qiurui
/
glibc
mirror of git://sourceware.org/git/glibc.git
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Update. 

2000-10-25  Ulrich Drepper  <drepper@redhat.com>

	* sysdeps/ieee754/dbl-64/e_jn.c: Use __ieee754_sqrt instead of __sqrt.
	* sysdeps/ieee754/dbl-64/e_j1.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_j0.c: Likewise.
	* sysdeps/ieee754/flt-32/e_j1f.c: Likewise.
	* sysdeps/ieee754/flt-32/e_j0f.c: Likewise.
This commit is contained in:
Ulrich Drepper 2000-10-25 22:17:16 +00:00
parent 6a39d02719
commit 106599818f
6 changed files with 67 additions and 59 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
ChangeLog
View File

@ -1,3 +1,11 @@
2000-10-25 Ulrich Drepper <drepper@redhat.com>
* sysdeps/ieee754/dbl-64/e_jn.c: Use __ieee754_sqrt instead of __sqrt.
* sysdeps/ieee754/dbl-64/e_j1.c: Likewise.
* sysdeps/ieee754/dbl-64/e_j0.c: Likewise.
* sysdeps/ieee754/flt-32/e_j1f.c: Likewise.
* sysdeps/ieee754/flt-32/e_j0f.c: Likewise.
2000-10-25 David Mosberger <davidm@hpl.hp.com> 2000-10-25 David Mosberger <davidm@hpl.hp.com>
* sysdeps/unix/sysv/linux/ia64/profil-counter.h: Multiply slot * sysdeps/unix/sysv/linux/ia64/profil-counter.h: Multiply slot

8
sysdeps/ieee754/dbl-64/e_j0.c
View File

@ -124,10 +124,10 @@ static double zero = 0.0;
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) * 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) * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/ */
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(x); if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x);
else { else {
u = pzero(x); v = qzero(x); u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/__sqrt(x); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x);
} }
return z; return z;
} }
@ -215,10 +215,10 @@ V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
if ((s*c)<zero) cc = z/ss; if ((s*c)<zero) cc = z/ss;
else ss = z/cc; else ss = z/cc;
} }
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else { else {
u = pzero(x); v = qzero(x); u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/__sqrt(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
} }
return z; return z;
} }

8
sysdeps/ieee754/dbl-64/e_j1.c
View File

@ -125,10 +125,10 @@ static double zero = 0.0;
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) * 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) * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/ */
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(y); if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
else { else {
u = pone(y); v = qone(y); u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/__sqrt(y); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
} }
if(hx<0) return -z; if(hx<0) return -z;
else return z; else return z;
@ -214,10 +214,10 @@ static double V0[5] = {
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one. * to compute the worse one.
*/ */
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else { else {
u = pone(x); v = qone(x); u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/__sqrt(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
} }
return z; return z;
} }

46
sysdeps/ieee754/dbl-64/e_jn.c
View File

@ -5,7 +5,7 @@
* *
* Developed at SunPro, a Sun Microsystems, Inc. business. * Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this * Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice * software is freely granted, provided that this notice
* is preserved. * is preserved.
* ==================================================== * ====================================================
*/ */
@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
* __ieee754_jn(n, x), __ieee754_yn(n, x) * __ieee754_jn(n, x), __ieee754_yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind * floating point Bessel's function of the 1st and 2nd kind
* of order n * of order n
* *
* Special cases: * Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
* yn(n,x) is similar in all respects, except * yn(n,x) is similar in all respects, except
* that forward recursion is used for all * that forward recursion is used for all
* values of n>1. * values of n>1.
* *
*/ */
#include "math.h" #include "math.h"
@ -76,7 +76,7 @@ static double zero = 0.00000000000000000000e+00;
ix = 0x7fffffff&hx; ix = 0x7fffffff&hx;
/* if J(n,NaN) is NaN */ /* if J(n,NaN) is NaN */
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
if(n<0){ if(n<0){
n = -n; n = -n;
x = -x; x = -x;
hx ^= 0x80000000; hx ^= 0x80000000;
@ -87,13 +87,13 @@ static double zero = 0.00000000000000000000e+00;
x = fabs(x); x = fabs(x);
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
b = zero; b = zero;
else if((double)n<=x) { else if((double)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if(ix>=0x52D00000) { /* x > 2**302 */ if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2) /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x), * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
* *
* n sin(xn)*sqt2 cos(xn)*sqt2 * n sin(xn)*sqt2 cos(xn)*sqt2
@ -109,8 +109,8 @@ static double zero = 0.00000000000000000000e+00;
case 2: temp = -__cos(x)-__sin(x); break; case 2: temp = -__cos(x)-__sin(x); break;
case 3: temp = __cos(x)-__sin(x); break; case 3: temp = __cos(x)-__sin(x); break;
} }
b = invsqrtpi*temp/__sqrt(x); b = invsqrtpi*temp/__ieee754_sqrt(x);
} else { } else {
a = __ieee754_j0(x); a = __ieee754_j0(x);
b = __ieee754_j1(x); b = __ieee754_j1(x);
for(i=1;i<n;i++){ for(i=1;i<n;i++){
@ -121,7 +121,7 @@ static double zero = 0.00000000000000000000e+00;
} }
} else { } else {
if(ix<0x3e100000) { /* x < 2**-29 */ if(ix<0x3e100000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x) /* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ... * J(n,x) = 1/n!*(x/2)^n - ...
*/ */
if(n>33) /* underflow */ if(n>33) /* underflow */
@ -136,14 +136,14 @@ static double zero = 0.00000000000000000000e+00;
} }
} else { } else {
/* use backward recurrence */ /* use backward recurrence */
/* x x^2 x^2 /* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ ..... * J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2) * 2n - 2(n+1) - 2(n+2)
* *
* 1 1 1 * 1 1 1
* (for large x) = ---- ------ ------ ..... * (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2) * 2n 2(n+1) 2(n+2)
* -- - ------ - ------ - * -- - ------ - ------ -
* x x x * x x x
* *
* Let w = 2n/x and h=2/x, then the above quotient * Let w = 2n/x and h=2/x, then the above quotient
@ -159,9 +159,9 @@ static double zero = 0.00000000000000000000e+00;
* To determine how many terms needed, let * To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1, * Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2), * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single * When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double * When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple * When Q(k) > 1e17 good for quadruple
*/ */
/* determine k */ /* determine k */
double t,v; double t,v;
@ -183,7 +183,7 @@ static double zero = 0.00000000000000000000e+00;
* single 8.8722839355e+01 * single 8.8722839355e+01
* double 7.09782712893383973096e+02 * double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04 * long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is * then recurrent value may overflow and the result is
* likely underflow to zero * likely underflow to zero
*/ */
tmp = n; tmp = n;
@ -219,9 +219,9 @@ static double zero = 0.00000000000000000000e+00;
} }
#ifdef __STDC__ #ifdef __STDC__
double __ieee754_yn(int n, double x) double __ieee754_yn(int n, double x)
#else #else
double __ieee754_yn(n,x) double __ieee754_yn(n,x)
int n; double x; int n; double x;
#endif #endif
{ {
@ -244,10 +244,10 @@ static double zero = 0.00000000000000000000e+00;
if(n==1) return(sign*__ieee754_y1(x)); if(n==1) return(sign*__ieee754_y1(x));
if(ix==0x7ff00000) return zero; if(ix==0x7ff00000) return zero;
if(ix>=0x52D00000) { /* x > 2**302 */ if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2) /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x), * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
* *
* n sin(xn)*sqt2 cos(xn)*sqt2 * n sin(xn)*sqt2 cos(xn)*sqt2
@ -263,14 +263,14 @@ static double zero = 0.00000000000000000000e+00;
case 2: temp = -__sin(x)+__cos(x); break; case 2: temp = -__sin(x)+__cos(x); break;
case 3: temp = __sin(x)+__cos(x); break; case 3: temp = __sin(x)+__cos(x); break;
} }
b = invsqrtpi*temp/__sqrt(x); b = invsqrtpi*temp/__ieee754_sqrt(x);
} else { } else {
u_int32_t high; u_int32_t high;
a = __ieee754_y0(x); a = __ieee754_y0(x);
b = __ieee754_y1(x); b = __ieee754_y1(x);
/* quit if b is -inf */ /* quit if b is -inf */
GET_HIGH_WORD(high,b); GET_HIGH_WORD(high,b);
for(i=1;i<n&&high!=0xfff00000;i++){ for(i=1;i<n&&high!=0xfff00000;i++){
temp = b; temp = b;
b = ((double)(i+i)/x)*b - a; b = ((double)(i+i)/x)*b - a;
GET_HIGH_WORD(high,b); GET_HIGH_WORD(high,b);

26
sysdeps/ieee754/flt-32/e_j0f.c
View File

@ -8,7 +8,7 @@
* *
* Developed at SunPro, a Sun Microsystems, Inc. business. * Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this * Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice * software is freely granted, provided that this notice
* is preserved. * is preserved.
* ==================================================== * ====================================================
*/ */
@ -27,9 +27,9 @@ static float pzerof(), qzerof();
#endif #endif
#ifdef __STDC__ #ifdef __STDC__
static const float static const float
#else #else
static float static float
#endif #endif
huge = 1e30, huge = 1e30,
one = 1.0, one = 1.0,
@ -52,9 +52,9 @@ static float zero = 0.0;
#endif #endif
#ifdef __STDC__ #ifdef __STDC__
float __ieee754_j0f(float x) float __ieee754_j0f(float x)
#else #else
float __ieee754_j0f(x) float __ieee754_j0f(x)
float x; float x;
#endif #endif
{ {
@ -79,10 +79,10 @@ static float zero = 0.0;
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) * 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) * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/ */
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(x); if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x);
else { else {
u = pzerof(x); v = qzerof(x); u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*cc-v*ss)/__sqrtf(x); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
} }
return z; return z;
} }
@ -121,9 +121,9 @@ v03 = 2.5915085189e-07, /* 0x348b216c */
v04 = 4.4111031494e-10; /* 0x2ff280c2 */ v04 = 4.4111031494e-10; /* 0x2ff280c2 */
#ifdef __STDC__ #ifdef __STDC__
float __ieee754_y0f(float x) float __ieee754_y0f(float x)
#else #else
float __ieee754_y0f(x) float __ieee754_y0f(x)
float x; float x;
#endif #endif
{ {
@ -133,7 +133,7 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */
GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx; ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(ix>=0x7f800000) return one/(x+x*x); if(ix>=0x7f800000) return one/(x+x*x);
if(ix==0) return -one/zero; if(ix==0) return -one/zero;
if(hx<0) return zero/zero; if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */ if(ix >= 0x40000000) { /* |x| >= 2.0 */
@ -161,10 +161,10 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */
if ((s*c)<zero) cc = z/ss; if ((s*c)<zero) cc = z/ss;
else ss = z/cc; else ss = z/cc;
} }
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x); if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else { else {
u = pzerof(x); v = qzerof(x); u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
} }
return z; return z;
} }
@ -306,7 +306,7 @@ static float pS2[5] = {
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s; return one+ r/s;
} }
/* For x >= 8, the asymptotic expansions of qzero is /* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x. * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.

30
sysdeps/ieee754/flt-32/e_j1f.c
View File

@ -8,7 +8,7 @@
* *
* Developed at SunPro, a Sun Microsystems, Inc. business. * Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this * Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice * software is freely granted, provided that this notice
* is preserved. * is preserved.
* ==================================================== * ====================================================
*/ */
@ -27,9 +27,9 @@ static float ponef(), qonef();
#endif #endif
#ifdef __STDC__ #ifdef __STDC__
static const float static const float
#else #else
static float static float
#endif #endif
huge = 1e30, huge = 1e30,
one = 1.0, one = 1.0,
@ -53,9 +53,9 @@ static float zero = 0.0;
#endif #endif
#ifdef __STDC__ #ifdef __STDC__
float __ieee754_j1f(float x) float __ieee754_j1f(float x)
#else #else
float __ieee754_j1f(x) float __ieee754_j1f(x)
float x; float x;
#endif #endif
{ {
@ -80,10 +80,10 @@ static float zero = 0.0;
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) * 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) * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/ */
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(y); if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y);
else { else {
u = ponef(y); v = qonef(y); u = ponef(y); v = qonef(y);
z = invsqrtpi*(u*cc-v*ss)/__sqrtf(y); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
} }
if(hx<0) return -z; if(hx<0) return -z;
else return z; else return z;
@ -122,9 +122,9 @@ static float V0[5] = {
}; };
#ifdef __STDC__ #ifdef __STDC__
float __ieee754_y1f(float x) float __ieee754_y1f(float x)
#else #else
float __ieee754_y1f(x) float __ieee754_y1f(x)
float x; float x;
#endif #endif
{ {
@ -134,7 +134,7 @@ static float V0[5] = {
GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx; ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(ix>=0x7f800000) return one/(x+x*x); if(ix>=0x7f800000) return one/(x+x*x);
if(ix==0) return -one/zero; if(ix==0) return -one/zero;
if(hx<0) return zero/zero; if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */ if(ix >= 0x40000000) { /* |x| >= 2.0 */
@ -158,16 +158,16 @@ static float V0[5] = {
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one. * to compute the worse one.
*/ */
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x); if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else { else {
u = ponef(x); v = qonef(x); u = ponef(x); v = qonef(x);
z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
} }
return z; return z;
} }
if(ix<=0x24800000) { /* x < 2**-54 */ if(ix<=0x24800000) { /* x < 2**-54 */
return(-tpi/x); return(-tpi/x);
} }
z = x*x; z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
@ -305,7 +305,7 @@ static float ps2[5] = {
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s; return one+ r/s;
} }
/* For x >= 8, the asymptotic expansions of qone is /* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x. * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.