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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 | /* IEEE754 floating point arithmetic * double precision square root */ /* * MIPS floating point support * Copyright (C) 1994-2000 Algorithmics Ltd. * * This program is free software; you can distribute it and/or modify it * under the terms of the GNU General Public License (Version 2) as * published by the Free Software Foundation. * * This program is distributed in the hope it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. */ #include "ieee754dp.h" static const unsigned int table[] = { 0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, 16499, 12183, 8588, 5674, 3403, 1742, 661, 130 }; union ieee754dp ieee754dp_sqrt(union ieee754dp x) { struct _ieee754_csr oldcsr; union ieee754dp y, z, t; unsigned int scalx, yh; COMPXDP; EXPLODEXDP; ieee754_clearcx(); FLUSHXDP; /* x == INF or NAN? */ switch (xc) { case IEEE754_CLASS_SNAN: return ieee754dp_nanxcpt(x); case IEEE754_CLASS_QNAN: /* sqrt(Nan) = Nan */ return x; case IEEE754_CLASS_ZERO: /* sqrt(0) = 0 */ return x; case IEEE754_CLASS_INF: if (xs) { /* sqrt(-Inf) = Nan */ ieee754_setcx(IEEE754_INVALID_OPERATION); return ieee754dp_indef(); } /* sqrt(+Inf) = Inf */ return x; case IEEE754_CLASS_DNORM: DPDNORMX; /* fall through */ case IEEE754_CLASS_NORM: if (xs) { /* sqrt(-x) = Nan */ ieee754_setcx(IEEE754_INVALID_OPERATION); return ieee754dp_indef(); } break; } /* save old csr; switch off INX enable & flag; set RN rounding */ oldcsr = ieee754_csr; ieee754_csr.mx &= ~IEEE754_INEXACT; ieee754_csr.sx &= ~IEEE754_INEXACT; ieee754_csr.rm = FPU_CSR_RN; /* adjust exponent to prevent overflow */ scalx = 0; if (xe > 512) { /* x > 2**-512? */ xe -= 512; /* x = x / 2**512 */ scalx += 256; } else if (xe < -512) { /* x < 2**-512? */ xe += 512; /* x = x * 2**512 */ scalx -= 256; } x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); y = x; /* magic initial approximation to almost 8 sig. bits */ yh = y.bits >> 32; yh = (yh >> 1) + 0x1ff80000; yh = yh - table[(yh >> 15) & 31]; y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff); /* Heron's rule once with correction to improve to ~18 sig. bits */ /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */ t = ieee754dp_div(x, y); y = ieee754dp_add(y, t); y.bits -= 0x0010000600000000LL; y.bits &= 0xffffffff00000000LL; /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */ /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */ t = ieee754dp_mul(y, y); z = t; t.bexp += 0x001; t = ieee754dp_add(t, z); z = ieee754dp_mul(ieee754dp_sub(x, z), y); /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */ t = ieee754dp_div(z, ieee754dp_add(t, x)); t.bexp += 0x001; y = ieee754dp_add(y, t); /* twiddle last bit to force y correctly rounded */ /* set RZ, clear INEX flag */ ieee754_csr.rm = FPU_CSR_RZ; ieee754_csr.sx &= ~IEEE754_INEXACT; /* t=x/y; ...chopped quotient, possibly inexact */ t = ieee754dp_div(x, y); if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) { if (!(ieee754_csr.sx & IEEE754_INEXACT)) /* t = t-ulp */ t.bits -= 1; /* add inexact to result status */ oldcsr.cx |= IEEE754_INEXACT; oldcsr.sx |= IEEE754_INEXACT; switch (oldcsr.rm) { case FPU_CSR_RU: y.bits += 1; /* fall through */ case FPU_CSR_RN: t.bits += 1; break; } /* y=y+t; ...chopped sum */ y = ieee754dp_add(y, t); /* adjust scalx for correctly rounded sqrt(x) */ scalx -= 1; } /* py[n0]=py[n0]+scalx; ...scale back y */ y.bexp += scalx; /* restore rounding mode, possibly set inexact */ ieee754_csr = oldcsr; return y; } |