1/* k_rem_pio2f.c -- float version of k_rem_pio2.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
17static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_rem_pio2f.c,v 1.8 2005/10/11 07:56:05 bde Exp $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23/* In the float version, the input parameter x contains 8 bit
24   integers, not 24 bit integers.  113 bit precision is not supported.  */
25
26static const int init_jk[] = {4,7,9}; /* initial value for jk */
27
28static const float PIo2[] = {
29  1.5703125000e+00, /* 0x3fc90000 */
30  4.5776367188e-04, /* 0x39f00000 */
31  2.5987625122e-05, /* 0x37da0000 */
32  7.5437128544e-08, /* 0x33a20000 */
33  6.0026650317e-11, /* 0x2e840000 */
34  7.3896444519e-13, /* 0x2b500000 */
35  5.3845816694e-15, /* 0x27c20000 */
36  5.6378512969e-18, /* 0x22d00000 */
37  8.3009228831e-20, /* 0x1fc40000 */
38  3.2756352257e-22, /* 0x1bc60000 */
39  6.3331015649e-25, /* 0x17440000 */
40};
41
42static const float
43zero   = 0.0,
44one    = 1.0,
45two8   =  2.5600000000e+02, /* 0x43800000 */
46twon8  =  3.9062500000e-03; /* 0x3b800000 */
47
48	int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
49{
50	int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
51	float z,fw,f[20],fq[20],q[20];
52
53    /* initialize jk*/
54	jk = init_jk[prec];
55	jp = jk;
56
57    /* determine jx,jv,q0, note that 3>q0 */
58	jx =  nx-1;
59	jv = (e0-3)/8; if(jv<0) jv=0;
60	q0 =  e0-8*(jv+1);
61
62    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
63	j = jv-jx; m = jx+jk;
64	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
65
66    /* compute q[0],q[1],...q[jk] */
67	for (i=0;i<=jk;i++) {
68	    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
69	}
70
71	jz = jk;
72recompute:
73    /* distill q[] into iq[] reversingly */
74	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
75	    fw    =  (float)((int32_t)(twon8* z));
76	    iq[i] =  (int32_t)(z-two8*fw);
77	    z     =  q[j-1]+fw;
78	}
79
80    /* compute n */
81	z  = scalbnf(z,q0);		/* actual value of z */
82	z -= (float)8.0*floorf(z*(float)0.125);	/* trim off integer >= 8 */
83	n  = (int32_t) z;
84	z -= (float)n;
85	ih = 0;
86	if(q0>0) {	/* need iq[jz-1] to determine n */
87	    i  = (iq[jz-1]>>(8-q0)); n += i;
88	    iq[jz-1] -= i<<(8-q0);
89	    ih = iq[jz-1]>>(7-q0);
90	}
91	else if(q0==0) ih = iq[jz-1]>>7;
92	else if(z>=(float)0.5) ih=2;
93
94	if(ih>0) {	/* q > 0.5 */
95	    n += 1; carry = 0;
96	    for(i=0;i<jz ;i++) {	/* compute 1-q */
97		j = iq[i];
98		if(carry==0) {
99		    if(j!=0) {
100			carry = 1; iq[i] = 0x100- j;
101		    }
102		} else  iq[i] = 0xff - j;
103	    }
104	    if(q0>0) {		/* rare case: chance is 1 in 12 */
105	        switch(q0) {
106	        case 1:
107	    	   iq[jz-1] &= 0x7f; break;
108	    	case 2:
109	    	   iq[jz-1] &= 0x3f; break;
110	        }
111	    }
112	    if(ih==2) {
113		z = one - z;
114		if(carry!=0) z -= scalbnf(one,q0);
115	    }
116	}
117
118    /* check if recomputation is needed */
119	if(z==zero) {
120	    j = 0;
121	    for (i=jz-1;i>=jk;i--) j |= iq[i];
122	    if(j==0) { /* need recomputation */
123		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
124
125		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
126		    f[jx+i] = (float) ipio2[jv+i];
127		    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
128		    q[i] = fw;
129		}
130		jz += k;
131		goto recompute;
132	    }
133	}
134
135    /* chop off zero terms */
136	if(z==(float)0.0) {
137	    jz -= 1; q0 -= 8;
138	    while(iq[jz]==0) { jz--; q0-=8;}
139	} else { /* break z into 8-bit if necessary */
140	    z = scalbnf(z,-q0);
141	    if(z>=two8) {
142		fw = (float)((int32_t)(twon8*z));
143		iq[jz] = (int32_t)(z-two8*fw);
144		jz += 1; q0 += 8;
145		iq[jz] = (int32_t) fw;
146	    } else iq[jz] = (int32_t) z ;
147	}
148
149    /* convert integer "bit" chunk to floating-point value */
150	fw = scalbnf(one,q0);
151	for(i=jz;i>=0;i--) {
152	    q[i] = fw*(float)iq[i]; fw*=twon8;
153	}
154
155    /* compute PIo2[0,...,jp]*q[jz,...,0] */
156	for(i=jz;i>=0;i--) {
157	    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
158	    fq[jz-i] = fw;
159	}
160
161    /* compress fq[] into y[] */
162	switch(prec) {
163	    case 0:
164		fw = 0.0;
165		for (i=jz;i>=0;i--) fw += fq[i];
166		y[0] = (ih==0)? fw: -fw;
167		break;
168	    case 1:
169	    case 2:
170		fw = 0.0;
171		for (i=jz;i>=0;i--) fw += fq[i];
172		fw = *(volatile float *)&fw;	/* clip any extra precision */
173		y[0] = (ih==0)? fw: -fw;
174		fw = fq[0]-fw;
175		for (i=1;i<=jz;i++) fw += fq[i];
176		y[1] = (ih==0)? fw: -fw;
177		break;
178	    case 3:	/* painful */
179		for (i=jz;i>0;i--) {
180		    fw      = fq[i-1]+fq[i];
181		    fq[i]  += fq[i-1]-fw;
182		    fq[i-1] = fw;
183		}
184		for (i=jz;i>1;i--) {
185		    fw      = fq[i-1]+fq[i];
186		    fq[i]  += fq[i-1]-fw;
187		    fq[i-1] = fw;
188		}
189		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
190		if(ih==0) {
191		    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
192		} else {
193		    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
194		}
195	}
196	return n&7;
197}
198