1 /* kf_rem_pio2.c -- float version of k_rem_pio2.c
2  * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
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 "fdlibm.h"
17 
18 /* In the float version, the input parameter x contains 8 bit
19    integers, not 24 bit integers.  113 bit precision is not supported.  */
20 
21 #ifdef __STDC__
22 static const int init_jk[] = {4,7,9}; /* initial value for jk */
23 #else
24 static int init_jk[] = {4,7,9};
25 #endif
26 
27 #ifdef __STDC__
28 static const float PIo2[] = {
29 #else
30 static float PIo2[] = {
31 #endif
32   1.5703125000e+00, /* 0x3fc90000 */
33   4.5776367188e-04, /* 0x39f00000 */
34   2.5987625122e-05, /* 0x37da0000 */
35   7.5437128544e-08, /* 0x33a20000 */
36   6.0026650317e-11, /* 0x2e840000 */
37   7.3896444519e-13, /* 0x2b500000 */
38   5.3845816694e-15, /* 0x27c20000 */
39   5.6378512969e-18, /* 0x22d00000 */
40   8.3009228831e-20, /* 0x1fc40000 */
41   3.2756352257e-22, /* 0x1bc60000 */
42   6.3331015649e-25, /* 0x17440000 */
43 };
44 
45 #ifdef __STDC__
46 static const float
47 #else
48 static float
49 #endif
50 zero   = 0.0,
51 one    = 1.0,
52 two8   =  2.5600000000e+02, /* 0x43800000 */
53 twon8  =  3.9062500000e-03; /* 0x3b800000 */
54 
55 #ifdef __STDC__
__kernel_rem_pio2f(float * x,float * y,int e0,int nx,int prec,const __int32_t * ipio2)56 	int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
57 #else
58 	int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
59 	float x[], y[]; int e0,nx,prec; __int32_t ipio2[];
60 #endif
61 {
62 	__int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
63 	float z,fw,f[20],fq[20],q[20];
64 
65     /* initialize jk*/
66 	jk = init_jk[prec];
67 	jp = jk;
68 
69     /* determine jx,jv,q0, note that 3>q0 */
70 	jx =  nx-1;
71 	jv = (e0-3)/8; if(jv<0) jv=0;
72 	q0 =  e0-8*(jv+1);
73 
74     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
75 	j = jv-jx; m = jx+jk;
76 	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
77 
78     /* compute q[0],q[1],...q[jk] */
79 	for (i=0;i<=jk;i++) {
80 	    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
81 	    q[i] = fw;
82 	}
83 
84 	jz = jk;
85 recompute:
86     /* distill q[] into iq[] reversingly */
87 	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
88 	    fw    =  (float)((__int32_t)(twon8* z));
89 	    iq[i] =  (__int32_t)(z-two8*fw);
90 	    z     =  q[j-1]+fw;
91 	}
92 
93     /* compute n */
94 	z  = scalbnf(z,(int)q0);	/* actual value of z */
95 	z -= (float)8.0*floorf(z*(float)0.125);	/* trim off integer >= 8 */
96 	n  = (__int32_t) z;
97 	z -= (float)n;
98 	ih = 0;
99 	if(q0>0) {	/* need iq[jz-1] to determine n */
100 	    i  = (iq[jz-1]>>(8-q0)); n += i;
101 	    iq[jz-1] -= i<<(8-q0);
102 	    ih = iq[jz-1]>>(7-q0);
103 	}
104 	else if(q0==0) ih = iq[jz-1]>>8;
105 	else if(z>=(float)0.5) ih=2;
106 
107 	if(ih>0) {	/* q > 0.5 */
108 	    n += 1; carry = 0;
109 	    for(i=0;i<jz ;i++) {	/* compute 1-q */
110 		j = iq[i];
111 		if(carry==0) {
112 		    if(j!=0) {
113 			carry = 1; iq[i] = 0x100- j;
114 		    }
115 		} else  iq[i] = 0xff - j;
116 	    }
117 	    if(q0>0) {		/* rare case: chance is 1 in 12 */
118 	        switch(q0) {
119 	        case 1:
120 	    	   iq[jz-1] &= 0x7f; break;
121 	    	case 2:
122 	    	   iq[jz-1] &= 0x3f; break;
123 	        }
124 	    }
125 	    if(ih==2) {
126 		z = one - z;
127 		if(carry!=0) z -= scalbnf(one,(int)q0);
128 	    }
129 	}
130 
131     /* check if recomputation is needed */
132 	if(z==zero) {
133 	    j = 0;
134 	    for (i=jz-1;i>=jk;i--) j |= iq[i];
135 	    if(j==0) { /* need recomputation */
136 		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
137 
138 		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
139 		    f[jx+i] = (float) ipio2[jv+i];
140 		    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
141 		    q[i] = fw;
142 		}
143 		jz += k;
144 		goto recompute;
145 	    }
146 	}
147 
148     /* chop off zero terms */
149 	if(z==(float)0.0) {
150 	    jz -= 1; q0 -= 8;
151 	    while(iq[jz]==0) { jz--; q0-=8;}
152 	} else { /* break z into 8-bit if necessary */
153 	    z = scalbnf(z,-(int)q0);
154 	    if(z>=two8) {
155 		fw = (float)((__int32_t)(twon8*z));
156 		iq[jz] = (__int32_t)(z-two8*fw);
157 		jz += 1; q0 += 8;
158 		iq[jz] = (__int32_t) fw;
159 	    } else iq[jz] = (__int32_t) z ;
160 	}
161 
162     /* convert integer "bit" chunk to floating-point value */
163 	fw = scalbnf(one,(int)q0);
164 	for(i=jz;i>=0;i--) {
165 	    q[i] = fw*(float)iq[i]; fw*=twon8;
166 	}
167 
168     /* compute PIo2[0,...,jp]*q[jz,...,0] */
169 	for(i=jz;i>=0;i--) {
170 	    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
171 	    fq[jz-i] = fw;
172 	}
173 
174     /* compress fq[] into y[] */
175 	switch(prec) {
176 	    case 0:
177 		fw = 0.0;
178 		for (i=jz;i>=0;i--) fw += fq[i];
179 		y[0] = (ih==0)? fw: -fw;
180 		break;
181 	    case 1:
182 	    case 2:
183 		fw = 0.0;
184 		for (i=jz;i>=0;i--) fw += fq[i];
185 		y[0] = (ih==0)? fw: -fw;
186 		fw = fq[0]-fw;
187 		for (i=1;i<=jz;i++) fw += fq[i];
188 		y[1] = (ih==0)? fw: -fw;
189 		break;
190 	    case 3:	/* painful */
191 		for (i=jz;i>0;i--) {
192 		    fw      = fq[i-1]+fq[i];
193 		    fq[i]  += fq[i-1]-fw;
194 		    fq[i-1] = fw;
195 		}
196 		for (i=jz;i>1;i--) {
197 		    fw      = fq[i-1]+fq[i];
198 		    fq[i]  += fq[i-1]-fw;
199 		    fq[i-1] = fw;
200 		}
201 		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
202 		if(ih==0) {
203 		    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
204 		} else {
205 		    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
206 		}
207 	}
208 	return n&7;
209 }
210