ReactOS 0.4.15-dev-8349-g6f277e9
exp2.c File Reference
#include "libm.h"
#include "libm_util.h"
#include "libm_inlines.h"
#include "libm_errno.h"
Include dependency graph for exp2.c:

Go to the source code of this file.

Macros

#define USE_SPLITEXP
 
#define USE_SCALEDOUBLE_1
 
#define USE_SCALEDOUBLE_2
 
#define USE_ZERO_WITH_FLAGS
 
#define USE_INFINITY_WITH_FLAGS
 
#define USE_HANDLE_ERROR
 

Functions

double FN_PROTOTYPE() _exp2 (double x)
 

Macro Definition Documentation

◆ USE_HANDLE_ERROR

#define USE_HANDLE_ERROR

Definition at line 35 of file exp2.c.

◆ USE_INFINITY_WITH_FLAGS

#define USE_INFINITY_WITH_FLAGS

Definition at line 34 of file exp2.c.

◆ USE_SCALEDOUBLE_1

#define USE_SCALEDOUBLE_1

Definition at line 31 of file exp2.c.

◆ USE_SCALEDOUBLE_2

#define USE_SCALEDOUBLE_2

Definition at line 32 of file exp2.c.

◆ USE_SPLITEXP

#define USE_SPLITEXP

Definition at line 30 of file exp2.c.

◆ USE_ZERO_WITH_FLAGS

#define USE_ZERO_WITH_FLAGS

Definition at line 33 of file exp2.c.

Function Documentation

◆ _exp2()

double FN_PROTOTYPE() _exp2 ( double  x)

Definition at line 49 of file exp2.c.

50{
51 static const double
52 max_exp2_arg = 1024.0, /* 0x4090000000000000 */
53 min_exp2_arg = -1074.0, /* 0xc090c80000000000 */
54 log2 = 6.931471805599453094178e-01, /* 0x3fe62e42fefa39ef */
55 log2_lead = 6.93147167563438415527E-01, /* 0x3fe62e42f8000000 */
56 log2_tail = 1.29965068938898869640E-08, /* 0x3e4be8e7bcd5e4f1 */
57 one_by_32_lead = 0.03125;
58
59 double y, z1, z2, z, hx, tx, y1, y2;
60 int m;
61 unsigned long long ux, ax;
62
63 /*
64 Computation of exp2(x).
65
66 We compute the values m, z1, and z2 such that
67 exp2(x) = 2**m * (z1 + z2), where exp2(x) is 2**x.
68
69 Computations needed in order to obtain m, z1, and z2
70 involve three steps.
71
72 First, we reduce the argument x to the form
73 x = n/32 + remainder,
74 where n has the value of an integer and |remainder| <= 1/64.
75 The value of n = x * 32 rounded to the nearest integer and
76 the remainder = x - n/32.
77
78 Second, we approximate exp2(r1 + r2) - 1 where r1 is the leading
79 part of the remainder and r2 is the trailing part of the remainder.
80
81 Third, we reconstruct exp2(x) so that
82 exp2(x) = 2**m * (z1 + z2).
83 */
84
85
86 GET_BITS_DP64(x, ux);
87 ax = ux & (~SIGNBIT_DP64);
88
89 if (ax >= 0x4090000000000000) /* abs(x) >= 1024.0 */
90 {
91 if(ax >= 0x7ff0000000000000)
92 {
93 /* x is either NaN or infinity */
94 if (ux & MANTBITS_DP64)
95 /* x is NaN */
96 return _handle_error("exp2", OP_EXP, ux|0x0008000000000000, _DOMAIN,
97 0, EDOM, x, 0.0, 1);
98 else if (ux & SIGNBIT_DP64)
99 /* x is negative infinity; return 0.0 with no flags. */
100 return 0.0;
101 else
102 /* x is positive infinity */
103 return x;
104 }
105 if (x > max_exp2_arg)
106 /* Return +infinity with overflow flag */
107 return _handle_error("exp2", OP_EXP, PINFBITPATT_DP64, _OVERFLOW,
109 else if (x < min_exp2_arg)
110 /* x is negative. Return +zero with underflow and inexact flags */
111 return _handle_error("exp2", OP_EXP, 0, _UNDERFLOW,
113 }
114
115
116 /* Handle small arguments separately */
117 if (ax < 0x3fb7154764ee6c2f) /* abs(x) < 1/(16*log2) */
118 {
119 if (ax < 0x3c00000000000000) /* abs(x) < 2^(-63) */
120 return 1.0 + x; /* Raises inexact if x is non-zero */
121 else
122 {
123 /* Split x into hx (head) and tx (tail). */
124 unsigned long long u;
125 hx = x;
126 GET_BITS_DP64(hx, u);
127 u &= 0xfffffffff8000000;
128 PUT_BITS_DP64(u, hx);
129 tx = x - hx;
130 /* Carefully multiply x by log2. y1 is the most significant
131 part of the result, and y2 the least significant part */
132 y1 = x * log2_lead;
133 y2 = (((hx * log2_lead - y1) + hx * log2_tail) +
134 tx * log2_lead) + tx * log2_tail;
135
136 y = y1 + y2;
137 z = (9.99564649780173690e-1 +
138 (1.61251249355268050e-5 +
139 (2.37986978239838493e-2 +
140 2.68724774856111190e-7*y)*y)*y)/
141 (9.99564649780173692e-1 +
142 (-4.99766199765151309e-1 +
143 (1.070876894098586184e-1 +
144 (-1.189773642681502232e-2 +
145 5.9480622371960190616e-4*y)*y)*y)*y);
146 z = ((z * y1) + (z * y2)) + 1.0;
147 }
148 }
149 else
150 {
151 /* Find m, z1 and z2 such that exp2(x) = 2**m * (z1 + z2) */
152
153 splitexp(x, log2, 32.0, one_by_32_lead, 0.0, &m, &z1, &z2);
154
155 /* Scale (z1 + z2) by 2.0**m */
156 if (m > EMIN_DP64 && m < EMAX_DP64)
157 z = scaleDouble_1((z1+z2),m);
158 else
159 z = scaleDouble_2((z1+z2),m);
160 }
161 return z;
162}
double __cdecl _handle_error(char *fname, int opcode, unsigned long long value, int type, int flags, int error, double arg1, double arg2, int nargs)
Handles an error condition.
Definition: _handle_error.c:34
#define ERANGE
Definition: acclib.h:92
#define EDOM
Definition: errno.h:39
GLint GLint GLint GLint GLint x
Definition: gl.h:1548
GLint GLint GLint GLint GLint GLint y
Definition: gl.h:1548
GLdouble GLdouble z
Definition: glext.h:5874
const GLfloat * m
Definition: glext.h:10848
GLsizei GLenum const GLvoid GLsizei GLenum GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLint GLint GLint GLshort GLshort GLshort GLubyte GLubyte GLubyte GLuint GLuint GLuint GLushort GLushort GLushort GLbyte GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLfloat GLint GLint GLint GLint GLshort GLshort GLshort GLshort GLubyte GLubyte GLubyte GLubyte GLuint GLuint GLuint GLuint GLushort GLushort GLushort GLushort GLboolean const GLdouble const GLfloat const GLint const GLshort const GLbyte const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLdouble const GLfloat const GLfloat const GLint const GLint const GLshort const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort GLenum GLenum GLenum GLfloat GLenum GLint GLenum GLenum GLenum GLfloat GLenum GLenum GLint GLenum GLfloat GLenum GLint GLint GLushort GLenum GLenum GLfloat GLenum GLenum GLint GLfloat const GLubyte GLenum GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLint GLint GLsizei GLsizei GLint GLenum GLenum const GLvoid GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLenum const GLdouble GLenum GLenum const GLfloat GLenum GLenum const GLint GLsizei GLuint GLfloat GLuint GLbitfield GLfloat GLint GLuint GLboolean GLenum GLfloat GLenum GLbitfield GLenum GLfloat GLfloat GLint GLint const GLfloat GLenum GLfloat GLfloat GLint GLint GLfloat GLfloat GLint GLint const GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat const GLdouble * u
Definition: glfuncs.h:240
#define _DOMAIN
Definition: math.h:39
#define _UNDERFLOW
Definition: math.h:42
_Check_return_ __CRT_INLINE double log2(_In_ double x)
Definition: math.h:301
#define _OVERFLOW
Definition: math.h:41
#define AMD_F_INEXACT
Definition: libm_new.h:82
#define AMD_F_UNDERFLOW
Definition: libm_new.h:84
#define AMD_F_OVERFLOW
Definition: libm_new.h:83
#define GET_BITS_DP64(x, ux)
Definition: libm_util.h:118
#define PINFBITPATT_DP64
Definition: libm_util.h:53
#define SIGNBIT_DP64
Definition: libm_util.h:44
#define EMAX_DP64
Definition: libm_util.h:60
#define EMIN_DP64
Definition: libm_util.h:58
#define MANTBITS_DP64
Definition: libm_util.h:46
#define PUT_BITS_DP64(ux, x)
Definition: libm_util.h:124
ecx edi movl ebx edx edi decl ecx esi eax jecxz decl eax andl eax esi movl edx movl TEMP incl eax andl eax ecx incl ebx testl eax jnz xchgl ecx incl TEMP esp ecx subl ebx pushl ecx ecx edx ecx shrl ecx mm0 mm4 mm0 mm4 mm1 mm5 mm1 mm5 mm2 mm6 mm2 mm6 mm3 mm7 mm3 mm7 paddd mm0 paddd mm4 paddd mm0 paddd mm4 paddd mm0 paddd mm4 movq mm1 movq mm5 psrlq mm1 psrlq mm5 paddd mm0 paddd mm4 psrad mm0 psrad mm4 packssdw mm0 packssdw mm4 mm1 punpckldq mm0 pand mm1 pand mm0 por mm1 movq edi esi edx edi decl ecx jnz popl ecx andl ecx jecxz mm0 mm0 mm1 mm1 mm2 mm2 mm3 mm3 paddd mm0 paddd mm0 paddd mm0 movq mm1 psrlq mm1 paddd mm0 psrad mm0 packssdw mm0 movd eax movw ax
Definition: synth_sse3d.h:180
_In_ CLIPOBJ _In_ BRUSHOBJ _In_ LONG _In_ LONG y1
Definition: winddi.h:3709
_In_ CLIPOBJ _In_ BRUSHOBJ _In_ LONG _In_ LONG _In_ LONG _In_ LONG y2
Definition: winddi.h:3711