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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
parent
6a39d02719
commit
106599818f
@ -1,3 +1,11 @@
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2000-10-25 Ulrich Drepper <drepper@redhat.com>
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* sysdeps/ieee754/dbl-64/e_jn.c: Use __ieee754_sqrt instead of __sqrt.
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* sysdeps/ieee754/dbl-64/e_j1.c: Likewise.
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* sysdeps/ieee754/dbl-64/e_j0.c: Likewise.
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* sysdeps/ieee754/flt-32/e_j1f.c: Likewise.
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* sysdeps/ieee754/flt-32/e_j0f.c: Likewise.
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2000-10-25 David Mosberger <davidm@hpl.hp.com>
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* sysdeps/unix/sysv/linux/ia64/profil-counter.h: Multiply slot
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@ -124,10 +124,10 @@ static double zero = 0.0;
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* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
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* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
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*/
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if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(x);
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if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x);
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else {
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u = pzero(x); v = qzero(x);
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z = invsqrtpi*(u*cc-v*ss)/__sqrt(x);
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z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x);
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}
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return z;
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}
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@ -215,10 +215,10 @@ V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
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if ((s*c)<zero) cc = z/ss;
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else ss = z/cc;
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}
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if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x);
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if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
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else {
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u = pzero(x); v = qzero(x);
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z = invsqrtpi*(u*ss+v*cc)/__sqrt(x);
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z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
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}
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return z;
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}
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@ -125,10 +125,10 @@ static double zero = 0.0;
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* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
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* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
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*/
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if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(y);
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if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
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else {
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u = pone(y); v = qone(y);
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z = invsqrtpi*(u*cc-v*ss)/__sqrt(y);
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z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
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}
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if(hx<0) return -z;
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else return z;
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@ -214,10 +214,10 @@ static double V0[5] = {
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* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
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* to compute the worse one.
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*/
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if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x);
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if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
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else {
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u = pone(x); v = qone(x);
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z = invsqrtpi*(u*ss+v*cc)/__sqrt(x);
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z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
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}
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return z;
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}
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@ -5,7 +5,7 @@
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
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* __ieee754_jn(n, x), __ieee754_yn(n, x)
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* floating point Bessel's function of the 1st and 2nd kind
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* of order n
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*
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*
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* Special cases:
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* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
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* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
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@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
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* yn(n,x) is similar in all respects, except
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* that forward recursion is used for all
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* values of n>1.
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*
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*
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*/
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#include "math.h"
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@ -76,7 +76,7 @@ static double zero = 0.00000000000000000000e+00;
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ix = 0x7fffffff&hx;
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/* if J(n,NaN) is NaN */
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if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
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if(n<0){
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if(n<0){
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n = -n;
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x = -x;
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hx ^= 0x80000000;
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@ -87,13 +87,13 @@ static double zero = 0.00000000000000000000e+00;
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x = fabs(x);
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if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
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b = zero;
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else if((double)n<=x) {
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else if((double)n<=x) {
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/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
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if(ix>=0x52D00000) { /* x > 2**302 */
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/* (x >> n**2)
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/* (x >> n**2)
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* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Let s=sin(x), c=cos(x),
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* Let s=sin(x), c=cos(x),
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* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
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*
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* n sin(xn)*sqt2 cos(xn)*sqt2
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@ -109,8 +109,8 @@ static double zero = 0.00000000000000000000e+00;
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case 2: temp = -__cos(x)-__sin(x); break;
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case 3: temp = __cos(x)-__sin(x); break;
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}
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b = invsqrtpi*temp/__sqrt(x);
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} else {
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b = invsqrtpi*temp/__ieee754_sqrt(x);
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} else {
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a = __ieee754_j0(x);
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b = __ieee754_j1(x);
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for(i=1;i<n;i++){
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@ -121,7 +121,7 @@ static double zero = 0.00000000000000000000e+00;
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}
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} else {
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if(ix<0x3e100000) { /* x < 2**-29 */
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/* x is tiny, return the first Taylor expansion of J(n,x)
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/* x is tiny, return the first Taylor expansion of J(n,x)
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* J(n,x) = 1/n!*(x/2)^n - ...
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*/
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if(n>33) /* underflow */
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@ -136,14 +136,14 @@ static double zero = 0.00000000000000000000e+00;
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}
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} else {
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/* use backward recurrence */
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/* x x^2 x^2
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/* x x^2 x^2
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* J(n,x)/J(n-1,x) = ---- ------ ------ .....
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* 2n - 2(n+1) - 2(n+2)
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*
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* 1 1 1
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* 1 1 1
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* (for large x) = ---- ------ ------ .....
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* 2n 2(n+1) 2(n+2)
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* -- - ------ - ------ -
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* -- - ------ - ------ -
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* x x x
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*
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* Let w = 2n/x and h=2/x, then the above quotient
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@ -159,9 +159,9 @@ static double zero = 0.00000000000000000000e+00;
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* To determine how many terms needed, let
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* Q(0) = w, Q(1) = w(w+h) - 1,
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* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
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* When Q(k) > 1e4 good for single
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* When Q(k) > 1e9 good for double
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* When Q(k) > 1e17 good for quadruple
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* When Q(k) > 1e4 good for single
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* When Q(k) > 1e9 good for double
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* When Q(k) > 1e17 good for quadruple
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*/
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/* determine k */
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double t,v;
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@ -183,7 +183,7 @@ static double zero = 0.00000000000000000000e+00;
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* single 8.8722839355e+01
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* double 7.09782712893383973096e+02
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* long double 1.1356523406294143949491931077970765006170e+04
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* then recurrent value may overflow and the result is
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* then recurrent value may overflow and the result is
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* likely underflow to zero
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*/
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tmp = n;
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@ -219,9 +219,9 @@ static double zero = 0.00000000000000000000e+00;
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}
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#ifdef __STDC__
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double __ieee754_yn(int n, double x)
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double __ieee754_yn(int n, double x)
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#else
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double __ieee754_yn(n,x)
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double __ieee754_yn(n,x)
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int n; double x;
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#endif
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{
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@ -244,10 +244,10 @@ static double zero = 0.00000000000000000000e+00;
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if(n==1) return(sign*__ieee754_y1(x));
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if(ix==0x7ff00000) return zero;
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if(ix>=0x52D00000) { /* x > 2**302 */
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/* (x >> n**2)
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/* (x >> n**2)
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* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Let s=sin(x), c=cos(x),
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* Let s=sin(x), c=cos(x),
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* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
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*
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* n sin(xn)*sqt2 cos(xn)*sqt2
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@ -263,14 +263,14 @@ static double zero = 0.00000000000000000000e+00;
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case 2: temp = -__sin(x)+__cos(x); break;
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case 3: temp = __sin(x)+__cos(x); break;
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}
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b = invsqrtpi*temp/__sqrt(x);
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b = invsqrtpi*temp/__ieee754_sqrt(x);
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} else {
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u_int32_t high;
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a = __ieee754_y0(x);
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b = __ieee754_y1(x);
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/* quit if b is -inf */
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GET_HIGH_WORD(high,b);
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for(i=1;i<n&&high!=0xfff00000;i++){
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for(i=1;i<n&&high!=0xfff00000;i++){
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temp = b;
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b = ((double)(i+i)/x)*b - a;
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GET_HIGH_WORD(high,b);
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@ -8,7 +8,7 @@
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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@ -27,9 +27,9 @@ static float pzerof(), qzerof();
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#endif
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#ifdef __STDC__
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static const float
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static const float
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#else
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static float
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static float
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#endif
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huge = 1e30,
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one = 1.0,
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@ -52,9 +52,9 @@ static float zero = 0.0;
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#endif
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#ifdef __STDC__
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float __ieee754_j0f(float x)
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float __ieee754_j0f(float x)
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#else
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float __ieee754_j0f(x)
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float __ieee754_j0f(x)
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float x;
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#endif
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{
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@ -79,10 +79,10 @@ static float zero = 0.0;
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* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
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* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
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*/
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if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(x);
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if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x);
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else {
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u = pzerof(x); v = qzerof(x);
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z = invsqrtpi*(u*cc-v*ss)/__sqrtf(x);
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z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
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}
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return z;
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}
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@ -121,9 +121,9 @@ v03 = 2.5915085189e-07, /* 0x348b216c */
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v04 = 4.4111031494e-10; /* 0x2ff280c2 */
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#ifdef __STDC__
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float __ieee754_y0f(float x)
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float __ieee754_y0f(float x)
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#else
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float __ieee754_y0f(x)
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float __ieee754_y0f(x)
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float x;
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#endif
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{
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@ -133,7 +133,7 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */
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GET_FLOAT_WORD(hx,x);
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ix = 0x7fffffff&hx;
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/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
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if(ix>=0x7f800000) return one/(x+x*x);
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if(ix>=0x7f800000) return one/(x+x*x);
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if(ix==0) return -one/zero;
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if(hx<0) return zero/zero;
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if(ix >= 0x40000000) { /* |x| >= 2.0 */
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@ -161,10 +161,10 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */
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if ((s*c)<zero) cc = z/ss;
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else ss = z/cc;
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}
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if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x);
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if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
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else {
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u = pzerof(x); v = qzerof(x);
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z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x);
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z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
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}
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return z;
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}
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@ -306,7 +306,7 @@ static float pS2[5] = {
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s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
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return one+ r/s;
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}
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/* For x >= 8, the asymptotic expansions of qzero is
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* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
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@ -8,7 +8,7 @@
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
|
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* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* software is freely granted, provided that this notice
|
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* is preserved.
|
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* ====================================================
|
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*/
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@ -27,9 +27,9 @@ static float ponef(), qonef();
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#endif
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#ifdef __STDC__
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static const float
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static const float
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#else
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static float
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static float
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#endif
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huge = 1e30,
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one = 1.0,
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@ -53,9 +53,9 @@ static float zero = 0.0;
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#endif
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#ifdef __STDC__
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float __ieee754_j1f(float x)
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float __ieee754_j1f(float x)
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#else
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float __ieee754_j1f(x)
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float __ieee754_j1f(x)
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float x;
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#endif
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{
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@ -80,10 +80,10 @@ static float zero = 0.0;
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* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
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* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
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*/
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if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrtf(y);
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if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y);
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else {
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u = ponef(y); v = qonef(y);
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z = invsqrtpi*(u*cc-v*ss)/__sqrtf(y);
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z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
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}
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if(hx<0) return -z;
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else return z;
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@ -122,9 +122,9 @@ static float V0[5] = {
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};
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#ifdef __STDC__
|
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float __ieee754_y1f(float x)
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float __ieee754_y1f(float x)
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#else
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float __ieee754_y1f(x)
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float __ieee754_y1f(x)
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float x;
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#endif
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{
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@ -134,7 +134,7 @@ static float V0[5] = {
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GET_FLOAT_WORD(hx,x);
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ix = 0x7fffffff&hx;
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/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
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if(ix>=0x7f800000) return one/(x+x*x);
|
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if(ix>=0x7f800000) return one/(x+x*x);
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if(ix==0) return -one/zero;
|
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if(hx<0) return zero/zero;
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if(ix >= 0x40000000) { /* |x| >= 2.0 */
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@ -158,16 +158,16 @@ static float V0[5] = {
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* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
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* to compute the worse one.
|
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*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x);
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
|
||||
else {
|
||||
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;
|
||||
}
|
||||
}
|
||||
if(ix<=0x24800000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
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]))));
|
||||
@ -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]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
|
||||
Loading…
Reference in New Issue
Block a user