diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c | 233 |
1 files changed, 233 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c b/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c new file mode 100644 index 0000000000..4e634778d3 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/flt-32/e_jnf.c @@ -0,0 +1,233 @@ +/* e_jnf.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 <errno.h> +#include <float.h> +#include <math.h> +#include <math_private.h> + +static const float +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +float +__ieee754_jnf(int n, float x) +{ + float ret; + { + 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(__builtin_expect(ix>0x7f800000, 0)) 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); + SET_RESTORE_ROUNDF (FE_TONEAREST); + if(__builtin_expect(ix==0||ix>=0x7f800000, 0)) /* if x is 0 or inf */ + return sgn == 1 ? -zero : 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*((double)(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; + } + } + } + /* j0() and j1() suffer enormous loss of precision at and + * near zero; however, we know that their zero points never + * coincide, so just choose the one further away from zero. + */ + z = __ieee754_j0f (x); + w = __ieee754_j1f (x); + if (fabsf (z) >= fabsf (w)) + b = (t * z / b); + else + b = (t * w / a); + } + } + if(sgn==1) ret = -b; else ret = b; + ret = math_narrow_eval (ret); + } + if (ret == 0) + { + ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN); + __set_errno (ERANGE); + } + else + math_check_force_underflow (ret); + return ret; +} +strong_alias (__ieee754_jnf, __jnf_finite) + +float +__ieee754_ynf(int n, float x) +{ + float ret; + { + int32_t i,hx,ix; + u_int32_t ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(__builtin_expect(ix>0x7f800000, 0)) return x+x; + if(__builtin_expect(ix==0, 0)) + return -HUGE_VALF+x; /* -inf and overflow exception. */ + if(__builtin_expect(hx<0, 0)) return zero/(zero*x); + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + SET_RESTORE_ROUNDF (FE_TONEAREST); + if(n==1) { + ret = sign*__ieee754_y1f(x); + goto out; + } + if(__builtin_expect(ix==0x7f800000, 0)) 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 = ((double)(i+i)/x)*b - a; + GET_FLOAT_WORD(ib,b); + a = temp; + } + /* If B is +-Inf, set up errno accordingly. */ + if (! isfinite (b)) + __set_errno (ERANGE); + if(sign>0) ret = b; else ret = -b; + } + out: + if (isinf (ret)) + ret = __copysignf (FLT_MAX, ret) * FLT_MAX; + return ret; +} +strong_alias (__ieee754_ynf, __ynf_finite) |