e_jnf.c - vx32 - Local 9vx git repository for patches.
(HTM) git clone git://r-36.net/vx32
(DIR) Log
(DIR) Files
(DIR) Refs
---
e_jnf.c (4830B)
---
1 /* e_jnf.c -- float version of e_jn.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_jnf.c,v 1.8 2002/05/28 18:15:04 alfred Exp $";
18 #endif
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const float
24 invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
25 two = 2.0000000000e+00, /* 0x40000000 */
26 one = 1.0000000000e+00; /* 0x3F800000 */
27
28 static const float zero = 0.0000000000e+00;
29
30 float
31 __ieee754_jnf(int n, float x)
32 {
33 int32_t i,hx,ix, sgn;
34 float a, b, temp, di;
35 float z, w;
36
37 /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
38 * Thus, J(-n,x) = J(n,-x)
39 */
40 GET_FLOAT_WORD(hx,x);
41 ix = 0x7fffffff&hx;
42 /* if J(n,NaN) is NaN */
43 if(ix>0x7f800000) return x+x;
44 if(n<0){
45 n = -n;
46 x = -x;
47 hx ^= 0x80000000;
48 }
49 if(n==0) return(__ieee754_j0f(x));
50 if(n==1) return(__ieee754_j1f(x));
51 sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
52 x = fabsf(x);
53 if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */
54 b = zero;
55 else if((float)n<=x) {
56 /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
57 a = __ieee754_j0f(x);
58 b = __ieee754_j1f(x);
59 for(i=1;i<n;i++){
60 temp = b;
61 b = b*((float)(i+i)/x) - a; /* avoid underflow */
62 a = temp;
63 }
64 } else {
65 if(ix<0x30800000) { /* x < 2**-29 */
66 /* x is tiny, return the first Taylor expansion of J(n,x)
67 * J(n,x) = 1/n!*(x/2)^n - ...
68 */
69 if(n>33) /* underflow */
70 b = zero;
71 else {
72 temp = x*(float)0.5; b = temp;
73 for (a=one,i=2;i<=n;i++) {
74 a *= (float)i; /* a = n! */
75 b *= temp; /* b = (x/2)^n */
76 }
77 b = b/a;
78 }
79 } else {
80 /* use backward recurrence */
81 /* x x^2 x^2
82 * J(n,x)/J(n-1,x) = ---- ------ ------ .....
83 * 2n - 2(n+1) - 2(n+2)
84 *
85 * 1 1 1
86 * (for large x) = ---- ------ ------ .....
87 * 2n 2(n+1) 2(n+2)
88 * -- - ------ - ------ -
89 * x x x
90 *
91 * Let w = 2n/x and h=2/x, then the above quotient
92 * is equal to the continued fraction:
93 * 1
94 * = -----------------------
95 * 1
96 * w - -----------------
97 * 1
98 * w+h - ---------
99 * w+2h - ...
100 *
101 * To determine how many terms needed, let
102 * Q(0) = w, Q(1) = w(w+h) - 1,
103 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
104 * When Q(k) > 1e4 good for single
105 * When Q(k) > 1e9 good for double
106 * When Q(k) > 1e17 good for quadruple
107 */
108 /* determine k */
109 float t,v;
110 float q0,q1,h,tmp; int32_t k,m;
111 w = (n+n)/(float)x; h = (float)2.0/(float)x;
112 q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
113 while(q1<(float)1.0e9) {
114 k += 1; z += h;
115 tmp = z*q1 - q0;
116 q0 = q1;
117 q1 = tmp;
118 }
119 m = n+n;
120 for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
121 a = t;
122 b = one;
123 /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
124 * Hence, if n*(log(2n/x)) > ...
125 * single 8.8722839355e+01
126 * double 7.09782712893383973096e+02
127 * long double 1.1356523406294143949491931077970765006170e+04
128 * then recurrent value may overflow and the result is
129 * likely underflow to zero
130 */
131 tmp = n;
132 v = two/x;
133 tmp = tmp*__ieee754_logf(fabsf(v*tmp));
134 if(tmp<(float)8.8721679688e+01) {
135 for(i=n-1,di=(float)(i+i);i>0;i--){
136 temp = b;
137 b *= di;
138 b = b/x - a;
139 a = temp;
140 di -= two;
141 }
142 } else {
143 for(i=n-1,di=(float)(i+i);i>0;i--){
144 temp = b;
145 b *= di;
146 b = b/x - a;
147 a = temp;
148 di -= two;
149 /* scale b to avoid spurious overflow */
150 if(b>(float)1e10) {
151 a /= b;
152 t /= b;
153 b = one;
154 }
155 }
156 }
157 b = (t*__ieee754_j0f(x)/b);
158 }
159 }
160 if(sgn==1) return -b; else return b;
161 }
162
163 float
164 __ieee754_ynf(int n, float x)
165 {
166 int32_t i,hx,ix,ib;
167 int32_t sign;
168 float a, b, temp;
169
170 GET_FLOAT_WORD(hx,x);
171 ix = 0x7fffffff&hx;
172 /* if Y(n,NaN) is NaN */
173 if(ix>0x7f800000) return x+x;
174 if(ix==0) return -one/zero;
175 if(hx<0) return zero/zero;
176 sign = 1;
177 if(n<0){
178 n = -n;
179 sign = 1 - ((n&1)<<1);
180 }
181 if(n==0) return(__ieee754_y0f(x));
182 if(n==1) return(sign*__ieee754_y1f(x));
183 if(ix==0x7f800000) return zero;
184
185 a = __ieee754_y0f(x);
186 b = __ieee754_y1f(x);
187 /* quit if b is -inf */
188 GET_FLOAT_WORD(ib,b);
189 for(i=1;i<n&&ib!=0xff800000;i++){
190 temp = b;
191 b = ((float)(i+i)/x)*b - a;
192 GET_FLOAT_WORD(ib,b);
193 a = temp;
194 }
195 if(sign>0) return b; else return -b;
196 }