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Diffstat (limited to 'src/math/jnf.c')
| -rw-r--r-- | src/math/jnf.c | 213 |
1 files changed, 213 insertions, 0 deletions
diff --git a/src/math/jnf.c b/src/math/jnf.c new file mode 100644 index 00000000..7db93ae7 --- /dev/null +++ b/src/math/jnf.c @@ -0,0 +1,213 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.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 "libm.h" + +static const float +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +float jnf(int n, float x) +{ + 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 (ix > 0x7f800000) + return x+x; + if (n < 0) { + n = -n; + x = -x; + hx ^= 0x80000000; + } + if (n == 0) return j0f(x); + if (n == 1) return j1f(x); + + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if (ix == 0 || ix >= 0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n <= x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = j0f(x); + b = 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; + z = w+h; + q0 = w; + 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*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; + } + } + } + z = j0f(x); + w = j1f(x); + if (fabsf(z) >= fabsf(w)) + b = t*z/b; + else + b = t*w/a; + } + } + if (sgn == 1) return -b; + return b; +} + +float ynf(int n, float x) +{ + 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 (ix > 0x7f800000) + return x+x; + if (ix == 0) + 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 y0f(x); + if (n == 1) + return sign*y1f(x); + if (ix == 0x7f800000) + return zero; + + a = y0f(x); + b = 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; + return -b; +} |