/cln-1.3.2/src/float/transcendental/cl_F_ln.cc

 1// ln().
 2
 3// General includes.
 4#include "base/cl_sysdep.h"
 5
 6// Specification.
 7#include "cln/float.h"
 8
 9
10// Implementation.
11
12#include "float/transcendental/cl_F_tran.h"
13#include "float/cl_F.h"
14#include "float/sfloat/cl_SF.h"
15#include "cln/integer.h"
16#include "cln/lfloat.h"
17#include "float/lfloat/cl_LF.h"
18
19namespace cln {
20
21const cl_F ln (const cl_F& x)
22{
23// Methode:
24// d := (float-digits x),
25// Genauigkeit um sqrt(d)+max(integer-length(e)) Bits erhöhen,
26// (m,e) := (decode-float x), so daß 1/2 <= m < 1.
27// m<2/3 -> m:=2m, e:=e-1, so daß 2/3 <= m <= 4/3.
28// ln(m) errechnen, ln(x)=ln(m)+e*ln(2) als Ergebnis.
29
30	// Rechengenauigkeit erhöhen und m,e,s bestimmen:
31	if (longfloatp(x) && (TheLfloat(x)->len >= 110)) {
32		DeclareType(cl_LF,x);
33		var decoded_lfloat m_e_s = decode_float(extend(x,TheLfloat(x)->len+1));
34		var cl_LF& m = m_e_s.mantissa;
35		var cl_I& e = m_e_s.exponent;
36		if (m < make_SF(0,0+SF_exp_mid,floor(bit(SF_mant_len+2),3))) { // Short-Float 2/3
37			m = scale_float(m,1); // m verdoppeln
38			e = minus1(e); // e decrementieren
39		}
40		var cl_F res = lnx_ratseries(m);
41		if (!zerop(e))
42			res = res + cl_float(e,m)*cl_ln2(m); // ln(m)+e*ln(2)
43		return cl_float(res,x);
44	} else {
45		var decoded_float m_e_s = decode_float(cl_F_extendsqrtx(x));
46		var cl_F& m = m_e_s.mantissa;
47		var cl_I& e = m_e_s.exponent;
48		if (m < make_SF(0,0+SF_exp_mid,floor(bit(SF_mant_len+2),3))) { // Short-Float 2/3
49			m = scale_float(m,1); // m verdoppeln
50			e = minus1(e); // e decrementieren
51		}
52		var cl_F res = lnx_naive(m);
53		if (!zerop(e))
54			res = res + cl_float(e,m)*cl_ln2(m); // ln(m)+e*ln(2)
55		return cl_float(res,x);
56	}
57}
58
59}  // namespace cln