| [469] | 1 | /* |
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| 2 | * ==================================================== |
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| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 4 | * |
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| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 6 | * Permission to use, copy, modify, and distribute this |
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| 7 | * software is freely granted, provided that this notice |
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| 8 | * is preserved. |
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| 9 | * ==================================================== |
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| 10 | */ |
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| 11 | |
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| 12 | /* |
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| 13 | * Modified for ALMOS-MKH OS at UPMC, France, August 2018. (Alain Greiner) |
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| 14 | */ |
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| 15 | |
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| 16 | /* __ieee754_rem_pio2(x,y) |
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| 17 | * |
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| 18 | * return the remainder of x rem pi/2 in y[0]+y[1] |
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| 19 | * use __kernel_rem_pio2() |
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| 20 | */ |
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| 21 | |
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| 22 | #include "math.h" |
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| 23 | #include "math_private.h" |
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| 24 | |
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| 25 | /* |
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| 26 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
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| 27 | */ |
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| 28 | static const int32_t two_over_pi[] = { |
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| 29 | 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
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| 30 | 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
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| 31 | 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
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| 32 | 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
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| 33 | 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
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| 34 | 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
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| 35 | 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
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| 36 | 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
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| 37 | 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
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| 38 | 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
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| 39 | 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
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| 40 | }; |
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| 41 | |
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| 42 | static const int32_t npio2_hw[] = { |
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| 43 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
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| 44 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
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| 45 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
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| 46 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
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| 47 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
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| 48 | 0x404858EB, 0x404921FB, |
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| 49 | }; |
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| 50 | |
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| 51 | /* |
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| 52 | * invpio2: 53 bits of 2/pi |
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| 53 | * pio2_1: first 33 bit of pi/2 |
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| 54 | * pio2_1t: pi/2 - pio2_1 |
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| 55 | * pio2_2: second 33 bit of pi/2 |
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| 56 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
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| 57 | * pio2_3: third 33 bit of pi/2 |
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| 58 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
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| 59 | */ |
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| 60 | |
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| 61 | static const double |
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| 62 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 63 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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| 64 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
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| 65 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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| 66 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
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| 67 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
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| 68 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
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| 69 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
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| 70 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
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| 71 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
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| 72 | |
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| 73 | int __ieee754_rem_pio2(double x, double *y) |
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| 74 | { |
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| 75 | double z=0.0,w,t,r,fn; |
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| 76 | double tx[3]; |
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| 77 | int32_t e0,i,j,nx,n,ix,hx; |
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| 78 | uint32_t low; |
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| 79 | |
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| 80 | GET_HIGH_WORD(hx,x); /* high word of x */ |
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| 81 | ix = hx&0x7fffffff; |
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| 82 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
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| 83 | {y[0] = x; y[1] = 0; return 0;} |
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| 84 | if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
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| 85 | if(hx>0) { |
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| 86 | z = x - pio2_1; |
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| 87 | if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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| 88 | y[0] = z - pio2_1t; |
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| 89 | y[1] = (z-y[0])-pio2_1t; |
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| 90 | } else { /* near pi/2, use 33+33+53 bit pi */ |
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| 91 | z -= pio2_2; |
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| 92 | y[0] = z - pio2_2t; |
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| 93 | y[1] = (z-y[0])-pio2_2t; |
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| 94 | } |
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| 95 | return 1; |
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| 96 | } else { /* negative x */ |
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| 97 | z = x + pio2_1; |
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| 98 | if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
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| 99 | y[0] = z + pio2_1t; |
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| 100 | y[1] = (z-y[0])+pio2_1t; |
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| 101 | } else { /* near pi/2, use 33+33+53 bit pi */ |
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| 102 | z += pio2_2; |
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| 103 | y[0] = z + pio2_2t; |
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| 104 | y[1] = (z-y[0])+pio2_2t; |
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| 105 | } |
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| 106 | return -1; |
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| 107 | } |
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| 108 | } |
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| 109 | if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
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| 110 | t = fabs(x); |
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| 111 | n = (int32_t) (t*invpio2+half); |
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| 112 | fn = (double)n; |
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| 113 | r = t-fn*pio2_1; |
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| 114 | w = fn*pio2_1t; /* 1st round good to 85 bit */ |
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| 115 | if(n<32&&ix!=npio2_hw[n-1]) { |
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| 116 | y[0] = r-w; /* quick check no cancellation */ |
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| 117 | } else { |
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| 118 | uint32_t high; |
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| 119 | j = ix>>20; |
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| 120 | y[0] = r-w; |
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| 121 | GET_HIGH_WORD(high,y[0]); |
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| 122 | i = j-((high>>20)&0x7ff); |
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| 123 | if(i>16) { /* 2nd iteration needed, good to 118 */ |
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| 124 | t = r; |
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| 125 | w = fn*pio2_2; |
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| 126 | r = t-w; |
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| 127 | w = fn*pio2_2t-((t-r)-w); |
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| 128 | y[0] = r-w; |
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| 129 | GET_HIGH_WORD(high,y[0]); |
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| 130 | i = j-((high>>20)&0x7ff); |
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| 131 | if(i>49) { /* 3rd iteration need, 151 bits acc */ |
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| 132 | t = r; /* will cover all possible cases */ |
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| 133 | w = fn*pio2_3; |
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| 134 | r = t-w; |
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| 135 | w = fn*pio2_3t-((t-r)-w); |
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| 136 | y[0] = r-w; |
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| 137 | } |
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| 138 | } |
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| 139 | } |
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| 140 | y[1] = (r-y[0])-w; |
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| 141 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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| 142 | else return n; |
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| 143 | } |
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| 144 | /* |
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| 145 | * all other (large) arguments |
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| 146 | */ |
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| 147 | if(ix>=0x7ff00000) { /* x is inf or NaN */ |
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| 148 | y[0]=y[1]=x-x; return 0; |
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| 149 | } |
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| 150 | /* set z = scalbn(|x|,ilogb(x)-23) */ |
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| 151 | GET_LOW_WORD(low,x); |
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| 152 | SET_LOW_WORD(z,low); |
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| 153 | e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
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| 154 | SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); |
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| 155 | for(i=0;i<2;i++) { |
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| 156 | tx[i] = (double)((int32_t)(z)); |
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| 157 | z = (z-tx[i])*two24; |
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| 158 | } |
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| 159 | tx[2] = z; |
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| 160 | nx = 3; |
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| 161 | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
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| 162 | n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
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| 163 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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| 164 | return n; |
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| 165 | } |
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