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Diffstat (limited to 'newlib/libm/math/ef_jn.c')
| -rw-r--r-- | newlib/libm/math/ef_jn.c | 207 |
1 files changed, 0 insertions, 207 deletions
diff --git a/newlib/libm/math/ef_jn.c b/newlib/libm/math/ef_jn.c deleted file mode 100644 index bedfb3ed5..000000000 --- a/newlib/libm/math/ef_jn.c +++ /dev/null @@ -1,207 +0,0 @@ -/* ef_jn.c -- float version of e_jn.c. - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const float -#else -static float -#endif -invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ -two = 2.0000000000e+00, /* 0x40000000 */ -one = 1.0000000000e+00; /* 0x3F800000 */ - -#ifdef __STDC__ -static const float zero = 0.0000000000e+00; -#else -static float zero = 0.0000000000e+00; -#endif - -#ifdef __STDC__ - float __ieee754_jnf(int n, float x) -#else - float __ieee754_jnf(n,x) - int n; float x; -#endif -{ - __int32_t i,hx,ix, sgn; - float a, b, temp, di; - float z, w; - - /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) - * Thus, J(-n,x) = J(n,-x) - */ - GET_FLOAT_WORD(hx,x); - ix = 0x7fffffff&hx; - /* if J(n,NaN) is NaN */ - if(FLT_UWORD_IS_NAN(ix)) return x+x; - if(n<0){ - n = -n; - x = -x; - hx ^= 0x80000000; - } - if(n==0) return(__ieee754_j0f(x)); - if(n==1) return(__ieee754_j1f(x)); - sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ - x = fabsf(x); - if(FLT_UWORD_IS_ZERO(ix)||FLT_UWORD_IS_INFINITE(ix)) - b = zero; - else if((float)n<=x) { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - a = __ieee754_j0f(x); - b = __ieee754_j1f(x); - for(i=1;i<n;i++){ - temp = b; - b = b*((float)(i+i)/x) - a; /* avoid underflow */ - a = temp; - } - } else { - if(ix<0x30800000) { /* x < 2**-29 */ - /* x is tiny, return the first Taylor expansion of J(n,x) - * J(n,x) = 1/n!*(x/2)^n - ... - */ - if(n>33) /* underflow */ - b = zero; - else { - temp = x*(float)0.5; b = temp; - for (a=one,i=2;i<=n;i++) { - a *= (float)i; /* a = n! */ - b *= temp; /* b = (x/2)^n */ - } - b = b/a; - } - } else { - /* use backward recurrence */ - /* x x^2 x^2 - * J(n,x)/J(n-1,x) = ---- ------ ------ ..... - * 2n - 2(n+1) - 2(n+2) - * - * 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 - * is equal to the continued fraction: - * 1 - * = ----------------------- - * 1 - * w - ----------------- - * 1 - * w+h - --------- - * w+2h - ... - * - * 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 - */ - /* determine k */ - float t,v; - float q0,q1,h,tmp; __int32_t k,m; - w = (n+n)/(float)x; h = (float)2.0/(float)x; - q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; - while(q1<(float)1.0e9) { - k += 1; z += h; - tmp = z*q1 - q0; - q0 = q1; - q1 = tmp; - } - m = n+n; - for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); - a = t; - b = one; - /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) - * Hence, if n*(log(2n/x)) > ... - * single 8.8722839355e+01 - * double 7.09782712893383973096e+02 - * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is - * likely underflow to zero - */ - tmp = n; - v = two/x; - tmp = tmp*__ieee754_logf(fabsf(v*tmp)); - if(tmp<(float)8.8721679688e+01) { - for(i=n-1,di=(float)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - } - } else { - for(i=n-1,di=(float)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - /* scale b to avoid spurious overflow */ - if(b>(float)1e10) { - a /= b; - t /= b; - b = one; - } - } - } - b = (t*__ieee754_j0f(x)/b); - } - } - if(sgn==1) return -b; else return b; -} - -#ifdef __STDC__ - float __ieee754_ynf(int n, float x) -#else - float __ieee754_ynf(n,x) - int n; float x; -#endif -{ - __int32_t i,hx,ix,ib; - __int32_t sign; - float a, b, temp; - - GET_FLOAT_WORD(hx,x); - ix = 0x7fffffff&hx; - /* if Y(n,NaN) is NaN */ - if(FLT_UWORD_IS_NAN(ix)) return x+x; - if(FLT_UWORD_IS_ZERO(ix)) return -one/zero; - if(hx<0) return zero/zero; - sign = 1; - if(n<0){ - n = -n; - sign = 1 - ((n&1)<<1); - } - if(n==0) return(__ieee754_y0f(x)); - if(n==1) return(sign*__ieee754_y1f(x)); - if(FLT_UWORD_IS_INFINITE(ix)) return zero; - - a = __ieee754_y0f(x); - b = __ieee754_y1f(x); - /* quit if b is -inf */ - GET_FLOAT_WORD(ib,b); - for(i=1;i<n&&ib!=0xff800000;i++){ - temp = b; - b = ((float)(i+i)/x)*b - a; - GET_FLOAT_WORD(ib,b); - a = temp; - } - if(sign>0) return b; else return -b; -} |