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#include <sys/cdefs.h>
17#if defined(LIBM_SCCS) && !defined(lint)
18__RCSID("$NetBSD: k_rem_pio2f.c,v 1.10 2023/08/08 06:31:17 mrg Exp $");
19#endif
20
21#include "namespace.h"
22#include "math.h"
23#include "math_private.h"
24
25/* In the float version, the input parameter x contains 8 bit
26   integers, not 24 bit integers.  113 bit precision is not supported.  */
27
28static const int init_jk[] = {4,7,9}; /* initial value for jk */
29
30static const float PIo2[] = {
31  1.5703125000e+00, /* 0x3fc90000 */
32  4.5776367188e-04, /* 0x39f00000 */
33  2.5987625122e-05, /* 0x37da0000 */
34  7.5437128544e-08, /* 0x33a20000 */
35  6.0026650317e-11, /* 0x2e840000 */
36  7.3896444519e-13, /* 0x2b500000 */
37  5.3845816694e-15, /* 0x27c20000 */
38  5.6378512969e-18, /* 0x22d00000 */
39  8.3009228831e-20, /* 0x1fc40000 */
40  3.2756352257e-22, /* 0x1bc60000 */
41  6.3331015649e-25, /* 0x17440000 */
42};
43
44static const float
45zero   = 0.0,
46one    = 1.0,
47two8   =  2.5600000000e+02, /* 0x43800000 */
48twon8  =  3.9062500000e-03; /* 0x3b800000 */
49
50int
51__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
52{
53	int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
54	float z,fw,f[20],fq[20],q[20];
55
56    /* if nx < 2, fq[0] may be accessed uninitialised */
57	if (nx < 2) {
58	    fq[0] = 0;
59	}
60
61    /* initialize jk*/
62	jk = init_jk[prec];
63	jp = jk;
64
65    /* determine jx,jv,q0, note that 3>q0 */
66	jx =  nx-1;
67	jv = (e0-3)/8; if(jv<0) jv=0;
68	q0 =  e0-8*(jv+1);
69
70    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
71	j = jv-jx; m = jx+jk;
72	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
73
74    /* compute q[0],q[1],...q[jk] */
75	for (i=0;i<=jk;i++) {
76	    for(j=0,fw=0.0;j<=jx;j++)
77		    fw += x[j]*f[jx+i-j];
78	    q[i] = fw;
79	}
80
81	jz = jk;
82recompute:
83    /* distill q[] into iq[] reversingly */
84	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
85	    fw    =  (float)((int32_t)(twon8* z));
86	    iq[i] =  (int32_t)(z-two8*fw);
87	    z     =  q[j-1]+fw;
88	}
89
90    /* compute n */
91	z  = scalbnf(z,q0);		/* actual value of z */
92	z -= (float)8.0*floorf(z*(float)0.125);	/* trim off integer >= 8 */
93	n  = (int32_t) z;
94	z -= (float)n;
95	ih = 0;
96	if(q0>0) {	/* need iq[jz-1] to determine n */
97	    i  = (iq[jz-1]>>(8-q0)); n += i;
98	    iq[jz-1] -= i<<(8-q0);
99	    ih = iq[jz-1]>>(7-q0);
100	}
101	else if(q0==0) ih = iq[jz-1]>>8;
102	else if(z>=(float)0.5) ih=2;
103
104	if(ih>0) {	/* q > 0.5 */
105	    n += 1; carry = 0;
106	    for(i=0;i<jz ;i++) {	/* compute 1-q */
107		j = iq[i];
108		if(carry==0) {
109		    if(j!=0) {
110			carry = 1; iq[i] = 0x100- j;
111		    }
112		} else  iq[i] = 0xff - j;
113	    }
114	    if(q0>0) {		/* rare case: chance is 1 in 12 */
115	        switch(q0) {
116	        case 1:
117	    	   iq[jz-1] &= 0x7f; break;
118	    	case 2:
119	    	   iq[jz-1] &= 0x3f; break;
120	        }
121	    }
122	    if(ih==2) {
123		z = one - z;
124		if(carry!=0) z -= scalbnf(one,q0);
125	    }
126	}
127
128    /* check if recomputation is needed */
129	if(z==zero) {
130	    j = 0;
131	    for (i=jz-1;i>=jk;i--) j |= iq[i];
132	    if(j==0) { /* need recomputation */
133		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
134
135		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
136		    f[jx+i] = (float) ipio2[jv+i];
137		    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
138		    q[i] = fw;
139		}
140		jz += k;
141		goto recompute;
142	    }
143	}
144
145    /* chop off zero terms */
146	if(z==(float)0.0) {
147	    jz -= 1; q0 -= 8;
148	    while(iq[jz]==0) { jz--; q0-=8;}
149	} else { /* break z into 8-bit if necessary */
150	    z = scalbnf(z,-q0);
151	    if(z>=two8) {
152		fw = (float)((int32_t)(twon8*z));
153		iq[jz] = (int32_t)(z-two8*fw);
154		jz += 1; q0 += 8;
155		iq[jz] = (int32_t) fw;
156	    } else iq[jz] = (int32_t) z ;
157	}
158
159    /* convert integer "bit" chunk to floating-point value */
160	fw = scalbnf(one,q0);
161	for(i=jz;i>=0;i--) {
162	    q[i] = fw*(float)iq[i]; fw*=twon8;
163	}
164
165    /* compute PIo2[0,...,jp]*q[jz,...,0] */
166	for(i=jz;i>=0;i--) {
167	    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
168	    fq[jz-i] = fw;
169	}
170
171    /* compress fq[] into y[] */
172	switch(prec) {
173	    case 0:
174		fw = 0.0;
175		for (i=jz;i>=0;i--) fw += fq[i];
176		y[0] = (ih==0)? fw: -fw;
177		break;
178	    case 1:
179	    case 2:
180		fw = 0.0;
181		for (i=jz;i>=0;i--) fw += fq[i];
182		y[0] = (ih==0)? fw: -fw;
183		fw = fq[0]-fw;
184		for (i=1;i<=jz;i++) fw += fq[i];
185		y[1] = (ih==0)? fw: -fw;
186		break;
187	    case 3:	/* painful */
188		for (i=jz;i>0;i--) {
189		    fw      = fq[i-1]+fq[i];
190		    fq[i]  += fq[i-1]-fw;
191		    fq[i-1] = fw;
192		}
193		for (i=jz;i>1;i--) {
194		    fw      = fq[i-1]+fq[i];
195		    fq[i]  += fq[i-1]-fw;
196		    fq[i-1] = fw;
197		}
198		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
199		if(ih==0) {
200		    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
201		} else {
202		    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
203		}
204	}
205	return n&7;
206}
207