1 /* kf_rem_pio2.c -- float version of k_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
18 /* In the float version, the input parameter x contains 8 bit
19 integers, not 24 bit integers. 113 bit precision is not supported. */
22 static const int init_jk[] = {4,7,9}; /* initial value for jk */
24 static int init_jk[] = {4,7,9};
28 static const float PIo2[] = {
30 static float PIo2[] = {
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 */
52 two8 = 2.5600000000e+02, /* 0x43800000 */
53 twon8 = 3.9062500000e-03; /* 0x3b800000 */
56 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
58 int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
59 float x[], y[]; int e0,nx,prec; __int32_t ipio2[];
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];
69 /* determine jx,jv,q0, note that 3>q0 */
71 jv = (e0-3)/8; if(jv<0) jv=0;
74 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
76 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
78 /* compute q[0],q[1],...q[jk] */
80 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
85 /* distill q[] into iq[] reversingly */
86 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
87 fw = (float)((__int32_t)(twon8* z));
88 iq[i] = (__int32_t)(z-two8*fw);
93 z = scalbnf(z,(int)q0); /* actual value of z */
94 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
98 if(q0>0) { /* need iq[jz-1] to determine n */
99 i = (iq[jz-1]>>(8-q0)); n += i;
100 iq[jz-1] -= i<<(8-q0);
101 ih = iq[jz-1]>>(7-q0);
103 else if(q0==0) ih = iq[jz-1]>>8;
104 else if(z>=(float)0.5) ih=2;
106 if(ih>0) { /* q > 0.5 */
108 for(i=0;i<jz ;i++) { /* compute 1-q */
112 carry = 1; iq[i] = 0x100- j;
114 } else iq[i] = 0xff - j;
116 if(q0>0) { /* rare case: chance is 1 in 12 */
119 iq[jz-1] &= 0x7f; break;
121 iq[jz-1] &= 0x3f; break;
126 if(carry!=0) z -= scalbnf(one,(int)q0);
130 /* check if recomputation is needed */
133 for (i=jz-1;i>=jk;i--) j |= iq[i];
134 if(j==0) { /* need recomputation */
135 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
137 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
138 f[jx+i] = (float) ipio2[jv+i];
139 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
147 /* chop off zero terms */
150 while(iq[jz]==0) { jz--; q0-=8;}
151 } else { /* break z into 8-bit if necessary */
152 z = scalbnf(z,-(int)q0);
154 fw = (float)((__int32_t)(twon8*z));
155 iq[jz] = (__int32_t)(z-two8*fw);
157 iq[jz] = (__int32_t) fw;
158 } else iq[jz] = (__int32_t) z ;
161 /* convert integer "bit" chunk to floating-point value */
162 fw = scalbnf(one,(int)q0);
164 q[i] = fw*(float)iq[i]; fw*=twon8;
167 /* compute PIo2[0,...,jp]*q[jz,...,0] */
169 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
173 /* compress fq[] into y[] */
177 for (i=jz;i>=0;i--) fw += fq[i];
178 y[0] = (ih==0)? fw: -fw;
183 for (i=jz;i>=0;i--) fw += fq[i];
184 y[0] = (ih==0)? fw: -fw;
186 for (i=1;i<=jz;i++) fw += fq[i];
187 y[1] = (ih==0)? fw: -fw;
189 case 3: /* painful */
200 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
202 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
204 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;