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181 lines
3.6 KiB
181 lines
3.6 KiB
/***
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*sqrt.c - square root
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*
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* Copyright (c) 1991-2001, Microsoft Corporation. All rights reserved.
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*
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*Purpose:
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*
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*Revision History:
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* 8-15-91 GDP written
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* 1-29-91 GDP Kahan's algorithm for final rounding
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* 3-11-92 GDP new interval and initial approximation
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* 10-07-97 RDL Added IA64.
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*
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*******************************************************************************/
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#ifndef R4000
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#include <math.h>
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#include <trans.h>
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#if defined(_M_IA64)
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#pragma function(sqrt)
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#endif
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//
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// Coefficients for initial approximation (Hart & al)
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//
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static double p00 = .2592768763e+0;
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static double p01 = .1052021187e+1;
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static double p02 = -.3163221431e+0;
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/***
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*double sqrt(double x) - square root
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*
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*Purpose:
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* Compute the square root of a number.
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* This function should be provided by the underlying
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* hardware (IEEE spec).
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*Entry:
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*
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*Exit:
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*
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*Exceptions:
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* I P
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*******************************************************************************/
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double sqrt(double x)
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{
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uintptr_t savedcw, sw;
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double result,t;
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uintptr_t stat,rc;
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savedcw = _ctrlfp(ICW, IMCW);
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if (IS_D_SPECIAL(x)){
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switch (_sptype(x)) {
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case T_PINF:
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RETURN(savedcw, x);
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case T_QNAN:
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return _handle_qnan1(OP_SQRT, x, savedcw);
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case T_SNAN:
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return _except1(FP_I,OP_SQRT,x,QNAN_SQRT,savedcw);
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}
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/* -INF will be handled in the x<0 case */
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}
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if (x < 0.0) {
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return _except1(FP_I, OP_SQRT, x, QNAN_SQRT,savedcw);
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}
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if (x == 0.0) {
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RETURN (savedcw, x);
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}
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result = _fsqrt(x);
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_ctrlfp(IRC_DOWN, IMCW_RC);
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//
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// Kahan's algorithm
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//
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sw = _clrfp();
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t = x / result;
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stat = _statfp();
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if (! (stat & ISW_INEXACT)) {
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// exact
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if (t == result) {
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_set_statfp(sw); // restore status word
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RETURN(savedcw, result);
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}
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else {
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// t = t-1
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if (*D_LO(t) == 0) {
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(*D_HI(t)) --;
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}
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(*D_LO(t)) --;
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}
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}
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rc = savedcw & IMCW_RC;
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if (rc == IRC_UP || rc == IRC_NEAR) {
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// t = t+1
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(*D_LO(t)) ++;
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if (*D_LO(t) == 0) {
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(*D_HI(t)) ++;
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}
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if (rc == IRC_UP) {
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// y = y+1
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(*D_LO(t)) ++;
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if (*D_LO(t) == 0) {
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(*D_HI(t)) ++;
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}
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}
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}
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result = 0.5 * (t + result);
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_set_statfp(sw | ISW_INEXACT); // update status word
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RETURN_INEXACT1(OP_SQRT, x, result, savedcw);
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}
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/***
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* _fsqrt - non IEEE conforming square root
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*
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*Purpose:
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* compute a square root of a normal number without performing
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* IEEE rounding. The argument is a finite number (no NaN or INF)
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*
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*Entry:
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*
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*Exit:
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*
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*Exceptions:
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*
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*******************************************************************************/
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double _fsqrt(double x)
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{
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double f,y,result;
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int n;
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f = _decomp(x,&n);
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if (n & 0x1) {
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// n is odd
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n++;
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f = _add_exp(f, -1);
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}
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//
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// approximation for sqrt in the interval [.25, 1]
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// (Computer Approximationsn, Hart & al.)
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// gives more than 7 bits of accuracy
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//
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y = p00 + f * (p01 + f * p02);
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y += f / y;
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y = _add_exp(y, -1);
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y += f / y;
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y = _add_exp(y, -1);
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y += f / y;
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y = _add_exp(y, -1);
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n >>= 1;
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result = _add_exp(y,n);
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return result;
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}
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#endif
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