11da177e4SLinus Torvalds /* IEEE754 floating point arithmetic 21da177e4SLinus Torvalds * single precision square root 31da177e4SLinus Torvalds */ 41da177e4SLinus Torvalds /* 51da177e4SLinus Torvalds * MIPS floating point support 61da177e4SLinus Torvalds * Copyright (C) 1994-2000 Algorithmics Ltd. 71da177e4SLinus Torvalds * 81da177e4SLinus Torvalds * ######################################################################## 91da177e4SLinus Torvalds * 101da177e4SLinus Torvalds * This program is free software; you can distribute it and/or modify it 111da177e4SLinus Torvalds * under the terms of the GNU General Public License (Version 2) as 121da177e4SLinus Torvalds * published by the Free Software Foundation. 131da177e4SLinus Torvalds * 141da177e4SLinus Torvalds * This program is distributed in the hope it will be useful, but WITHOUT 151da177e4SLinus Torvalds * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 161da177e4SLinus Torvalds * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 171da177e4SLinus Torvalds * for more details. 181da177e4SLinus Torvalds * 191da177e4SLinus Torvalds * You should have received a copy of the GNU General Public License along 201da177e4SLinus Torvalds * with this program; if not, write to the Free Software Foundation, Inc., 211da177e4SLinus Torvalds * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA. 221da177e4SLinus Torvalds * 231da177e4SLinus Torvalds * ######################################################################## 241da177e4SLinus Torvalds */ 251da177e4SLinus Torvalds 261da177e4SLinus Torvalds 271da177e4SLinus Torvalds #include "ieee754sp.h" 281da177e4SLinus Torvalds 292209bcb1SRalf Baechle union ieee754sp ieee754sp_sqrt(union ieee754sp x) 301da177e4SLinus Torvalds { 311da177e4SLinus Torvalds int ix, s, q, m, t, i; 321da177e4SLinus Torvalds unsigned int r; 331da177e4SLinus Torvalds COMPXSP; 341da177e4SLinus Torvalds 351da177e4SLinus Torvalds /* take care of Inf and NaN */ 361da177e4SLinus Torvalds 371da177e4SLinus Torvalds EXPLODEXSP; 389e8bad1fSRalf Baechle ieee754_clearcx(); 391da177e4SLinus Torvalds FLUSHXSP; 401da177e4SLinus Torvalds 411da177e4SLinus Torvalds /* x == INF or NAN? */ 421da177e4SLinus Torvalds switch (xc) { 431da177e4SLinus Torvalds case IEEE754_CLASS_QNAN: 441da177e4SLinus Torvalds /* sqrt(Nan) = Nan */ 4590efba36SRalf Baechle return ieee754sp_nanxcpt(x); 461da177e4SLinus Torvalds case IEEE754_CLASS_SNAN: 479e8bad1fSRalf Baechle ieee754_setcx(IEEE754_INVALID_OPERATION); 4890efba36SRalf Baechle return ieee754sp_nanxcpt(ieee754sp_indef()); 491da177e4SLinus Torvalds case IEEE754_CLASS_ZERO: 501da177e4SLinus Torvalds /* sqrt(0) = 0 */ 511da177e4SLinus Torvalds return x; 521da177e4SLinus Torvalds case IEEE754_CLASS_INF: 531da177e4SLinus Torvalds if (xs) { 541da177e4SLinus Torvalds /* sqrt(-Inf) = Nan */ 559e8bad1fSRalf Baechle ieee754_setcx(IEEE754_INVALID_OPERATION); 5690efba36SRalf Baechle return ieee754sp_nanxcpt(ieee754sp_indef()); 571da177e4SLinus Torvalds } 581da177e4SLinus Torvalds /* sqrt(+Inf) = Inf */ 591da177e4SLinus Torvalds return x; 601da177e4SLinus Torvalds case IEEE754_CLASS_DNORM: 611da177e4SLinus Torvalds case IEEE754_CLASS_NORM: 621da177e4SLinus Torvalds if (xs) { 631da177e4SLinus Torvalds /* sqrt(-x) = Nan */ 649e8bad1fSRalf Baechle ieee754_setcx(IEEE754_INVALID_OPERATION); 6590efba36SRalf Baechle return ieee754sp_nanxcpt(ieee754sp_indef()); 661da177e4SLinus Torvalds } 671da177e4SLinus Torvalds break; 681da177e4SLinus Torvalds } 691da177e4SLinus Torvalds 701da177e4SLinus Torvalds ix = x.bits; 711da177e4SLinus Torvalds 721da177e4SLinus Torvalds /* normalize x */ 731da177e4SLinus Torvalds m = (ix >> 23); 741da177e4SLinus Torvalds if (m == 0) { /* subnormal x */ 751da177e4SLinus Torvalds for (i = 0; (ix & 0x00800000) == 0; i++) 761da177e4SLinus Torvalds ix <<= 1; 771da177e4SLinus Torvalds m -= i - 1; 781da177e4SLinus Torvalds } 791da177e4SLinus Torvalds m -= 127; /* unbias exponent */ 801da177e4SLinus Torvalds ix = (ix & 0x007fffff) | 0x00800000; 811da177e4SLinus Torvalds if (m & 1) /* odd m, double x to make it even */ 821da177e4SLinus Torvalds ix += ix; 831da177e4SLinus Torvalds m >>= 1; /* m = [m/2] */ 841da177e4SLinus Torvalds 851da177e4SLinus Torvalds /* generate sqrt(x) bit by bit */ 861da177e4SLinus Torvalds ix += ix; 871da177e4SLinus Torvalds q = s = 0; /* q = sqrt(x) */ 881da177e4SLinus Torvalds r = 0x01000000; /* r = moving bit from right to left */ 891da177e4SLinus Torvalds 901da177e4SLinus Torvalds while (r != 0) { 911da177e4SLinus Torvalds t = s + r; 921da177e4SLinus Torvalds if (t <= ix) { 931da177e4SLinus Torvalds s = t + r; 941da177e4SLinus Torvalds ix -= t; 951da177e4SLinus Torvalds q += r; 961da177e4SLinus Torvalds } 971da177e4SLinus Torvalds ix += ix; 981da177e4SLinus Torvalds r >>= 1; 991da177e4SLinus Torvalds } 1001da177e4SLinus Torvalds 1011da177e4SLinus Torvalds if (ix != 0) { 1029e8bad1fSRalf Baechle ieee754_setcx(IEEE754_INEXACT); 1031da177e4SLinus Torvalds switch (ieee754_csr.rm) { 1041da177e4SLinus Torvalds case IEEE754_RP: 1051da177e4SLinus Torvalds q += 2; 1061da177e4SLinus Torvalds break; 1071da177e4SLinus Torvalds case IEEE754_RN: 1081da177e4SLinus Torvalds q += (q & 1); 1091da177e4SLinus Torvalds break; 1101da177e4SLinus Torvalds } 1111da177e4SLinus Torvalds } 1121da177e4SLinus Torvalds ix = (q >> 1) + 0x3f000000; 1131da177e4SLinus Torvalds ix += (m << 23); 1141da177e4SLinus Torvalds x.bits = ix; 1151da177e4SLinus Torvalds return x; 1161da177e4SLinus Torvalds } 117