Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | /* IEEE754 floating point arithmetic |
| 2 | * double precision square root |
| 3 | */ |
| 4 | /* |
| 5 | * MIPS floating point support |
| 6 | * Copyright (C) 1994-2000 Algorithmics Ltd. |
| 7 | * http://www.algor.co.uk |
| 8 | * |
| 9 | * ######################################################################## |
| 10 | * |
| 11 | * This program is free software; you can distribute it and/or modify it |
| 12 | * under the terms of the GNU General Public License (Version 2) as |
| 13 | * published by the Free Software Foundation. |
| 14 | * |
| 15 | * This program is distributed in the hope it will be useful, but WITHOUT |
| 16 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| 17 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 18 | * for more details. |
| 19 | * |
| 20 | * You should have received a copy of the GNU General Public License along |
| 21 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 22 | * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA. |
| 23 | * |
| 24 | * ######################################################################## |
| 25 | */ |
| 26 | |
| 27 | |
| 28 | #include "ieee754dp.h" |
| 29 | |
| 30 | static const unsigned table[] = { |
| 31 | 0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, |
| 32 | 29598, 36145, 43202, 50740, 58733, 67158, 75992, |
| 33 | 85215, 83599, 71378, 60428, 50647, 41945, 34246, |
| 34 | 27478, 21581, 16499, 12183, 8588, 5674, 3403, |
| 35 | 1742, 661, 130 |
| 36 | }; |
| 37 | |
| 38 | ieee754dp ieee754dp_sqrt(ieee754dp x) |
| 39 | { |
Ralf Baechle | cd21dfc | 2005-04-28 13:39:10 +0000 | [diff] [blame^] | 40 | struct _ieee754_csr oldcsr; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 41 | ieee754dp y, z, t; |
| 42 | unsigned scalx, yh; |
| 43 | COMPXDP; |
| 44 | |
| 45 | EXPLODEXDP; |
| 46 | CLEARCX; |
| 47 | FLUSHXDP; |
| 48 | |
| 49 | /* x == INF or NAN? */ |
| 50 | switch (xc) { |
| 51 | case IEEE754_CLASS_QNAN: |
| 52 | /* sqrt(Nan) = Nan */ |
| 53 | return ieee754dp_nanxcpt(x, "sqrt"); |
| 54 | case IEEE754_CLASS_SNAN: |
| 55 | SETCX(IEEE754_INVALID_OPERATION); |
| 56 | return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt"); |
| 57 | case IEEE754_CLASS_ZERO: |
| 58 | /* sqrt(0) = 0 */ |
| 59 | return x; |
| 60 | case IEEE754_CLASS_INF: |
| 61 | if (xs) { |
| 62 | /* sqrt(-Inf) = Nan */ |
| 63 | SETCX(IEEE754_INVALID_OPERATION); |
| 64 | return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt"); |
| 65 | } |
| 66 | /* sqrt(+Inf) = Inf */ |
| 67 | return x; |
| 68 | case IEEE754_CLASS_DNORM: |
| 69 | DPDNORMX; |
| 70 | /* fall through */ |
| 71 | case IEEE754_CLASS_NORM: |
| 72 | if (xs) { |
| 73 | /* sqrt(-x) = Nan */ |
| 74 | SETCX(IEEE754_INVALID_OPERATION); |
| 75 | return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt"); |
| 76 | } |
| 77 | break; |
| 78 | } |
| 79 | |
| 80 | /* save old csr; switch off INX enable & flag; set RN rounding */ |
| 81 | oldcsr = ieee754_csr; |
| 82 | ieee754_csr.mx &= ~IEEE754_INEXACT; |
| 83 | ieee754_csr.sx &= ~IEEE754_INEXACT; |
| 84 | ieee754_csr.rm = IEEE754_RN; |
| 85 | |
| 86 | /* adjust exponent to prevent overflow */ |
| 87 | scalx = 0; |
| 88 | if (xe > 512) { /* x > 2**-512? */ |
| 89 | xe -= 512; /* x = x / 2**512 */ |
| 90 | scalx += 256; |
| 91 | } else if (xe < -512) { /* x < 2**-512? */ |
| 92 | xe += 512; /* x = x * 2**512 */ |
| 93 | scalx -= 256; |
| 94 | } |
| 95 | |
| 96 | y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); |
| 97 | |
| 98 | /* magic initial approximation to almost 8 sig. bits */ |
| 99 | yh = y.bits >> 32; |
| 100 | yh = (yh >> 1) + 0x1ff80000; |
| 101 | yh = yh - table[(yh >> 15) & 31]; |
| 102 | y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff); |
| 103 | |
| 104 | /* Heron's rule once with correction to improve to ~18 sig. bits */ |
| 105 | /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */ |
| 106 | t = ieee754dp_div(x, y); |
| 107 | y = ieee754dp_add(y, t); |
| 108 | y.bits -= 0x0010000600000000LL; |
| 109 | y.bits &= 0xffffffff00000000LL; |
| 110 | |
| 111 | /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */ |
| 112 | /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */ |
| 113 | z = t = ieee754dp_mul(y, y); |
| 114 | t.parts.bexp += 0x001; |
| 115 | t = ieee754dp_add(t, z); |
| 116 | z = ieee754dp_mul(ieee754dp_sub(x, z), y); |
| 117 | |
| 118 | /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */ |
| 119 | t = ieee754dp_div(z, ieee754dp_add(t, x)); |
| 120 | t.parts.bexp += 0x001; |
| 121 | y = ieee754dp_add(y, t); |
| 122 | |
| 123 | /* twiddle last bit to force y correctly rounded */ |
| 124 | |
| 125 | /* set RZ, clear INEX flag */ |
| 126 | ieee754_csr.rm = IEEE754_RZ; |
| 127 | ieee754_csr.sx &= ~IEEE754_INEXACT; |
| 128 | |
| 129 | /* t=x/y; ...chopped quotient, possibly inexact */ |
| 130 | t = ieee754dp_div(x, y); |
| 131 | |
| 132 | if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) { |
| 133 | |
| 134 | if (!(ieee754_csr.sx & IEEE754_INEXACT)) |
| 135 | /* t = t-ulp */ |
| 136 | t.bits -= 1; |
| 137 | |
| 138 | /* add inexact to result status */ |
| 139 | oldcsr.cx |= IEEE754_INEXACT; |
| 140 | oldcsr.sx |= IEEE754_INEXACT; |
| 141 | |
| 142 | switch (oldcsr.rm) { |
| 143 | case IEEE754_RP: |
| 144 | y.bits += 1; |
| 145 | /* drop through */ |
| 146 | case IEEE754_RN: |
| 147 | t.bits += 1; |
| 148 | break; |
| 149 | } |
| 150 | |
| 151 | /* y=y+t; ...chopped sum */ |
| 152 | y = ieee754dp_add(y, t); |
| 153 | |
| 154 | /* adjust scalx for correctly rounded sqrt(x) */ |
| 155 | scalx -= 1; |
| 156 | } |
| 157 | |
| 158 | /* py[n0]=py[n0]+scalx; ...scale back y */ |
| 159 | y.parts.bexp += scalx; |
| 160 | |
| 161 | /* restore rounding mode, possibly set inexact */ |
| 162 | ieee754_csr = oldcsr; |
| 163 | |
| 164 | return y; |
| 165 | } |