137 lines
2.9 KiB
C
137 lines
2.9 KiB
C
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/*++
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Copyright (c) 1999 Microsoft Corporation
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Module Name:
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log.c
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Abstract:
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logarithmic functions
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Author:
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Revision History:
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29-sept-1999 ATM Shafiqul Khalid [askhalid] copied from rtl library.
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--*/
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#include <math.h>
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#include <trans.h>
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static double _log_hlp( double x, int flag);
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/* constants */
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static double const c0 = 0.70710678118654752440; /* sqrt(0.5) */
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static double const c1 = 0.69335937500000000000;
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static double const c2 = -2.121944400546905827679e-4;
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static double const c3 = 0.43429448190325182765;
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/* coefficients for rational approximation */
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static double const a0 = -0.64124943423745581147e2 ;
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static double const a1 = 0.16383943563021534222e2 ;
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static double const a2 = -0.78956112887491257267e0 ;
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static double const b0 = -0.76949932108494879777e3 ;
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static double const b1 = 0.31203222091924532844e3 ;
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static double const b2 = -0.35667977739034646171e2 ;
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/* b3=1.0 is not used -avoid multiplication by 1.0 */
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#define A(w) (((w) * a2 + a1) * (w) + a0)
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#define B(w) ((((w) + b2) * (w) + b1) * (w) + b0)
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/***
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*double log(double x) - natural logarithm
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*double log10(double x) - base-10 logarithm
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*
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*Purpose:
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* Compute the natural and base-10 logarithm of a number.
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* The algorithm (reduction / rational approximation) is
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* taken from Cody & Waite.
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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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* I P Z
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*******************************************************************************/
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double Proxylog10(double x)
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{
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return(_log_hlp(x,OP_LOG10));
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}
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double Proxylog(double x)
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{
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return(_log_hlp(x,OP_LOG));
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}
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static double _log_hlp(double x, int opcode)
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{
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unsigned int savedcw;
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int n;
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double f,result;
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double z,w,znum,zden;
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double rz,rzsq;
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/* save user fp control word */
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savedcw = _maskfp();
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/* check for infinity or NAN */
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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(opcode, x, savedcw);
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case T_SNAN:
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return _except1(FP_I, opcode, x, _s2qnan(x), savedcw);
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}
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/* NINF will be handled in the x<0 case */
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}
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if (x <= 0.0) {
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double qnan;
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if (x == 0.0) {
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return _except1(FP_Z,opcode,x,-D_INF,savedcw);
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}
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qnan = (opcode == OP_LOG ? QNAN_LOG : QNAN_LOG10);
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return _except1(FP_I,opcode,x,qnan,savedcw);
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}
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if (x == 1.0) {
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// no precision ecxeption
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RETURN(savedcw, 0.0);
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}
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f = _decomp(x, &n);
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if (f > c0) {
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znum = (f - 0.5) - 0.5;
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zden = f * 0.5 + 0.5;
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}
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else {
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n--;
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znum = f - 0.5;
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zden = znum * 0.5 + 0.5;
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}
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z = znum / zden;
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w = z * z;
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rzsq = w * A(w)/B(w) ;
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rz = z + z*rzsq;
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result = (n * c2 + rz) + n * c1;
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if (opcode == OP_LOG10) {
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result *= c3;
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}
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RETURN_INEXACT1(opcode,x,result,savedcw);
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}
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