[__USE_ISOC99] (llrintf): Likewise.
[__USE_ISOC99] (llrintl): Likewise.
+2018-03-15 Wilco Dijkstra <wdijkstr@arm.com>
+
+ * sysdeps/ieee754/dbl-64/e_acosh.c (__ieee754_acosh): Use sqrt.
+ * sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Likewise.
+ * sysdeps/ieee754/dbl-64/e_hypot.c (__ieee754_hypot): Likewise.
+ * sysdeps/ieee754/dbl-64/e_j0.c (__ieee754_j0): Likewise.
+ * sysdeps/ieee754/dbl-64/e_j1.c (__ieee754_j1): Likewise.
+ * sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
+ * sysdeps/ieee754/dbl-64/s_asinh.c (__asinh): Likewise.
+ * sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c (__ieee754_acosh):
+ Likewise.
+ * sysdeps/ieee754/flt-32/e_acosf.c (__ieee754_acosf): Likewise.
+ * sysdeps/ieee754/flt-32/e_acoshf.c (__ieee754_acoshf): Likewise.
+ * sysdeps/ieee754/flt-32/e_asinf.c (__ieee754_asinf): Likewise.
+ * sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Likewise.
+ * sysdeps/ieee754/flt-32/e_hypotf.c (__ieee754_hypotf): Likewise.
+ * sysdeps/ieee754/flt-32/e_j0f.c (__ieee754_j0f): Likewise.
+ * sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_j1f): Likewise.
+ * sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Likewise.
+ * sysdeps/ieee754/flt-32/s_asinhf.c (__asinhf): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_acoshl.c (__ieee754_acoshl): Use sqrtl.
+ * sysdeps/ieee754/ldbl-128/e_acosl.c (__ieee754_acosl): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_hypotl.c (__ieee754_hypotl): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_j0l.c (__ieee754_j0l): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
+ * sysdeps/ieee754/ldbl-128/e_powl.c (__ieee754_powl): Likewise.
+ * sysdeps/ieee754/ldbl-128/s_asinhl.c (__ieee754_asinhl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (__ieee754_acoshl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_acosl.c (__ieee754_acosl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_j0l.c (__ieee754_j0l): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_j1l.c (__ieee754_j1l): Likewise
+ * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__ieee754_asinhl): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_acoshl.c (__ieee754_acoshl): Use sqrtl.
+ * sysdeps/ieee754/ldbl-96/e_asinl.c (__ieee754_asinl): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_hypotl.c (__ieee754_hypotl): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_j0l.c (__ieee754_j0l): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_j1l.c (__ieee754_j1l): Likewise.
+ * sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
+ * sysdeps/ieee754/ldbl-96/s_asinhl.c (__ieee754_asinhl): Likewise.
+ * sysdeps/m68k/m680x0/fpu/e_pow.c (__ieee754_pow): Likewise.
+ * sysdeps/powerpc/fpu/e_hypot.c (__ieee754_hypot): Likewise.
+ * sysdeps/powerpc/fpu/e_hypotf.c (__ieee754_hypotf): Likewise.
+
2018-03-15 Wilco Dijkstra <wdijkstr@arm.com>
* include/math.h (sqrt): Declare with asm redirect.
else if (hx > 0x40000000) /* 2**28 > x > 2 */
{
t = x * x;
- return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
+ return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
}
else /* 1<x<2 */
{
t = x - one;
- return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
+ return __log1p (t + sqrt (2.0 * t + t * t));
}
}
strong_alias (__ieee754_acosh, __acosh_finite)
double ret = (__ieee754_pow (x_adj_mant, x_adj)
* __ieee754_exp2 (x_adj_log2 * x_adj_frac)
* __ieee754_exp (-x_adj)
- * __ieee754_sqrt (2 * M_PI / x_adj)
+ * sqrt (2 * M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_log (x_adj);
double bsum = gamma_coeff[NCOEFF - 1];
t1 = 0;
SET_HIGH_WORD (t1, ha);
t2 = a - t1;
- w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
+ w = sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
}
else
{
t1 = 0;
SET_HIGH_WORD (t1, ha + 0x00100000);
t2 = a - t1;
- w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
+ w = sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
}
if (k != 0)
{
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if (ix > 0x48000000)
- z = (invsqrtpi * cc) / __ieee754_sqrt (x);
+ z = (invsqrtpi * cc) / sqrt (x);
else
{
u = pzero (x); v = qzero (x);
- z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (x);
+ z = invsqrtpi * (u * cc - v * ss) / sqrt (x);
}
return z;
}
ss = z / cc;
}
if (ix > 0x48000000)
- z = (invsqrtpi * ss) / __ieee754_sqrt (x);
+ z = (invsqrtpi * ss) / sqrt (x);
else
{
u = pzero (x); v = qzero (x);
- z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x);
+ z = invsqrtpi * (u * ss + v * cc) / sqrt (x);
}
return z;
}
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if (ix > 0x48000000)
- z = (invsqrtpi * cc) / __ieee754_sqrt (y);
+ z = (invsqrtpi * cc) / sqrt (y);
else
{
u = pone (y); v = qone (y);
- z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (y);
+ z = invsqrtpi * (u * cc - v * ss) / sqrt (y);
}
if (hx < 0)
return -z;
* to compute the worse one.
*/
if (ix > 0x48000000)
- z = (invsqrtpi * ss) / __ieee754_sqrt (x);
+ z = (invsqrtpi * ss) / sqrt (x);
else
{
u = pone (x); v = qone (x);
- z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x);
+ z = invsqrtpi * (u * ss + v * cc) / sqrt (x);
}
return z;
}
case 2: temp = -c - s; break;
case 3: temp = c - s; break;
}
- b = invsqrtpi * temp / __ieee754_sqrt (x);
+ b = invsqrtpi * temp / sqrt (x);
}
else
{
case 2: temp = -s + c; break;
case 3: temp = s + c; break;
}
- b = invsqrtpi * temp / __ieee754_sqrt (x);
+ b = invsqrtpi * temp / sqrt (x);
}
else
{
double xa = fabs (x);
if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */
{
- w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) +
+ w = __ieee754_log (2.0 * xa + one / (sqrt (xa * xa + one) +
xa));
}
else /* 2.0 > |x| > 2**-28 */
{
double t = xa * xa;
- w = __log1p (xa + t / (one + __ieee754_sqrt (one + t)));
+ w = __log1p (xa + t / (one + sqrt (one + t)));
}
}
return __copysign (w, x);
/* 2**28 > x > 2 */
double t = x * x;
- return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
+ return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
}
else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000)))
{
/* 1<x<2 */
double t = x - one;
- return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
+ return __log1p (t + sqrt (2.0 * t + t * t));
}
else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000)))
return 0.0; /* acosh(1) = 0 */
z = (one+x)*(float)0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
- s = __ieee754_sqrtf(z);
+ s = sqrtf(z);
r = p/q;
w = r*s-pio2_lo;
return pi - (float)2.0*(s+w);
} else { /* x > 0.5 */
int32_t idf;
z = (one-x)*(float)0.5;
- s = __ieee754_sqrtf(z);
+ s = sqrtf(z);
df = s;
GET_FLOAT_WORD(idf,df);
SET_FLOAT_WORD(df,idf&0xfffff000);
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
- return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one)));
+ return __ieee754_logf((float)2.0*x-one/(x+sqrtf(t-one)));
} else { /* 1<x<2 */
t = x-one;
- return __log1pf(t+__ieee754_sqrtf((float)2.0*t+t*t));
+ return __log1pf(t+sqrtf((float)2.0*t+t*t));
}
}
strong_alias (__ieee754_acoshf, __acoshf_finite)
w = one-fabsf(x);
t = w*0.5f;
p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
- s = __ieee754_sqrtf(t);
+ s = sqrtf(t);
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
} else {
float ret = (__ieee754_powf (x_adj_mant, x_adj)
* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
* __ieee754_expf (-x_adj)
- * __ieee754_sqrtf (2 * (float) M_PI / x_adj)
+ * sqrtf (2 * (float) M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logf (x_adj);
float bsum = gamma_coeff[NCOEFF - 1];
d_x = (double) x;
d_y = (double) y;
- return (float) __ieee754_sqrt(d_x * d_x + d_y * d_y);
+ return (float) sqrt(d_x * d_x + d_y * d_y);
}
strong_alias (__ieee754_hypotf, __hypotf_finite)
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
- if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x);
+ if(ix>0x48000000) z = (invsqrtpi*cc)/sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
- z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
+ z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
}
return z;
}
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
- if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
+ if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
- z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
+ z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
}
return z;
}
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
- if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y);
+ if(ix>0x48000000) z = (invsqrtpi*cc)/sqrtf(y);
else {
u = ponef(y); v = qonef(y);
- z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
+ z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
}
if(hx<0) return -z;
else return z;
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
- if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
+ if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);
else {
u = ponef(x); v = qonef(x);
- z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
+ z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
}
return z;
}
} else {
float xa = fabsf(x);
if (ix>0x40000000) { /* 2**14 > |x| > 2.0 */
- w = __ieee754_logf(2.0f*xa+one/(__ieee754_sqrtf(xa*xa+one)+xa));
+ w = __ieee754_logf(2.0f*xa+one/(sqrtf(xa*xa+one)+xa));
} else { /* 2.0 > |x| > 2**-14 */
float t = xa*xa;
- w =__log1pf(xa+t/(one+__ieee754_sqrtf(one+t)));
+ w =__log1pf(xa+t/(one+sqrtf(one+t)));
}
}
return __copysignf(w, x);
return 0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
- return __ieee754_logl(2*x-one/(x+__ieee754_sqrtl(t-one)));
+ return __ieee754_logl(2*x-one/(x+sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
- return __log1pl(t+__sqrtl(2*t+t*t));
+ return __log1pl(t+sqrtl(2*t+t*t));
}
}
strong_alias (__ieee754_acoshl, __acoshl_finite)
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
- * Functions needed: __ieee754_sqrtl.
+ * Functions needed: sqrtl.
*/
#include <math.h>
else
{ /* |x| >= .625 */
z = (one - u.value) * 0.5;
- s = __ieee754_sqrtl (z);
+ s = sqrtl (z);
/* Compute an extended precision square root from
the Newton iteration s -> 0.5 * (s + z / s).
The change w from s to the improved value is
return x + x * w;
}
- s = __ieee754_sqrtl (t);
+ s = sqrtl (t);
if (ix >= 0x3ffef333) /* |x| > 0.975 */
{
w = p / q;
_Float128 ret = (__ieee754_powl (x_adj_mant, x_adj)
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
* __ieee754_expl (-x_adj)
- * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ * sqrtl (2 * M_PIl / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logl (x_adj);
_Float128 bsum = gamma_coeff[NCOEFF - 1];
t1 = 0;
SET_LDOUBLE_MSW64(t1,ha);
t2 = a-t1;
- w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
+ w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
t1 = 0;
SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
t2 = a - t1;
- w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
uint64_t high;
}
if (xx > L(0x1p256))
- return ONEOSQPI * cc / __ieee754_sqrtl (xx);
+ return ONEOSQPI * cc / sqrtl (xx);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * xinv * q;
q = q - L(0.125) * xinv;
- z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx);
return z;
}
strong_alias (__ieee754_j0l, __j0l_finite)
}
if (xx > L(0x1p256))
- return ONEOSQPI * ss / __ieee754_sqrtl (x);
+ return ONEOSQPI * ss / sqrtl (x);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * xinv * q;
q = q - L(0.125) * xinv;
- z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
+ z = ONEOSQPI * (p * ss + q * cc) / sqrtl (x);
return z;
}
strong_alias (__ieee754_y0l, __y0l_finite)
if (xx > L(0x1p256))
{
- z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * cc / sqrtl (xx);
if (x < 0)
z = -z;
return z;
p = 1 + z * p;
q = z * q;
q = q * xinv + L(0.375) * xinv;
- z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
if (xx > L(0x1p256))
- return ONEOSQPI * ss / __ieee754_sqrtl (xx);
+ return ONEOSQPI * ss / sqrtl (xx);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * q;
q = q * xinv + L(0.375) * xinv;
- z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * ss + q * cc) / sqrtl (xx);
return z;
}
strong_alias (__ieee754_y1l, __y1l_finite)
temp = c - s;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
temp = s + c;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
if (hy == 0x3ffe0000)
{ /* y is 0.5 */
if (hx >= 0) /* x >= +0 */
- return __ieee754_sqrtl (x);
+ return sqrtl (x);
}
}
else if (ix >0x40000000)
{ /* 2^ 54 > |x| > 2.0 */
t = u.value;
- w = __ieee754_logl (2.0 * t + one / (__ieee754_sqrtl (x * x + one) + t));
+ w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t));
}
else
{ /* 2.0 > |x| > 2 ^ -56 */
t = x * x;
- w = __log1pl (u.value + t / (one + __ieee754_sqrtl (one + t)));
+ w = __log1pl (u.value + t / (one + sqrtl (one + t)));
}
if (sign & 0x80000000)
return -w;
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */
t=x*x;
- return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
+ return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
- return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
+ return __log1pl(t+sqrtl(2.0*t+t*t));
}
}
strong_alias (__ieee754_acoshl, __acoshl_finite)
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
- * Functions needed: __ieee754_sqrtl.
+ * Functions needed: sqrtl.
*/
#include <math.h>
double shi, slo;
z = (one - a) * 0.5;
- s = __ieee754_sqrtl (z);
+ s = sqrtl (z);
/* Compute an extended precision square root from
the Newton iteration s -> 0.5 * (s + z / s).
The change w from s to the improved value is
#include <float.h>
#include <math.h>
#include <math_private.h>
-long double sqrtl (long double);
static const long double
one = 1.0L,
return x + x * w;
}
- s = __ieee754_sqrtl (t);
+ s = sqrtl (t);
if (a > 0.975L)
{
w = p / q;
long double ret = (__ieee754_powl (x_adj_mant, x_adj)
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
* __ieee754_expl (-x_adj)
- * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ * sqrtl (2 * M_PIl / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logl (x_adj);
long double bsum = gamma_coeff[NCOEFF - 1];
= a1*(a1+a2) + a2*a + b*b
= a1*a1 + a1*a2 + a2*a + b*b
= a1*a1 + a2*(a+a1) + b*b */
- w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
+ w = sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
} else {
a = a+a;
ldbl_unpack (b, &hi, &lo);
= w*w + a1*b + a2*b
= w*w + a1*(b1+b2) + a2*b
= w*w + a1*b1 + a1*b2 + a2*b */
- w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
+ w = sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
}
if(k!=0)
{
}
if (xx > 0x1p256L)
- return ONEOSQPI * cc / __ieee754_sqrtl (xx);
+ return ONEOSQPI * cc / sqrtl (xx);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
- z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx);
return z;
}
strong_alias (__ieee754_j0l, __j0l_finite)
}
if (xx > 0x1p256L)
- return ONEOSQPI * ss / __ieee754_sqrtl (x);
+ return ONEOSQPI * ss / sqrtl (x);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
- z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
+ z = ONEOSQPI * (p * ss + q * cc) / sqrtl (x);
return z;
}
strong_alias (__ieee754_y0l, __y0l_finite)
if (xx > 0x1p256L)
{
- z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * cc / sqrtl (xx);
if (x < 0)
z = -z;
return z;
p = 1 + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
- z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
if (xx > 0x1p256L)
- return ONEOSQPI * ss / __ieee754_sqrtl (xx);
+ return ONEOSQPI * ss / sqrtl (xx);
xinv = 1 / xx;
z = xinv * xinv;
p = 1 + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
- z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
+ z = ONEOSQPI * (p * ss + q * cc) / sqrtl (xx);
return z;
}
strong_alias (__ieee754_y1l, __y1l_finite)
temp = c - s;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
temp = s + c;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
if (hy == 0x3fe00000)
{ /* y is 0.5 */
if (hx >= 0) /* x >= +0 */
- return __ieee754_sqrtl (x);
+ return sqrtl (x);
}
}
}
w = __ieee754_logl(fabsl(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
t = fabs(x);
- w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
+ w = __ieee754_logl(2.0*t+one/(sqrtl(x*x+one)+t));
} else { /* 2.0 >= |x| >= 2**-56 */
t = x*x;
- w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
+ w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
return 0.0; /* acosh(1) = 0 */
} else if (se > 0x4000) { /* 2**28 > x > 2 */
t=x*x;
- return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
+ return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
- return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
+ return __log1pl(t+sqrtl(2.0*t+t*t));
}
}
strong_alias (__ieee754_acoshl, __acoshl_finite)
t = w * 0.5;
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t))));
- s = __ieee754_sqrtl (t);
+ s = sqrtl (t);
if (ix >= 0x3ffef999)
{ /* if |x| > 0.975 */
w = p / q;
long double ret = (__ieee754_powl (x_adj_mant, x_adj)
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
* __ieee754_expl (-x_adj)
- * __ieee754_sqrtl (2 * M_PIl / x_adj)
+ * sqrtl (2 * M_PIl / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logl (x_adj);
long double bsum = gamma_coeff[NCOEFF - 1];
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)));
+ w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
uint32_t high;
GET_LDOUBLE_MSW(high,b);
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)));
+ w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
uint32_t exp;
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if (__glibc_unlikely (ix > 0x4080)) /* 2^129 */
- z = (invsqrtpi * cc) / __ieee754_sqrtl (x);
+ z = (invsqrtpi * cc) / sqrtl (x);
else
{
u = pzero (x);
v = qzero (x);
- z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (x);
+ z = invsqrtpi * (u * cc - v * ss) / sqrtl (x);
}
return z;
}
ss = z / cc;
}
if (__glibc_unlikely (ix > 0x4080)) /* 1e39 */
- z = (invsqrtpi * ss) / __ieee754_sqrtl (x);
+ z = (invsqrtpi * ss) / sqrtl (x);
else
{
u = pzero (x);
v = qzero (x);
- z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x);
+ z = invsqrtpi * (u * ss + v * cc) / sqrtl (x);
}
return z;
}
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if (__glibc_unlikely (ix > 0x4080))
- z = (invsqrtpi * cc) / __ieee754_sqrtl (y);
+ z = (invsqrtpi * cc) / sqrtl (y);
else
{
u = pone (y);
v = qone (y);
- z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (y);
+ z = invsqrtpi * (u * cc - v * ss) / sqrtl (y);
}
if (se & 0x8000)
return -z;
* to compute the worse one.
*/
if (__glibc_unlikely (ix > 0x4080))
- z = (invsqrtpi * ss) / __ieee754_sqrtl (x);
+ z = (invsqrtpi * ss) / sqrtl (x);
else
{
u = pone (x);
v = qone (x);
- z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x);
+ z = invsqrtpi * (u * ss + v * cc) / sqrtl (x);
}
return z;
}
temp = c - s;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
temp = s + c;
break;
}
- b = invsqrtpi * temp / __ieee754_sqrtl (x);
+ b = invsqrtpi * temp / sqrtl (x);
}
else
{
} else {
long double xa = fabsl(x);
if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
- w = __ieee754_logl(2.0*xa+one/(__ieee754_sqrtl(xa*xa+one)+xa));
+ w = __ieee754_logl(2.0*xa+one/(sqrtl(xa*xa+one)+xa));
} else { /* 2.0 > |x| > 2**-28 */
t = xa*xa;
- w =__log1pl(xa+t/(one+__ieee754_sqrtl(one+t)));
+ w =__log1pl(xa+t/(one+sqrtl(one+t)));
}
}
return __copysignl(w, x);
if (y == 2)
return x * x;
if (y == 0.5 && !(x_cond & __M81_COND_NEG))
- return m81(__ieee754_sqrt) (x);
+ return m81(sqrt) (x);
if (x == 10.0)
{
{
x *= twoM600;
y *= twoM600;
- return __ieee754_sqrt (x * x + y * y) / twoM600;
+ return sqrt (x * x + y * y) / twoM600;
}
if (y < twoM500)
{
{
x *= two1022;
y *= two1022;
- double ret = __ieee754_sqrt (x * x + y * y) / two1022;
+ double ret = sqrt (x * x + y * y) / two1022;
math_check_force_underflow_nonneg (ret);
return ret;
}
{
x *= two600;
y *= two600;
- return __ieee754_sqrt (x * x + y * y) / two600;
+ return sqrt (x * x + y * y) / two600;
}
}
- return __ieee754_sqrt (x * x + y * y);
+ return sqrt (x * x + y * y);
}
strong_alias (__ieee754_hypot, __hypot_finite)
{
TEST_INF_NAN (x, y);
- return __ieee754_sqrt ((double) x * x + (double) y * y);
+ return sqrt ((double) x * x + (double) y * y);
}
strong_alias (__ieee754_hypotf, __hypotf_finite)