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