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| Rev | Author | Line No. | Line |
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| 2 | pj | 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. |
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| 3 | */ |
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| 4 | |||
| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | */ |
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| 15 | |||
| 16 | #ifndef lint |
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| 17 | static char rcsid[] = "$\Id: k_rem_pio2f.c,v 1.2 1995/05/30 05:49:00 rgrimes Exp $"; |
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| 18 | #endif |
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| 19 | |||
| 20 | #include "math.h" |
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| 21 | #include "math_private.h" |
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| 22 | |||
| 23 | /* In the float version, the input parameter x contains 8 bit |
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| 24 | integers, not 24 bit integers. 113 bit precision is not supported. */ |
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| 25 | |||
| 26 | #ifdef __STDC__ |
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| 27 | static const int init_jk[] = {4,7,9}; /* initial value for jk */ |
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| 28 | #else |
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| 29 | static int init_jk[] = {4,7,9}; |
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| 30 | #endif |
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| 31 | |||
| 32 | #ifdef __STDC__ |
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| 33 | static const float PIo2[] = { |
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| 34 | #else |
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| 35 | static float PIo2[] = { |
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| 36 | #endif |
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| 37 | 1.5703125000e+00, /* 0x3fc90000 */ |
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| 38 | 4.5776367188e-04, /* 0x39f00000 */ |
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| 39 | 2.5987625122e-05, /* 0x37da0000 */ |
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| 40 | 7.5437128544e-08, /* 0x33a20000 */ |
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| 41 | 6.0026650317e-11, /* 0x2e840000 */ |
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| 42 | 7.3896444519e-13, /* 0x2b500000 */ |
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| 43 | 5.3845816694e-15, /* 0x27c20000 */ |
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| 44 | 5.6378512969e-18, /* 0x22d00000 */ |
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| 45 | 8.3009228831e-20, /* 0x1fc40000 */ |
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| 46 | 3.2756352257e-22, /* 0x1bc60000 */ |
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| 47 | 6.3331015649e-25, /* 0x17440000 */ |
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| 48 | }; |
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| 49 | |||
| 50 | #ifdef __STDC__ |
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| 51 | static const float |
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| 52 | #else |
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| 53 | static float |
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| 54 | #endif |
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| 55 | zero = 0.0, |
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| 56 | one = 1.0, |
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| 57 | two8 = 2.5600000000e+02, /* 0x43800000 */ |
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| 58 | twon8 = 3.9062500000e-03; /* 0x3b800000 */ |
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| 59 | |||
| 60 | #ifdef __STDC__ |
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| 61 | int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) |
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| 62 | #else |
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| 63 | int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) |
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| 64 | float x[], y[]; int e0,nx,prec; int32_t ipio2[]; |
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| 65 | #endif |
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| 66 | { |
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| 67 | int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; |
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| 68 | float z,fw,f[20],fq[20],q[20]; |
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| 69 | |||
| 70 | /* initialize jk*/ |
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| 71 | jk = init_jk[prec]; |
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| 72 | jp = jk; |
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| 73 | |||
| 74 | /* determine jx,jv,q0, note that 3>q0 */ |
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| 75 | jx = nx-1; |
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| 76 | jv = (e0-3)/8; if(jv<0) jv=0; |
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| 77 | q0 = e0-8*(jv+1); |
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| 78 | |||
| 79 | /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ |
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| 80 | j = jv-jx; m = jx+jk; |
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| 81 | for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; |
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| 82 | |||
| 83 | /* compute q[0],q[1],...q[jk] */ |
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| 84 | for (i=0;i<=jk;i++) { |
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| 85 | for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; |
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| 86 | } |
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| 87 | |||
| 88 | jz = jk; |
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| 89 | recompute: |
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| 90 | /* distill q[] into iq[] reversingly */ |
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| 91 | for(i=0,j=jz,z=q[jz];j>0;i++,j--) { |
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| 92 | fw = (float)((int32_t)(twon8* z)); |
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| 93 | iq[i] = (int32_t)(z-two8*fw); |
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| 94 | z = q[j-1]+fw; |
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| 95 | } |
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| 96 | |||
| 97 | /* compute n */ |
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| 98 | z = scalbnf(z,q0); /* actual value of z */ |
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| 99 | z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ |
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| 100 | n = (int32_t) z; |
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| 101 | z -= (float)n; |
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| 102 | ih = 0; |
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| 103 | if(q0>0) { /* need iq[jz-1] to determine n */ |
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| 104 | i = (iq[jz-1]>>(8-q0)); n += i; |
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| 105 | iq[jz-1] -= i<<(8-q0); |
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| 106 | ih = iq[jz-1]>>(7-q0); |
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| 107 | } |
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| 108 | else if(q0==0) ih = iq[jz-1]>>8; |
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| 109 | else if(z>=(float)0.5) ih=2; |
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| 110 | |||
| 111 | if(ih>0) { /* q > 0.5 */ |
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| 112 | n += 1; carry = 0; |
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| 113 | for(i=0;i<jz ;i++) { /* compute 1-q */ |
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| 114 | j = iq[i]; |
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| 115 | if(carry==0) { |
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| 116 | if(j!=0) { |
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| 117 | carry = 1; iq[i] = 0x100- j; |
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| 118 | } |
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| 119 | } else iq[i] = 0xff - j; |
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| 120 | } |
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| 121 | if(q0>0) { /* rare case: chance is 1 in 12 */ |
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| 122 | switch(q0) { |
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| 123 | case 1: |
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| 124 | iq[jz-1] &= 0x7f; break; |
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| 125 | case 2: |
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| 126 | iq[jz-1] &= 0x3f; break; |
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| 127 | } |
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| 128 | } |
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| 129 | if(ih==2) { |
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| 130 | z = one - z; |
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| 131 | if(carry!=0) z -= scalbnf(one,q0); |
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| 132 | } |
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| 133 | } |
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| 134 | |||
| 135 | /* check if recomputation is needed */ |
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| 136 | if(z==zero) { |
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| 137 | j = 0; |
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| 138 | for (i=jz-1;i>=jk;i--) j |= iq[i]; |
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| 139 | if(j==0) { /* need recomputation */ |
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| 140 | for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ |
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| 141 | |||
| 142 | for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ |
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| 143 | f[jx+i] = (float) ipio2[jv+i]; |
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| 144 | for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; |
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| 145 | q[i] = fw; |
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| 146 | } |
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| 147 | jz += k; |
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| 148 | goto recompute; |
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| 149 | } |
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| 150 | } |
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| 151 | |||
| 152 | /* chop off zero terms */ |
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| 153 | if(z==(float)0.0) { |
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| 154 | jz -= 1; q0 -= 8; |
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| 155 | while(iq[jz]==0) { jz--; q0-=8;} |
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| 156 | } else { /* break z into 8-bit if necessary */ |
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| 157 | z = scalbnf(z,-q0); |
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| 158 | if(z>=two8) { |
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| 159 | fw = (float)((int32_t)(twon8*z)); |
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| 160 | iq[jz] = (int32_t)(z-two8*fw); |
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| 161 | jz += 1; q0 += 8; |
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| 162 | iq[jz] = (int32_t) fw; |
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| 163 | } else iq[jz] = (int32_t) z ; |
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| 164 | } |
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| 165 | |||
| 166 | /* convert integer "bit" chunk to floating-point value */ |
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| 167 | fw = scalbnf(one,q0); |
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| 168 | for(i=jz;i>=0;i--) { |
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| 169 | q[i] = fw*(float)iq[i]; fw*=twon8; |
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| 170 | } |
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| 171 | |||
| 172 | /* compute PIo2[0,...,jp]*q[jz,...,0] */ |
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| 173 | for(i=jz;i>=0;i--) { |
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| 174 | for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; |
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| 175 | fq[jz-i] = fw; |
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| 176 | } |
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| 177 | |||
| 178 | /* compress fq[] into y[] */ |
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| 179 | switch(prec) { |
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| 180 | case 0: |
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| 181 | fw = 0.0; |
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| 182 | for (i=jz;i>=0;i--) fw += fq[i]; |
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| 183 | y[0] = (ih==0)? fw: -fw; |
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| 184 | break; |
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| 185 | case 1: |
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| 186 | case 2: |
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| 187 | fw = 0.0; |
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| 188 | for (i=jz;i>=0;i--) fw += fq[i]; |
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| 189 | y[0] = (ih==0)? fw: -fw; |
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| 190 | fw = fq[0]-fw; |
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| 191 | for (i=1;i<=jz;i++) fw += fq[i]; |
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| 192 | y[1] = (ih==0)? fw: -fw; |
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| 193 | break; |
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| 194 | case 3: /* painful */ |
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| 195 | for (i=jz;i>0;i--) { |
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| 196 | fw = fq[i-1]+fq[i]; |
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| 197 | fq[i] += fq[i-1]-fw; |
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| 198 | fq[i-1] = fw; |
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| 199 | } |
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| 200 | for (i=jz;i>1;i--) { |
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| 201 | fw = fq[i-1]+fq[i]; |
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| 202 | fq[i] += fq[i-1]-fw; |
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| 203 | fq[i-1] = fw; |
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| 204 | } |
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| 205 | for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; |
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| 206 | if(ih==0) { |
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| 207 | y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; |
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| 208 | } else { |
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| 209 | y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; |
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| 210 | } |
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| 211 | } |
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| 212 | return n&7; |
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| 213 | } |