SDL  2.0
Data Structures | Macros | Typedefs | Functions
math_private.h File Reference
#include "SDL_endian.h"
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Data Structures

union  ieee_double_shape_type
 
union  ieee_float_shape_type
 

Macros

#define attribute_hidden
 
#define libm_hidden_proto(x)
 
#define libm_hidden_def(x)
 
#define atan   SDL_uclibc_atan
 
#define __ieee754_atan2   SDL_uclibc_atan2
 
#define copysign   SDL_uclibc_copysign
 
#define cos   SDL_uclibc_cos
 
#define fabs   SDL_uclibc_fabs
 
#define floor   SDL_uclibc_floor
 
#define __ieee754_log   SDL_uclibc_log
 
#define __ieee754_pow   SDL_uclibc_pow
 
#define scalbn   SDL_uclibc_scalbn
 
#define sin   SDL_uclibc_sin
 
#define __ieee754_sqrt   SDL_uclibc_sqrt
 
#define tan   SDL_uclibc_tan
 
#define EXTRACT_WORDS(ix0, ix1, d)
 
#define GET_HIGH_WORD(i, d)
 
#define GET_LOW_WORD(i, d)
 
#define INSERT_WORDS(d, ix0, ix1)
 
#define SET_HIGH_WORD(d, v)
 
#define SET_LOW_WORD(d, v)
 
#define GET_FLOAT_WORD(i, d)
 
#define SET_FLOAT_WORD(d, i)
 

Typedefs

typedef unsigned int u_int32_t
 

Functions

double __ieee754_sqrt (double) attribute_hidden
 
double __ieee754_acos (double) attribute_hidden
 
double __ieee754_acosh (double) attribute_hidden
 
double __ieee754_log (double) attribute_hidden
 
double __ieee754_atanh (double) attribute_hidden
 
double __ieee754_asin (double) attribute_hidden
 
double __ieee754_atan2 (double, double) attribute_hidden
 
double __ieee754_exp (double) attribute_hidden
 
double __ieee754_cosh (double) attribute_hidden
 
double __ieee754_fmod (double, double) attribute_hidden
 
double __ieee754_pow (double, double) attribute_hidden
 
double __ieee754_lgamma_r (double, int *) attribute_hidden
 
double __ieee754_gamma_r (double, int *) attribute_hidden
 
double __ieee754_lgamma (double) attribute_hidden
 
double __ieee754_gamma (double) attribute_hidden
 
double __ieee754_log10 (double) attribute_hidden
 
double __ieee754_sinh (double) attribute_hidden
 
double __ieee754_hypot (double, double) attribute_hidden
 
double __ieee754_j0 (double) attribute_hidden
 
double __ieee754_j1 (double) attribute_hidden
 
double __ieee754_y0 (double) attribute_hidden
 
double __ieee754_y1 (double) attribute_hidden
 
double __ieee754_jn (int, double) attribute_hidden
 
double __ieee754_yn (int, double) attribute_hidden
 
double __ieee754_remainder (double, double) attribute_hidden
 
int __ieee754_rem_pio2 (double, double *) attribute_hidden
 
double __ieee754_scalb (double, double) attribute_hidden
 
double __kernel_standard (double, double, int) attribute_hidden
 
double __kernel_sin (double, double, int) attribute_hidden
 
double __kernel_cos (double, double) attribute_hidden
 
double __kernel_tan (double, double, int) attribute_hidden
 
int __kernel_rem_pio2 (double *, double *, int, int, int, const int *) attribute_hidden
 

Macro Definition Documentation

#define __ieee754_atan2   SDL_uclibc_atan2

Definition at line 33 of file math_private.h.

#define __ieee754_log   SDL_uclibc_log

Definition at line 38 of file math_private.h.

#define __ieee754_pow   SDL_uclibc_pow

Definition at line 39 of file math_private.h.

#define __ieee754_sqrt   SDL_uclibc_sqrt

Definition at line 42 of file math_private.h.

Referenced by __ieee754_pow().

#define atan   SDL_uclibc_atan

Definition at line 32 of file math_private.h.

#define attribute_hidden

Definition at line 24 of file math_private.h.

#define copysign   SDL_uclibc_copysign

Definition at line 34 of file math_private.h.

Referenced by libm_hidden_proto(), and SDL_copysign().

#define cos   SDL_uclibc_cos

Definition at line 35 of file math_private.h.

Referenced by SDL_cos().

#define EXTRACT_WORDS (   ix0,
  ix1,
  d 
)
Value:
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121

Definition at line 93 of file math_private.h.

Referenced by __ieee754_atan2(), __ieee754_log(), __ieee754_pow(), __ieee754_sqrt(), and libm_hidden_proto().

#define fabs   SDL_uclibc_fabs

Definition at line 36 of file math_private.h.

Referenced by __ieee754_atan2(), __ieee754_pow(), __ieee754_rem_pio2(), __kernel_tan(), atan(), and SDL_fabs().

#define floor   SDL_uclibc_floor

Definition at line 37 of file math_private.h.

Referenced by __kernel_rem_pio2(), and SDL_floor().

#define GET_FLOAT_WORD (   i,
  d 
)
Value:
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121
i
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:42

Definition at line 160 of file math_private.h.

#define GET_HIGH_WORD (   i,
  d 
)
Value:
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121
i
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:42

Definition at line 103 of file math_private.h.

Referenced by __ieee754_atan2(), __ieee754_log(), __ieee754_pow(), __ieee754_rem_pio2(), __kernel_cos(), __kernel_sin(), __kernel_tan(), atan(), libm_hidden_proto(), and tan().

#define GET_LOW_WORD (   i,
  d 
)
Value:
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121
i
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:42

Definition at line 112 of file math_private.h.

Referenced by __ieee754_rem_pio2(), __kernel_tan(), and atan().

#define INSERT_WORDS (   d,
  ix0,
  ix1 
)
Value:
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121

Definition at line 121 of file math_private.h.

Referenced by __ieee754_sqrt(), __kernel_cos(), and libm_hidden_proto().

#define libm_hidden_def (   x)

Definition at line 26 of file math_private.h.

#define libm_hidden_proto (   x)

Definition at line 25 of file math_private.h.

#define scalbn   SDL_uclibc_scalbn

Definition at line 40 of file math_private.h.

Referenced by __ieee754_pow(), __kernel_rem_pio2(), and SDL_scalbn().

#define SET_FLOAT_WORD (   d,
  i 
)
Value:
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121
i
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:42

Definition at line 169 of file math_private.h.

#define SET_HIGH_WORD (   d,
  v 
)
Value:
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
v
const GLdouble * v
Definition: SDL_opengl.h:2057
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121

Definition at line 131 of file math_private.h.

Referenced by __ieee754_atan2(), __ieee754_log(), __ieee754_pow(), __ieee754_rem_pio2(), and libm_hidden_proto().

#define SET_LOW_WORD (   d,
  v 
)
Value:
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
v
const GLdouble * v
Definition: SDL_opengl.h:2057
d
SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char int SDL_PRINTF_FORMAT_STRING const char const char SDL_SCANF_FORMAT_STRING const char return SDL_ThreadFunction const char void return Uint32 return Uint32 SDL_AssertionHandler void SDL_SpinLock SDL_atomic_t int int return SDL_atomic_t return void void void return void return int return SDL_AudioSpec SDL_AudioSpec return int int return return int SDL_RWops int SDL_AudioSpec Uint8 ** d
Definition: SDL_dynapi_procs.h:121

Definition at line 141 of file math_private.h.

Referenced by __ieee754_pow(), __ieee754_rem_pio2(), and __kernel_tan().

#define sin   SDL_uclibc_sin

Definition at line 41 of file math_private.h.

Referenced by SDL_sin().

#define tan   SDL_uclibc_tan

Definition at line 43 of file math_private.h.

Typedef Documentation

typedef unsigned int u_int32_t

Definition at line 29 of file math_private.h.

Function Documentation

double __ieee754_acos ( double  )
double __ieee754_acosh ( double  )
double __ieee754_asin ( double  )
double __ieee754_atan2 ( double  ,
double   
)

Definition at line 50 of file e_atan2.c.

References atan(), EXTRACT_WORDS, fabs, GET_HIGH_WORD, pi, pi_lo, pi_o_2, pi_o_4, SET_HIGH_WORD, tiny, and zero.

51 {
52  double z;
53  int32_t k,m,hx,hy,ix,iy;
54  u_int32_t lx,ly;
55 
56  EXTRACT_WORDS(hx,lx,x);
57  ix = hx&0x7fffffff;
58  EXTRACT_WORDS(hy,ly,y);
59  iy = hy&0x7fffffff;
60  if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
61  ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */
62  return x+y;
63  if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
64  m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
65 
66  /* when y = 0 */
67  if((iy|ly)==0) {
68  switch(m) {
69  case 0:
70  case 1: return y; /* atan(+-0,+anything)=+-0 */
71  case 2: return pi+tiny;/* atan(+0,-anything) = pi */
72  case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
73  }
74  }
75  /* when x = 0 */
76  if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
77 
78  /* when x is INF */
79  if(ix==0x7ff00000) {
80  if(iy==0x7ff00000) {
81  switch(m) {
82  case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
83  case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
84  case 2: return 3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
85  case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
86  }
87  } else {
88  switch(m) {
89  case 0: return zero ; /* atan(+...,+INF) */
90  case 1: return -zero ; /* atan(-...,+INF) */
91  case 2: return pi+tiny ; /* atan(+...,-INF) */
92  case 3: return -pi-tiny ; /* atan(-...,-INF) */
93  }
94  }
95  }
96  /* when y is INF */
97  if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
98 
99  /* compute y/x */
100  k = (iy-ix)>>20;
101  if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
102  else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
103  else z=atan(fabs(y/x)); /* safe to do y/x */
104  switch (m) {
105  case 0: return z ; /* atan(+,+) */
106  case 1: {
107  u_int32_t zh;
108  GET_HIGH_WORD(zh,z);
109  SET_HIGH_WORD(z,zh ^ 0x80000000);
110  }
111  return z ; /* atan(-,+) */
112  case 2: return pi-(z-pi_lo);/* atan(+,-) */
113  default: /* case 3 */
114  return (z-pi_lo)-pi;/* atan(-,-) */
115  }
116 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
pi
static const double pi
Definition: e_atan2.c:47
tiny
static const double tiny
Definition: e_atan2.c:43
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
m
const GLfloat * m
Definition: SDL_opengl_glext.h:6092
pi_o_4
static const double pi_o_4
Definition: e_atan2.c:45
SET_HIGH_WORD
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:131
pi_lo
static const double pi_lo
Definition: e_atan2.c:48
zero
static const double zero
Definition: e_atan2.c:44
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
EXTRACT_WORDS
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:93
pi_o_2
static const double pi_o_2
Definition: e_atan2.c:46
fabs
#define fabs
Definition: math_private.h:36
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
atan
double atan(double x)
Definition: s_atan.c:67
double __ieee754_atanh ( double  )
double __ieee754_cosh ( double  )
double __ieee754_exp ( double  )
double __ieee754_fmod ( double  ,
double   
)
double __ieee754_gamma ( double  )
double __ieee754_gamma_r ( double  ,
int *   
)
double __ieee754_hypot ( double  ,
double   
)
double __ieee754_j0 ( double  )
double __ieee754_j1 ( double  )
double __ieee754_jn ( int  ,
double   
)
double __ieee754_lgamma ( double  )
double __ieee754_lgamma_r ( double  ,
int *   
)
double __ieee754_log ( double  )

Definition at line 99 of file e_log.c.

References EXTRACT_WORDS, GET_HIGH_WORD, i, j, Lg1, Lg2, Lg3, Lg4, Lg5, Lg6, Lg7, ln2_hi, ln2_lo, SET_HIGH_WORD, two54, and zero.

102 {
103  double hfsq, f, s, z, R, w, t1, t2, dk;
104  int32_t k, hx, i, j;
105  u_int32_t lx;
106 
107  EXTRACT_WORDS(hx, lx, x);
108 
109  k = 0;
110  if (hx < 0x00100000) { /* x < 2**-1022 */
111  if (((hx & 0x7fffffff) | lx) == 0)
112  return -two54 / zero; /* log(+-0)=-inf */
113  if (hx < 0)
114  return (x - x) / zero; /* log(-#) = NaN */
115  k -= 54;
116  x *= two54; /* subnormal number, scale up x */
117  GET_HIGH_WORD(hx, x);
118  }
119  if (hx >= 0x7ff00000)
120  return x + x;
121  k += (hx >> 20) - 1023;
122  hx &= 0x000fffff;
123  i = (hx + 0x95f64) & 0x100000;
124  SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
125  k += (i >> 20);
126  f = x - 1.0;
127  if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
128  if (f == zero) {
129  if (k == 0)
130  return zero;
131  else {
132  dk = (double) k;
133  return dk * ln2_hi + dk * ln2_lo;
134  }
135  }
136  R = f * f * (0.5 - 0.33333333333333333 * f);
137  if (k == 0)
138  return f - R;
139  else {
140  dk = (double) k;
141  return dk * ln2_hi - ((R - dk * ln2_lo) - f);
142  }
143  }
144  s = f / (2.0 + f);
145  dk = (double) k;
146  z = s * s;
147  i = hx - 0x6147a;
148  w = z * z;
149  j = 0x6b851 - hx;
150  t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
151  t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
152  i |= j;
153  R = t2 + t1;
154  if (i > 0) {
155  hfsq = 0.5 * f * f;
156  if (k == 0)
157  return f - (hfsq - s * (hfsq + R));
158  else
159  return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
160  f);
161  } else {
162  if (k == 0)
163  return f - s * (f - R);
164  else
165  return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
166  }
167 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
zero
static double zero
Definition: e_log.c:91
s
GLdouble s
Definition: SDL_opengl.h:2056
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
Lg1
static double Lg1
Definition: e_log.c:80
ln2_lo
static double ln2_lo
Definition: e_log.c:78
f
GLfloat f
Definition: SDL_opengl_glext.h:1870
Lg6
static double Lg6
Definition: e_log.c:85
SET_HIGH_WORD
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:131
t1
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat t1
Definition: SDL_opengl_glext.h:8583
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
EXTRACT_WORDS
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:93
Lg5
static double Lg5
Definition: e_log.c:84
Lg4
static double Lg4
Definition: e_log.c:83
i
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:42
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
Lg3
static double Lg3
Definition: e_log.c:82
Lg7
static double Lg7
Definition: e_log.c:86
two54
static double two54
Definition: e_log.c:79
w
GLubyte GLubyte GLubyte GLubyte w
Definition: SDL_opengl_glext.h:731
Lg2
static double Lg2
Definition: e_log.c:81
ln2_hi
static double ln2_hi
Definition: e_log.c:77
j
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 in j)
Definition: SDL_x11sym.h:42
double __ieee754_log10 ( double  )
double __ieee754_pow ( double  ,
double   
)

Definition at line 106 of file e_pow.c.

References __ieee754_sqrt, cp, cp_h, cp_l, dp_h, dp_l, EXTRACT_WORDS, fabs, GET_HIGH_WORD, huge_val, i, ivln2, ivln2_h, ivln2_l, j, L1, L2, L3, L4, L5, L6, lg2, lg2_h, lg2_l, one, ovt, P1, P2, P3, P4, P5, scalbn, SET_HIGH_WORD, SET_LOW_WORD, tiny, two, two53, and zero.

109  {
110  double z, ax, z_h, z_l, p_h, p_l;
111  double y1, t1, t2, r, s, t, u, v, w;
112  int32_t i, j, k, yisint, n;
113  int32_t hx, hy, ix, iy;
114  u_int32_t lx, ly;
115 
116  EXTRACT_WORDS(hx, lx, x);
117  EXTRACT_WORDS(hy, ly, y);
118  ix = hx & 0x7fffffff;
119  iy = hy & 0x7fffffff;
120 
121  /* y==zero: x**0 = 1 */
122  if ((iy | ly) == 0)
123  return one;
124 
125  /* +-NaN return x+y */
126  if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
127  iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
128  return x + y;
129 
130  /* determine if y is an odd int when x < 0
131  * yisint = 0 ... y is not an integer
132  * yisint = 1 ... y is an odd int
133  * yisint = 2 ... y is an even int
134  */
135  yisint = 0;
136  if (hx < 0) {
137  if (iy >= 0x43400000)
138  yisint = 2; /* even integer y */
139  else if (iy >= 0x3ff00000) {
140  k = (iy >> 20) - 0x3ff; /* exponent */
141  if (k > 20) {
142  j = ly >> (52 - k);
143  if ((j << (52 - k)) == ly)
144  yisint = 2 - (j & 1);
145  } else if (ly == 0) {
146  j = iy >> (20 - k);
147  if ((j << (20 - k)) == iy)
148  yisint = 2 - (j & 1);
149  }
150  }
151  }
152 
153  /* special value of y */
154  if (ly == 0) {
155  if (iy == 0x7ff00000) { /* y is +-inf */
156  if (((ix - 0x3ff00000) | lx) == 0)
157  return y - y; /* inf**+-1 is NaN */
158  else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
159  return (hy >= 0) ? y : zero;
160  else /* (|x|<1)**-,+inf = inf,0 */
161  return (hy < 0) ? -y : zero;
162  }
163  if (iy == 0x3ff00000) { /* y is +-1 */
164  if (hy < 0)
165  return one / x;
166  else
167  return x;
168  }
169  if (hy == 0x40000000)
170  return x * x; /* y is 2 */
171  if (hy == 0x3fe00000) { /* y is 0.5 */
172  if (hx >= 0) /* x >= +0 */
173  return __ieee754_sqrt(x);
174  }
175  }
176 
177  ax = fabs(x);
178  /* special value of x */
179  if (lx == 0) {
180  if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
181  z = ax; /* x is +-0,+-inf,+-1 */
182  if (hy < 0)
183  z = one / z; /* z = (1/|x|) */
184  if (hx < 0) {
185  if (((ix - 0x3ff00000) | yisint) == 0) {
186  z = (z - z) / (z - z); /* (-1)**non-int is NaN */
187  } else if (yisint == 1)
188  z = -z; /* (x<0)**odd = -(|x|**odd) */
189  }
190  return z;
191  }
192  }
193 
194  /* (x<0)**(non-int) is NaN */
195  if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
196  return (x - x) / (x - x);
197 
198  /* |y| is huge */
199  if (iy > 0x41e00000) { /* if |y| > 2**31 */
200  if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
201  if (ix <= 0x3fefffff)
202  return (hy < 0) ? huge_val * huge_val : tiny * tiny;
203  if (ix >= 0x3ff00000)
204  return (hy > 0) ? huge_val * huge_val : tiny * tiny;
205  }
206  /* over/underflow if x is not close to one */
207  if (ix < 0x3fefffff)
208  return (hy < 0) ? huge_val * huge_val : tiny * tiny;
209  if (ix > 0x3ff00000)
210  return (hy > 0) ? huge_val * huge_val : tiny * tiny;
211  /* now |1-x| is tiny <= 2**-20, suffice to compute
212  log(x) by x-x^2/2+x^3/3-x^4/4 */
213  t = x - 1; /* t has 20 trailing zeros */
214  w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
215  u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
216  v = t * ivln2_l - w * ivln2;
217  t1 = u + v;
218  SET_LOW_WORD(t1, 0);
219  t2 = v - (t1 - u);
220  } else {
221  double s2, s_h, s_l, t_h, t_l;
222  n = 0;
223  /* take care subnormal number */
224  if (ix < 0x00100000) {
225  ax *= two53;
226  n -= 53;
227  GET_HIGH_WORD(ix, ax);
228  }
229  n += ((ix) >> 20) - 0x3ff;
230  j = ix & 0x000fffff;
231  /* determine interval */
232  ix = j | 0x3ff00000; /* normalize ix */
233  if (j <= 0x3988E)
234  k = 0; /* |x|<sqrt(3/2) */
235  else if (j < 0xBB67A)
236  k = 1; /* |x|<sqrt(3) */
237  else {
238  k = 0;
239  n += 1;
240  ix -= 0x00100000;
241  }
242  SET_HIGH_WORD(ax, ix);
243 
244  /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
245  u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
246  v = one / (ax + bp[k]);
247  s = u * v;
248  s_h = s;
249  SET_LOW_WORD(s_h, 0);
250  /* t_h=ax+bp[k] High */
251  t_h = zero;
252  SET_HIGH_WORD(t_h,
253  ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
254  t_l = ax - (t_h - bp[k]);
255  s_l = v * ((u - s_h * t_h) - s_h * t_l);
256  /* compute log(ax) */
257  s2 = s * s;
258  r = s2 * s2 * (L1 +
259  s2 * (L2 +
260  s2 * (L3 +
261  s2 * (L4 + s2 * (L5 + s2 * L6)))));
262  r += s_l * (s_h + s);
263  s2 = s_h * s_h;
264  t_h = 3.0 + s2 + r;
265  SET_LOW_WORD(t_h, 0);
266  t_l = r - ((t_h - 3.0) - s2);
267  /* u+v = s*(1+...) */
268  u = s_h * t_h;
269  v = s_l * t_h + t_l * s;
270  /* 2/(3log2)*(s+...) */
271  p_h = u + v;
272  SET_LOW_WORD(p_h, 0);
273  p_l = v - (p_h - u);
274  z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
275  z_l = cp_l * p_h + p_l * cp + dp_l[k];
276  /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
277  t = (double) n;
278  t1 = (((z_h + z_l) + dp_h[k]) + t);
279  SET_LOW_WORD(t1, 0);
280  t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
281  }
282 
283  s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
284  if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
285  s = -one; /* (-ve)**(odd int) */
286 
287  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
288  y1 = y;
289  SET_LOW_WORD(y1, 0);
290  p_l = (y - y1) * t1 + y * t2;
291  p_h = y1 * t1;
292  z = p_l + p_h;
293  EXTRACT_WORDS(j, i, z);
294  if (j >= 0x40900000) { /* z >= 1024 */
295  if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
296  return s * huge_val * huge_val; /* overflow */
297  else {
298  if (p_l + ovt > z - p_h)
299  return s * huge_val * huge_val; /* overflow */
300  }
301  } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
302  if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
303  return s * tiny * tiny; /* underflow */
304  else {
305  if (p_l <= z - p_h)
306  return s * tiny * tiny; /* underflow */
307  }
308  }
309  /*
310  * compute 2**(p_h+p_l)
311  */
312  i = j & 0x7fffffff;
313  k = (i >> 20) - 0x3ff;
314  n = 0;
315  if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
316  n = j + (0x00100000 >> (k + 1));
317  k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
318  t = zero;
319  SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
320  n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
321  if (j < 0)
322  n = -n;
323  p_h -= t;
324  }
325  t = p_l + p_h;
326  SET_LOW_WORD(t, 0);
327  u = t * lg2_h;
328  v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
329  z = u + v;
330  w = v - (z - u);
331  t = z * z;
332  t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
333  r = (z * t1) / (t1 - two) - (w + z * w);
334  z = one - (r - z);
335  GET_HIGH_WORD(j, z);
336  j += (n << 20);
337  if ((j >> 20) <= 0)
338  z = scalbn(z, n); /* subnormal output */
339  else
340  SET_HIGH_WORD(z, j);
341  return s * z;
342  }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
ovt
ovt
Definition: e_pow.c:95
one
one
Definition: e_pow.c:78
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
s
GLdouble s
Definition: SDL_opengl.h:2056
ivln2_l
ivln2_l
Definition: e_pow.c:101
n
GLdouble n
Definition: SDL_opengl_glext.h:1952
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
tiny
tiny
Definition: e_pow.c:79
two
two
Definition: e_pow.c:78
cp_l
cp_l
Definition: e_pow.c:98
P3
P3
Definition: e_pow.c:89
__ieee754_sqrt
#define __ieee754_sqrt
Definition: math_private.h:42
lg2
lg2
Definition: e_pow.c:92
SET_HIGH_WORD
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:131
t1
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat t1
Definition: SDL_opengl_glext.h:8583
scalbn
#define scalbn
Definition: math_private.h:40
y1
GLfixed y1
Definition: SDL_opengl_glext.h:4583
v
const GLdouble * v
Definition: SDL_opengl.h:2057
P2
P2
Definition: e_pow.c:88
dp_l
dp_l[]
Definition: e_pow.c:75
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
ivln2
ivln2
Definition: e_pow.c:99
cp
cp
Definition: e_pow.c:96
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
SET_LOW_WORD
#define SET_LOW_WORD(d, v)
Definition: math_private.h:141
EXTRACT_WORDS
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:93
L3
L3
Definition: e_pow.c:83
P5
P5
Definition: e_pow.c:91
lg2_h
lg2_h
Definition: e_pow.c:93
P4
P4
Definition: e_pow.c:90
fabs
#define fabs
Definition: math_private.h:36
L6
L6
Definition: e_pow.c:86
i
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:42
ivln2_h
ivln2_h
Definition: e_pow.c:100
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
L5
L5
Definition: e_pow.c:85
lg2_l
lg2_l
Definition: e_pow.c:94
P1
P1
Definition: e_pow.c:87
dp_h
dp_h[]
Definition: e_pow.c:72
w
GLubyte GLubyte GLubyte GLubyte w
Definition: SDL_opengl_glext.h:731
cp_h
cp_h
Definition: e_pow.c:97
huge_val
huge_val
Definition: e_pow.c:79
L4
L4
Definition: e_pow.c:84
zero
zero
Definition: e_pow.c:78
L1
L1
Definition: e_pow.c:81
t
GLdouble GLdouble t
Definition: SDL_opengl.h:2064
L2
L2
Definition: e_pow.c:82
two53
two53
Definition: e_pow.c:78
j
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 in j)
Definition: SDL_x11sym.h:42
int __ieee754_rem_pio2 ( double  ,
double *   
)
double __ieee754_remainder ( double  ,
double   
)
double __ieee754_scalb ( double  ,
double   
)
double __ieee754_sinh ( double  )
double __ieee754_sqrt ( double  )

Definition at line 102 of file e_sqrt.c.

References EXTRACT_WORDS, i, INSERT_WORDS, one, and tiny.

105 {
106  double z;
107  int32_t sign = (int) 0x80000000;
108  int32_t ix0, s0, q, m, t, i;
109  u_int32_t r, t1, s1, ix1, q1;
110 
111  EXTRACT_WORDS(ix0, ix1, x);
112 
113  /* take care of Inf and NaN */
114  if ((ix0 & 0x7ff00000) == 0x7ff00000) {
115  return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
116  sqrt(-inf)=sNaN */
117  }
118  /* take care of zero */
119  if (ix0 <= 0) {
120  if (((ix0 & (~sign)) | ix1) == 0)
121  return x; /* sqrt(+-0) = +-0 */
122  else if (ix0 < 0)
123  return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
124  }
125  /* normalize x */
126  m = (ix0 >> 20);
127  if (m == 0) { /* subnormal x */
128  while (ix0 == 0) {
129  m -= 21;
130  ix0 |= (ix1 >> 11);
131  ix1 <<= 21;
132  }
133  for (i = 0; (ix0 & 0x00100000) == 0; i++)
134  ix0 <<= 1;
135  m -= i - 1;
136  ix0 |= (ix1 >> (32 - i));
137  ix1 <<= i;
138  }
139  m -= 1023; /* unbias exponent */
140  ix0 = (ix0 & 0x000fffff) | 0x00100000;
141  if (m & 1) { /* odd m, double x to make it even */
142  ix0 += ix0 + ((ix1 & sign) >> 31);
143  ix1 += ix1;
144  }
145  m >>= 1; /* m = [m/2] */
146 
147  /* generate sqrt(x) bit by bit */
148  ix0 += ix0 + ((ix1 & sign) >> 31);
149  ix1 += ix1;
150  q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
151  r = 0x00200000; /* r = moving bit from right to left */
152 
153  while (r != 0) {
154  t = s0 + r;
155  if (t <= ix0) {
156  s0 = t + r;
157  ix0 -= t;
158  q += r;
159  }
160  ix0 += ix0 + ((ix1 & sign) >> 31);
161  ix1 += ix1;
162  r >>= 1;
163  }
164 
165  r = sign;
166  while (r != 0) {
167  t1 = s1 + r;
168  t = s0;
169  if ((t < ix0) || ((t == ix0) && (t1 <= ix1))) {
170  s1 = t1 + r;
171  if (((t1 & sign) == sign) && (s1 & sign) == 0)
172  s0 += 1;
173  ix0 -= t;
174  if (ix1 < t1)
175  ix0 -= 1;
176  ix1 -= t1;
177  q1 += r;
178  }
179  ix0 += ix0 + ((ix1 & sign) >> 31);
180  ix1 += ix1;
181  r >>= 1;
182  }
183 
184  /* use floating add to find out rounding direction */
185  if ((ix0 | ix1) != 0) {
186  z = one - tiny; /* trigger inexact flag */
187  if (z >= one) {
188  z = one + tiny;
189  if (q1 == (u_int32_t) 0xffffffff) {
190  q1 = 0;
191  q += 1;
192  } else if (z > one) {
193  if (q1 == (u_int32_t) 0xfffffffe)
194  q += 1;
195  q1 += 2;
196  } else
197  q1 += (q1 & 1);
198  }
199  }
200  ix0 = (q >> 1) + 0x3fe00000;
201  ix1 = q1 >> 1;
202  if ((q & 1) == 1)
203  ix1 |= sign;
204  ix0 += (m << 20);
205  INSERT_WORDS(z, ix0, ix1);
206  return z;
207 }
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
q
GLdouble GLdouble GLdouble GLdouble q
Definition: SDL_opengl.h:2080
m
const GLfloat * m
Definition: SDL_opengl_glext.h:6092
t1
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat t1
Definition: SDL_opengl_glext.h:8583
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
EXTRACT_WORDS
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:93
INSERT_WORDS
#define INSERT_WORDS(d, ix0, ix1)
Definition: math_private.h:121
s1
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat s1
Definition: SDL_opengl_glext.h:8583
s0
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat GLfloat s0
Definition: SDL_opengl_glext.h:8583
i
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:42
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
tiny
static double tiny
Definition: e_sqrt.c:94
t
GLdouble GLdouble t
Definition: SDL_opengl.h:2064
one
static double one
Definition: e_sqrt.c:94
double __ieee754_y0 ( double  )
double __ieee754_y1 ( double  )
double __ieee754_yn ( int  ,
double   
)
double __kernel_cos ( double  ,
double   
)

Definition at line 74 of file k_cos.c.

References C1, C2, C3, C4, C5, C6, GET_HIGH_WORD, INSERT_WORDS, and one.

Referenced by libm_hidden_proto().

77 {
78  double a, hz, z, r, qx;
79  int32_t ix;
80  GET_HIGH_WORD(ix, x);
81  ix &= 0x7fffffff; /* ix = |x|'s high word */
82  if (ix < 0x3e400000) { /* if x < 2**27 */
83  if (((int) x) == 0)
84  return one; /* generate inexact */
85  }
86  z = x * x;
87  r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
88  if (ix < 0x3FD33333) /* if |x| < 0.3 */
89  return one - (0.5 * z - (z * r - x * y));
90  else {
91  if (ix > 0x3fe90000) { /* x > 0.78125 */
92  qx = 0.28125;
93  } else {
94  INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
95  }
96  hz = 0.5 * z - qx;
97  a = one - qx;
98  return a - (hz - (z * r - x * y));
99  }
100 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
one
static double one
Definition: k_cos.c:61
C2
static double C2
Definition: k_cos.c:63
C5
static double C5
Definition: k_cos.c:66
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
C4
static double C4
Definition: k_cos.c:65
INSERT_WORDS
#define INSERT_WORDS(d, ix0, ix1)
Definition: math_private.h:121
C3
static double C3
Definition: k_cos.c:64
C6
static double C6
Definition: k_cos.c:67
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
C1
static double C1
Definition: k_cos.c:62
a
GLboolean GLboolean GLboolean GLboolean a
Definition: SDL_opengl_glext.h:1109
int __kernel_rem_pio2 ( double *  ,
double *  ,
int  ,
int  ,
int  ,
const int *   
)
double __kernel_sin ( double  ,
double  ,
int   
)

Definition at line 67 of file k_sin.c.

References GET_HIGH_WORD, half, S1, S2, S3, S4, S5, and S6.

Referenced by libm_hidden_proto().

71 {
72  double z, r, v;
73  int32_t ix;
74  GET_HIGH_WORD(ix, x);
75  ix &= 0x7fffffff; /* high word of x */
76  if (ix < 0x3e400000) { /* |x| < 2**-27 */
77  if ((int) x == 0)
78  return x;
79  } /* generate inexact */
80  z = x * x;
81  v = z * x;
82  r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
83  if (iy == 0)
84  return x + v * (S1 + z * r);
85  else
86  return x - ((z * (half * y - v * r) - y) - v * S1);
87 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
S3
static double S3
Definition: k_sin.c:57
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
S1
static double S1
Definition: k_sin.c:55
v
const GLdouble * v
Definition: SDL_opengl.h:2057
S4
static double S4
Definition: k_sin.c:58
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
S6
static double S6
Definition: k_sin.c:60
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
half
static double half
Definition: k_sin.c:54
S5
static double S5
Definition: k_sin.c:59
S2
static double S2
Definition: k_sin.c:56
double __kernel_standard ( double  ,
double  ,
int   
)
double __kernel_tan ( double  ,
double  ,
int   
)

Definition at line 69 of file k_tan.c.

References fabs, GET_HIGH_WORD, GET_LOW_WORD, one, pio4, pio4lo, SET_LOW_WORD, and T.

Referenced by tan().

70 {
71  double z,r,v,w,s;
72  int32_t ix,hx;
73  GET_HIGH_WORD(hx,x);
74  ix = hx&0x7fffffff; /* high word of |x| */
75  if(ix<0x3e300000) /* x < 2**-28 */
76  {if((int)x==0) { /* generate inexact */
77  u_int32_t low;
78  GET_LOW_WORD(low,x);
79  if(((ix|low)|(iy+1))==0) return one/fabs(x);
80  else return (iy==1)? x: -one/x;
81  }
82  }
83  if(ix>=0x3FE59428) { /* |x|>=0.6744 */
84  if(hx<0) {x = -x; y = -y;}
85  z = pio4-x;
86  w = pio4lo-y;
87  x = z+w; y = 0.0;
88  }
89  z = x*x;
90  w = z*z;
91  /* Break x^5*(T[1]+x^2*T[2]+...) into
92  * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
93  * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
94  */
95  r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
96  v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
97  s = z*x;
98  r = y + z*(s*(r+v)+y);
99  r += T[0]*s;
100  w = x+r;
101  if(ix>=0x3FE59428) {
102  v = (double)iy;
103  return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
104  }
105  if(iy==1) return w;
106  else { /* if allow error up to 2 ulp,
107  simply return -1.0/(x+r) here */
108  /* compute -1.0/(x+r) accurately */
109  double a,t;
110  z = w;
111  SET_LOW_WORD(z,0);
112  v = r-(z - x); /* z+v = r+x */
113  t = a = -1.0/w; /* a = -1.0/w */
114  SET_LOW_WORD(t,0);
115  s = 1.0+t*z;
116  return t+a*(s+t*v);
117  }
118 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
s
GLdouble s
Definition: SDL_opengl.h:2056
pio4lo
static const double pio4lo
Definition: k_tan.c:52
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
T
static const double T[]
Definition: k_tan.c:53
v
const GLdouble * v
Definition: SDL_opengl.h:2057
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
SET_LOW_WORD
#define SET_LOW_WORD(d, v)
Definition: math_private.h:141
fabs
#define fabs
Definition: math_private.h:36
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
GET_LOW_WORD
#define GET_LOW_WORD(i, d)
Definition: math_private.h:112
pio4
static const double pio4
Definition: k_tan.c:51
w
GLubyte GLubyte GLubyte GLubyte w
Definition: SDL_opengl_glext.h:731
one
static const double one
Definition: k_tan.c:50
a
GLboolean GLboolean GLboolean GLboolean a
Definition: SDL_opengl_glext.h:1109
t
GLdouble GLdouble t
Definition: SDL_opengl.h:2064