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4:
5: 6: 7: 8: 9: 10: 11: 12: 13: 14:
15:
16: #include "math.h"
17: #include "math_private.h"
18:
19: 20:
21:
22: static const int init_jk[] = {4,7,9};
23:
24: static const float PIo2[] = {
25: 1.5703125000e+00,
26: 4.5776367188e-04,
27: 2.5987625122e-05,
28: 7.5437128544e-08,
29: 6.0026650317e-11,
30: 7.3896444519e-13,
31: 5.3845816694e-15,
32: 5.6378512969e-18,
33: 8.3009228831e-20,
34: 3.2756352257e-22,
35: 6.3331015649e-25,
36: };
37:
38: static const float
39: zero = 0.0,
40: one = 1.0,
41: two8 = 2.5600000000e+02,
42: twon8 = 3.9062500000e-03;
43:
44: int
45: __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec,
46: const int32_t *ipio2)
47: {
48: int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
49: float z,fw,f[20],fq[20],q[20];
50:
51:
52: jk = init_jk[prec];
53: jp = jk;
54:
55:
56: jx = nx-1;
57: jv = (e0-3)/8; if(jv<0) jv=0;
58: q0 = e0-8*(jv+1);
59:
60:
61: j = jv-jx; m = jx+jk;
62: for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
63:
64:
65: for (i=0;i<=jk;i++) {
66: for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
67: }
68:
69: jz = jk;
70: recompute:
71:
72: for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
73: fw = (float)((int32_t)(twon8* z));
74: iq[i] = (int32_t)(z-two8*fw);
75: z = q[j-1]+fw;
76: }
77:
78:
79: z = scalbnf(z,q0);
80: z -= (float)8.0*floorf(z*(float)0.125);
81: n = (int32_t) z;
82: z -= (float)n;
83: ih = 0;
84: if(q0>0) {
85: i = (iq[jz-1]>>(8-q0)); n += i;
86: iq[jz-1] -= i<<(8-q0);
87: ih = iq[jz-1]>>(7-q0);
88: }
89: else if(q0==0) ih = iq[jz-1]>>8;
90: else if(z>=(float)0.5) ih=2;
91:
92: if(ih>0) {
93: n += 1; carry = 0;
94: for(i=0;i<jz ;i++) {
95: j = iq[i];
96: if(carry==0) {
97: if(j!=0) {
98: carry = 1; iq[i] = 0x100- j;
99: }
100: } else iq[i] = 0xff - j;
101: }
102: if(q0>0) {
103: switch(q0) {
104: case 1:
105: iq[jz-1] &= 0x7f; break;
106: case 2:
107: iq[jz-1] &= 0x3f; break;
108: }
109: }
110: if(ih==2) {
111: z = one - z;
112: if(carry!=0) z -= scalbnf(one,q0);
113: }
114: }
115:
116:
117: if(z==zero) {
118: j = 0;
119: for (i=jz-1;i>=jk;i--) j |= iq[i];
120: if(j==0) {
121: for(k=1;iq[jk-k]==0;k++);
122:
123: for(i=jz+1;i<=jz+k;i++) {
124: f[jx+i] = (float) ipio2[jv+i];
125: for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
126: q[i] = fw;
127: }
128: jz += k;
129: goto recompute;
130: }
131: }
132:
133:
134: if(z==(float)0.0) {
135: jz -= 1; q0 -= 8;
136: while(iq[jz]==0) { jz--; q0-=8;}
137: } else {
138: z = scalbnf(z,-q0);
139: if(z>=two8) {
140: fw = (float)((int32_t)(twon8*z));
141: iq[jz] = (int32_t)(z-two8*fw);
142: jz += 1; q0 += 8;
143: iq[jz] = (int32_t) fw;
144: } else iq[jz] = (int32_t) z ;
145: }
146:
147:
148: fw = scalbnf(one,q0);
149: for(i=jz;i>=0;i--) {
150: q[i] = fw*(float)iq[i]; fw*=twon8;
151: }
152:
153:
154: for(i=jz;i>=0;i--) {
155: for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
156: fq[jz-i] = fw;
157: }
158:
159:
160: switch(prec) {
161: case 0:
162: fw = 0.0;
163: for (i=jz;i>=0;i--) fw += fq[i];
164: y[0] = (ih==0)? fw: -fw;
165: break;
166: case 1:
167: case 2:
168: fw = 0.0;
169: for (i=jz;i>=0;i--) fw += fq[i];
170: y[0] = (ih==0)? fw: -fw;
171: fw = fq[0]-fw;
172: for (i=1;i<=jz;i++) fw += fq[i];
173: y[1] = (ih==0)? fw: -fw;
174: break;
175: case 3:
176: for (i=jz;i>0;i--) {
177: fw = fq[i-1]+fq[i];
178: fq[i] += fq[i-1]-fw;
179: fq[i-1] = fw;
180: }
181: for (i=jz;i>1;i--) {
182: fw = fq[i-1]+fq[i];
183: fq[i] += fq[i-1]-fw;
184: fq[i-1] = fw;
185: }
186: for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
187: if(ih==0) {
188: y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
189: } else {
190: y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
191: }
192: }
193: return n&7;
194: }