diff options
Diffstat (limited to 'sysdeps/ieee754')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_j0.c | 8 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_j1.c | 8 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_jn.c | 46 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_j0f.c | 26 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_j1f.c | 30 |
5 files changed, 59 insertions, 59 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_j0.c b/sysdeps/ieee754/dbl-64/e_j0.c index 55e8294bb9..00caf3f0d3 100644 --- a/sysdeps/ieee754/dbl-64/e_j0.c +++ b/sysdeps/ieee754/dbl-64/e_j0.c @@ -124,10 +124,10 @@ static double zero = 0.0; * 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)/__sqrt(x); + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x); else { 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; } @@ -215,10 +215,10 @@ V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ if ((s*c)<zero) cc = z/ss; else ss = z/cc; } - if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); else { 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; } diff --git a/sysdeps/ieee754/dbl-64/e_j1.c b/sysdeps/ieee754/dbl-64/e_j1.c index daf025fdb7..f5f5c28830 100644 --- a/sysdeps/ieee754/dbl-64/e_j1.c +++ b/sysdeps/ieee754/dbl-64/e_j1.c @@ -125,10 +125,10 @@ static double zero = 0.0; * 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)/__sqrt(y); + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y); else { 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; else return z; @@ -214,10 +214,10 @@ static double V0[5] = { * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one. */ - if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x); + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); else { 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; } diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c index d63d7688a3..68abc90462 100644 --- a/sysdeps/ieee754/dbl-64/e_jn.c +++ b/sysdeps/ieee754/dbl-64/e_jn.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * 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. * ==================================================== */ @@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; * __ieee754_jn(n, x), __ieee754_yn(n, x) * floating point Bessel's function of the 1st and 2nd kind * of order n - * + * * Special cases: * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. @@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; * yn(n,x) is similar in all respects, except * that forward recursion is used for all * values of n>1. - * + * */ #include "math.h" @@ -76,7 +76,7 @@ static double zero = 0.00000000000000000000e+00; ix = 0x7fffffff&hx; /* if J(n,NaN) is NaN */ if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; - if(n<0){ + if(n<0){ n = -n; x = -x; hx ^= 0x80000000; @@ -87,13 +87,13 @@ static double zero = 0.00000000000000000000e+00; x = fabs(x); if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ 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) */ if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) + /* (x >> n**2) * Jn(x) = cos(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 * * 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 3: temp = __cos(x)-__sin(x); break; } - b = invsqrtpi*temp/__sqrt(x); - } else { + b = invsqrtpi*temp/__ieee754_sqrt(x); + } else { a = __ieee754_j0(x); b = __ieee754_j1(x); for(i=1;i<n;i++){ @@ -121,7 +121,7 @@ static double zero = 0.00000000000000000000e+00; } } else { 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 - ... */ if(n>33) /* underflow */ @@ -136,14 +136,14 @@ static double zero = 0.00000000000000000000e+00; } } else { /* use backward recurrence */ - /* x x^2 x^2 + /* x x^2 x^2 * J(n,x)/J(n-1,x) = ---- ------ ------ ..... * 2n - 2(n+1) - 2(n+2) * - * 1 1 1 + * 1 1 1 * (for large x) = ---- ------ ------ ..... * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - + * -- - ------ - ------ - * x x x * * 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 * Q(0) = w, Q(1) = w(w+h) - 1, * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple */ /* determine k */ double t,v; @@ -183,7 +183,7 @@ static double zero = 0.00000000000000000000e+00; * single 8.8722839355e+01 * double 7.09782712893383973096e+02 * 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 */ tmp = n; @@ -219,9 +219,9 @@ static double zero = 0.00000000000000000000e+00; } #ifdef __STDC__ - double __ieee754_yn(int n, double x) + double __ieee754_yn(int n, double x) #else - double __ieee754_yn(n,x) + double __ieee754_yn(n,x) int n; double x; #endif { @@ -244,10 +244,10 @@ static double zero = 0.00000000000000000000e+00; if(n==1) return(sign*__ieee754_y1(x)); if(ix==0x7ff00000) return zero; if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) + /* (x >> n**2) * Jn(x) = cos(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 * * 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 3: temp = __sin(x)+__cos(x); break; } - b = invsqrtpi*temp/__sqrt(x); + b = invsqrtpi*temp/__ieee754_sqrt(x); } else { u_int32_t high; a = __ieee754_y0(x); b = __ieee754_y1(x); /* quit if b is -inf */ GET_HIGH_WORD(high,b); - for(i=1;i<n&&high!=0xfff00000;i++){ + for(i=1;i<n&&high!=0xfff00000;i++){ temp = b; b = ((double)(i+i)/x)*b - a; GET_HIGH_WORD(high,b); diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c index eed171cc90..c767318e3a 100644 --- a/sysdeps/ieee754/flt-32/e_j0f.c +++ b/sysdeps/ieee754/flt-32/e_j0f.c @@ -8,7 +8,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * 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. * ==================================================== */ @@ -27,9 +27,9 @@ static float pzerof(), qzerof(); #endif #ifdef __STDC__ -static const float +static const float #else -static float +static float #endif huge = 1e30, one = 1.0, @@ -52,9 +52,9 @@ static float zero = 0.0; #endif #ifdef __STDC__ - float __ieee754_j0f(float x) + float __ieee754_j0f(float x) #else - float __ieee754_j0f(x) + float __ieee754_j0f(x) float x; #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) * 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 { 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; } @@ -121,9 +121,9 @@ v03 = 2.5915085189e-07, /* 0x348b216c */ v04 = 4.4111031494e-10; /* 0x2ff280c2 */ #ifdef __STDC__ - float __ieee754_y0f(float x) + float __ieee754_y0f(float x) #else - float __ieee754_y0f(x) + float __ieee754_y0f(x) float x; #endif { @@ -133,7 +133,7 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */ GET_FLOAT_WORD(hx,x); ix = 0x7fffffff&hx; /* 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(hx<0) return zero/zero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ @@ -161,10 +161,10 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */ if ((s*c)<zero) cc = z/ss; else ss = z/cc; } - if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x); + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); else { 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; } @@ -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])))); return one+ r/s; } - + /* For x >= 8, the asymptotic expansions of qzero is * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. diff --git a/sysdeps/ieee754/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c index e6f14a16ac..a227bc09f1 100644 --- a/sysdeps/ieee754/flt-32/e_j1f.c +++ b/sysdeps/ieee754/flt-32/e_j1f.c @@ -8,7 +8,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * 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. * ==================================================== */ @@ -27,9 +27,9 @@ static float ponef(), qonef(); #endif #ifdef __STDC__ -static const float +static const float #else -static float +static float #endif huge = 1e30, one = 1.0, @@ -53,9 +53,9 @@ static float zero = 0.0; #endif #ifdef __STDC__ - float __ieee754_j1f(float x) + float __ieee754_j1f(float x) #else - float __ieee754_j1f(x) + float __ieee754_j1f(x) float x; #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) * 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 { 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; else return z; @@ -122,9 +122,9 @@ static float V0[5] = { }; #ifdef __STDC__ - float __ieee754_y1f(float x) + float __ieee754_y1f(float x) #else - float __ieee754_y1f(x) + float __ieee754_y1f(x) float x; #endif { @@ -134,7 +134,7 @@ static float V0[5] = { GET_FLOAT_WORD(hx,x); ix = 0x7fffffff&hx; /* 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(hx<0) return zero/zero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ @@ -158,16 +158,16 @@ static float V0[5] = { * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one. */ - 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. |