SDL  2.0
e_log10.c
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1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
13 /* C4723: potential divide by zero. */
14 #pragma warning ( disable : 4723 )
15 #endif
16 
17 /* __ieee754_log10(x)
18  * Return the base 10 logarithm of x
19  *
20  * Method :
21  * Let log10_2hi = leading 40 bits of log10(2) and
22  * log10_2lo = log10(2) - log10_2hi,
23  * ivln10 = 1/log(10) rounded.
24  * Then
25  * n = ilogb(x),
26  * if(n<0) n = n+1;
27  * x = scalbn(x,-n);
28  * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
29  *
30  * Note 1:
31  * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
32  * mode must set to Round-to-Nearest.
33  * Note 2:
34  * [1/log(10)] rounded to 53 bits has error .198 ulps;
35  * log10 is monotonic at all binary break points.
36  *
37  * Special cases:
38  * log10(x) is NaN with signal if x < 0;
39  * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
40  * log10(NaN) is that NaN with no signal;
41  * log10(10**N) = N for N=0,1,...,22.
42  *
43  * Constants:
44  * The hexadecimal values are the intended ones for the following constants.
45  * The decimal values may be used, provided that the compiler will convert
46  * from decimal to binary accurately enough to produce the hexadecimal values
47  * shown.
48  */
49 
50 #include "math_libm.h"
51 #include "math_private.h"
52 
53 static const double
54 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
55 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
56 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
57 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
58 
59 static const double zero = 0.0;
60 
62 {
63  double y,z;
64  int32_t i,k,hx;
65  u_int32_t lx;
66 
67  EXTRACT_WORDS(hx,lx,x);
68 
69  k=0;
70  if (hx < 0x00100000) { /* x < 2**-1022 */
71  if (((hx&0x7fffffff)|lx)==0)
72  return -two54/zero; /* log(+-0)=-inf */
73  if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
74  k -= 54; x *= two54; /* subnormal number, scale up x */
75  GET_HIGH_WORD(hx,x);
76  }
77  if (hx >= 0x7ff00000) return x+x;
78  k += (hx>>20)-1023;
79  i = ((u_int32_t)k&0x80000000)>>31;
80  hx = (hx&0x000fffff)|((0x3ff-i)<<20);
81  y = (double)(k+i);
82  SET_HIGH_WORD(x,hx);
83  z = y*log10_2lo + ivln10*__ieee754_log(x);
84  return z+y*log10_2hi;
85 }
86 
87 /*
88  * wrapper log10(X)
89  */
90 #ifndef _IEEE_LIBM
91 double log10(double x)
92 {
93  double z = __ieee754_log10(x);
94  if (_LIB_VERSION == _IEEE_ || isnan(x))
95  return z;
96  if (x <= 0.0) {
97  if(x == 0.0)
98  return __kernel_standard(x, x, 18); /* log10(0) */
99  return __kernel_standard(x, x, 19); /* log10(x<0) */
100  }
101  return z;
102 }
103 #else
105 #endif
106 libm_hidden_def(log10)
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:108
#define __ieee754_log
Definition: math_private.h:41
GLdouble GLdouble z
static const double log10_2hi
Definition: e_log10.c:56
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1574
signed int int32_t
#define strong_alias(x, y)
Definition: math_private.h:28
static const double ivln10
Definition: e_log10.c:55
#define attribute_hidden
Definition: math_private.h:25
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:136
double attribute_hidden __ieee754_log10(double x)
Definition: e_log10.c:61
unsigned int u_int32_t
Definition: math_private.h:31
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:98
static const double log10_2lo
Definition: e_log10.c:57
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1574
static const double zero
Definition: e_log10.c:59
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int in i)
Definition: SDL_x11sym.h:50
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int int int return Display Window Cursor return Display Window return Display Drawable GC int int unsigned int unsigned int return Display Drawable GC int int _Xconst char int return Display Drawable GC int int unsigned int unsigned int return Display return Display Cursor return Display GC return XModifierKeymap return char Display Window int return Display return Display Atom return Display Window XWindowAttributes return Display Window return Display XEvent Bool(*) XPointer return Display Window Bool unsigned int int int Window Cursor Time return Display Window int return KeySym return Display _Xconst char Bool return Display _Xconst char return XKeyEvent char int KeySym XComposeStatus return Display int int int XVisualInfo return Display Window int int return _Xconst char return Display XEvent return Display Drawable GC XImage int int int int unsigned int unsigned int return Display Window Window Window int int int int unsigned int return Display Window Window int int return Display Window unsigned int unsigned int return Display Window Bool long XEvent return Display GC unsigned long return Display Window int Time return Display Window Window return Display Window unsigned long return Display Window XSizeHints Display Colormap XColor int return char int XTextProperty return XFontStruct _Xconst char int int int int XCharStruct return Display Window return Display Time return Display Colormap return Display Window Window int int unsigned int unsigned int int int return Display Window int return XExtensionInfo Display char XExtensionHooks int XPointer return XExtensionInfo XExtensionInfo Display return Display return Display unsigned long Display GC Display char long Display xReply int Bool return Display Bool return Display int SDL_X11_XESetEventToWireRetType return Display Window Window Window Window unsigned int return Display XShmSegmentInfo return Display Drawable GC XImage int int int int unsigned int unsigned int Boo k)
Definition: SDL_x11sym.h:213
static const double two54
Definition: e_log10.c:54
libm_hidden_def(scalbln)
Definition: s_scalbn.c:62