is
0.5000262 ulp.
union ieee854_long_double ex3_u;
#ifdef FE_TONEAREST
fesetround (FE_TONEAREST);
#endif
ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d;
ex2_u.d = result;
ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS
- ex2_u.ieee.exponent;
n_i = abs (ex3_u.d);
n_i = (n_i + 1) / 2;
fesetenv (&oldenv);
#ifdef FE_TONEAREST
if (fegetround () == FE_TONEAREST)
n_i -= 0x4000;
#endif
if (!n_i) {
return __ieee754_expl_proc2 (origx);
}
*/
if (!unsafe)
return result;
else
{
result *= scale_u.d;
math_check_force_underflow_nonneg (result);
return result;
}
}
CFLOAT
M_DECL_FUNC (__clog) (CFLOAT x)
{
CFLOAT result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? (FLOAT) M_MLIT (M_PI) : 0;
__imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1 / M_FABS (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
int scale = 0;
if (absx < absy)
{
FLOAT t = absx;
absx = absy;
absy = t;
}
if (absx > M_MAX / 2)
{
scale = -1;
absx = M_SCALBN (absx, scale);
absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
}
else if (absx < M_MIN && absy < M_MIN)
{
scale = M_MANT_DIG;
absx = M_SCALBN (absx, scale);
absy = M_SCALBN (absy, scale);
}
if (absx == 1 && scale == 0)
{
__real__ result = M_LOG1P (absy * absy) / 2;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
{
FLOAT d2m1 = (absx - 1) * (absx + 1);
if (absy >= M_EPSILON)
d2m1 += absy * absy;
__real__ result = M_LOG1P (d2m1) / 2;
}
else if (absx < 1
&& absx >= M_LIT (0.5)
&& absy < M_EPSILON / 2
&& scale == 0)
{
FLOAT d2m1 = (absx - 1) * (absx + 1);
__real__ result = M_LOG1P (d2m1) / 2;
}
else if (absx < 1
&& absx >= M_LIT (0.5)
&& scale == 0
&& absx * absx + absy * absy >= M_LIT (0.5))
{
FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
__real__ result = M_LOG1P (d2m1) / 2;
}
else
{
FLOAT d = M_HYPOT (absx, absy);
__real__ result = M_LOG (d) - scale * (FLOAT) M_MLIT (M_LN2);
}
__imag__ result = M_ATAN2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = M_NAN;
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = M_HUGE_VAL;
else
__real__ result = M_NAN;
}
return result;
}
long double
__kernel_tanl (long double x, long double y, int iy)
{
long double z, r, v, w, s;
long double absx = fabsl (x);
int sign;
if (absx < 0x1p-33)
{
if ((int) x == 0)
{ /* generate inexact */
if (x == 0 && iy == -1)
return one / fabsl (x);
else if (iy == 1)
{
math_check_force_underflow_nonneg (absx);
return x;
}
else
return -one / x;
}
}
if (absx >= 0.6743316650390625L)
{
if (signbit (x))
{
x = -x;
y = -y;
sign = -1;
}
else
sign = 1;
z = pio4hi - x;
w = pio4lo - y;
x = z + w;
y = 0.0;
}
z = x * x;
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
r = r / v;
s = z * x;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
if (absx >= 0.6743316650390625L)
{
v = (long double) iy;
w = (v - 2.0 * (x - (w * w / (w + v) - r)));
/* SIGN is set for arguments that reach this code, but not
otherwise, resulting in warnings that it may be used
uninitialized although in the cases where it is used it has
always been set. */
DIAG_PUSH_NEEDS_COMMENT;
DIAG_IGNORE_NEEDS_COMMENT (4.8, "-Wmaybe-uninitialized");
if (sign < 0)
w = -w;
DIAG_POP_NEEDS_COMMENT;
return w;
}
if (iy == 1)
return w;
else
return -1.0 / (x + r);
}
long double
__ieee754_hypotl(long double x, long double y)
{
long double a,b,a1,a2,b1,b2,w,kld;
int64_t j,k,ha,hb;
double xhi, yhi, hi, lo;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (ha, xhi);
yhi = ldbl_high (y);
EXTRACT_WORDS64 (hb, yhi);
ha &= 0x7fffffffffffffffLL;
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsl(a); /* a <- |a| */
b = fabsl(b); /* b <- |b| */
if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
kld = 1.0L;
if(ha > 0x5f30000000000000LL) { /* a>2**500 */
if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */
w = a+b; /* for sNaN */
if (issignaling (a) || issignaling (b))
return w;
if(ha == 0x7ff0000000000000LL)
w = a;
if(hb == 0x7ff0000000000000LL)
w = b;
return w;
}
/* scale a and b by 2**-600 */
a *= 0x1p-600L;
b *= 0x1p-600L;
k = 600;
kld = 0x1p+600L;
}
else if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */
if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */
if(hb==0) return a;
a *= 0x1p+1022L;
b *= 0x1p+1022L;
k = -1022;
kld = 0x1p-1022L;
} else { /* scale a and b by 2^600 */
a *= 0x1p+600L;
b *= 0x1p+600L;
k = -600;
kld = 0x1p-600L;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
ldbl_unpack (a, &hi, &lo);
a1 = hi;
a2 = lo;
/* a*a + b*b
= (a1+a2)*a + b*b
= a1*a + a2*a + b*b
= a1*(a1+a2) + a2*a + b*b
= a1*a1 + a1*a2 + a2*a + b*b
= a1*a1 + a2*(a+a1) + b*b */
w = sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
} else {
a = a+a;
ldbl_unpack (b, &hi, &lo);
b1 = hi;
b2 = lo;
ldbl_unpack (a, &hi, &lo);
a1 = hi;
a2 = lo;
/* a*a + b*b
= a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b
= a*a + w*w - (a*a - 2*a*b + b*b) + b*b
= w*w + 2*a*b
= w*w + (a1+a2)*b
= w*w + a1*b + a2*b
= w*w + a1*(b1+b2) + a2*b
= w*w + a1*b1 + a1*b2 + a2*b */
w = sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
}
if(k!=0)
{
w *= kld;
math_check_force_underflow_nonneg (w);
return w;
}
else
return w;
}
double
__ieee754_hypot (double x, double y)
{
double a, b, t1, t2, y1, y2, w;
int32_t j, k, ha, hb;
GET_HIGH_WORD (ha, x);
ha &= 0x7fffffff;
GET_HIGH_WORD (hb, y);
hb &= 0x7fffffff;
if (hb > ha)
{
a = y; b = x; j = ha; ha = hb; hb = j;
}
else
{
a = x; b = y;
}
SET_HIGH_WORD (a, ha); /* a <- |a| */
SET_HIGH_WORD (b, hb); /* b <- |b| */
if ((ha - hb) > 0x3c00000)
{
return a + b;
} /* x/y > 2**60 */
k = 0;
if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */
{
if (ha >= 0x7ff00000) /* Inf or NaN */
{
u_int32_t low;
w = a + b; /* for sNaN */
GET_LOW_WORD (low, a);
if (((ha & 0xfffff) | low) == 0)
w = a;
GET_LOW_WORD (low, b);
if (((hb ^ 0x7ff00000) | low) == 0)
w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
SET_HIGH_WORD (a, ha);
SET_HIGH_WORD (b, hb);
}
if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */
{
if (hb <= 0x000fffff) /* subnormal b or 0 */
{
u_int32_t low;
GET_LOW_WORD (low, b);
if ((hb | low) == 0)
return a;
t1 = 0;
SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
GET_HIGH_WORD (ha, a);
GET_HIGH_WORD (hb, b);
if (hb > ha)
{
t1 = a;
a = b;
b = t1;
j = ha;
ha = hb;
hb = j;
}
}
else /* scale a and b by 2^600 */
{
ha += 0x25800000; /* a *= 2^600 */
hb += 0x25800000; /* b *= 2^600 */
k -= 600;
SET_HIGH_WORD (a, ha);
SET_HIGH_WORD (b, hb);
}
}
/* medium size a and b */
w = a - b;
if (w > b)
{
t1 = 0;
SET_HIGH_WORD (t1, ha);
t2 = a - t1;
w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
}
else
{
a = a + a;
y1 = 0;
SET_HIGH_WORD (y1, hb);
y2 = b - y1;
t1 = 0;
SET_HIGH_WORD (t1, ha + 0x00100000);
t2 = a - t1;
w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
}
if (k != 0)
{
u_int32_t high;
t1 = 1.0;
GET_HIGH_WORD (high, t1);
SET_HIGH_WORD (t1, high + (k << 20));
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
}
else
return w;
}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
u_int32_t es, hx, lx;
long double ret;
GET_LDOUBLE_WORDS (es, hx, lx, x);
if (__glibc_unlikely (((es & 0x7fff) | hx | lx) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__glibc_unlikely (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((es & 0x7fff) == 0x7fff))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (__builtin_expect ((es & 0x8000) != 0, 0) && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (x >= 1756.0L)
{
/* Overflow. */
*signgamp = 0;
return LDBL_MAX * LDBL_MAX;
}
else
{
SET_RESTORE_ROUNDL (FE_TONEAREST);
if (x > 0.0L)
{
*signgamp = 0;
int exp2_adj;
ret = gammal_positive (x, &exp2_adj);
ret = __scalbnl (ret, exp2_adj);
}
else if (x >= -LDBL_EPSILON / 4.0L)
{
*signgamp = 0;
ret = 1.0L / x;
}
else
{
long double tx = __truncl (x);
*signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
if (x <= -1766.0L)
/* Underflow. */
ret = LDBL_MIN * LDBL_MIN;
else
{
long double frac = tx - x;
if (frac > 0.5L)
frac = 1.0L - frac;
long double sinpix = (frac <= 0.25L
? __sinl (M_PIl * frac)
: __cosl (M_PIl * (0.5L - frac)));
int exp2_adj;
ret = M_PIl / (-x * sinpix
* gammal_positive (-x, &exp2_adj));
ret = __scalbnl (ret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
}
}
if (isinf (ret) && x != 0)
{
if (*signgamp < 0)
return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX);
else
return __copysignl (LDBL_MAX, ret) * LDBL_MAX;
}
else if (ret == 0)
{
if (*signgamp < 0)
return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN);
else
return __copysignl (LDBL_MIN, ret) * LDBL_MIN;
}
else
return ret;
}
/* routine computes the correctly rounded (to nearest) value of atan(x). */
double
atan (double x)
{
double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
v, vv, w, ww, y, yy, z, zz;
#ifndef DLA_FMS
double t4, t5, t6;
#endif
int i, ux, dx;
static const int pr[M] = { 6, 8, 10, 32 };
number num;
num.d = x;
ux = num.i[HIGH_HALF];
dx = num.i[LOW_HALF];
/* x=NaN */
if (((ux & 0x7ff00000) == 0x7ff00000)
&& (((ux & 0x000fffff) | dx) != 0x00000000))
return x + x;
/* Regular values of x, including denormals +-0 and +-INF */
SET_RESTORE_ROUND (FE_TONEAREST);
u = (x < 0) ? -x : x;
if (u < C)
{
if (u < B)
{
if (u < A)
{
math_check_force_underflow_nonneg (u);
return x;
}
else
{ /* A <= u < B */
v = x * x;
yy = d11.d + v * d13.d;
yy = d9.d + v * yy;
yy = d7.d + v * yy;
yy = d5.d + v * yy;
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, t1, t2, t3, t4, t5); /* 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, t3, t4, t5, t6, t7, t8);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
t8);
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);
}
}
else
{ /* B <= u < C */
i = (TWO52 + TWO8 * u) - TWO52;
i -= 16;
z = u - cij[i][0].d;
yy = cij[i][5].d + z * cij[i][6].d;
yy = cij[i][4].d + z * yy;
yy = cij[i][3].d + z * yy;
yy = cij[i][2].d + z * yy;
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, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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);
}
}
else
{
if (u < D)
{ /* C <= u < D */
w = 1 / u;
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
ww = w * ((1 - t1) - t2);
i = (TWO52 + TWO8 * w) - TWO52;
i -= 16;
z = (w - cij[i][0].d) + ww;
yy = cij[i][5].d + z * cij[i][6].d;
yy = cij[i][4].d + z * yy;
yy = cij[i][3].d + z * yy;
yy = cij[i][2].d + z * yy;
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, t5, t6, t7, t8, t9,
t10);
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, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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);
}
else
{
if (u < E)
{ /* D <= u < E */
w = 1 / u;
v = w * w;
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
yy = d11.d + v * d13.d;
yy = d9.d + v * yy;
yy = d7.d + v * yy;
yy = d5.d + v * yy;
yy = d3.d + v * yy;
yy *= w * v;
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, t5, t6, t7, t8,
t9, t10);
MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
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, t3, t4, t5, t6, t7, t8);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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);
}
else
{
/* u >= E */
if (x > 0)
return HPI;
else
return MHPI;
}
}
}
}
