Include dependency graph for math.h:
Go to the source code of this file.
Classes | |
| struct | _exception |
| struct | _complex |
Variables | |
| union { | |
| unsigned int __i | |
| float __f | |
| } | __inff = { 0x7f800000 } |
| union { | |
| unsigned int __i | |
| float __f | |
| } | __nanf = { 0x7fc00000 } |
Macro Definition Documentation
◆ _C2
◆ _COMPLEX_DEFINED
◆ _DOMAIN
◆ _EXCEPTION_DEFINED
◆ _MATH_DEFINES_DEFINED
◆ _OVERFLOW
◆ _PLOSS
◆ _SING
◆ _TLOSS
◆ _UNDERFLOW
◆ copysign
◆ copysignf
◆ FP_ILOGB0
◆ FP_ILOGBNAN
◆ FP_INFINITE
◆ FP_NAN
◆ FP_NORMAL
◆ FP_SUBNORMAL
◆ FP_ZERO
◆ HUGE_VAL
◆ INFINITY
| #define INFINITY (__inff.__f) |
◆ isfinite
◆ isinf
◆ isnan
◆ isnormal
| #define isnormal | ( | x | ) | (sizeof(x) == sizeof(float) ? __isnormalf(x) : __isnormal(x)) |
◆ M_1_PI
◆ M_2_PI
◆ M_2_SQRTPI
◆ M_E
◆ M_LN10
◆ M_LN2
◆ M_LOG10E
◆ M_LOG2E
◆ M_PI
◆ M_PI_2
◆ M_PI_4
◆ M_SQRT1_2
◆ M_SQRT2
◆ NAN
| #define NAN (__nanf.__f) |
◆ signbit
Function Documentation
◆ __isinf()
Definition at line 333 of file math.h.
334{
337}
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 const GLfloat const GLdouble const GLfloat GLint i
Definition: glfuncs.h:248
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
◆ __isinff()
◆ __isnan()
◆ __isnanf()
◆ __isnormal()
◆ __isnormalf()
◆ __signbit()
◆ __signbitf()
◆ _cabs()
◆ _chgsign()
Definition at line 1227 of file math.c.
Referenced by _chgsignf(), and _chgsignl().
◆ _chgsignf()
◆ _copysign()
Definition at line 17 of file copysign.c.
18{
19 union
20 {
21 double* __d;
23 } d;
24 union
25 {
26 double* __s;
28 } s;
29 d.__d = &__d;
30 s.__s = &__s;
31
33
34 return __d;
35}
Referenced by _copysignf(), and _copysignl().
◆ _copysignf()
Definition at line 34 of file _copysignf.c.
35{
36 unsigned int ux, uy;
42}
◆ _dtest()
◆ _fdtest()
◆ _finite()
◆ _finitef()
◆ _fpclass()
◆ _fpclassf()
◆ _hypot()
Definition at line 34 of file hypot.c.
35{
37 double ratio;
38
39 /* Make abig = max(|x|, |y|), asmall = min(|x|, |y|). */
40 if (abig < asmall)
41 {
43
44 abig = asmall;
45 asmall = temp;
46 }
47
48 /* Trivial case. */
49 if (asmall == 0.)
50 return abig;
51
52 /* Scale the numbers as much as possible by using its ratio.
53 For example, if both ABIG and ASMALL are VERY small, then
54 X^2 + Y^2 might be VERY inaccurate due to loss of
55 significant digits. Dividing ASMALL by ABIG scales them
56 to a certain degree, so that accuracy is better. */
57
60 else
61 {
62 /* Slower but safer algorithm due to Moler and Morrison. Never
63 produces any intermediate result greater than roughly the
64 larger of X and Y. Should converge to machine-precision
65 accuracy in 3 iterations. */
66
68
69 do {
72 break;
77 } while (1);
78
80 }
81}
_ACRTIMP double __cdecl fabs(double)
Referenced by _cabs(), _hypotf(), _hypotl(), hypot(), and hypotl().
◆ _hypotf()
Definition at line 45 of file hypotf.c.
46{
47 /* Returns sqrt(x*x + y*y) with no overflow or underflow unless
48 the result warrants it */
49
50 /* Do intermediate computations in double precision
51 and use sqrt instruction from chip if available. */
53
54 /* The largest finite float, stored as a double */
55 const double large = 3.40282346638528859812e+38; /* 0x47efffffe0000000 */
56
57
59
61 avx &= ~SIGNBIT_DP64;
63 avy &= ~SIGNBIT_DP64;
65 uy = (avy >> EXPSHIFTBITS_DP64);
66
68 {
70 /* One or both of the arguments are NaN or infinity. The
71 result will also be NaN or infinity. */
74 /* x or y is infinity. ISO C99 defines that we must
75 return +infinity, even if the other argument is NaN.
76 Note that the computation of x*x + y*y above will already
77 have raised invalid if either x or y is a signalling NaN. */
78 return infinityf_with_flags(0);
79 else
80 /* One or both of x or y is NaN, and neither is infinity.
81 Raise invalid if it's a signalling NaN */
83 }
84
86
87#if USE_SOFTWARE_SQRT
89#else
90 /* VC++ intrinsic call */
92#endif
93
97 else
99}
float __cdecl _handle_errorf(char *fname, int opcode, unsigned long long value, int type, int flags, int error, float arg1, float arg2, int nargs)
Definition: _handle_error.c:56
Referenced by hypotf().
◆ _isnan()
◆ _isnanf()
◆ _j0()
◆ _j1()
◆ _jn()
◆ _ldtest()
◆ _logb()
◆ _logbf()
Definition at line 38 of file logbf.c.
39{
40 unsigned int ux;
45 /* x is +/-zero. Return -infinity with div-by-zero flag. */
49 /* x is a normal number */
52 {
53 /* x is infinity or NaN */
55 /* x is +/-infinity. For VC++, return infinity of same sign. */
57 else
58 /* x is NaN, result is NaN */
61 }
62 else
63 {
64 /* x is denormalized. */
65#ifdef FOLLOW_IEEE754_LOGB
66 /* Return the value of the minimum exponent to ensure that
67 the relationship between logb and scalb, defined in
68 IEEE 754, holds. */
70#else
71 /* Follow the rule set by IEEE 854 for logb */
72 ux &= MANTBITS_SP32;
75 {
76 ux <<= 1;
77 u--;
78 }
80#endif
81 }
82}
◆ _matherr()
| _ACRTIMP int __cdecl _matherr | ( | struct _exception * | e | ) |
◆ _nextafter()
◆ _scalb()
| _ACRTIMP double __cdecl _scalb | ( | double | num, |
| __msvcrt_long | power | ||
| ) |
◆ _y0()
◆ _y1()
◆ _yn()
◆ acos()
Definition at line 28 of file acos.c.
29{
31}
Referenced by __libm_sse2_acos(), __libm_sse2_acosf(), _CIacos(), _libm_sse2_acos_precise(), acosf(), acosl(), AngleBetweenVectorsRad(), D3DRMQuaternionSlerp(), fpu_invalid_operation(), Math_acos(), CDrvDefExt::PaintStaticControls(), pres_acos(), rpn_acos(), Test_acos_approx(), Test_acos_exact(), test_math_errors(), and ValarrayTest::transcendentals().
◆ acosf()
Definition at line 47 of file acosf.c.
48{
49 /* Computes arccos(x).
50 The argument is first reduced by noting that arccos(x)
51 is invalid for abs(x) > 1. For denormal and small
52 arguments arccos(x) = pi/2 to machine accuracy.
53 Remaining argument ranges are handled as follows.
54 For abs(x) <= 0.5 use
55 arccos(x) = pi/2 - arcsin(x)
56 = pi/2 - (x + x^3*R(x^2))
57 where R(x^2) is a rational minimax approximation to
58 (arcsin(x) - x)/x^3.
59 For abs(x) > 0.5 exploit the identity:
60 arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
61 together with the above rational approximation, and
62 reconstruct the terms carefully.
63 */
64
65 /* Some constants and split constants. */
66
67 static const float
68 piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */
69 static const double
71 piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */
72 piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */
73
76
77 unsigned int ux, aux, xneg;
78
80 aux = ux & ~SIGNBIT_SP32;
81 xneg = (ux & SIGNBIT_SP32);
82 xnan = (aux > PINFBITPATT_SP32);
84
85 /* Special cases */
86
87 if (xnan)
88 {
91 }
92 else if (xexp < -26)
93 /* y small enough that arccos(x) = pi/2 */
95 else if (xexp >= 0)
96 { /* abs(x) >= 1.0 */
98 return 0.0F;
101 else
104 }
105
108
110
112 { /* Transform y into the range [0,0.5) */
114 /* VC++ intrinsic call */
117 }
118 else
120
121 /* Use a rational approximation for [0.0, 0.5] */
122
124 (-0.0565298683201845211985026327361F +
125 (-0.0133819288943925804214011424456F -
127 (1.10496961524520294485512696706F -
128 0.836411276854206731913362287293F*r);
129
131 {
132 /* Reconstruct acos carefully in transformed region */
133 if (xneg)
135 else
136 {
143 }
144 }
145 else
147}
unsigned int(__cdecl typeof(jpeg_read_scanlines))(struct jpeg_decompress_struct *
Definition: typeof.h:31
struct S1 s1
Referenced by D3DXComputeTangentFrameEx(), D3DXQuaternionLn(), D3DXQuaternionSlerp(), D3DXQuaternionToAxisAngle(), Test_acosf_approx(), and Test_acosf_exact().
◆ acosh()
◆ acoshf()
◆ asin()
Definition at line 31 of file asin.c.
32{
34
35 /* Check range */
37
38 /* Calculate the square of x */
40
41 /* Start with 0, compiler will optimize this away */
42 result = 0;
43
44 result += (15*13*11*9*7*5*3*1./(16*14*12*10*8*6*4*2*17));
46
47 result += (13*11*9*7*5*3*1./(14*12*10*8*6*4*2*15));
49
50 result += (11*9*7*5*3*1./(12*10*8*6*4*2*13));
52
53 result += (9*7*5*3*1./(10*8*6*4*2*11));
55
56 result += (7*5*3*1./(8*6*4*2*9));
58
59 result += (5*3*1./(6*4*2*7));
61
62 result += (3*1./(4*2*5));
64
65 result += (1./(2*3));
67
68 result += 1.;
70
72}
Referenced by __libm_sse2_asin(), __libm_sse2_asinf(), _CIasin(), _libm_sse2_asin_precise(), asinf(), asinl(), Math_asin(), MSVCRT_asin(), pres_asin(), rpn_asin(), Test_asin_approx(), Test_asin_exact(), and ValarrayTest::transcendentals().
◆ asinf()
Definition at line 47 of file asinf.c.
48{
49 /* Computes arcsin(x).
50 The argument is first reduced by noting that arcsin(x)
51 is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
52 For denormal and small arguments arcsin(x) = x to machine
53 accuracy. Remaining argument ranges are handled as follows.
54 For abs(x) <= 0.5 use
55 arcsin(x) = x + x^3*R(x^2)
56 where R(x^2) is a rational minimax approximation to
57 (arcsin(x) - x)/x^3.
58 For abs(x) > 0.5 exploit the identity:
59 arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
60 together with the above rational approximation, and
61 reconstruct the terms carefully.
62 */
63
64 /* Some constants and split constants. */
65
66 static const float
67 piby2_tail = 7.5497894159e-08F, /* 0x33a22168 */
68 hpiby2_head = 7.8539812565e-01F, /* 0x3f490fda */
69 piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */
72
73 unsigned int ux, aux, xneg;
75 aux = ux & ~SIGNBIT_SP32;
76 xneg = (ux & SIGNBIT_SP32);
77 xnan = (aux > PINFBITPATT_SP32);
79
80 /* Special cases */
81
82 if (xnan)
83 {
86 }
87 else if (xexp < -14)
88 /* y small enough that arcsin(x) = x */
90 else if (xexp >= 0)
91 {
92 /* abs(x) >= 1.0 */
97 else
100 }
101
104
106
108 { /* Transform y into the range [0,0.5) */
110 /* VC++ intrinsic call */
113 }
114 else
116
117 /* Use a rational approximation for [0.0, 0.5] */
118
120 (-0.0565298683201845211985026327361F +
121 (-0.0133819288943925804214011424456F -
123 (1.10496961524520294485512696706F -
124 0.836411276854206731913362287293F*r);
125
127 {
128 /* Reconstruct asin carefully in transformed region */
137 }
138 else
139 {
140 /* Use a temporary variable to prevent VC++ rearranging
141 y + y*u
142 into
143 y * (1 + u)
144 and getting an incorrectly rounded result */
145 float tmp;
148 }
149
152}
Referenced by D3DXSHEvalSphericalLight(), Test_asinf_approx(), and Test_asinf_exact().
◆ asinh()
◆ asinhf()
◆ atan()
Definition at line 44 of file atan.c.
45{
46
47 /* Some constants and split constants. */
48
49 static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
51
52 /* Find properties of argument x. */
53
54 unsigned long long ux, aux, xneg;
56 aux = ux & ~SIGNBIT_DP64;
57 xneg = (ux != aux);
58
61
62 /* Argument reduction to range [-7/16,7/16] */
63
64 if (aux > 0x4003800000000000) /* v > 39./16. */
65 {
66
68 {
69 /* x is NaN */
72 }
74 { /* abs(x) > 2^56 => arctan(1/x) is
75 insignificant compared to piby2 */
76 if (xneg)
78 else
80 }
81
83 /* (chi + clo) = arctan(infinity) */
84 chi = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */
85 clo = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */
86 }
87 else if (aux > 0x3ff3000000000000) /* 39./16. > v > 19./16. */
88 {
90 /* (chi + clo) = arctan(1.5) */
91 chi = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */
92 clo = 1.39033110312309953701e-17; /* 0x3c7007887af0cbbc */
93 }
94 else if (aux > 0x3fe6000000000000) /* 19./16. > v > 11./16. */
95 {
97 /* (chi + clo) = arctan(1.) */
98 chi = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */
99 clo = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */
100 }
101 else if (aux > 0x3fdc000000000000) /* 11./16. > v > 7./16. */
102 {
104 /* (chi + clo) = arctan(0.5) */
105 chi = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */
106 clo = 2.26987774529616809294e-17; /* 0x3c7a2b7f222f65e0 */
107 }
108 else /* v < 7./16. */
109 {
111 chi = 0.0;
112 clo = 0.0;
113 }
114
115 /* Core approximation: Remez(4,4) on [-7/16,7/16] */
116
119 (0.268297920532545909e0 +
120 (0.447677206805497472e0 +
121 (0.220638780716667420e0 +
122 (0.304455919504853031e-1 +
124 (0.804893761597637733e0 +
125 (0.182596787737507063e1 +
126 (0.141254259931958921e1 +
127 (0.424602594203847109e0 +
129
131
134}
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
Referenced by __libm_sse2_atan(), __libm_sse2_atanf(), _CIatan(), _libm_sse2_atan_precise(), atanf(), atanl(), GdipCreateLineBrushFromRectWithAngle(), Global_Atn(), Math_atan(), MSVCRT_atan(), pres_atan(), rpn_atan(), Test_atan_approx(), Test_atan_exact(), and ValarrayTest::transcendentals().
◆ atan2()
Definition at line 52 of file atan2.c.
53{
54 /* Arrays atan_jby256_lead and atan_jby256_tail contain
55 leading and trailing parts respectively of precomputed
56 values of atan(j/256), for j = 16, 17, ..., 256.
57 atan_jby256_lead contains the first 21 bits of precision,
58 and atan_jby256_tail contains a further 53 bits precision. */
59
60 static const double atan_jby256_lead[ 241] = {
61 6.24187886714935302734e-02, /* 0x3faff55b00000000 */
62 6.63088560104370117188e-02, /* 0x3fb0f99e00000000 */
63 7.01969265937805175781e-02, /* 0x3fb1f86d00000000 */
64 7.40829110145568847656e-02, /* 0x3fb2f71900000000 */
65 7.79666304588317871094e-02, /* 0x3fb3f59f00000000 */
66 8.18479657173156738281e-02, /* 0x3fb4f3fd00000000 */
67 8.57268571853637695312e-02, /* 0x3fb5f23200000000 */
68 8.96031260490417480469e-02, /* 0x3fb6f03b00000000 */
69 9.34767723083496093750e-02, /* 0x3fb7ee1800000000 */
70 9.73475575447082519531e-02, /* 0x3fb8ebc500000000 */
71 1.01215422153472900391e-01, /* 0x3fb9e94100000000 */
72 1.05080246925354003906e-01, /* 0x3fbae68a00000000 */
73 1.08941912651062011719e-01, /* 0x3fbbe39e00000000 */
74 1.12800359725952148438e-01, /* 0x3fbce07c00000000 */
75 1.16655409336090087891e-01, /* 0x3fbddd2100000000 */
76 1.20507001876831054688e-01, /* 0x3fbed98c00000000 */
77 1.24354958534240722656e-01, /* 0x3fbfd5ba00000000 */
78 1.28199219703674316406e-01, /* 0x3fc068d500000000 */
79 1.32039666175842285156e-01, /* 0x3fc0e6ad00000000 */
80 1.35876297950744628906e-01, /* 0x3fc1646500000000 */
81 1.39708757400512695312e-01, /* 0x3fc1e1fa00000000 */
82 1.43537282943725585938e-01, /* 0x3fc25f6e00000000 */
83 1.47361397743225097656e-01, /* 0x3fc2dcbd00000000 */
84 1.51181221008300781250e-01, /* 0x3fc359e800000000 */
85 1.54996633529663085938e-01, /* 0x3fc3d6ee00000000 */
86 1.58807516098022460938e-01, /* 0x3fc453ce00000000 */
87 1.62613749504089355469e-01, /* 0x3fc4d08700000000 */
88 1.66415214538574218750e-01, /* 0x3fc54d1800000000 */
89 1.70211911201477050781e-01, /* 0x3fc5c98100000000 */
90 1.74003481864929199219e-01, /* 0x3fc645bf00000000 */
91 1.77790164947509765625e-01, /* 0x3fc6c1d400000000 */
92 1.81571602821350097656e-01, /* 0x3fc73dbd00000000 */
93 1.85347914695739746094e-01, /* 0x3fc7b97b00000000 */
94 1.89118742942810058594e-01, /* 0x3fc8350b00000000 */
95 1.92884206771850585938e-01, /* 0x3fc8b06e00000000 */
96 1.96644186973571777344e-01, /* 0x3fc92ba300000000 */
97 2.00398445129394531250e-01, /* 0x3fc9a6a800000000 */
98 2.04147100448608398438e-01, /* 0x3fca217e00000000 */
99 2.07889914512634277344e-01, /* 0x3fca9c2300000000 */
100 2.11626768112182617188e-01, /* 0x3fcb169600000000 */
101 2.15357661247253417969e-01, /* 0x3fcb90d700000000 */
102 2.19082474708557128906e-01, /* 0x3fcc0ae500000000 */
103 2.22801089286804199219e-01, /* 0x3fcc84bf00000000 */
104 2.26513504981994628906e-01, /* 0x3fccfe6500000000 */
105 2.30219483375549316406e-01, /* 0x3fcd77d500000000 */
106 2.33919143676757812500e-01, /* 0x3fcdf11000000000 */
107 2.37612247467041015625e-01, /* 0x3fce6a1400000000 */
108 2.41298794746398925781e-01, /* 0x3fcee2e100000000 */
109 2.44978547096252441406e-01, /* 0x3fcf5b7500000000 */
110 2.48651623725891113281e-01, /* 0x3fcfd3d100000000 */
111 2.52317905426025390625e-01, /* 0x3fd025fa00000000 */
112 2.55977153778076171875e-01, /* 0x3fd061ee00000000 */
113 2.59629487991333007812e-01, /* 0x3fd09dc500000000 */
114 2.63274669647216796875e-01, /* 0x3fd0d97e00000000 */
115 2.66912937164306640625e-01, /* 0x3fd1151a00000000 */
116 2.70543813705444335938e-01, /* 0x3fd1509700000000 */
117 2.74167299270629882812e-01, /* 0x3fd18bf500000000 */
118 2.77783632278442382812e-01, /* 0x3fd1c73500000000 */
119 2.81392335891723632812e-01, /* 0x3fd2025500000000 */
120 2.84993648529052734375e-01, /* 0x3fd23d5600000000 */
121 2.88587331771850585938e-01, /* 0x3fd2783700000000 */
122 2.92173147201538085938e-01, /* 0x3fd2b2f700000000 */
123 2.95751571655273437500e-01, /* 0x3fd2ed9800000000 */
124 2.99322128295898437500e-01, /* 0x3fd3281800000000 */
125 3.02884817123413085938e-01, /* 0x3fd3627700000000 */
126 3.06439399719238281250e-01, /* 0x3fd39cb400000000 */
127 3.09986352920532226562e-01, /* 0x3fd3d6d100000000 */
128 3.13524961471557617188e-01, /* 0x3fd410cb00000000 */
129 3.17055702209472656250e-01, /* 0x3fd44aa400000000 */
130 3.20578098297119140625e-01, /* 0x3fd4845a00000000 */
131 3.24092388153076171875e-01, /* 0x3fd4bdee00000000 */
132 3.27598333358764648438e-01, /* 0x3fd4f75f00000000 */
133 3.31095933914184570312e-01, /* 0x3fd530ad00000000 */
134 3.34585189819335937500e-01, /* 0x3fd569d800000000 */
135 3.38066101074218750000e-01, /* 0x3fd5a2e000000000 */
136 3.41538190841674804688e-01, /* 0x3fd5dbc300000000 */
137 3.45002174377441406250e-01, /* 0x3fd6148400000000 */
138 3.48457098007202148438e-01, /* 0x3fd64d1f00000000 */
139 3.51903676986694335938e-01, /* 0x3fd6859700000000 */
140 3.55341434478759765625e-01, /* 0x3fd6bdea00000000 */
141 3.58770608901977539062e-01, /* 0x3fd6f61900000000 */
142 3.62190723419189453125e-01, /* 0x3fd72e2200000000 */
143 3.65602254867553710938e-01, /* 0x3fd7660700000000 */
144 3.69004726409912109375e-01, /* 0x3fd79dc600000000 */
145 3.72398376464843750000e-01, /* 0x3fd7d56000000000 */
146 3.75782966613769531250e-01, /* 0x3fd80cd400000000 */
147 3.79158496856689453125e-01, /* 0x3fd8442200000000 */
148 3.82525205612182617188e-01, /* 0x3fd87b4b00000000 */
149 3.85882616043090820312e-01, /* 0x3fd8b24d00000000 */
150 3.89230966567993164062e-01, /* 0x3fd8e92900000000 */
151 3.92570018768310546875e-01, /* 0x3fd91fde00000000 */
152 3.95900011062622070312e-01, /* 0x3fd9566d00000000 */
153 3.99220705032348632812e-01, /* 0x3fd98cd500000000 */
154 4.02532100677490234375e-01, /* 0x3fd9c31600000000 */
155 4.05834197998046875000e-01, /* 0x3fd9f93000000000 */
156 4.09126996994018554688e-01, /* 0x3fda2f2300000000 */
157 4.12410259246826171875e-01, /* 0x3fda64ee00000000 */
158 4.15684223175048828125e-01, /* 0x3fda9a9200000000 */
159 4.18948888778686523438e-01, /* 0x3fdad00f00000000 */
160 4.22204017639160156250e-01, /* 0x3fdb056400000000 */
161 4.25449609756469726562e-01, /* 0x3fdb3a9100000000 */
162 4.28685665130615234375e-01, /* 0x3fdb6f9600000000 */
163 4.31912183761596679688e-01, /* 0x3fdba47300000000 */
164 4.35129165649414062500e-01, /* 0x3fdbd92800000000 */
165 4.38336372375488281250e-01, /* 0x3fdc0db400000000 */
166 4.41534280776977539062e-01, /* 0x3fdc421900000000 */
167 4.44722414016723632812e-01, /* 0x3fdc765500000000 */
168 4.47900772094726562500e-01, /* 0x3fdcaa6800000000 */
169 4.51069593429565429688e-01, /* 0x3fdcde5300000000 */
170 4.54228639602661132812e-01, /* 0x3fdd121500000000 */
171 4.57377910614013671875e-01, /* 0x3fdd45ae00000000 */
172 4.60517644882202148438e-01, /* 0x3fdd791f00000000 */
173 4.63647603988647460938e-01, /* 0x3fddac6700000000 */
174 4.66767549514770507812e-01, /* 0x3fdddf8500000000 */
175 4.69877958297729492188e-01, /* 0x3fde127b00000000 */
176 4.72978591918945312500e-01, /* 0x3fde454800000000 */
177 4.76069211959838867188e-01, /* 0x3fde77eb00000000 */
178 4.79150056838989257812e-01, /* 0x3fdeaa6500000000 */
179 4.82221126556396484375e-01, /* 0x3fdedcb600000000 */
180 4.85282421112060546875e-01, /* 0x3fdf0ede00000000 */
181 4.88333940505981445312e-01, /* 0x3fdf40dd00000000 */
182 4.91375446319580078125e-01, /* 0x3fdf72b200000000 */
183 4.94406938552856445312e-01, /* 0x3fdfa45d00000000 */
184 4.97428894042968750000e-01, /* 0x3fdfd5e000000000 */
185 5.00440597534179687500e-01, /* 0x3fe0039c00000000 */
186 5.03442764282226562500e-01, /* 0x3fe01c3400000000 */
187 5.06434917449951171875e-01, /* 0x3fe034b700000000 */
188 5.09417057037353515625e-01, /* 0x3fe04d2500000000 */
189 5.12389183044433593750e-01, /* 0x3fe0657e00000000 */
190 5.15351772308349609375e-01, /* 0x3fe07dc300000000 */
191 5.18304347991943359375e-01, /* 0x3fe095f300000000 */
192 5.21246910095214843750e-01, /* 0x3fe0ae0e00000000 */
193 5.24179458618164062500e-01, /* 0x3fe0c61400000000 */
194 5.27101993560791015625e-01, /* 0x3fe0de0500000000 */
195 5.30014991760253906250e-01, /* 0x3fe0f5e200000000 */
196 5.32917976379394531250e-01, /* 0x3fe10daa00000000 */
197 5.35810947418212890625e-01, /* 0x3fe1255d00000000 */
198 5.38693904876708984375e-01, /* 0x3fe13cfb00000000 */
199 5.41567325592041015625e-01, /* 0x3fe1548500000000 */
200 5.44430732727050781250e-01, /* 0x3fe16bfa00000000 */
201 5.47284126281738281250e-01, /* 0x3fe1835a00000000 */
202 5.50127506256103515625e-01, /* 0x3fe19aa500000000 */
203 5.52961349487304687500e-01, /* 0x3fe1b1dc00000000 */
204 5.55785179138183593750e-01, /* 0x3fe1c8fe00000000 */
205 5.58598995208740234375e-01, /* 0x3fe1e00b00000000 */
206 5.61403274536132812500e-01, /* 0x3fe1f70400000000 */
207 5.64197540283203125000e-01, /* 0x3fe20de800000000 */
208 5.66981792449951171875e-01, /* 0x3fe224b700000000 */
209 5.69756031036376953125e-01, /* 0x3fe23b7100000000 */
210 5.72520732879638671875e-01, /* 0x3fe2521700000000 */
211 5.75275897979736328125e-01, /* 0x3fe268a900000000 */
212 5.78021049499511718750e-01, /* 0x3fe27f2600000000 */
213 5.80756187438964843750e-01, /* 0x3fe2958e00000000 */
214 5.83481788635253906250e-01, /* 0x3fe2abe200000000 */
215 5.86197376251220703125e-01, /* 0x3fe2c22100000000 */
216 5.88903427124023437500e-01, /* 0x3fe2d84c00000000 */
217 5.91599464416503906250e-01, /* 0x3fe2ee6200000000 */
218 5.94285964965820312500e-01, /* 0x3fe3046400000000 */
219 5.96962928771972656250e-01, /* 0x3fe31a5200000000 */
220 5.99629878997802734375e-01, /* 0x3fe3302b00000000 */
221 6.02287292480468750000e-01, /* 0x3fe345f000000000 */
222 6.04934692382812500000e-01, /* 0x3fe35ba000000000 */
223 6.07573032379150390625e-01, /* 0x3fe3713d00000000 */
224 6.10201358795166015625e-01, /* 0x3fe386c500000000 */
225 6.12820148468017578125e-01, /* 0x3fe39c3900000000 */
226 6.15428924560546875000e-01, /* 0x3fe3b19800000000 */
227 6.18028640747070312500e-01, /* 0x3fe3c6e400000000 */
228 6.20618820190429687500e-01, /* 0x3fe3dc1c00000000 */
229 6.23198986053466796875e-01, /* 0x3fe3f13f00000000 */
230 6.25770092010498046875e-01, /* 0x3fe4064f00000000 */
231 6.28331184387207031250e-01, /* 0x3fe41b4a00000000 */
232 6.30883216857910156250e-01, /* 0x3fe4303200000000 */
233 6.33425712585449218750e-01, /* 0x3fe4450600000000 */
234 6.35958671569824218750e-01, /* 0x3fe459c600000000 */
235 6.38482093811035156250e-01, /* 0x3fe46e7200000000 */
236 6.40995979309082031250e-01, /* 0x3fe4830a00000000 */
237 6.43500804901123046875e-01, /* 0x3fe4978f00000000 */
238 6.45996093750000000000e-01, /* 0x3fe4ac0000000000 */
239 6.48482322692871093750e-01, /* 0x3fe4c05e00000000 */
240 6.50959014892578125000e-01, /* 0x3fe4d4a800000000 */
241 6.53426170349121093750e-01, /* 0x3fe4e8de00000000 */
242 6.55884265899658203125e-01, /* 0x3fe4fd0100000000 */
243 6.58332824707031250000e-01, /* 0x3fe5111000000000 */
244 6.60772323608398437500e-01, /* 0x3fe5250c00000000 */
245 6.63202762603759765625e-01, /* 0x3fe538f500000000 */
246 6.65623664855957031250e-01, /* 0x3fe54cca00000000 */
247 6.68035984039306640625e-01, /* 0x3fe5608d00000000 */
248 6.70438766479492187500e-01, /* 0x3fe5743c00000000 */
249 6.72832489013671875000e-01, /* 0x3fe587d800000000 */
250 6.75216674804687500000e-01, /* 0x3fe59b6000000000 */
251 6.77592277526855468750e-01, /* 0x3fe5aed600000000 */
252 6.79958820343017578125e-01, /* 0x3fe5c23900000000 */
253 6.82316303253173828125e-01, /* 0x3fe5d58900000000 */
254 6.84664726257324218750e-01, /* 0x3fe5e8c600000000 */
255 6.87004089355468750000e-01, /* 0x3fe5fbf000000000 */
256 6.89334869384765625000e-01, /* 0x3fe60f0800000000 */
257 6.91656589508056640625e-01, /* 0x3fe6220d00000000 */
258 6.93969249725341796875e-01, /* 0x3fe634ff00000000 */
259 6.96272850036621093750e-01, /* 0x3fe647de00000000 */
260 6.98567867279052734375e-01, /* 0x3fe65aab00000000 */
261 7.00854301452636718750e-01, /* 0x3fe66d6600000000 */
262 7.03131675720214843750e-01, /* 0x3fe6800e00000000 */
263 7.05400466918945312500e-01, /* 0x3fe692a400000000 */
264 7.07660198211669921875e-01, /* 0x3fe6a52700000000 */
265 7.09911346435546875000e-01, /* 0x3fe6b79800000000 */
266 7.12153911590576171875e-01, /* 0x3fe6c9f700000000 */
267 7.14387893676757812500e-01, /* 0x3fe6dc4400000000 */
268 7.16613292694091796875e-01, /* 0x3fe6ee7f00000000 */
269 7.18829631805419921875e-01, /* 0x3fe700a700000000 */
270 7.21037864685058593750e-01, /* 0x3fe712be00000000 */
271 7.23237514495849609375e-01, /* 0x3fe724c300000000 */
272 7.25428581237792968750e-01, /* 0x3fe736b600000000 */
273 7.27611064910888671875e-01, /* 0x3fe7489700000000 */
274 7.29785442352294921875e-01, /* 0x3fe75a6700000000 */
275 7.31950759887695312500e-01, /* 0x3fe76c2400000000 */
276 7.34108448028564453125e-01, /* 0x3fe77dd100000000 */
277 7.36257076263427734375e-01, /* 0x3fe78f6b00000000 */
278 7.38397598266601562500e-01, /* 0x3fe7a0f400000000 */
279 7.40530014038085937500e-01, /* 0x3fe7b26c00000000 */
280 7.42654323577880859375e-01, /* 0x3fe7c3d300000000 */
281 7.44770050048828125000e-01, /* 0x3fe7d52800000000 */
282 7.46877670288085937500e-01, /* 0x3fe7e66c00000000 */
283 7.48976707458496093750e-01, /* 0x3fe7f79e00000000 */
284 7.51068115234375000000e-01, /* 0x3fe808c000000000 */
285 7.53150939941406250000e-01, /* 0x3fe819d000000000 */
286 7.55226135253906250000e-01, /* 0x3fe82ad000000000 */
287 7.57292747497558593750e-01, /* 0x3fe83bbe00000000 */
288 7.59351730346679687500e-01, /* 0x3fe84c9c00000000 */
289 7.61402606964111328125e-01, /* 0x3fe85d6900000000 */
290 7.63445377349853515625e-01, /* 0x3fe86e2500000000 */
291 7.65480041503906250000e-01, /* 0x3fe87ed000000000 */
292 7.67507076263427734375e-01, /* 0x3fe88f6b00000000 */
293 7.69526004791259765625e-01, /* 0x3fe89ff500000000 */
294 7.71537303924560546875e-01, /* 0x3fe8b06f00000000 */
295 7.73540973663330078125e-01, /* 0x3fe8c0d900000000 */
296 7.75536537170410156250e-01, /* 0x3fe8d13200000000 */
297 7.77523994445800781250e-01, /* 0x3fe8e17a00000000 */
298 7.79504299163818359375e-01, /* 0x3fe8f1b300000000 */
299 7.81476497650146484375e-01, /* 0x3fe901db00000000 */
300 7.83441066741943359375e-01, /* 0x3fe911f300000000 */
301 7.85398006439208984375e-01}; /* 0x3fe921fb00000000 */
302
303 static const double atan_jby256_tail[ 241] = {
304 2.13244638182005395671e-08, /* 0x3e56e59fbd38db2c */
305 3.89093864761712760656e-08, /* 0x3e64e3aa54dedf96 */
306 4.44780900009437454576e-08, /* 0x3e67e105ab1bda88 */
307 1.15344768460112754160e-08, /* 0x3e48c5254d013fd0 */
308 3.37271051945395312705e-09, /* 0x3e2cf8ab3ad62670 */
309 2.40857608736109859459e-08, /* 0x3e59dca4bec80468 */
310 1.85853810450623807768e-08, /* 0x3e53f4b5ec98a8da */
311 5.14358299969225078306e-08, /* 0x3e6b9d49619d81fe */
312 8.85023985412952486748e-09, /* 0x3e43017887460934 */
313 1.59425154214358432060e-08, /* 0x3e511e3eca0b9944 */
314 1.95139937737755753164e-08, /* 0x3e54f3f73c5a332e */
315 2.64909755273544319715e-08, /* 0x3e5c71c8ae0e00a6 */
316 4.43388037881231070144e-08, /* 0x3e67cde0f86fbdc7 */
317 2.14757072421821274557e-08, /* 0x3e570f328c889c72 */
318 2.61049792670754218852e-08, /* 0x3e5c07ae9b994efe */
319 7.81439350674466302231e-09, /* 0x3e40c8021d7b1698 */
320 3.60125207123751024094e-08, /* 0x3e635585edb8cb22 */
321 6.15276238179343767917e-08, /* 0x3e70842567b30e96 */
322 9.54387964641184285058e-08, /* 0x3e799e811031472e */
323 3.02789566851502754129e-08, /* 0x3e6041821416bcee */
324 1.16888650949870856331e-07, /* 0x3e7f6086e4dc96f4 */
325 1.07580956468653338863e-08, /* 0x3e471a535c5f1b58 */
326 8.33454265379535427653e-08, /* 0x3e765f743fe63ca1 */
327 1.10790279272629526068e-07, /* 0x3e7dbd733472d014 */
328 1.08394277896366207424e-07, /* 0x3e7d18cc4d8b0d1d */
329 9.22176086126841098800e-08, /* 0x3e78c12553c8fb29 */
330 7.90938592199048786990e-08, /* 0x3e753b49e2e8f991 */
331 8.66445407164293125637e-08, /* 0x3e77422ae148c141 */
332 1.40839973537092438671e-08, /* 0x3e4e3ec269df56a8 */
333 1.19070438507307600689e-07, /* 0x3e7ff6754e7e0ac9 */
334 6.40451663051716197071e-08, /* 0x3e7131267b1b5aad */
335 1.08338682076343674522e-07, /* 0x3e7d14fa403a94bc */
336 3.52999550187922736222e-08, /* 0x3e62f396c089a3d8 */
337 1.05983273930043077202e-07, /* 0x3e7c731d78fa95bb */
338 1.05486124078259553339e-07, /* 0x3e7c50f385177399 */
339 5.82167732281776477773e-08, /* 0x3e6f41409c6f2c20 */
340 1.08696483983403942633e-07, /* 0x3e7d2d90c4c39ec0 */
341 4.47335086122377542835e-08, /* 0x3e680420696f2106 */
342 1.26896287162615723528e-08, /* 0x3e4b40327943a2e8 */
343 4.06534471589151404531e-08, /* 0x3e65d35e02f3d2a2 */
344 3.84504846300557026690e-08, /* 0x3e64a498288117b0 */
345 3.60715006404807269080e-08, /* 0x3e635da119afb324 */
346 6.44725903165522722801e-08, /* 0x3e714e85cdb9a908 */
347 3.63749249976409461305e-08, /* 0x3e638754e5547b9a */
348 1.03901294413833913794e-07, /* 0x3e7be40ae6ce3246 */
349 6.25379756302167880580e-08, /* 0x3e70c993b3bea7e7 */
350 6.63984302368488828029e-08, /* 0x3e71d2dd89ac3359 */
351 3.21844598971548278059e-08, /* 0x3e61476603332c46 */
352 1.16030611712765830905e-07, /* 0x3e7f25901bac55b7 */
353 1.17464622142347730134e-07, /* 0x3e7f881b7c826e28 */
354 7.54604017965808996596e-08, /* 0x3e7441996d698d20 */
355 1.49234929356206556899e-07, /* 0x3e8407ac521ea089 */
356 1.41416924523217430259e-07, /* 0x3e82fb0c6c4b1723 */
357 2.13308065617483489011e-07, /* 0x3e8ca135966a3e18 */
358 5.04230937933302320146e-08, /* 0x3e6b1218e4d646e4 */
359 5.45874922281655519035e-08, /* 0x3e6d4e72a350d288 */
360 1.51849028914786868886e-07, /* 0x3e84617e2f04c329 */
361 3.09004308703769273010e-08, /* 0x3e6096ec41e82650 */
362 9.67574548184738317664e-08, /* 0x3e79f91f25773e6e */
363 4.02508285529322212824e-08, /* 0x3e659c0820f1d674 */
364 3.01222268096861091157e-08, /* 0x3e602bf7a2df1064 */
365 2.36189860670079288680e-07, /* 0x3e8fb36bfc40508f */
366 1.14095158111080887695e-07, /* 0x3e7ea08f3f8dc892 */
367 7.42349089746573467487e-08, /* 0x3e73ed6254656a0e */
368 5.12515583196230380184e-08, /* 0x3e6b83f5e5e69c58 */
369 2.19290391828763918102e-07, /* 0x3e8d6ec2af768592 */
370 3.83263512187553886471e-08, /* 0x3e6493889a226f94 */
371 1.61513486284090523855e-07, /* 0x3e85ad8fa65279ba */
372 5.09996743535589922261e-08, /* 0x3e6b615784d45434 */
373 1.23694037861246766534e-07, /* 0x3e809a184368f145 */
374 8.23367955351123783984e-08, /* 0x3e761a2439b0d91c */
375 1.07591766213053694014e-07, /* 0x3e7ce1a65e39a978 */
376 1.42789947524631815640e-07, /* 0x3e832a39a93b6a66 */
377 1.32347123024711878538e-07, /* 0x3e81c3699af804e7 */
378 2.17626067316598149229e-08, /* 0x3e575e0f4e44ede8 */
379 2.34454866923044288656e-07, /* 0x3e8f77ced1a7a83b */
380 2.82966370261766916053e-09, /* 0x3e284e7f0cb1b500 */
381 2.29300919890907632975e-07, /* 0x3e8ec6b838b02dfe */
382 1.48428270450261284915e-07, /* 0x3e83ebf4dfbeda87 */
383 1.87937408574313982512e-07, /* 0x3e89397aed9cb475 */
384 6.13685946813334055347e-08, /* 0x3e707937bc239c54 */
385 1.98585022733583817493e-07, /* 0x3e8aa754553131b6 */
386 7.68394131623752961662e-08, /* 0x3e74a05d407c45dc */
387 1.28119052312436745644e-07, /* 0x3e8132231a206dd0 */
388 7.02119104719236502733e-08, /* 0x3e72d8ecfdd69c88 */
389 9.87954793820636301943e-08, /* 0x3e7a852c74218606 */
390 1.72176752381034986217e-07, /* 0x3e871bf2baeebb50 */
391 1.12877225146169704119e-08, /* 0x3e483d7db7491820 */
392 5.33549829555851737993e-08, /* 0x3e6ca50d92b6da14 */
393 2.13833275710816521345e-08, /* 0x3e56f5cde8530298 */
394 1.16243518048290556393e-07, /* 0x3e7f343198910740 */
395 6.29926408369055877943e-08, /* 0x3e70e8d241ccd80a */
396 6.45429039328021963791e-08, /* 0x3e71535ac619e6c8 */
397 8.64001922814281933403e-08, /* 0x3e77316041c36cd2 */
398 9.50767572202325800240e-08, /* 0x3e7985a000637d8e */
399 5.80851497508121135975e-08, /* 0x3e6f2f29858c0a68 */
400 1.82350561135024766232e-07, /* 0x3e8879847f96d909 */
401 1.98948680587390608655e-07, /* 0x3e8ab3d319e12e42 */
402 7.83548663450197659846e-08, /* 0x3e75088162dfc4c2 */
403 3.04374234486798594427e-08, /* 0x3e605749a1cd9d8c */
404 2.76135725629797411787e-08, /* 0x3e5da65c6c6b8618 */
405 4.32610105454203065470e-08, /* 0x3e6739bf7df1ad64 */
406 5.17107515324127256994e-08, /* 0x3e6bc31252aa3340 */
407 2.82398327875841444660e-08, /* 0x3e5e528191ad3aa8 */
408 1.87482469524195595399e-07, /* 0x3e8929d93df19f18 */
409 2.97481891662714096139e-08, /* 0x3e5ff11eb693a080 */
410 9.94421570843584316402e-09, /* 0x3e455ae3f145a3a0 */
411 1.07056210730391848428e-07, /* 0x3e7cbcd8c6c0ca82 */
412 6.25589580466881163081e-08, /* 0x3e70cb04d425d304 */
413 9.56641013869464593803e-08, /* 0x3e79adfcab5be678 */
414 1.88056307148355440276e-07, /* 0x3e893d90c5662508 */
415 8.38850689379557880950e-08, /* 0x3e768489bd35ff40 */
416 5.01215865527674122924e-09, /* 0x3e3586ed3da2b7e0 */
417 1.74166095998522089762e-07, /* 0x3e87604d2e850eee */
418 9.96779574395363585849e-08, /* 0x3e7ac1d12bfb53d8 */
419 5.98432026368321460686e-09, /* 0x3e39b3d468274740 */
420 1.18362922366887577169e-07, /* 0x3e7fc5d68d10e53c */
421 1.86086833284154215946e-07, /* 0x3e88f9e51884becb */
422 1.97671457251348941011e-07, /* 0x3e8a87f0869c06d1 */
423 1.42447160717199237159e-07, /* 0x3e831e7279f685fa */
424 1.05504240785546574184e-08, /* 0x3e46a8282f9719b0 */
425 3.13335218371639189324e-08, /* 0x3e60d2724a8a44e0 */
426 1.96518418901914535399e-07, /* 0x3e8a60524b11ad4e */
427 2.17692035039173536059e-08, /* 0x3e575fdf832750f0 */
428 2.15613114426529981675e-07, /* 0x3e8cf06902e4cd36 */
429 5.68271098300441214948e-08, /* 0x3e6e82422d4f6d10 */
430 1.70331455823369124256e-08, /* 0x3e524a091063e6c0 */
431 9.17590028095709583247e-08, /* 0x3e78a1a172dc6f38 */
432 2.77266304112916566247e-07, /* 0x3e929b6619f8a92d */
433 9.37041937614656939690e-08, /* 0x3e79274d9c1b70c8 */
434 1.56116346368316796511e-08, /* 0x3e50c34b1fbb7930 */
435 4.13967433808382727413e-08, /* 0x3e6639866c20eb50 */
436 1.70164749185821616276e-07, /* 0x3e86d6d0f6832e9e */
437 4.01708788545600086008e-07, /* 0x3e9af54def99f25e */
438 2.59663539226050551563e-07, /* 0x3e916cfc52a00262 */
439 2.22007487655027469542e-07, /* 0x3e8dcc1e83569c32 */
440 2.90542250809644081369e-07, /* 0x3e937f7a551ed425 */
441 4.67720537666628903341e-07, /* 0x3e9f6360adc98887 */
442 2.79799803956772554802e-07, /* 0x3e92c6ec8d35a2c1 */
443 2.07344552327432547723e-07, /* 0x3e8bd44df84cb036 */
444 2.54705698692735196368e-07, /* 0x3e9117cf826e310e */
445 4.26848589539548450728e-07, /* 0x3e9ca533f332cfc9 */
446 2.52506723633552216197e-07, /* 0x3e90f208509dbc2e */
447 2.14684129933849704964e-07, /* 0x3e8cd07d93c945de */
448 3.20134822201596505431e-07, /* 0x3e957bdfd67e6d72 */
449 9.93537565749855712134e-08, /* 0x3e7aab89c516c658 */
450 3.70792944827917252327e-08, /* 0x3e63e823b1a1b8a0 */
451 1.41772749369083698972e-07, /* 0x3e8307464a9d6d3c */
452 4.22446601490198804306e-07, /* 0x3e9c5993cd438843 */
453 4.11818433724801511540e-07, /* 0x3e9ba2fca02ab554 */
454 1.19976381502605310519e-07, /* 0x3e801a5b6983a268 */
455 3.43703078571520905265e-08, /* 0x3e6273d1b350efc8 */
456 1.66128705555453270379e-07, /* 0x3e864c238c37b0c6 */
457 5.00499610023283006540e-08, /* 0x3e6aded07370a300 */
458 1.75105139941208062123e-07, /* 0x3e878091197eb47e */
459 7.70807146729030327334e-08, /* 0x3e74b0f245e0dabc */
460 2.45918607526895836121e-07, /* 0x3e9080d9794e2eaf */
461 2.18359020958626199345e-07, /* 0x3e8d4ec242b60c76 */
462 8.44342887976445333569e-09, /* 0x3e4221d2f940caa0 */
463 1.07506148687888629299e-07, /* 0x3e7cdbc42b2bba5c */
464 5.36544954316820904572e-08, /* 0x3e6cce37bb440840 */
465 3.39109101518396596341e-07, /* 0x3e96c1d999cf1dd0 */
466 2.60098720293920613340e-08, /* 0x3e5bed8a07eb0870 */
467 8.42678991664621455827e-08, /* 0x3e769ed88f490e3c */
468 5.36972237470183633197e-08, /* 0x3e6cd41719b73ef0 */
469 4.28192558171921681288e-07, /* 0x3e9cbc4ac95b41b7 */
470 2.71535491483955143294e-07, /* 0x3e9238f1b890f5d7 */
471 7.84094998145075780203e-08, /* 0x3e750c4282259cc4 */
472 3.43880599134117431863e-07, /* 0x3e9713d2de87b3e2 */
473 1.32878065060366481043e-07, /* 0x3e81d5a7d2255276 */
474 4.18046802627967629428e-07, /* 0x3e9c0dfd48227ac1 */
475 2.65042411765766019424e-07, /* 0x3e91c964dab76753 */
476 1.70383695347518643694e-07, /* 0x3e86de56d5704496 */
477 1.54096497259613515678e-07, /* 0x3e84aeb71fd19968 */
478 2.36543402412459813461e-07, /* 0x3e8fbf91c57b1918 */
479 4.38416350106876736790e-07, /* 0x3e9d6bef7fbe5d9a */
480 3.03892161339927775731e-07, /* 0x3e9464d3dc249066 */
481 3.31136771605664899240e-07, /* 0x3e9638e2ec4d9073 */
482 6.49494294526590682218e-08, /* 0x3e716f4a7247ea7c */
483 4.10423429887181345747e-09, /* 0x3e31a0a740f1d440 */
484 1.70831640869113847224e-07, /* 0x3e86edbb0114a33c */
485 1.10811512657909180966e-07, /* 0x3e7dbee8bf1d513c */
486 3.23677724749783611964e-07, /* 0x3e95b8bdb0248f73 */
487 3.55662734259192678528e-07, /* 0x3e97de3d3f5eac64 */
488 2.30102333489738219140e-07, /* 0x3e8ee24187ae448a */
489 4.47429004000738629714e-07, /* 0x3e9e06c591ec5192 */
490 7.78167135617329598659e-08, /* 0x3e74e3861a332738 */
491 9.90345291908535415737e-08, /* 0x3e7a9599dcc2bfe4 */
492 5.85800913143113728314e-08, /* 0x3e6f732fbad43468 */
493 4.57859062410871843857e-07, /* 0x3e9eb9f573b727d9 */
494 3.67993069723390929794e-07, /* 0x3e98b212a2eb9897 */
495 2.90836464322977276043e-07, /* 0x3e9384884c167215 */
496 2.51621574250131388318e-07, /* 0x3e90e2d363020051 */
497 2.75789824740652815545e-07, /* 0x3e92820879fbd022 */
498 3.88985776250314403593e-07, /* 0x3e9a1ab9893e4b30 */
499 1.40214080183768019611e-07, /* 0x3e82d1b817a24478 */
500 3.23451432223550478373e-08, /* 0x3e615d7b8ded4878 */
501 9.15979180730608444470e-08, /* 0x3e78968f9db3a5e4 */
502 3.44371402498640470421e-07, /* 0x3e971c4171fe135f */
503 3.40401897215059498077e-07, /* 0x3e96d80f605d0d8c */
504 1.06431813453707950243e-07, /* 0x3e7c91f043691590 */
505 1.46204238932338846248e-07, /* 0x3e839f8a15fce2b2 */
506 9.94610376972039046878e-09, /* 0x3e455beda9d94b80 */
507 2.01711528092681771039e-07, /* 0x3e8b12c15d60949a */
508 2.72027977986191568296e-07, /* 0x3e924167b312bfe3 */
509 2.48402602511693757964e-07, /* 0x3e90ab8633070277 */
510 1.58480011219249621715e-07, /* 0x3e854554ebbc80ee */
511 3.00372828113368713281e-08, /* 0x3e60204aef5a4bb8 */
512 3.67816204583541976394e-07, /* 0x3e98af08c679cf2c */
513 2.46169793032343824291e-07, /* 0x3e90852a330ae6c8 */
514 1.70080468270204253247e-07, /* 0x3e86d3eb9ec32916 */
515 1.67806717763872914315e-07, /* 0x3e8685cb7fcbbafe */
516 2.67715622006907942620e-07, /* 0x3e91f751c1e0bd95 */
517 2.14411342550299170574e-08, /* 0x3e5705b1b0f72560 */
518 4.11228221283669073277e-07, /* 0x3e9b98d8d808ca92 */
519 3.52311752396749662260e-08, /* 0x3e62ea22c75cc980 */
520 3.52718000397367821054e-07, /* 0x3e97aba62bca0350 */
521 4.38857387992911129814e-07, /* 0x3e9d73833442278c */
522 3.22574606753482540743e-07, /* 0x3e95a5ca1fb18bf9 */
523 3.28730371182804296828e-08, /* 0x3e61a6092b6ecf28 */
524 7.56672470607639279700e-08, /* 0x3e744fd049aac104 */
525 3.26750155316369681821e-09, /* 0x3e2c114fd8df5180 */
526 3.21724445362095284743e-07, /* 0x3e95972f130feae5 */
527 1.06639427371776571151e-07, /* 0x3e7ca034a55fe198 */
528 3.41020788139524715063e-07, /* 0x3e96e2b149990227 */
529 1.00582838631232552824e-07, /* 0x3e7b00000294592c */
530 3.68439433859276640065e-07, /* 0x3e98b9bdc442620e */
531 2.20403078342388012027e-07, /* 0x3e8d94fdfabf3e4e */
532 1.62841467098298142534e-07, /* 0x3e85db30b145ad9a */
533 2.25325348296680733838e-07, /* 0x3e8e3e1eb95022b0 */
534 4.37462238226421614339e-07, /* 0x3e9d5b8b45442bd6 */
535 3.52055880555040706500e-07, /* 0x3e97a046231ecd2e */
536 4.75614398494781776825e-07, /* 0x3e9feafe3ef55232 */
537 3.60998399033215317516e-07, /* 0x3e9839e7bfd78267 */
538 3.79292434611513945954e-08, /* 0x3e645cf49d6fa900 */
539 1.29859015528549300061e-08, /* 0x3e4be3132b27f380 */
540 3.15927546985474913188e-07, /* 0x3e9533980bb84f9f */
541 2.28533679887379668031e-08, /* 0x3e5889e2ce3ba390 */
542 1.17222541823553133877e-07, /* 0x3e7f7778c3ad0cc8 */
543 1.51991208405464415857e-07, /* 0x3e846660cec4eba2 */
544 1.56958239325240655564e-07}; /* 0x3e85110b4611a626 */
545
546 /* Some constants and split constants. */
547
549 piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */
550 piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */
551 three_piby4 = 2.3561944901923449e+00, /* 0x4002d97c7f3321d2 */
552 pi_head = 3.1415926218032836e+00, /* 0x400921fb50000000 */
553 pi_tail = 3.1786509547056392e-08, /* 0x3e6110b4611a6263 */
554 piby2_head = 1.5707963267948965e+00, /* 0x3ff921fb54442d18 */
555 piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */
556
560
561 /* Find properties of arguments x and y. */
562
564
567 aux = ux & ~SIGNBIT_DP64;
568 auy = uy & ~SIGNBIT_DP64;
571 xneg = ux & SIGNBIT_DP64;
572 yneg = uy & SIGNBIT_DP64;
573 xzero = (aux == 0);
574 yzero = (auy == 0);
575 xnan = (aux > PINFBITPATT_DP64);
576 ynan = (auy > PINFBITPATT_DP64);
577 xinf = (aux == PINFBITPATT_DP64);
578 yinf = (auy == PINFBITPATT_DP64);
579
580 diffexp = yexp - xexp;
581
582 /* Special cases */
583
584 if (xnan)
587 else if (ynan)
590 else if (yzero)
591 { /* Zero y gives +-0 for positive x
592 and +-pi for negative x */
593 if (xneg)
594 {
597 }
599 }
600 else if (xzero)
601 { /* Zero x gives +- pi/2
602 depending on sign of y */
605 }
606
607 /* Scale up both x and y if they are both below 1/4.
608 This avoids any possible later denormalised arithmetic. */
609
610 if ((xexp < 1021 && yexp < 1021))
611 {
612 scaleUpDouble1024(ux, &ux);
613 scaleUpDouble1024(uy, &uy);
618 diffexp = yexp - xexp;
619 }
620
621 if (diffexp > 56)
622 { /* abs(y)/abs(x) > 2^56 => arctan(x/y)
623 is insignificant compared to piby2 */
626 }
627 else if (diffexp < -28 && (!xneg))
628 { /* x positive and dominant over y by a factor of 2^28.
629 In this case atan(y/x) is y/x to machine accuracy. */
630
631 if (diffexp < -1074) /* Result underflows */
632 {
633 if (yneg)
635 else
637 }
638 else
639 {
640 if (diffexp < -1022)
641 {
642 /* Result will likely be denormalized */
645 /* Now y is 2^100 times the true result. Scale it back down. */
647 scaleDownDouble(uy, 100, &uy);
651 else
653 }
654 else
656 }
657 }
658 else if (diffexp < -56 && xneg)
659 { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x)
660 is insignificant compared to pi */
663 }
664 else if (yinf && xinf)
665 { /* If abs(x) and abs(y) are both infinity
666 return +-pi/4 or +- 3pi/4 according to
667 signs. */
668 if (xneg)
669 {
672 }
673 else
674 {
677 }
678 }
679
680 /* General case: take absolute values of arguments */
681
685
686 /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */
687
691
692 if (vbyu > 0.0625)
693 { /* General values of v/u. Use a look-up
694 table and series expansion. */
695
697 q1 = atan_jby256_lead[index-16];
698 q2 = atan_jby256_tail[index-16];
707
709
710 /* Polynomial approximation to atan(r) */
711
714 }
715 else if (vbyu < 1.e-8)
716 { /* v/u is small enough that atan(v/u) = v/u */
717 q1 = 0.0;
718 q2 = vbyu;
719 }
720 else /* vbyu <= 0.0625 */
721 {
722 /* Small values of v/u. Use a series expansion
723 computed carefully to minimise cancellation */
724
730 vu2 = vbyu - vu1;
731
732 q1 = 0.0;
733 s = vbyu*vbyu;
734 q2 = vbyu +
736 (vbyu*s*(0.33333333333333170500 -
737 s*(0.19999999999393223405 -
738 s*(0.14285713561807169030 -
739 s*(0.11110736283514525407 -
740 s*(0.90029810285449784439E-01)))))));
741 }
742
743 /* Tidy-up according to which quadrant the arguments lie in */
744
745 if (swap_vu) {q1 = piby2_head - q1; q2 = piby2_tail - q2;}
746 if (xneg) {q1 = pi_head - q1; q2 = pi_tail - q2;}
747 q1 = q1 + q2;
748
749 if (yneg) q1 = - q1;
750
751 return q1;
752}
Referenced by __libm_sse2_atan2(), _CIatan2(), acos(), asin(), atan2f(), atan2l(), EMFDRV_ArcChordPie(), gdiplus_atan2(), GetDirection(), IntArc(), IntGdiWidenPath(), log10T(), logT(), Math_atan2(), PATH_Arc(), powT(), pres_atan2(), and ValarrayTest::transcendentals().
◆ atan2f()
Definition at line 51 of file atan2f.c.
52{
53 /* Array atan_jby256 contains precomputed values of atan(j/256),
54 for j = 16, 17, ..., 256. */
55
56 static const double atan_jby256[ 241] = {
57 6.24188099959573430842e-02, /* 0x3faff55bb72cfde9 */
58 6.63088949198234745008e-02, /* 0x3fb0f99ea71d52a6 */
59 7.01969710718705064423e-02, /* 0x3fb1f86dbf082d58 */
60 7.40829225490337306415e-02, /* 0x3fb2f719318a4a9a */
61 7.79666338315423007588e-02, /* 0x3fb3f59f0e7c559d */
62 8.18479898030765457007e-02, /* 0x3fb4f3fd677292fb */
63 8.57268757707448092464e-02, /* 0x3fb5f2324fd2d7b2 */
64 8.96031774848717321724e-02, /* 0x3fb6f03bdcea4b0c */
65 9.34767811585894559112e-02, /* 0x3fb7ee182602f10e */
66 9.73475734872236708739e-02, /* 0x3fb8ebc54478fb28 */
67 1.01215441667466668485e-01, /* 0x3fb9e94153cfdcf1 */
68 1.05080273416329528224e-01, /* 0x3fbae68a71c722b8 */
69 1.08941956989865793015e-01, /* 0x3fbbe39ebe6f07c3 */
70 1.12800381201659388752e-01, /* 0x3fbce07c5c3cca32 */
71 1.16655435441069349478e-01, /* 0x3fbddd21701eba6e */
72 1.20507009691224548087e-01, /* 0x3fbed98c2190043a */
73 1.24354994546761424279e-01, /* 0x3fbfd5ba9aac2f6d */
74 1.28199281231298117811e-01, /* 0x3fc068d584212b3d */
75 1.32039761614638734288e-01, /* 0x3fc0e6adccf40881 */
76 1.35876328229701304195e-01, /* 0x3fc1646541060850 */
77 1.39708874289163620386e-01, /* 0x3fc1e1fafb043726 */
78 1.43537293701821222491e-01, /* 0x3fc25f6e171a535c */
79 1.47361481088651630200e-01, /* 0x3fc2dcbdb2fba1ff */
80 1.51181331798580037562e-01, /* 0x3fc359e8edeb99a3 */
81 1.54996741923940972718e-01, /* 0x3fc3d6eee8c6626c */
82 1.58807608315631065832e-01, /* 0x3fc453cec6092a9e */
83 1.62613828597948567589e-01, /* 0x3fc4d087a9da4f17 */
84 1.66415301183114927586e-01, /* 0x3fc54d18ba11570a */
85 1.70211925285474380276e-01, /* 0x3fc5c9811e3ec269 */
86 1.74003600935367680469e-01, /* 0x3fc645bfffb3aa73 */
87 1.77790228992676047071e-01, /* 0x3fc6c1d4898933d8 */
88 1.81571711160032150945e-01, /* 0x3fc73dbde8a7d201 */
89 1.85347949995694760705e-01, /* 0x3fc7b97b4bce5b02 */
90 1.89118848926083965578e-01, /* 0x3fc8350be398ebc7 */
91 1.92884312257974643856e-01, /* 0x3fc8b06ee2879c28 */
92 1.96644245190344985064e-01, /* 0x3fc92ba37d050271 */
93 2.00398553825878511514e-01, /* 0x3fc9a6a8e96c8626 */
94 2.04147145182116990236e-01, /* 0x3fca217e601081a5 */
95 2.07889927202262986272e-01, /* 0x3fca9c231b403279 */
96 2.11626808765629753628e-01, /* 0x3fcb1696574d780b */
97 2.15357699697738047551e-01, /* 0x3fcb90d7529260a2 */
98 2.19082510780057748701e-01, /* 0x3fcc0ae54d768466 */
99 2.22801153759394493514e-01, /* 0x3fcc84bf8a742e6d */
100 2.26513541356919617664e-01, /* 0x3fccfe654e1d5395 */
101 2.30219587276843717927e-01, /* 0x3fcd77d5df205736 */
102 2.33919206214733416127e-01, /* 0x3fcdf110864c9d9d */
103 2.37612313865471241892e-01, /* 0x3fce6a148e96ec4d */
104 2.41298826930858800743e-01, /* 0x3fcee2e1451d980c */
105 2.44978663126864143473e-01, /* 0x3fcf5b75f92c80dd */
106 2.48651741190513253521e-01, /* 0x3fcfd3d1fc40dbe4 */
107 2.52317980886427151166e-01, /* 0x3fd025fa510665b5 */
108 2.55977303013005474952e-01, /* 0x3fd061eea03d6290 */
109 2.59629629408257511791e-01, /* 0x3fd09dc597d86362 */
110 2.63274882955282396590e-01, /* 0x3fd0d97ee509acb3 */
111 2.66912987587400396539e-01, /* 0x3fd1151a362431c9 */
112 2.70543868292936529052e-01, /* 0x3fd150973a9ce546 */
113 2.74167451119658789338e-01, /* 0x3fd18bf5a30bf178 */
114 2.77783663178873208022e-01, /* 0x3fd1c735212dd883 */
115 2.81392432649178403370e-01, /* 0x3fd2025567e47c95 */
116 2.84993688779881237938e-01, /* 0x3fd23d562b381041 */
117 2.88587361894077354396e-01, /* 0x3fd278372057ef45 */
118 2.92173383391398755471e-01, /* 0x3fd2b2f7fd9b5fe2 */
119 2.95751685750431536626e-01, /* 0x3fd2ed987a823cfe */
120 2.99322202530807379706e-01, /* 0x3fd328184fb58951 */
121 3.02884868374971361060e-01, /* 0x3fd362773707ebcb */
122 3.06439619009630070945e-01, /* 0x3fd39cb4eb76157b */
123 3.09986391246883430384e-01, /* 0x3fd3d6d129271134 */
124 3.13525122985043869228e-01, /* 0x3fd410cbad6c7d32 */
125 3.17055753209146973237e-01, /* 0x3fd44aa436c2af09 */
126 3.20578221991156986359e-01, /* 0x3fd4845a84d0c21b */
127 3.24092470489871664618e-01, /* 0x3fd4bdee586890e6 */
128 3.27598440950530811477e-01, /* 0x3fd4f75f73869978 */
129 3.31096076704132047386e-01, /* 0x3fd530ad9951cd49 */
130 3.34585322166458920545e-01, /* 0x3fd569d88e1b4cd7 */
131 3.38066122836825466713e-01, /* 0x3fd5a2e0175e0f4e */
132 3.41538425296541714449e-01, /* 0x3fd5dbc3fbbe768d */
133 3.45002177207105076295e-01, /* 0x3fd614840309cfe1 */
134 3.48457327308122011278e-01, /* 0x3fd64d1ff635c1c5 */
135 3.51903825414964732676e-01, /* 0x3fd685979f5fa6fd */
136 3.55341622416168290144e-01, /* 0x3fd6bdeac9cbd76c */
137 3.58770670270572189509e-01, /* 0x3fd6f61941e4def0 */
138 3.62190922004212156882e-01, /* 0x3fd72e22d53aa2a9 */
139 3.65602331706966821034e-01, /* 0x3fd7660752817501 */
140 3.69004854528964421068e-01, /* 0x3fd79dc6899118d1 */
141 3.72398446676754202311e-01, /* 0x3fd7d5604b63b3f7 */
142 3.75783065409248884237e-01, /* 0x3fd80cd46a14b1d0 */
143 3.79158669033441808605e-01, /* 0x3fd84422b8df95d7 */
144 3.82525216899905096124e-01, /* 0x3fd87b4b0c1ebedb */
145 3.85882669398073752109e-01, /* 0x3fd8b24d394a1b25 */
146 3.89230987951320717144e-01, /* 0x3fd8e92916f5cde8 */
147 3.92570135011828580396e-01, /* 0x3fd91fde7cd0c662 */
148 3.95900074055262896078e-01, /* 0x3fd9566d43a34907 */
149 3.99220769575252543149e-01, /* 0x3fd98cd5454d6b18 */
150 4.02532187077682512832e-01, /* 0x3fd9c3165cc58107 */
151 4.05834293074804064450e-01, /* 0x3fd9f93066168001 */
152 4.09127055079168300278e-01, /* 0x3fda2f233e5e530b */
153 4.12410441597387267265e-01, /* 0x3fda64eec3cc23fc */
154 4.15684422123729413467e-01, /* 0x3fda9a92d59e98cf */
155 4.18948967133552840902e-01, /* 0x3fdad00f5422058b */
156 4.22204048076583571270e-01, /* 0x3fdb056420ae9343 */
157 4.25449637370042266227e-01, /* 0x3fdb3a911da65c6c */
158 4.28685708391625730496e-01, /* 0x3fdb6f962e737efb */
159 4.31912235472348193799e-01, /* 0x3fdba473378624a5 */
160 4.35129193889246812521e-01, /* 0x3fdbd9281e528191 */
161 4.38336559857957774877e-01, /* 0x3fdc0db4c94ec9ef */
162 4.41534310525166673322e-01, /* 0x3fdc42191ff11eb6 */
163 4.44722423960939305942e-01, /* 0x3fdc76550aad71f8 */
164 4.47900879150937292206e-01, /* 0x3fdcaa6872f3631b */
165 4.51069655988523443568e-01, /* 0x3fdcde53432c1350 */
166 4.54228735266762495559e-01, /* 0x3fdd121566b7f2ad */
167 4.57378098670320809571e-01, /* 0x3fdd45aec9ec862b */
168 4.60517728767271039558e-01, /* 0x3fdd791f5a1226f4 */
169 4.63647609000806093515e-01, /* 0x3fddac670561bb4f */
170 4.66767723680866497560e-01, /* 0x3fdddf85bb026974 */
171 4.69878057975686880265e-01, /* 0x3fde127b6b0744af */
172 4.72978597903265574054e-01, /* 0x3fde4548066cf51a */
173 4.76069330322761219421e-01, /* 0x3fde77eb7f175a34 */
174 4.79150242925822533735e-01, /* 0x3fdeaa65c7cf28c4 */
175 4.82221324227853687105e-01, /* 0x3fdedcb6d43f8434 */
176 4.85282563559221225002e-01, /* 0x3fdf0ede98f393cf */
177 4.88333951056405479729e-01, /* 0x3fdf40dd0b541417 */
178 4.91375477653101910835e-01, /* 0x3fdf72b221a4e495 */
179 4.94407135071275316562e-01, /* 0x3fdfa45dd3029258 */
180 4.97428915812172245392e-01, /* 0x3fdfd5e0175fdf83 */
181 5.00440813147294050189e-01, /* 0x3fe0039c73c1a40b */
182 5.03442821109336358099e-01, /* 0x3fe01c341e82422d */
183 5.06434934483096732549e-01, /* 0x3fe034b709250488 */
184 5.09417148796356245022e-01, /* 0x3fe04d25314342e5 */
185 5.12389460310737621107e-01, /* 0x3fe0657e94db30cf */
186 5.15351866012543347040e-01, /* 0x3fe07dc3324e9b38 */
187 5.18304363603577900044e-01, /* 0x3fe095f30861a58f */
188 5.21246951491958210312e-01, /* 0x3fe0ae0e1639866c */
189 5.24179628782913242802e-01, /* 0x3fe0c6145b5b43da */
190 5.27102395269579471204e-01, /* 0x3fe0de05d7aa6f7c */
191 5.30015251423793132268e-01, /* 0x3fe0f5e28b67e295 */
192 5.32918198386882147055e-01, /* 0x3fe10daa77307a0d */
193 5.35811237960463593311e-01, /* 0x3fe1255d9bfbd2a8 */
194 5.38694372597246617929e-01, /* 0x3fe13cfbfb1b056e */
195 5.41567605391844897333e-01, /* 0x3fe1548596376469 */
196 5.44430940071603086672e-01, /* 0x3fe16bfa6f5137e1 */
197 5.47284380987436924748e-01, /* 0x3fe1835a88be7c13 */
198 5.50127933104692989907e-01, /* 0x3fe19aa5e5299f99 */
199 5.52961601994028217888e-01, /* 0x3fe1b1dc87904284 */
200 5.55785393822313511514e-01, /* 0x3fe1c8fe7341f64f */
201 5.58599315343562330405e-01, /* 0x3fe1e00babdefeb3 */
202 5.61403373889889367732e-01, /* 0x3fe1f7043557138a */
203 5.64197577362497537656e-01, /* 0x3fe20de813e823b1 */
204 5.66981934222700489912e-01, /* 0x3fe224b74c1d192a */
205 5.69756453482978431069e-01, /* 0x3fe23b71e2cc9e6a */
206 5.72521144698072359525e-01, /* 0x3fe25217dd17e501 */
207 5.75276017956117824426e-01, /* 0x3fe268a940696da6 */
208 5.78021083869819540801e-01, /* 0x3fe27f261273d1b3 */
209 5.80756353567670302596e-01, /* 0x3fe2958e59308e30 */
210 5.83481838685214859730e-01, /* 0x3fe2abe21aded073 */
211 5.86197551356360535557e-01, /* 0x3fe2c2215e024465 */
212 5.88903504204738026395e-01, /* 0x3fe2d84c2961e48b */
213 5.91599710335111383941e-01, /* 0x3fe2ee628406cbca */
214 5.94286183324841177367e-01, /* 0x3fe30464753b090a */
215 5.96962937215401501234e-01, /* 0x3fe31a52048874be */
216 5.99629986503951384336e-01, /* 0x3fe3302b39b78856 */
217 6.02287346134964152178e-01, /* 0x3fe345f01cce37bb */
218 6.04935031491913965951e-01, /* 0x3fe35ba0b60eccce */
219 6.07573058389022313541e-01, /* 0x3fe3713d0df6c503 */
220 6.10201443063065118722e-01, /* 0x3fe386c52d3db11e */
221 6.12820202165241245673e-01, /* 0x3fe39c391cd41719 */
222 6.15429352753104952356e-01, /* 0x3fe3b198e5e2564a */
223 6.18028912282561737612e-01, /* 0x3fe3c6e491c78dc4 */
224 6.20618898599929469384e-01, /* 0x3fe3dc1c2a188504 */
225 6.23199329934065904268e-01, /* 0x3fe3f13fb89e96f4 */
226 6.25770224888563042498e-01, /* 0x3fe4064f47569f48 */
227 6.28331602434009650615e-01, /* 0x3fe41b4ae06fea41 */
228 6.30883481900321840818e-01, /* 0x3fe430328e4b26d5 */
229 6.33425882969144482537e-01, /* 0x3fe445065b795b55 */
230 6.35958825666321447834e-01, /* 0x3fe459c652badc7f */
231 6.38482330354437466191e-01, /* 0x3fe46e727efe4715 */
232 6.40996417725432032775e-01, /* 0x3fe4830aeb5f7bfd */
233 6.43501108793284370968e-01, /* 0x3fe4978fa3269ee1 */
234 6.45996424886771558604e-01, /* 0x3fe4ac00b1c71762 */
235 6.48482387642300484032e-01, /* 0x3fe4c05e22de94e4 */
236 6.50959018996812410762e-01, /* 0x3fe4d4a8023414e8 */
237 6.53426341180761927063e-01, /* 0x3fe4e8de5bb6ec04 */
238 6.55884376711170835605e-01, /* 0x3fe4fd013b7dd17e */
239 6.58333148384755983962e-01, /* 0x3fe51110adc5ed81 */
240 6.60772679271132590273e-01, /* 0x3fe5250cbef1e9fa */
241 6.63202992706093175102e-01, /* 0x3fe538f57b89061e */
242 6.65624112284960989250e-01, /* 0x3fe54ccaf0362c8f */
243 6.68036061856020157990e-01, /* 0x3fe5608d29c70c34 */
244 6.70438865514021320458e-01, /* 0x3fe5743c352b33b9 */
245 6.72832547593763097282e-01, /* 0x3fe587d81f732fba */
246 6.75217132663749830535e-01, /* 0x3fe59b60f5cfab9d */
247 6.77592645519925151909e-01, /* 0x3fe5aed6c5909517 */
248 6.79959111179481823228e-01, /* 0x3fe5c2399c244260 */
249 6.82316554874748071313e-01, /* 0x3fe5d58987169b18 */
250 6.84665002047148862907e-01, /* 0x3fe5e8c6941043cf */
251 6.87004478341244895212e-01, /* 0x3fe5fbf0d0d5cc49 */
252 6.89335009598845749323e-01, /* 0x3fe60f084b46e05e */
253 6.91656621853199760075e-01, /* 0x3fe6220d115d7b8d */
254 6.93969341323259825138e-01, /* 0x3fe634ff312d1f3b */
255 6.96273194408023488045e-01, /* 0x3fe647deb8e20b8f */
256 6.98568207680949848637e-01, /* 0x3fe65aabb6c07b02 */
257 7.00854407884450081312e-01, /* 0x3fe66d663923e086 */
258 7.03131821924453670469e-01, /* 0x3fe6800e4e7e2857 */
259 7.05400476865049030906e-01, /* 0x3fe692a40556fb6a */
260 7.07660399923197958039e-01, /* 0x3fe6a5276c4b0575 */
261 7.09911618463524796141e-01, /* 0x3fe6b798920b3d98 */
262 7.12154159993178659249e-01, /* 0x3fe6c9f7855c3198 */
263 7.14388052156768926793e-01, /* 0x3fe6dc44551553ae */
264 7.16613322731374569052e-01, /* 0x3fe6ee7f10204aef */
265 7.18829999621624415873e-01, /* 0x3fe700a7c5784633 */
266 7.21038110854851588272e-01, /* 0x3fe712be84295198 */
267 7.23237684576317874097e-01, /* 0x3fe724c35b4fae7b */
268 7.25428749044510712274e-01, /* 0x3fe736b65a172dff */
269 7.27611332626510676214e-01, /* 0x3fe748978fba8e0f */
270 7.29785463793429123314e-01, /* 0x3fe75a670b82d8d8 */
271 7.31951171115916565668e-01, /* 0x3fe76c24dcc6c6c0 */
272 7.34108483259739652560e-01, /* 0x3fe77dd112ea22c7 */
273 7.36257428981428097003e-01, /* 0x3fe78f6bbd5d315e */
274 7.38398037123989547936e-01, /* 0x3fe7a0f4eb9c19a2 */
275 7.40530336612692630105e-01, /* 0x3fe7b26cad2e50fd */
276 7.42654356450917929600e-01, /* 0x3fe7c3d311a6092b */
277 7.44770125716075148681e-01, /* 0x3fe7d528289fa093 */
278 7.46877673555587429099e-01, /* 0x3fe7e66c01c114fd */
279 7.48977029182941400620e-01, /* 0x3fe7f79eacb97898 */
280 7.51068221873802288613e-01, /* 0x3fe808c03940694a */
281 7.53151280962194302759e-01, /* 0x3fe819d0b7158a4c */
282 7.55226235836744863583e-01, /* 0x3fe82ad036000005 */
283 7.57293115936992444759e-01, /* 0x3fe83bbec5cdee22 */
284 7.59351950749757920178e-01, /* 0x3fe84c9c7653f7ea */
285 7.61402769805578416573e-01, /* 0x3fe85d69576cc2c5 */
286 7.63445602675201784315e-01, /* 0x3fe86e2578f87ae5 */
287 7.65480478966144461950e-01, /* 0x3fe87ed0eadc5a2a */
288 7.67507428319308182552e-01, /* 0x3fe88f6bbd023118 */
289 7.69526480405658186434e-01, /* 0x3fe89ff5ff57f1f7 */
290 7.71537664922959498526e-01, /* 0x3fe8b06fc1cf3dfe */
291 7.73541011592573490852e-01, /* 0x3fe8c0d9145cf49d */
292 7.75536550156311621507e-01, /* 0x3fe8d13206f8c4ca */
293 7.77524310373347682379e-01, /* 0x3fe8e17aa99cc05d */
294 7.79504322017186335181e-01, /* 0x3fe8f1b30c44f167 */
295 7.81476614872688268854e-01, /* 0x3fe901db3eeef187 */
296 7.83441218733151756304e-01, /* 0x3fe911f35199833b */
297 7.85398163397448278999e-01}; /* 0x3fe921fb54442d18 */
298
299 /* Some constants. */
300
302 piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */
303 piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */
304 three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */
305
308 int xexp, yexp, diffexp;
309
312
313 /* Find properties of arguments x and y. */
314
315 unsigned long long ux, aux, xneg, uy, auy, yneg;
316
319 aux = ux & ~SIGNBIT_DP64;
320 auy = uy & ~SIGNBIT_DP64;
323 xneg = ux & SIGNBIT_DP64;
324 yneg = uy & SIGNBIT_DP64;
325 xzero = (aux == 0);
326 yzero = (auy == 0);
327 xnan = (aux > PINFBITPATT_DP64);
328 ynan = (auy > PINFBITPATT_DP64);
329 xinf = (aux == PINFBITPATT_DP64);
330 yinf = (auy == PINFBITPATT_DP64);
331
332 diffexp = yexp - xexp;
333
334 /* Special cases */
335
336 if (xnan)
337 {
338 unsigned int ufx;
342 }
343 else if (ynan)
344 {
345 unsigned int ufy;
349 }
350 else if (yzero)
351 { /* Zero y gives +-0 for positive x
352 and +-pi for negative x */
353 if (xneg)
354 {
357 }
359 }
360 else if (xzero)
361 { /* Zero x gives +- pi/2
362 depending on sign of y */
365 }
366
367 if (diffexp > 26)
368 { /* abs(y)/abs(x) > 2^26 => arctan(x/y)
369 is insignificant compared to piby2 */
372 }
373 else if (diffexp < -13 && (!xneg))
374 { /* x positive and dominant over y by a factor of 2^13.
375 In this case atan(y/x) is y/x to machine accuracy. */
376
377 if (diffexp < -150) /* Result underflows */
378 {
379 if (yneg)
381 else
383 }
384 else
385 {
386 if (diffexp < -126)
387 {
388 /* Result will likely be denormalized */
391 /* Now y is 2^100 times the true result. Scale it back down. */
393 scaleDownDouble(uy, 100, &uy);
397 else
399 }
400 else
402 }
403 }
404 else if (diffexp < -26 && xneg)
405 { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x)
406 is insignificant compared to pi */
409 }
410 else if (yinf && xinf)
411 { /* If abs(x) and abs(y) are both infinity
412 return +-pi/4 or +- 3pi/4 according to
413 signs. */
414 if (xneg)
415 {
418 }
419 else
420 {
423 }
424 }
425
426 /* General case: take absolute values of arguments */
427
431
432 /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */
433
437
438 if (vbyu > 0.0625)
439 { /* General values of v/u. Use a look-up
440 table and series expansion. */
441
444
445 /* Polynomial approximation to atan(vbyu) */
446
449 }
450 else if (vbyu < 1.e-4)
451 { /* v/u is small enough that atan(v/u) = v/u */
452 q = vbyu;
453 }
454 else /* vbyu <= 0.0625 */
455 {
456 /* Small values of v/u. Use a series expansion */
457
458 s = vbyu*vbyu;
459 q = vbyu -
460 vbyu*s*(0.33333333333333170500 -
461 s*(0.19999999999393223405 -
462 s*0.14285713561807169030));
463 }
464
465 /* Tidy-up according to which quadrant the arguments lie in */
466
471}
Referenced by D3DXSHRotate().
◆ atan2l()
◆ atanf()
Definition at line 47 of file atanf.c.
48{
49
50 /* Some constants and split constants. */
51
52 static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
53
55 unsigned int xnan;
56
58
59 /* Find properties of argument fx. */
60
61 unsigned long long ux, aux, xneg;
62
64 aux = ux & ~SIGNBIT_DP64;
65 xneg = ux & SIGNBIT_DP64;
66
69
70 /* Argument reduction to range [-7/16,7/16] */
71
72 if (aux < 0x3fdc000000000000) /* v < 7./16. */
73 {
75 c = 0.0;
76 }
77 else if (aux < 0x3fe6000000000000) /* v < 11./16. */
78 {
80 /* c = arctan(0.5) */
82 }
83 else if (aux < 0x3ff3000000000000) /* v < 19./16. */
84 {
86 /* c = arctan(1.) */
88 }
89 else if (aux < 0x4003800000000000) /* v < 39./16. */
90 {
92 /* c = arctan(1.5) */
94 }
95 else
96 {
97
98 xnan = (aux > PINFBITPATT_DP64);
99
100 if (xnan)
101 {
102 /* x is NaN */
103 unsigned int uhx;
107 }
109 { /* abs(x) > 2^26 => arctan(1/x) is
110 insignificant compared to piby2 */
111 if (xneg)
113 else
115 }
116
118 /* c = arctan(infinity) */
120 }
121
122 /* Core approximation: Remez(2,2) on [-7/16,7/16] */
123
126 (0.296528598819239217902158651186e0 +
127 (0.192324546402108583211697690500e0 +
129 (0.889585796862432286486651434570e0 +
130 (0.111072499995399550138837673349e1 +
132
134
137}
Referenced by MSVCRT_atanf(), Test_atanf_approx(), and Test_atanf_exact().
◆ atanh()
◆ atanhf()
◆ cbrt()
Referenced by rpn_cbrt().
◆ cbrtf()
◆ ceil()
Definition at line 18 of file ceil.c.
19{
20 /* Load the value as uint64 */
22
23 /* Check for NAN */
25 {
26 /* Set error bit */
27 u64 |= 0x0008000000000000ull;
29 }
30
31 /* Check if x is positive */
33 {
34 /* Check if it fits into an int64 */
36 {
37 /* Cast to int64 to truncate towards 0. If this matches the
38 input, return it as is, otherwise add 1 */
41 }
42 else
43 {
44 /* The exponent is larger than the fraction bits.
45 This means the number is already an integer. */
47 }
48 }
49 else
50 {
51 /* Check if it fits into an int64 */
53 {
54 /* Cast to int64 to truncate towards 0. */
57 }
58 else
59 {
60 /* The exponent is larger than the fraction bits.
61 This means the number is already an integer. */
63 }
64 }
65}
static const char mbstate_t *static wchar_t const char mbstate_t *static const wchar_t int *static double
Definition: string.c:91
Referenced by brush_fill_pixels(), ceilf(), ceill(), convert_to_fos_high_precision(), findRightGridIndices(), IntDrawArc(), IntFillArc(), Math_ceil(), PATH_Arc(), round(), rpn_dec2dms(), Test_ceil(), VarBstrFromDate(), VarFix(), VarR8Round(), VarRound(), and VarUdateFromDate().
◆ ceilf()
Definition at line 40 of file ceilf.c.
41{
43 int rexp, xneg;
45
47 ax = ux & (~SIGNBIT_SP32);
48 xneg = (ux != ax);
49
51 {
52 /* abs(x) is either NaN, infinity, or >= 2^24 */
54 /* x is NaN */
56 0.0F, 1);
57 else
59 }
61 {
63 /* x is +zero or -zero; return the same zero */
65 else if (xneg) /* x < 0.0 */
66 {
69 }
70 else
71 return 1.0F;
72 }
73 else
74 {
76 /* Mask out the bits of r that we don't want */
78 ur = (ux & ~mask);
80
82 else
83 /* We threw some bits away and x was positive */
85 }
86}
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
◆ cos()
Definition at line 21 of file cos.c.
22{
23 int quadrant;
25
26 /* Calculate the quadrant */
28
29 /* Get offset inside quadrant */
31
32 /* Normalize quadrant to [0..3] */
33 quadrant = quadrant & 0x3;
34
35 /* Fixup value for the generic function */
37
38 /* Calculate the negative of the square of x */
40
41 /* This is an unrolled taylor series using <PRECISION> iterations
42 * Example with 4 iterations:
43 * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
44 * To save multiplications and to keep the precision high, it's performed
45 * like this:
46 * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
47 */
48
49 /* Start with 0, compiler will optimize this away */
50 result = 0;
51
52#if (PRECISION >= 10)
53 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
55#endif
56#if (PRECISION >= 9)
57 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
59#endif
60#if (PRECISION >= 8)
61 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
63#endif
64#if (PRECISION >= 7)
65 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
67#endif
68#if (PRECISION >= 6)
69 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
71#endif
72#if (PRECISION >= 5)
73 result += 1./(1.*2*3*4*5*6*7*8*9*10);
75#endif
76 result += 1./(1.*2*3*4*5*6*7*8);
78
79 result += 1./(1.*2*3*4*5*6);
81
82 result += 1./(1.*2*3*4);
84
85 result += 1./(1.*2);
87
88 result += 1;
89
90 /* Apply correct sign */
92
94}
Referenced by __cos(), __libm_sse2_cos(), __libm_sse2_cosf(), __sincos(), _CIcos(), _libm_sse2_cos_precise(), add_arc_part(), AngleBetweenVectorsRad(), attempt_line_merge(), compute_sincos_table(), cosf(), cosl(), create_outline(), D3DRMQuaternionFromRotation(), D3DRMVectorRotate(), draw_cap(), draw_graphics(), DrawGLScene(), EMFDRV_ArcChordPie(), expT(), GdipRotateMatrix(), generateTestSignal(), gl_Lightfv(), gl_rotation_matrix(), Global_Cos(), init_layer3(), IntGdiAngleArc(), IntGdiWidenPath(), Math_cos(), CDrvDefExt::PaintStaticControls(), PATH_DoArcPart(), polar(), powT(), prepare_decode_tables(), pres_cos(), render(), RotatePoint(), rpn_cos(), shorten_line_percent(), sincos(), Test_cos_approx(), Test_cos_exact(), ValarrayTest::transcendentals(), and unstretch_angle().
◆ cosf()
This file has no copyright assigned and is placed in the Public Domain. This file is part of the w64 mingw-runtime package. No warranty is given; refer to the file DISCLAIMER.PD within this package.
Definition at line 13 of file cosf.c.
14{
16}
Referenced by compute_polygon(), compute_sincos_table(), compute_torus(), d3drm_matrix_set_rotation(), D3DXCreatePolygon(), D3DXCreateSphere(), D3DXCreateTextW(), D3DXCreateTorus(), D3DXMatrixAffineTransformation2D(), D3DXMatrixRotationAxis(), D3DXMatrixRotationX(), D3DXMatrixRotationY(), D3DXMatrixRotationYawPitchRoll(), D3DXMatrixRotationZ(), D3DXMatrixTransformation2D(), D3DXQuaternionExp(), D3DXQuaternionRotationAxis(), D3DXQuaternionRotationYawPitchRoll(), D3DXSHRotateZ(), GdipCreateLineBrushFromRectWithAngle(), set_rotation_xform(), shader_glsl_ffp_vertex_light_uniform(), sincosf(), Test_cosf_approx(), Test_cosf_exact(), Test_ExtCreateRegion_Transform(), weightedcapintegrale(), and wined3d_device_set_light().
◆ cosh()
Definition at line 11 of file cosh.c.
12{
14 return (ebig + 1.0/ebig) / 2.0;
15}
Referenced by _CIcosh(), coshf(), coshl(), rpn_cosh(), test_math_functions(), and ValarrayTest::transcendentals().
◆ coshf()
Definition at line 51 of file coshf.c.
52{
53 /*
54 After dealing with special cases the computation is split into
55 regions as follows:
56
57 abs(x) >= max_cosh_arg:
58 cosh(x) = sign(x)*Inf
59
60 abs(x) >= small_threshold:
61 cosh(x) = sign(x)*exp(abs(x))/2 computed using the
62 splitexp and scaleDouble functions as for exp_amd().
63
64 abs(x) < small_threshold:
65 compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
66 cosh(x) is then sign(x)*z. */
67
68 static const double
69 /* The max argument of coshf, but stored as a double */
70 max_cosh_arg = 8.94159862922329438106e+01, /* 0x40565a9f84f82e63 */
71 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
72 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
73 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
74
75 small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889;
76// small_threshold = 20.0;
77 /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */
78
79 /* Tabulated values of sinh(i) and cosh(i) for i = 0,...,36. */
80
81 static const double sinh_lead[ 37] = {
82 0.00000000000000000000e+00, /* 0x0000000000000000 */
83 1.17520119364380137839e+00, /* 0x3ff2cd9fc44eb982 */
84 3.62686040784701857476e+00, /* 0x400d03cf63b6e19f */
85 1.00178749274099008204e+01, /* 0x40240926e70949ad */
86 2.72899171971277496596e+01, /* 0x403b4a3803703630 */
87 7.42032105777887522891e+01, /* 0x40528d0166f07374 */
88 2.01713157370279219549e+02, /* 0x406936d22f67c805 */
89 5.48316123273246489589e+02, /* 0x408122876ba380c9 */
90 1.49047882578955000099e+03, /* 0x409749ea514eca65 */
91 4.05154190208278987484e+03, /* 0x40afa7157430966f */
92 1.10132328747033916443e+04, /* 0x40c5829dced69991 */
93 2.99370708492480553105e+04, /* 0x40dd3c4488cb48d6 */
94 8.13773957064298447222e+04, /* 0x40f3de1654d043f0 */
95 2.21206696003330085659e+05, /* 0x410b00b5916a31a5 */
96 6.01302142081972560845e+05, /* 0x412259ac48bef7e3 */
97 1.63450868623590236530e+06, /* 0x4138f0ccafad27f6 */
98 4.44305526025387924165e+06, /* 0x4150f2ebd0a7ffe3 */
99 1.20774763767876271158e+07, /* 0x416709348c0ea4ed */
100 3.28299845686652474105e+07, /* 0x417f4f22091940bb */
101 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
102 2.42582597704895108938e+08, /* 0x41aceb088b68e803 */
103 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
104 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
105 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
106 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
107 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
108 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
109 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
110 7.23128532145737548828e+11, /* 0x42650bba3796379a */
111 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
112 5.34323729076223046875e+12, /* 0x429370470aec28ec */
113 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
114 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
115 1.07321789892958031250e+14, /* 0x42d866f34a725782 */
116 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
117 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
118 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
119
120 static const double cosh_lead[ 37] = {
121 1.00000000000000000000e+00, /* 0x3ff0000000000000 */
122 1.54308063481524371241e+00, /* 0x3ff8b07551d9f550 */
123 3.76219569108363138810e+00, /* 0x400e18fa0df2d9bc */
124 1.00676619957777653269e+01, /* 0x402422a497d6185e */
125 2.73082328360164865444e+01, /* 0x403b4ee858de3e80 */
126 7.42099485247878334349e+01, /* 0x40528d6fcbeff3a9 */
127 2.01715636122455890700e+02, /* 0x406936e67db9b919 */
128 5.48317035155212010977e+02, /* 0x4081228949ba3a8b */
129 1.49047916125217807348e+03, /* 0x409749eaa93f4e76 */
130 4.05154202549259389343e+03, /* 0x40afa715845d8894 */
131 1.10132329201033226127e+04, /* 0x40c5829dd053712d */
132 2.99370708659497577173e+04, /* 0x40dd3c4489115627 */
133 8.13773957125740562333e+04, /* 0x40f3de1654d6b543 */
134 2.21206696005590405548e+05, /* 0x410b00b5916b6105 */
135 6.01302142082804115489e+05, /* 0x412259ac48bf13ca */
136 1.63450868623620807193e+06, /* 0x4138f0ccafad2d17 */
137 4.44305526025399193168e+06, /* 0x4150f2ebd0a8005c */
138 1.20774763767876680940e+07, /* 0x416709348c0ea503 */
139 3.28299845686652623117e+07, /* 0x417f4f22091940bf */
140 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
141 2.42582597704895138741e+08, /* 0x41aceb088b68e804 */
142 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
143 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
144 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
145 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
146 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
147 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
148 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
149 7.23128532145737548828e+11, /* 0x42650bba3796379a */
150 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
151 5.34323729076223046875e+12, /* 0x429370470aec28ec */
152 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
153 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
154 1.07321789892958031250e+14, /* 0x42d866f34a725782 */
155 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
156 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
157 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
158
159 unsigned long long ux, aux, xneg;
160 unsigned int uhx;
163
164 /* Special cases */
165
167 aux = ux & ~SIGNBIT_DP64;
168 if (aux < 0x3f10000000000000) /* |x| small enough that cosh(x) = 1 */
169 {
170 if (aux == 0) return (float)1.0; /* with no inexact */
171 if (LAMBDA_DP64 + x > 1.0) return valf_with_flags((float)1.0, AMD_F_INEXACT); /* with inexact */
172 }
174 {
176 {
180 }
181 else /* x is infinity */
182 return infinityf_with_flags(0);
183 }
184 xneg = (aux != ux);
185
188
190 /* Return +infinity with overflow flag. */
193// z = infinity_with_flags(AMD_F_OVERFLOW);
195 {
196 /* In this range y is large enough so that
197 the negative exponential is negligible,
198 so cosh(y) is approximated by sign(x)*exp(y)/2. The
199 code below is an inlined version of that from
200 exp() with two changes (it operates on
201 y instead of x, and the division by 2 is
202 done by reducing m by 1). */
203
204 splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
206 m -= 1;
207
208 /* scaleDouble_1 is always safe because the argument x was
209 float, rather than double */
211 }
212 else
213 {
214 /* In this range we find the integer part y0 of y
215 and the increment dy = y - y0. We then compute
216
217 z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
218 z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
219
220 where sinh(y0) and cosh(y0) are tabulated above. */
221
222 int ind;
224
227
229
231 (0.833333333333329931873097e-2 +
232 (0.198412698413242405162014e-3 +
233 (0.275573191913636406057211e-5 +
234 (0.250521176994133472333666e-7 +
235 (0.160576793121939886190847e-9 +
236 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
237
238 cdy = 1 + dy2*(0.500000000000000005911074e0 +
239 (0.416666666666660876512776e-1 +
240 (0.138888888889814854814536e-2 +
241 (0.248015872460622433115785e-4 +
242 (0.275573350756016588011357e-6 +
243 (0.208744349831471353536305e-8 +
244 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
245
246 z = cosh_lead[ind]*cdy + sinh_lead[ind]*sdy;
247 }
248
249// if (xneg) z = - z;
251}
Referenced by test_math_functions().
◆ erf()
Referenced by create_cab_file(), create_cc_test_files(), extract_cabinet(), extract_cabinet_stream(), ExtractCabinet(), GdipSetLineSigmaBlend(), GdipSetPathGradientSigmaBlend(), HResultFrom(), Init(), SetupIterateCabinetA(), SetupIterateCabinetW(), test_FDICopy(), test_FDICreate(), test_FDIDestroy(), and test_FDIIsCabinet().
◆ erff()
◆ exp()
◆ exp2()
◆ exp2f()
◆ expf()
Referenced by Test_expf_approx(), and Test_expf_exact().
◆ expm1()
◆ expm1f()
◆ fabs()
Referenced by __ieee754_j0(), __ieee754_j1(), __ieee754_jn(), _hypot(), brush_fill_pixels(), check_dc_state(), check_mat(), colors_match(), ColorTest(), compare(), compare_bitmap_data(), cosh(), DBG_is_U_direction(), EMF_FixIsotropic(), eto_scale_enum_proc(), fabsf(), fabsl(), fill_cube_positive_x(), findLeftGridIndices(), flatten_bezier(), GdipCreateLineBrush(), GdipGetPathWorldBounds(), GdipIsMatrixInvertible(), height_to_LP(), in_plane(), IntGdiWidenPath(), linear_vari_process(), linegradient_init_transform(), logic_dbl2int(), myequal(), ok_path(), PATH_DoArcPart(), prepare_rpn_result_2(), pres_log(), pres_rsq(), relative_error(), sampleCompTopSimpleOpt(), ScriptXtoCP(), sinc_hex_vari_process(), sinc_mono_vari_process(), sinc_multichan_vari_process(), sinc_quad_vari_process(), sinc_stereo_vari_process(), src_process(), sampledLine::tessellate(), test_BeginContainer2(), test_buffer(), test_buffer8(), test_clipping(), test_clipping_2(), test_D3DXSHEvalSphericalLight(), test_D3DXSHRotateZ(), test_decode_4bpp(), test_decode_bitfields(), test_decode_rle4(), test_decode_rle8(), Test_fabs(), test_font_height_scaling(), test_GdipMeasureString(), test_session_creation(), test_tiff_resolution(), test_transform(), unstretch_angle(), VarUdateFromDate(), width_to_LP(), xform_eq(), xform_near_match(), xsltFormatNumberConversion(), xsltNumberFormatDecimal(), zoh_vari_process(), and CardRegion::ZoomCard().
◆ fabsf()
Referenced by check_vertex_components(), d3dx9_mesh_GenerateAdjacency(), D3DXIntersectTri(), D3DXSHRotate(), float_32_to_16(), invert_matrix(), invert_matrix_3d(), near_equal(), test_channelvolume(), Test_fabsf(), test_simplevolume(), test_streamvolume(), test_volume_dependence(), weld_float1(), weld_float16_2(), weld_float16_4(), weld_float2(), weld_float3(), and weld_float4().
◆ fdim()
◆ fdimf()
◆ floor()
Definition at line 18 of file floor.c.
19{
20 /* Load the value as uint64 */
22
23 /* Check for NAN */
25 {
26 /* Set error bit */
27 u64 |= 0x0008000000000000ull;
29 }
30
31 /* Check if x is positive */
33 {
34 /* Check if it fits into an int64 */
36 {
37 /* Just cast to int64, which will truncate towards 0,
38 which is what we want here.*/
40 }
41 else
42 {
43 /* The exponent is larger than the fraction bits.
44 This means the number is already an integer. */
46 }
47 }
48 else
49 {
50 /* Check if it fits into an int64 */
52 {
53 /* Check if it is -0 */
55 {
56 return -0.;
57 }
58
59 /* Cast to int64 to truncate towards 0. If this matches the
60 input, return it as is, otherwise subtract 1 */
63 }
64 else
65 {
66 /* The exponent is larger than the fraction bits.
67 This means the number is already an integer. */
69 }
70 }
71}
Referenced by Array_set_length(), Array_slice(), d3drm_color_component(), Date_getTimezoneOffset(), Date_setYear(), day(), day_from_year(), EMF_FixIsotropic(), EmfEnumProc(), floorf(), floorl(), GDI_ROUND(), CAppScrnshotPreview::GetRequestedWidth(), hour_from_time(), HTMLRect_get_bottom(), HTMLRect_get_left(), HTMLRect_get_right(), HTMLRect_get_top(), I10_OUTPUT(), index_from_val(), JSON_stringify(), make_day(), Math_floor(), Math_round(), msl::utilities::SafeInt< T, E >::Min(), min_from_time(), number_to_str(), Number_toPrecision(), Number_toString(), PATH_Arc(), pres_frc(), round(), sample_1d_linear(), sample_2d_linear(), scale_internal(), scale_internal_byte(), scale_internal_float(), scale_internal_int(), scale_internal_short(), scale_internal_ubyte(), scale_internal_uint(), scale_internal_ushort(), scaleInternal3D(), scaleInternalPackedPixel(), sec_from_time(), set_style_pos(), StrFormatByteSizeW(), Test_floor(), TIFFDefaultTransferFunction(), time_clip(), to_integer(), TRACKBAR_ConvertPlaceToPosition(), translate(), VarBstrFromDate(), VarFix(), VarInt(), VarR8Round(), VarRound(), VarUdateFromDate(), wave_generate_tone(), xsltFormatNumberConversion(), and xsltNumberFormatInsertNumbers().
◆ floorf()
Definition at line 40 of file floorf.c.
41{
43 int rexp, xneg;
45
47 ax = ux & (~SIGNBIT_SP32);
48 xneg = (ux != ax);
49
51 {
52 /* abs(x) is either NaN, infinity, or >= 2^24 */
54 /* x is NaN */
57 else
59 }
61 {
63 /* x is +zero or -zero; return the same zero */
65 else if (xneg) /* x < 0.0 */
66 return -1.0F;
67 else
68 return 0.0F;
69 }
70 else
71 {
73 /* Mask out the bits of r that we don't want */
75 ur = (ux & ~mask);
77 if (xneg && (ux != ur))
78 /* We threw some bits away and x was negative */
80 else
82 }
83}
◆ fma()
◆ fmaf()
◆ fmax()
◆ fmaxf()
◆ fmin()
Referenced by GetMaxValue(), pres_min(), and test_DuplicateHandle().
◆ fminf()
◆ fmod()
Referenced by _CIfmod(), fmodf(), fmodl(), hour_from_time(), interp_mod(), make_day(), min_from_time(), ms_from_time(), Number_toString(), rpn_exp10(), sec_from_time(), time_within_day(), to_int32(), VarR8Round(), week_day(), xsltFormatNumberConversion(), xsltNumberFormatAlpha(), and xsltNumberFormatDecimal().
◆ fmodf()
Referenced by blend_line_gradient(), and GdipCreateLineBrushFromRectWithAngle().
◆ frexp()
◆ frexpf()
◆ hypot()
◆ hypotf()
◆ ilogb()
◆ ilogbf()
◆ j0()
Definition at line 421 of file math.h.
Referenced by generate_xa_rr_attributes(), modfl(), polygon_area(), render_clipped_polygon(), render_polygon(), sample_2d_linear(), and unfilled_polygon().
◆ j1()
Definition at line 422 of file math.h.
Referenced by _mesa_EvalMesh2(), Subdivider::ccwTurn_sl(), Subdivider::ccwTurn_sr(), Subdivider::ccwTurn_tl(), Subdivider::ccwTurn_tr(), generate_xa_rr_attributes(), gl_EvalMesh2(), gl_save_EvalMesh2(), polygon_area(), render_clipped_polygon(), render_polygon(), sample_2d_linear(), Test_WSAIoctl_GetInterfaceList(), and unfilled_polygon().
◆ jn()
◆ ldexp()
Definition at line 1204 of file math.c.
1205{
1207
1213}
double math_error(int type, const char *name, double arg1, double arg2, double retval)
Definition: math.c:125
◆ ldexpf()
◆ lgamma()
◆ lgammaf()
◆ llrint()
| __MINGW_EXTENSION __CRT_INLINE long long __cdecl llrint | ( | double | x | ) |
Definition at line 395 of file mingw_math.h.
396 {
398 __asm__ __volatile__ \
401 }
__asm__(".p2align 4, 0x90\n" ".seh_proc __seh2_global_filter_func\n" "__seh2_global_filter_func:\n" "\tsub %rbp, %rax\n" "\tpush %rbp\n" "\t.seh_pushreg %rbp\n" "\tsub $32, %rsp\n" "\t.seh_stackalloc 32\n" "\t.seh_endprologue\n" "\tsub %rax, %rdx\n" "\tmov %rdx, %rbp\n" "\tjmp *%r8\n" "__seh2_global_filter_func_exit:\n" "\t.p2align 4\n" "\tadd $32, %rsp\n" "\tpop %rbp\n" "\tret\n" "\t.seh_endproc")
◆ llrintf()
| __MINGW_EXTENSION __CRT_INLINE long long __cdecl llrintf | ( | float | x | ) |
Definition at line 403 of file mingw_math.h.
◆ llround()
◆ llroundf()
◆ log()
◆ log10()
Definition at line 190 of file freeldr.c.
Referenced by __libm_sse2_log10(), __libm_sse2_log10f(), _CIlog10(), _fcvt(), _fcvt_s(), _libm_sse2_log10_precise(), convert_to_fos_high_precision(), DSOUND_Calc3DBuffer(), I10_OUTPUT(), log10f(), log10l(), logic_dbl2int(), MCIQTZ_mciSetAudio(), number_to_fixed(), number_to_str(), Number_toPrecision(), prepare_rpn_result_2(), PrintOID(), rpn_log(), Test_log10_approx(), Test_log10_exact(), and ValarrayTest::transcendentals().
◆ log10f()
Referenced by Test_log10f_approx(), and Test_log10f_exact().
◆ log1p()
◆ log1pf()
◆ log2()
Definition at line 62 of file stubs.c.
63{
64 // Simplistic implementation: log2(x) = log(x) / log(2)
66}
Referenced by exp2(), logbase2(), and pres_log().
◆ log2f()
◆ logb()
Definition at line 243 of file mingw_math.h.
◆ logbf()
◆ logf()
This file has no copyright assigned and is placed in the Public Domain. This file is part of the w64 mingw-runtime package. No warranty is given; refer to the file DISCLAIMER.PD within this package.
Definition at line 12 of file logf.c.
Referenced by Test_logf_approx(), Test_logf_exact(), and wined3d_device_set_light().
◆ lrint()
Definition at line 371 of file mingw_math.h.
Referenced by double_to_fp(), exec_get_arg(), fmod_one(), linear_vari_process(), regstore_set_double(), sinc_hex_vari_process(), sinc_mono_vari_process(), sinc_multichan_vari_process(), sinc_quad_vari_process(), sinc_set_converter(), sinc_stereo_vari_process(), src_float_to_int_array(), src_float_to_short_array(), and zoh_vari_process().
◆ lrintf()
Definition at line 379 of file mingw_math.h.
Referenced by PerformSampleRateConversion().
◆ lround()
| _ACRTIMP __msvcrt_long __cdecl lround | ( | double | ) |
◆ lroundf()
| _ACRTIMP __msvcrt_long __cdecl lroundf | ( | float | ) |
◆ modf()
Definition at line 30 of file modf.c.
31{
32 /* modf splits the argument x into integer and fraction parts,
33 each with the same sign as x. */
34
35
36 long long xexp;
38
40 ax = ux & (~SIGNBIT_DP64);
41
43 {
44 /* abs(x) is either NaN, infinity, or >= 2^53 */
46 {
47 /* x is NaN */
48 *iptr = x;
50 }
51 else
52 {
53 /* x is infinity or large. Return zero with the sign of x */
54 *iptr = x;
57 }
58 }
60 {
61 /* abs(x) < 1.0. Set iptr to zero with the sign of x
62 and return x. */
65 }
66 else
67 {
69 /* Mask out the bits of x that we don't want */
70 mask = 1;
74 }
75
76}
Referenced by cvt(), logic_dbl2int(), modff(), modfl(), rpn_dec2dms(), rpn_dms2dec(), rpn_exp10(), rpn_frac(), rpn_int(), rpn_mod_f(), rpn_shl_f(), and rpn_shr_f().
◆ modff()
Definition at line 30 of file modff.c.
31{
32 /* modff splits the argument x into integer and fraction parts,
33 each with the same sign as x. */
34
36 int xexp;
37
40
41 if (xexp < 0)
42 {
43 /* abs(x) < 1.0. Set iptr to zero with the sign of x
44 and return x. */
47 }
49 {
50 /* x lies between 1.0 and 2**(24) */
51 /* Mask out the bits of x that we don't want */
55 }
57 {
58 /* x is NaN */
59 *iptr = x;
61 }
62 else
63 {
64 /* x is infinity or large. Set iptr to x and return zero
65 with the sign of x. */
66 *iptr = x;
69 }
70}
◆ nearbyint()
◆ nearbyintf()
◆ nextafter()
Definition at line 13 of file nextafter.c.
◆ nextafterf()
Definition at line 13 of file nextafterf.c.
14{
17
20 if (ux.i == uy.i)
22 ax = ux.i & 0x7fffffff;
23 ay = uy.i & 0x7fffffff;
25 if (ay == 0)
27 ux.i = (uy.i & 0x80000000) | 1;
29 ux.i--;
30 else
31 ux.i++;
32 e = ux.i & 0x7f800000;
33 /* raise overflow if ux.f is infinite and x is finite */
36 /* raise underflow if ux.f is subnormal or zero */
39 return ux.f;
40}
◆ pow()
◆ powf()
Definition at line 14 of file powf.c.
15{
17}
Referenced by __libm_sse2_powf(), apply_image_attributes(), exp2f(), flatten_bezier(), float_16_to_32(), float_24_to_32(), and to_sRGB_component().
◆ remainder()
Definition at line 75 of file remainder.c.
79{
83 unsigned int sw;
84
87
88
91 ax = ux & ~SIGNBIT_DP64;
92 ay = uy & ~SIGNBIT_DP64;
95
97 yexp < 1 || yexp > BIASEDEMAX_DP64)
98 {
99 /* x or y is zero, denormalized, NaN or infinity */
101 {
102 /* x is NaN or infinity */
104 {
105 /* x is NaN */
108 }
109 else
110 {
111 /* x is infinity; result is NaN */
114 }
115 }
117 {
118 /* y is NaN or infinity */
120 {
121 /* y is NaN */
124 }
125 else
126 {
127#ifdef _CRTBLD_C9X
128 /* C99 return for y = +-inf is x */
130#else
131 /* y is infinity; result is indefinite */
134#endif
135 }
136 }
138 {
139 /* x is zero */
140 if (ay == 0x0000000000000000)
141 {
142 /* y is zero */
145 }
146 else
147 /* C99 return for x = 0 must preserve sign */
149 }
150 else if (ay == 0x0000000000000000)
151 {
152 /* y is zero */
155 }
156
157 /* We've exhausted all other possibilities. One or both of x and
158 y must be denormalized */
159 if (xexp < 1)
160 {
161 /* x is denormalized. Figure out its exponent. */
164 {
165 xexp--;
166 u <<= 1;
167 }
168 }
169 if (yexp < 1)
170 {
171 /* y is denormalized. Figure out its exponent. */
172 u = ay;
174 {
175 yexp--;
176 u <<= 1;
177 }
178 }
179 }
181 {
182 /* abs(x) == abs(y); return zero with the sign of x */
185 }
186
187 /* Set x = abs(x), y = abs(y) */
190
192 {
193 /* abs(x) < abs(y) */
194#if !defined(COMPILING_FMOD)
197#endif
199 }
200
201 /* Save the current floating-point status word. We need
202 to do this because the remainder function is always
203 exact for finite arguments, but our algorithm causes
204 the inexact flag to be raised. We therefore need to
205 restore the entry status before exiting. */
206 sw = get_fpsw_inline();
207
208 /* Set ntimes to the number of times we need to do a
209 partial remainder. If the exponent of x is an exact multiple
210 of 52 larger than the exponent of y, and the mantissa of x is
211 less than the mantissa of y, ntimes will be one too large
212 but it doesn't matter - it just means that we'll go round
213 the loop below one extra time. */
214 if (xexp <= yexp)
215 ntimes = 0;
216 else
217 ntimes = (xexp - yexp) / 52;
218
219 if (ntimes == 0)
220 {
222 scale = 1.0;
223 }
224 else
225 {
226 /* Set w = y * 2^(52*ntimes) */
228
229 /* Set scale = 2^(-52) */
231 scale);
232 }
233
234
235 /* Each time round the loop we compute a partial remainder.
236 This is done by subtracting a large multiple of w
237 from x each time, where w is a scaled up version of y.
238 The subtraction must be performed exactly in quad
239 precision, though the result at each stage can
240 fit exactly in a double precision number. */
242 {
243 /* t is the integer multiple of w that we will subtract.
244 We use a truncated value for t.
245
246 N.B. w has been chosen so that the integer t will have
247 at most 52 significant bits. This is the amount by
248 which the exponent of the partial remainder dx gets reduced
249 every time around the loop. In theory we could use
250 53 bits in t, but the quad precision multiplication
251 routine dekker_mul12 does not allow us to do that because
252 it loses the last (106th) bit of its quad precision result. */
253
254 /* Set dx = dx - w * t, where t is equal to trunc(dx/w). */
256 /* At this point, t may be one too large due to
257 rounding of dx/w */
258
259 /* Compute w * t in quad precision */
261
262 /* Subtract w * t from dx */
265
266 /* If t was one too large, dx will be negative. Add back
267 one w */
268 /* It might be possible to speed up this loop by finding
269 a way to compute correctly truncated t directly from dx and w.
270 We would then avoid the need for this check on negative dx. */
273
274 /* Scale w down by 2^(-52) for the next iteration */
276 }
277
278 /* One more time */
279 /* Variable todd says whether the integer t is odd or not */
286 {
287 todd = !todd;
289 }
290
291 /* At this point, dx lies in the range [0,dy) */
292#if !defined(COMPILING_FMOD)
293 /* For the fmod function, we're done apart from setting
294 the correct sign. */
295 /* For the remainder function, we need to adjust dx
296 so that it lies in the range (-y/2, y/2] by carefully
297 subtracting w (== dy == y) if necessary. The rigmarole
298 with todd is to get the correct sign of the result
299 when x/y lies exactly half way between two integers,
300 when we need to choose the even integer. */
301 if (ay < 0x7fd0000000000000)
302 {
305 }
308
309#endif
310
311 /* **** N.B. for some reason this breaks the 32 bit version
312 of remainder when compiling with optimization. */
313 /* Restore the entry status flags */
314 set_fpsw_inline(sw);
315
316 /* Set the result sign according to input argument x */
318
319}
#define _FUNCNAME
#define _OPERATION
static void dekker_mul12(double x, double y, double *z, double *zz)
Definition: remainder.c:50
Referenced by cut_misaligned_tail(), IDirectSoundBufferImpl_Lock(), layout_recall_range(), memcmp_blocks(), positive_remainder(), stripe_next_unit(), TAB_SetItemBounds(), test_RegQueryValueExPerformanceData(), VARIANT_DecScale(), VARIANT_DI_div(), VARIANT_DI_mul(), VARIANT_DI_tostringW(), VARIANT_do_division(), VARIANT_int_addlossy(), VARIANT_int_divbychar(), widGetPosition(), wodGetPosition(), and write_integer().
◆ remainderf()
Definition at line 60 of file remainderf.c.
64{
68
69 unsigned int sw;
70
73
74
77 ax = ux & ~SIGNBIT_DP64;
78 ay = uy & ~SIGNBIT_DP64;
81
83 yexp < 1 || yexp > BIASEDEMAX_DP64)
84 {
85 /* x or y is zero, NaN or infinity (neither x nor y can be
86 denormalized because we promoted from float to double) */
88 {
89 /* x is NaN or infinity */
91 {
92 /* x is NaN */
93 unsigned int ufx;
97 }
98 else
99 {
100 /* x is infinity; result is NaN */
103 }
104 }
106 {
107 /* y is NaN or infinity */
109 {
110 /* y is NaN */
111 unsigned int ufy;
115 }
116 else
117 {
118#ifdef _CRTBLD_C9X
119 /* C99 return for y = +-inf is x */
121#else
122 /* y is infinity; result is indefinite */
125#endif
126 }
127 }
128 else if (xexp < 1)
129 {
130 /* x must be zero (cannot be denormalized) */
131 if (yexp < 1)
132 {
133 /* y must be zero (cannot be denormalized) */
136 }
137 else
138 /* C99 return for x = 0 must preserve sign */
140 }
141 else
142 {
143 /* y must be zero */
146 }
147 }
149 {
150 /* abs(x) == abs(y); return zero with the sign of x */
153 }
154
155 /* Set dx = abs(x), dy = abs(y) */
158
160 {
161 /* abs(x) < abs(y) */
162#if !defined(COMPILING_FMOD)
165#endif
167 }
168
169 /* Save the current floating-point status word. We need
170 to do this because the remainder function is always
171 exact for finite arguments, but our algorithm causes
172 the inexact flag to be raised. We therefore need to
173 restore the entry status before exiting. */
174 sw = get_fpsw_inline();
175
176 /* Set ntimes to the number of times we need to do a
177 partial remainder. If the exponent of x is an exact multiple
178 of 24 larger than the exponent of y, and the mantissa of x is
179 less than the mantissa of y, ntimes will be one too large
180 but it doesn't matter - it just means that we'll go round
181 the loop below one extra time. */
182 if (xexp <= yexp)
183 {
184 ntimes = 0;
186 scale = 1.0;
187 }
188 else
189 {
190 ntimes = (xexp - yexp) / 24;
191
192 /* Set w = y * 2^(24*ntimes) */
194 scale);
196 /* Set scale = 2^(-24) */
198 scale);
199 }
200
201
202 /* Each time round the loop we compute a partial remainder.
203 This is done by subtracting a large multiple of w
204 from x each time, where w is a scaled up version of y.
205 The subtraction can be performed exactly when performed
206 in double precision, and the result at each stage can
207 fit exactly in a single precision number. */
209 {
210 /* t is the integer multiple of w that we will subtract.
211 We use a truncated value for t. */
214 /* Scale w down by 2^(-24) for the next iteration */
216 }
217
218 /* One more time */
219#if defined(COMPILING_FMOD)
222#else
223 {
224 unsigned int todd;
225 /* Variable todd says whether the integer t is odd or not */
229
230 /* At this point, dx lies in the range [0,dy) */
231 /* For the remainder function, we need to adjust dx
232 so that it lies in the range (-y/2, y/2] by carefully
233 subtracting w (== dy == y) if necessary. */
236 }
237#endif
238
239 /* **** N.B. for some reason this breaks the 32 bit version
240 of remainder when compiling with optimization. */
241 /* Restore the entry status flags */
242 set_fpsw_inline(sw);
243
244 /* Set the result sign according to input argument x */
246
247}
#define _FUNCNAME
#define _OPERATION
◆ remquo()
◆ remquof()
◆ rint()
◆ rintf()
◆ round()
◆ roundf()
◆ scalbln()
| _ACRTIMP double __cdecl scalbln | ( | double | , |
| __msvcrt_long | |||
| ) |
◆ scalblnf()
| _ACRTIMP float __cdecl scalblnf | ( | float | , |
| __msvcrt_long | |||
| ) |
◆ scalbn()
Definition at line 14 of file scalbn.c.
15{
18
20 y *= 0x1p1023;
21 n -= 1023;
23 y *= 0x1p1023;
24 n -= 1023;
26 n = 1023;
27 }
29 /* make sure final n < -53 to avoid double
30 rounding in the subnormal range */
31 y *= 0x1p-1022 * 0x1p53;
32 n += 1022 - 53;
34 y *= 0x1p-1022 * 0x1p53;
35 n += 1022 - 53;
37 n = -1022;
38 }
39 }
43}
Definition: sprintf.c:30
Referenced by ldexp().
◆ scalbnf()
◆ sin()
Definition at line 21 of file sin.c.
22{
23 int quadrant;
25
26 /* Calculate the quadrant */
28
29 /* Get offset inside quadrant */
31
32 /* Normalize quadrant to [0..3] */
33 quadrant = (quadrant - 1) & 0x3;
34
35 /* Fixup value for the generic function */
37
38 /* Calculate the negative of the square of x */
40
41 /* This is an unrolled taylor series using <PRECISION> iterations
42 * Example with 4 iterations:
43 * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
44 * To save multiplications and to keep the precision high, it's performed
45 * like this:
46 * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
47 */
48
49 /* Start with 0, compiler will optimize this away */
50 result = 0;
51
52#if (PRECISION >= 10)
53 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
55#endif
56#if (PRECISION >= 9)
57 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
59#endif
60#if (PRECISION >= 8)
61 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
63#endif
64#if (PRECISION >= 7)
65 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
67#endif
68#if (PRECISION >= 6)
69 result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
71#endif
72#if (PRECISION >= 5)
73 result += 1./(1.*2*3*4*5*6*7*8*9*10);
75#endif
76 result += 1./(1.*2*3*4*5*6*7*8);
78
79 result += 1./(1.*2*3*4*5*6);
81
82 result += 1./(1.*2*3*4);
84
85 result += 1./(1.*2);
87
88 result += 1;
89
90 /* Apply correct sign */
92
94}
Referenced by __libm_sse2_sin(), __libm_sse2_sinf(), __rpc_get_time_offset(), __rpc_sockisbound(), __rpc_taddr2uaddr_af(), __rpc_uaddr2taddr_af(), __sincos(), _CIsin(), _libm_sse2_sin_precise(), add_arc_part(), bindresvport(), bindresvport_sa(), compute_sincos_table(), D3DRMQuaternionFromRotation(), D3DRMQuaternionSlerp(), D3DRMVectorRotate(), draw_cap(), draw_graphics(), DrawGLScene(), EMFDRV_ArcChordPie(), expT(), GdipRotateMatrix(), get_server(), CAppScrnshotPreview::GetFrameDotShift(), gl_rotation_matrix(), Global_Sin(), gluPerspective(), init_layer3(), IntGdiAngleArc(), IntGdiWidenPath(), main(), Math_sin(), NetBTCall(), NetBTSendNameQuery(), netfinger(), CDrvDefExt::PaintStaticControls(), PATH_DoArcPart(), polar(), powT(), pres_sin(), RotatePoint(), rpc_broadcast_exp(), rpcrt4_ip_tcp_get_top_of_tower(), rpn_sin(), shorten_line_percent(), sincos(), sinf(), sinl(), Test_sin_approx(), Test_sin_exact(), TestKs(), ValarrayTest::transcendentals(), uaddr_to_sockaddr(), unstretch_angle(), wave_generate_la(), and wave_generate_tone().
◆ sinf()
This file has no copyright assigned and is placed in the Public Domain. This file is part of the w64 mingw-runtime package. No warranty is given; refer to the file DISCLAIMER.PD within this package.
Definition at line 13 of file sinf.c.
14{
16}
Referenced by compute_polygon(), compute_sincos_table(), compute_torus(), d3drm_matrix_set_rotation(), D3DXCreatePolygon(), D3DXCreateSphere(), D3DXCreateTorus(), D3DXMatrixAffineTransformation2D(), D3DXMatrixRotationAxis(), D3DXMatrixRotationX(), D3DXMatrixRotationY(), D3DXMatrixRotationYawPitchRoll(), D3DXMatrixRotationZ(), D3DXMatrixTransformation2D(), D3DXQuaternionExp(), D3DXQuaternionRotationAxis(), D3DXQuaternionRotationYawPitchRoll(), D3DXQuaternionSlerp(), D3DXSHEvalConeLight(), D3DXSHRotateZ(), GdipCreateLineBrushFromRectWithAngle(), set_rotation_xform(), sincosf(), Test_ExtCreateRegion_Transform(), Test_sinf_approx(), Test_sinf_exact(), and weightedcapintegrale().
◆ sinh()
Definition at line 50 of file sinh.c.
51{
52 /*
53 After dealing with special cases the computation is split into
54 regions as follows:
55
56 abs(x) >= max_sinh_arg:
57 sinh(x) = sign(x)*Inf
58
59 abs(x) >= small_threshold:
60 sinh(x) = sign(x)*exp(abs(x))/2 computed using the
61 splitexp and scaleDouble functions as for exp_amd().
62
63 abs(x) < small_threshold:
64 compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
65 sinh(x) is then sign(x)*z. */
66
67 static const double
68 max_sinh_arg = 7.10475860073943977113e+02, /* 0x408633ce8fb9f87e */
69 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
70 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
71 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
72 small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889;
73 /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */
74
75 /* Lead and tail tabulated values of sinh(i) and cosh(i)
76 for i = 0,...,36. The lead part has 26 leading bits. */
77
78 static const double sinh_lead[37] = {
79 0.00000000000000000000e+00, /* 0x0000000000000000 */
80 1.17520117759704589844e+00, /* 0x3ff2cd9fc0000000 */
81 3.62686038017272949219e+00, /* 0x400d03cf60000000 */
82 1.00178747177124023438e+01, /* 0x40240926e0000000 */
83 2.72899169921875000000e+01, /* 0x403b4a3800000000 */
84 7.42032089233398437500e+01, /* 0x40528d0160000000 */
85 2.01713153839111328125e+02, /* 0x406936d228000000 */
86 5.48316116333007812500e+02, /* 0x4081228768000000 */
87 1.49047882080078125000e+03, /* 0x409749ea50000000 */
88 4.05154187011718750000e+03, /* 0x40afa71570000000 */
89 1.10132326660156250000e+04, /* 0x40c5829dc8000000 */
90 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */
91 8.13773945312500000000e+04, /* 0x40f3de1650000000 */
92 2.21206695312500000000e+05, /* 0x410b00b590000000 */
93 6.01302140625000000000e+05, /* 0x412259ac48000000 */
94 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */
95 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */
96 1.20774762500000000000e+07, /* 0x4167093488000000 */
97 3.28299845000000000000e+07, /* 0x417f4f2208000000 */
98 8.92411500000000000000e+07, /* 0x419546d8f8000000 */
99 2.42582596000000000000e+08, /* 0x41aceb0888000000 */
100 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */
101 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */
102 4.87240166400000000000e+09, /* 0x41f226af30000000 */
103 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */
104 3.60024494080000000000e+10, /* 0x4220c3d390000000 */
105 9.78648043520000000000e+10, /* 0x4236c93268000000 */
106 2.66024116224000000000e+11, /* 0x424ef822f0000000 */
107 7.23128516608000000000e+11, /* 0x42650bba30000000 */
108 1.96566712320000000000e+12, /* 0x427c9aae40000000 */
109 5.34323724288000000000e+12, /* 0x4293704708000000 */
110 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */
111 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */
112 1.07321789251584000000e+14, /* 0x42d866f348000000 */
113 2.91730863685632000000e+14, /* 0x42f0953e28000000 */
114 7.93006722514944000000e+14, /* 0x430689e220000000 */
115 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */
116
117 static const double sinh_tail[37] = {
118 0.00000000000000000000e+00, /* 0x0000000000000000 */
119 1.60467555584448807892e-08, /* 0x3e513ae6096a0092 */
120 2.76742892754807136947e-08, /* 0x3e5db70cfb79a640 */
121 2.09697499555224576530e-07, /* 0x3e8c2526b66dc067 */
122 2.04940252448908240062e-07, /* 0x3e8b81b18647f380 */
123 1.65444891522700935932e-06, /* 0x3ebbc1cdd1e1eb08 */
124 3.53116789999998198721e-06, /* 0x3ecd9f201534fb09 */
125 6.94023870987375490695e-06, /* 0x3edd1c064a4e9954 */
126 4.98876893611587449271e-06, /* 0x3ed4eca65d06ea74 */
127 3.19656024605152215752e-05, /* 0x3f00c259bcc0ecc5 */
128 2.08687768377236501204e-04, /* 0x3f2b5a6647cf9016 */
129 4.84668088325403796299e-05, /* 0x3f09691adefb0870 */
130 1.17517985422733832468e-03, /* 0x3f53410fc29cde38 */
131 6.90830086959560562415e-04, /* 0x3f46a31a50b6fb3c */
132 1.45697262451506548420e-03, /* 0x3f57defc71805c40 */
133 2.99859023684906737806e-02, /* 0x3f9eb49fd80e0bab */
134 1.02538800507941396667e-02, /* 0x3f84fffc7bcd5920 */
135 1.26787628407699110022e-01, /* 0x3fc03a93b6c63435 */
136 6.86652479544033744752e-02, /* 0x3fb1940bb255fd1c */
137 4.81593627621056619148e-01, /* 0x3fded26e14260b50 */
138 1.70489513795397629181e+00, /* 0x3ffb47401fc9f2a2 */
139 1.12416073482258713767e+01, /* 0x40267bb3f55634f1 */
140 7.06579578070110514432e+00, /* 0x401c435ff8194ddc */
141 5.91244512999659974639e+01, /* 0x404d8fee052ba63a */
142 1.68921736147050694399e+02, /* 0x40651d7edccde3f6 */
143 2.60692936262073658327e+02, /* 0x40704b1644557d1a */
144 3.62419382134885609048e+02, /* 0x4076a6b5ca0a9dc4 */
145 4.07689930834187271103e+03, /* 0x40afd9cc72249aba */
146 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */
147 2.53720210371943067003e+04, /* 0x40d8c70158ac6363 */
148 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */
149 1.81871712615542812273e+05, /* 0x4106337db36fc718 */
150 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */
151 6.41374032312148716301e+05, /* 0x412392bc108b37cc */
152 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */
153 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */
154 7.63580561355670914054e+06}; /* 0x415d20d76744835c */
155
156 static const double cosh_lead[37] = {
157 1.00000000000000000000e+00, /* 0x3ff0000000000000 */
158 1.54308062791824340820e+00, /* 0x3ff8b07550000000 */
159 3.76219564676284790039e+00, /* 0x400e18fa08000000 */
160 1.00676617622375488281e+01, /* 0x402422a490000000 */
161 2.73082327842712402344e+01, /* 0x403b4ee858000000 */
162 7.42099475860595703125e+01, /* 0x40528d6fc8000000 */
163 2.01715633392333984375e+02, /* 0x406936e678000000 */
164 5.48317031860351562500e+02, /* 0x4081228948000000 */
165 1.49047915649414062500e+03, /* 0x409749eaa8000000 */
166 4.05154199218750000000e+03, /* 0x40afa71580000000 */
167 1.10132329101562500000e+04, /* 0x40c5829dd0000000 */
168 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */
169 8.13773945312500000000e+04, /* 0x40f3de1650000000 */
170 2.21206695312500000000e+05, /* 0x410b00b590000000 */
171 6.01302140625000000000e+05, /* 0x412259ac48000000 */
172 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */
173 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */
174 1.20774762500000000000e+07, /* 0x4167093488000000 */
175 3.28299845000000000000e+07, /* 0x417f4f2208000000 */
176 8.92411500000000000000e+07, /* 0x419546d8f8000000 */
177 2.42582596000000000000e+08, /* 0x41aceb0888000000 */
178 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */
179 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */
180 4.87240166400000000000e+09, /* 0x41f226af30000000 */
181 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */
182 3.60024494080000000000e+10, /* 0x4220c3d390000000 */
183 9.78648043520000000000e+10, /* 0x4236c93268000000 */
184 2.66024116224000000000e+11, /* 0x424ef822f0000000 */
185 7.23128516608000000000e+11, /* 0x42650bba30000000 */
186 1.96566712320000000000e+12, /* 0x427c9aae40000000 */
187 5.34323724288000000000e+12, /* 0x4293704708000000 */
188 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */
189 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */
190 1.07321789251584000000e+14, /* 0x42d866f348000000 */
191 2.91730863685632000000e+14, /* 0x42f0953e28000000 */
192 7.93006722514944000000e+14, /* 0x430689e220000000 */
193 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */
194
195 static const double cosh_tail[37] = {
196 0.00000000000000000000e+00, /* 0x0000000000000000 */
197 6.89700037027478056904e-09, /* 0x3e3d9f5504c2bd28 */
198 4.43207835591715833630e-08, /* 0x3e67cb66f0a4c9fd */
199 2.33540217013828929694e-07, /* 0x3e8f58617928e588 */
200 5.17452463948269748331e-08, /* 0x3e6bc7d000c38d48 */
201 9.38728274131605919153e-07, /* 0x3eaf7f9d4e329998 */
202 2.73012191010840495544e-06, /* 0x3ec6e6e464885269 */
203 3.29486051438996307950e-06, /* 0x3ecba3a8b946c154 */
204 4.75803746362771416375e-06, /* 0x3ed3f4e76110d5a4 */
205 3.33050940471947692369e-05, /* 0x3f017622515a3e2b */
206 9.94707313972136215365e-06, /* 0x3ee4dc4b528af3d0 */
207 6.51685096227860253398e-05, /* 0x3f11156278615e10 */
208 1.18132406658066663359e-03, /* 0x3f535ad50ed821f5 */
209 6.93090416366541877541e-04, /* 0x3f46b61055f2935c */
210 1.45780415323416845386e-03, /* 0x3f57e2794a601240 */
211 2.99862082708111758744e-02, /* 0x3f9eb4b45f6aadd3 */
212 1.02539925859688602072e-02, /* 0x3f85000b967b3698 */
213 1.26787669807076286421e-01, /* 0x3fc03a940fadc092 */
214 6.86652631843830962843e-02, /* 0x3fb1940bf3bf874c */
215 4.81593633223853068159e-01, /* 0x3fded26e1a2a2110 */
216 1.70489514001513020602e+00, /* 0x3ffb4740205796d6 */
217 1.12416073489841270572e+01, /* 0x40267bb3f55cb85d */
218 7.06579578098005001152e+00, /* 0x401c435ff81e18ac */
219 5.91244513000686140458e+01, /* 0x404d8fee052bdea4 */
220 1.68921736147088438429e+02, /* 0x40651d7edccde926 */
221 2.60692936262087528121e+02, /* 0x40704b1644557e0e */
222 3.62419382134890611269e+02, /* 0x4076a6b5ca0a9e1c */
223 4.07689930834187453002e+03, /* 0x40afd9cc72249abe */
224 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */
225 2.53720210371943103382e+04, /* 0x40d8c70158ac6364 */
226 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */
227 1.81871712615542812273e+05, /* 0x4106337db36fc718 */
228 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */
229 6.41374032312148716301e+05, /* 0x412392bc108b37cc */
230 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */
231 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */
232 7.63580561355670914054e+06}; /* 0x415d20d76744835c */
233
234 unsigned long long ux, aux, xneg;
237
238 /* Special cases */
239
241 aux = ux & ~SIGNBIT_DP64;
242 if (aux < 0x3e30000000000000) /* |x| small enough that sinh(x) = x */
243 {
244 if (aux == 0)
245 /* with no inexact */
247 else
249 }
250 else if (aux >= 0x7ff0000000000000) /* |x| is NaN or Inf */
251 {
252 if (aux > 0x7ff0000000000000)
253 /* x is NaN */
256 else
258 }
259
260
261 xneg = (aux != ux);
262
265
267 {
268 if (xneg)
271 else
274 }
276 {
277 /* In this range y is large enough so that
278 the negative exponential is negligible,
279 so sinh(y) is approximated by sign(x)*exp(y)/2. The
280 code below is an inlined version of that from
281 exp() with two changes (it operates on
282 y instead of x, and the division by 2 is
283 done by reducing m by 1). */
284
285 splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
287 m -= 1;
288
291 else
293 }
294 else
295 {
296 /* In this range we find the integer part y0 of y
297 and the increment dy = y - y0. We then compute
298
299 z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
300
301 where sinh(y0) and cosh(y0) are tabulated above. */
302
303 int ind;
305
308
310 sdy = dy*dy2*(0.166666666666666667013899e0 +
311 (0.833333333333329931873097e-2 +
312 (0.198412698413242405162014e-3 +
313 (0.275573191913636406057211e-5 +
314 (0.250521176994133472333666e-7 +
315 (0.160576793121939886190847e-9 +
316 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
317
318 cdy = dy2*(0.500000000000000005911074e0 +
319 (0.416666666666660876512776e-1 +
320 (0.138888888889814854814536e-2 +
321 (0.248015872460622433115785e-4 +
322 (0.275573350756016588011357e-6 +
323 (0.208744349831471353536305e-8 +
324 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
325
326 /* At this point sinh(dy) is approximated by dy + sdy.
327 Shift some significant bits from dy to sdy. */
328
330 ux &= 0xfffffffff8000000;
331 PUT_BITS_DP64(ux, sdy1);
332 sdy2 = sdy + (dy - sdy1);
333
334 z = ((((((cosh_tail[ind]*sdy2 + sinh_tail[ind]*cdy)
335 + cosh_tail[ind]*sdy1) + sinh_tail[ind])
336 + cosh_lead[ind]*sdy2) + sinh_lead[ind]*cdy)
337 + cosh_lead[ind]*sdy1) + sinh_lead[ind];
338 }
339
342}
Referenced by _CIsinh(), rpn_sinh(), sinhf(), sinhl(), test_math_functions(), and ValarrayTest::transcendentals().
◆ sinhf()
Definition at line 51 of file sinhf.c.
52{
53 /*
54 After dealing with special cases the computation is split into
55 regions as follows:
56
57 abs(x) >= max_sinh_arg:
58 sinh(x) = sign(x)*Inf
59
60 abs(x) >= small_threshold:
61 sinh(x) = sign(x)*exp(abs(x))/2 computed using the
62 splitexp and scaleDouble functions as for exp_amd().
63
64 abs(x) < small_threshold:
65 compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
66 sinh(x) is then sign(x)*z. */
67
68 static const double
69 /* The max argument of sinhf, but stored as a double */
70 max_sinh_arg = 8.94159862922329438106e+01, /* 0x40565a9f84f82e63 */
71 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
72 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
73 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
74 small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889;
75 /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */
76
77 /* Tabulated values of sinh(i) and cosh(i) for i = 0,...,36. */
78
79 static const double sinh_lead[37] = {
80 0.00000000000000000000e+00, /* 0x0000000000000000 */
81 1.17520119364380137839e+00, /* 0x3ff2cd9fc44eb982 */
82 3.62686040784701857476e+00, /* 0x400d03cf63b6e19f */
83 1.00178749274099008204e+01, /* 0x40240926e70949ad */
84 2.72899171971277496596e+01, /* 0x403b4a3803703630 */
85 7.42032105777887522891e+01, /* 0x40528d0166f07374 */
86 2.01713157370279219549e+02, /* 0x406936d22f67c805 */
87 5.48316123273246489589e+02, /* 0x408122876ba380c9 */
88 1.49047882578955000099e+03, /* 0x409749ea514eca65 */
89 4.05154190208278987484e+03, /* 0x40afa7157430966f */
90 1.10132328747033916443e+04, /* 0x40c5829dced69991 */
91 2.99370708492480553105e+04, /* 0x40dd3c4488cb48d6 */
92 8.13773957064298447222e+04, /* 0x40f3de1654d043f0 */
93 2.21206696003330085659e+05, /* 0x410b00b5916a31a5 */
94 6.01302142081972560845e+05, /* 0x412259ac48bef7e3 */
95 1.63450868623590236530e+06, /* 0x4138f0ccafad27f6 */
96 4.44305526025387924165e+06, /* 0x4150f2ebd0a7ffe3 */
97 1.20774763767876271158e+07, /* 0x416709348c0ea4ed */
98 3.28299845686652474105e+07, /* 0x417f4f22091940bb */
99 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
100 2.42582597704895108938e+08, /* 0x41aceb088b68e803 */
101 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
102 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
103 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
104 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
105 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
106 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
107 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
108 7.23128532145737548828e+11, /* 0x42650bba3796379a */
109 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
110 5.34323729076223046875e+12, /* 0x429370470aec28ec */
111 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
112 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
113 1.07321789892958031250e+14, /* 0x42d866f34a725782 */
114 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
115 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
116 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
117
118 static const double cosh_lead[37] = {
119 1.00000000000000000000e+00, /* 0x3ff0000000000000 */
120 1.54308063481524371241e+00, /* 0x3ff8b07551d9f550 */
121 3.76219569108363138810e+00, /* 0x400e18fa0df2d9bc */
122 1.00676619957777653269e+01, /* 0x402422a497d6185e */
123 2.73082328360164865444e+01, /* 0x403b4ee858de3e80 */
124 7.42099485247878334349e+01, /* 0x40528d6fcbeff3a9 */
125 2.01715636122455890700e+02, /* 0x406936e67db9b919 */
126 5.48317035155212010977e+02, /* 0x4081228949ba3a8b */
127 1.49047916125217807348e+03, /* 0x409749eaa93f4e76 */
128 4.05154202549259389343e+03, /* 0x40afa715845d8894 */
129 1.10132329201033226127e+04, /* 0x40c5829dd053712d */
130 2.99370708659497577173e+04, /* 0x40dd3c4489115627 */
131 8.13773957125740562333e+04, /* 0x40f3de1654d6b543 */
132 2.21206696005590405548e+05, /* 0x410b00b5916b6105 */
133 6.01302142082804115489e+05, /* 0x412259ac48bf13ca */
134 1.63450868623620807193e+06, /* 0x4138f0ccafad2d17 */
135 4.44305526025399193168e+06, /* 0x4150f2ebd0a8005c */
136 1.20774763767876680940e+07, /* 0x416709348c0ea503 */
137 3.28299845686652623117e+07, /* 0x417f4f22091940bf */
138 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */
139 2.42582597704895138741e+08, /* 0x41aceb088b68e804 */
140 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */
141 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */
142 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */
143 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */
144 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */
145 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */
146 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */
147 7.23128532145737548828e+11, /* 0x42650bba3796379a */
148 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */
149 5.34323729076223046875e+12, /* 0x429370470aec28ec */
150 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */
151 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */
152 1.07321789892958031250e+14, /* 0x42d866f34a725782 */
153 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */
154 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */
155 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */
156
157 unsigned long long ux, aux, xneg;
160
161 /* Special cases */
162
164 aux = ux & ~SIGNBIT_DP64;
165 if (aux < 0x3f10000000000000) /* |x| small enough that sinh(x) = x */
166 {
167 if (aux == 0)
168 /* with no inexact */
170 else
172 }
173 else if (aux >= 0x7ff0000000000000) /* |x| is NaN or Inf */
174 {
175 if (aux > 0x7ff0000000000000)
176 {
177 /* x is NaN */
178 unsigned int uhx;
182 }
183 else
185 }
186
187 xneg = (aux != ux);
188
191
193 {
194 /* Return infinity with overflow flag. */
195 if (xneg)
198 else
201 }
203 {
204 /* In this range y is large enough so that
205 the negative exponential is negligible,
206 so sinh(y) is approximated by sign(x)*exp(y)/2. The
207 code below is an inlined version of that from
208 exp() with two changes (it operates on
209 y instead of x, and the division by 2 is
210 done by reducing m by 1). */
211
212 splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
214 m -= 1;
215 /* scaleDouble_1 is always safe because the argument x was
216 float, rather than double */
218 }
219 else
220 {
221 /* In this range we find the integer part y0 of y
222 and the increment dy = y - y0. We then compute
223
224 z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
225
226 where sinh(y0) and cosh(y0) are tabulated above. */
227
228 int ind;
230
233
235
237 (0.833333333333329931873097e-2 +
238 (0.198412698413242405162014e-3 +
239 (0.275573191913636406057211e-5 +
240 (0.250521176994133472333666e-7 +
241 (0.160576793121939886190847e-9 +
242 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
243
244 cdy = 1 + dy2*(0.500000000000000005911074e0 +
245 (0.416666666666660876512776e-1 +
246 (0.138888888889814854814536e-2 +
247 (0.248015872460622433115785e-4 +
248 (0.275573350756016588011357e-6 +
249 (0.208744349831471353536305e-8 +
250 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
251
252 z = sinh_lead[ind]*cdy + cosh_lead[ind]*sdy;
253 }
254
257}
Referenced by test_math_functions().
◆ sqrt()
Definition at line 5 of file sqrt.c.
7{
8 register union
9 {
10 __m128d x128d;
11 __m128i x128i;
12 } u ;
13 register union
14 {
15 unsigned long long ullx;
16 double dbl;
17 } u2;
18
19 /* Set the lower double-precision value of u to x.
20 All that we want, is that the compiler understands that we have the
21 function parameter in a register that we can address as an __m128.
22 Sadly there is no obvious way to do that. If we use the union, VS will
23 generate code to store xmm0 in memory and the read it into a GPR.
24 We avoid memory access by using a direct move. But even here we won't
25 get a simple MOVSD. We can either do:
26 a) _mm_set_sd: move x into the lower part of an xmm register and zero
27 out the upper part (XORPD+MOVSD)
28 b) _mm_set1_pd: move x into the lower and higher part of an xmm register
29 (MOVSD+UNPCKLPD)
30 c) _mm_set_pd, which either generates a memory access, when we try to
31 tell it to keep the upper 64 bits, or generate 2 MOVAPS + UNPCKLPD
32 We choose a, which is probably the fastest.
33 */
35
36 /* Move the contents of the lower 64 bit into a 64 bit GPR using MOVD */
38
39 /* Check for negative values */
41 {
42 /* Check if this is *really* negative and not just -0.0 */
44 {
45 /* Return -1.#IND00 */
46 u2.ullx = 0xfff8000000000000ULL;
47 }
48
49 /* Return what we have */
51 }
52
53 /* Check if this is a NaN (bits 52-62 are 1, bit 0-61 are not all 0) or
54 negative (bit 63 is 1) */
56 {
57 /* Set this bit. That's what MS function does. */
58 u2.ullx |= 0x8000000000000ULL;
60 }
61
62 /* Calculate the square root. */
63#ifdef _MSC_VER
64 /* Another YAY for the MS compiler. There are 2 instructions we could use:
65 SQRTPD (computes sqrt for 2 double values) or SQRTSD (computes sqrt for
66 only the lower 64 bit double value). Obviously we only need 1. And on
67 Some architectures SQRTPD is twice as slow as SQRTSD. On the other hand
68 the MS compiler is stupid and always generates an additional MOVAPS
69 instruction when SQRTSD is used. We choose to use SQRTPD here since on
70 modern hardware it's as fast as SQRTSD. */
72#else
74#endif
75
77}
__INTRIN_INLINE_SSE2 long long _mm_cvtsi128_si64(__m128i a)
Definition: emmintrin.h:1551
Referenced by __ieee754_sqrt(), _cabs(), _CIsqrt(), _hypot(), _libm_sse2_sqrt_precise(), _y0(), _y1(), _yn(), acos(), acosh(), asin(), asinh(), atanh(), bezier_deviation_squared(), D3DRMVectorModulus(), D3DXBoundProbeTest(), D3DXMatrixTest(), D3DXPlaneTest(), draw_cap(), NS1::f(), anonymous_namespace{resolve_name.cpp}::g(), GdipDrawString(), GdipGetLogFontW(), GdipMeasureCharacterRanges(), GdipMeasureDriverString(), GdipMeasureString(), GdipSetLineSigmaBlend(), GdipSetPathGradientSigmaBlend(), get_font_hfont(), CAppScrnshotPreview::GetFrameDotShift(), gl_sqrt(), Global_Sqr(), h(), OpenGLSurfaceEvaluator::inComputeNormal2(), init_layer3(), init_sqrt(), IntGdiWidenPath(), Math_sqrt(), normalize(), prepare_dc(), pres_rsq(), rpn_s_ex(), rpn_sqrt(), shorten_bezier_amt(), shorten_line_amt(), shorten_line_percent(), SOFTWARE_GdipDrawPath(), sq::sqroot(), sqrtf(), sqrtl(), test_printf_fp(), test_sprintf(), Test_sqrt_approx(), Test_sqrt_exact(), test_timer(), ValarrayTest::transcendentals(), VectorMagnitude(), and CardRegion::ZoomCard().
◆ sqrtf()
◆ tan()
Definition at line 122 of file tan.c.
123{
125 int region, xneg;
126
129 ax = (ux & ~SIGNBIT_DP64);
131 {
133 {
135 {
138 }
139 else
140 {
141 /* Using a temporary variable prevents 64-bit VC++ from
142 rearranging
143 x + x*x*x*0.333333333333333333;
144 into
145 x * (1 + x*x*0.333333333333333333);
146 The latter results in an incorrectly rounded answer. */
147 double tmp;
150 }
151 }
152 else
154 }
156 {
157 /* x is either NaN or infinity */
159 /* x is NaN */
162 else
163 /* x is infinity. Return a NaN */
166 }
167 xneg = (ax != ux);
168
169
170 if (xneg)
172
174 {
175 /* For these size arguments we can just carefully subtract the
176 appropriate multiple of pi/2, using extra precision where
177 x is close to an exact multiple of pi/2 */
178 static const double
179 twobypi = 6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */
180 piby2_1 = 1.57079632673412561417e+00, /* 0x3ff921fb54400000 */
181 piby2_1tail = 6.07710050650619224932e-11, /* 0x3dd0b4611a626331 */
182 piby2_2 = 6.07710050630396597660e-11, /* 0x3dd0b4611a600000 */
183 piby2_2tail = 2.02226624879595063154e-21, /* 0x3ba3198a2e037073 */
184 piby2_3 = 2.02226624871116645580e-21, /* 0x3ba3198a2e000000 */
185 piby2_3tail = 8.47842766036889956997e-32; /* 0x397b839a252049c1 */
187 int npi2;
188 unsigned long long uy, xexp, expdiff;
190 /* How many pi/2 is x a multiple of? */
192 {
194 npi2 = 1;
195 else
196 npi2 = 2;
197 }
199 {
201 npi2 = 3;
202 else
203 npi2 = 4;
204 }
205 else
207 /* Subtract the multiple from x to get an extra-precision remainder */
208 rhead = x - npi2 * piby2_1;
209 rtail = npi2 * piby2_1tail;
210 GET_BITS_DP64(rhead, uy);
212 if (expdiff > 15)
213 {
214 /* The remainder is pretty small compared with x, which
215 implies that x is a near multiple of pi/2
216 (x matches the multiple to at least 15 bits) */
217 t = rhead;
218 rtail = npi2 * piby2_2;
219 rhead = t - rtail;
220 rtail = npi2 * piby2_2tail - ((t - rhead) - rtail);
221 if (expdiff > 48)
222 {
223 /* x matches a pi/2 multiple to at least 48 bits */
224 t = rhead;
225 rtail = npi2 * piby2_3;
226 rhead = t - rtail;
227 rtail = npi2 * piby2_3tail - ((t - rhead) - rtail);
228 }
229 }
230 r = rhead - rtail;
231 rr = (rhead - r) - rtail;
232 region = npi2 & 3;
233 }
234 else
235 {
236 /* Reduce x into range [-pi/4,pi/4] */
238 }
239
240 if (xneg)
242 else
244}
void __remainder_piby2(double x, double *r, double *rr, int *region)
Definition: remainder_piby2.c:35
Referenced by __libm_sse2_tan(), __libm_sse2_tanf(), _CItan(), _libm_sse2_tan_precise(), app_boundary_point(), GdipCreateLineBrushFromRectWithAngle(), Global_Tan(), init_layer3(), Math_tan(), rpn_tan(), SkewDIB(), tanf(), tanl(), Test_tan_approx(), Test_tan_exact(), and ValarrayTest::transcendentals().
◆ tanf()
Definition at line 72 of file tanf.c.
73{
75 int region, xneg;
76
78
80
82 ax = (ux & ~SIGNBIT_DP64);
83
85 {
87 {
89 {
92 else
94 }
95 else
97 }
98 else
100 }
102 {
103 /* x is either NaN or infinity */
105 {
106 /* x is NaN */
107 unsigned int ufx;
111 }
112 else
113 {
114 /* x is infinity. Return a NaN */
117 }
118 }
119
120 xneg = (int)(ux >> 63);
121
122 if (xneg)
124
126 {
127 /* For these size arguments we can just carefully subtract the
128 appropriate multiple of pi/2, using extra precision where
129 dx is close to an exact multiple of pi/2 */
130 static const double
131 twobypi = 6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */
132 piby2_1 = 1.57079632673412561417e+00, /* 0x3ff921fb54400000 */
133 piby2_1tail = 6.07710050650619224932e-11, /* 0x3dd0b4611a626331 */
134 piby2_2 = 6.07710050630396597660e-11, /* 0x3dd0b4611a600000 */
135 piby2_2tail = 2.02226624879595063154e-21, /* 0x3ba3198a2e037073 */
136 piby2_3 = 2.02226624871116645580e-21, /* 0x3ba3198a2e000000 */
137 piby2_3tail = 8.47842766036889956997e-32; /* 0x397b839a252049c1 */
139 int npi2;
140 unsigned long long uy, xexp, expdiff;
142 /* How many pi/2 is dx a multiple of? */
144 {
146 npi2 = 1;
147 else
148 npi2 = 2;
149 }
151 {
153 npi2 = 3;
154 else
155 npi2 = 4;
156 }
157 else
159 /* Subtract the multiple from dx to get an extra-precision remainder */
160 rhead = dx - npi2 * piby2_1;
161 rtail = npi2 * piby2_1tail;
162 GET_BITS_DP64(rhead, uy);
164 if (expdiff > 15)
165 {
166 /* The remainder is pretty small compared with dx, which
167 implies that dx is a near multiple of pi/2
168 (dx matches the multiple to at least 15 bits) */
169 t = rhead;
170 rtail = npi2 * piby2_2;
171 rhead = t - rtail;
172 rtail = npi2 * piby2_2tail - ((t - rhead) - rtail);
173 if (expdiff > 48)
174 {
175 /* dx matches a pi/2 multiple to at least 48 bits */
176 t = rhead;
177 rtail = npi2 * piby2_3;
178 rhead = t - rtail;
179 rtail = npi2 * piby2_3tail - ((t - rhead) - rtail);
180 }
181 }
182 r = rhead - rtail;
183 region = npi2 & 3;
184 }
185 else
186 {
187 /* Reduce x into range [-pi/4,pi/4] */
189 }
190
191 if (xneg)
193 else
195}
Referenced by D3DXMatrixPerspectiveFovLH(), D3DXMatrixPerspectiveFovRH(), Test_tanf_approx(), and Test_tanf_exact().
◆ tanh()
Definition at line 46 of file tanh.c.
47{
48 /*
49 The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
50 to the following three formulae:
51 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
52 2. (1 - (2/(exp(2*x) + 1 )))
53 3. (exp(2*x) - 1)/(exp(2*x) + 1)
54 but computationally, some formulae are better on some ranges.
55 */
56 static const double
57 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
58 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
59 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
60 large_threshold = 20.0; /* 0x4034000000000000 */
61
62 unsigned long long ux, aux, xneg;
65
66 /* Special cases */
67
69 aux = ux & ~SIGNBIT_DP64;
70 if (aux < 0x3e30000000000000) /* |x| small enough that tanh(x) = x */
71 {
72 if (aux == 0)
74 else
76 }
77 else if (aux > 0x7ff0000000000000) /* |x| is NaN */
80// return x + x;
81
82 xneg = (aux != ux);
83
86
88 {
89 /* If x is large then exp(-x) is negligible and
90 formula 1 reduces to plus or minus 1.0 */
91 z = 1.0;
92 }
94 {
98 {
99 /* Use a [3,3] Remez approximation on [0,0.9]. */
101 (-0.274030424656179760118928e0 +
102 (-0.176016349003044679402273e-1 +
103 (-0.200047621071909498730453e-3 -
105 (0.822091273968539282568011e0 +
106 (0.381641414288328849317962e0 +
107 (0.201562166026937652780575e-1 +
109 }
110 else
111 {
112 /* Use a [3,3] Remez approximation on [0.9,1]. */
114 (-0.227793870659088295252442e0 +
115 (-0.146173047288731678404066e-1 +
116 (-0.165597043903549960486816e-3 -
118 (0.683381611977295894959554e0 +
119 (0.317204558977294374244770e0 +
120 (0.167358775461896562588695e-1 +
122 }
123 }
124 else
125 {
126 /* Compute p = exp(2*y) + 1. The code is basically inlined
127 from exp_amd. */
128
129 splitexp(2*y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
132
133 /* Now reconstruct tanh from p. */
135 }
136
139}
Referenced by _CItanh(), MSVCRT_tanh(), rpn_tanh(), tanhf(), tanhl(), test_math_functions(), and ValarrayTest::transcendentals().
◆ tanhf()
Definition at line 49 of file tanhf.c.
50{
51 /*
52 The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
53 to the following three formulae:
54 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
55 2. (1 - (2/(exp(2*x) + 1 )))
56 3. (exp(2*x) - 1)/(exp(2*x) + 1)
57 but computationally, some formulae are better on some ranges.
58 */
59 static const float
60 thirtytwo_by_log2 = 4.6166240692e+01F, /* 0x4238aa3b */
61 log2_by_32_lead = 2.1659851074e-02F, /* 0x3cb17000 */
62 log2_by_32_tail = 9.9831822808e-07F, /* 0x3585fdf4 */
63 large_threshold = 10.0F; /* 0x41200000 */
64
65 unsigned int ux, aux;
68
69 /* Special cases */
70
72 aux = ux & ~SIGNBIT_SP32;
73 if (aux < 0x39000000) /* |x| small enough that tanh(x) = x */
74 {
75 if (aux == 0)
77 else
79 }
80 else if (aux > 0x7f800000) /* |x| is NaN */
81 {
82 unsigned int ufx;
86 }
87// return x + x;
88
89 xneg = 1.0F - 2.0F * (aux != ux);
90
92
94 {
95 /* If x is large then exp(-x) is negligible and
96 formula 1 reduces to plus or minus 1.0 */
97 z = 1.0F;
98 }
100 {
103
105 {
106 /* Use a [2,1] Remez approximation on [0,0.9]. */
108 (-0.28192806108402678e0F +
109 (-0.14628356048797849e-2F +
111 (0.845784192581041099e0F +
112 0.3427017942262751343e0F*y2);
113 }
114 else
115 {
116 /* Use a [2,1] Remez approximation on [0.9,1]. */
118 (-0.24069858695196524e0F +
119 (-0.12325644183611929e-2F +
121 (0.72209738473684982e0F +
122 0.292529068698052819e0F*y2);
123 }
124 }
125 else
126 {
127 /* Compute p = exp(2*y) + 1. The code is basically inlined
128 from exp_amd. */
129
130 splitexpf(2*y, 1.0F, thirtytwo_by_log2, log2_by_32_lead,
133 /* Now reconstruct tanh from p. */
135 }
136
138}
Referenced by MSVCRT_tanhf(), and test_math_functions().
◆ tgamma()
◆ tgammaf()
◆ trunc()
Referenced by divide_ext().
◆ truncf()
◆ y0()
◆ y1()
◆ yn()
Variable Documentation
◆ __f
| float __f |
Definition at line 270 of file math.h.
Referenced by __construct_checker< _Container >::__construct_checker(), __do_put_bool(), __do_put_float(), __do_put_integer(), __DOUBLE_BITS(), __FLOAT_BITS(), __get_money_digits(), __get_money_digits_aux(), __put_float(), __put_integer(), __stlp_string_fill(), _FILE_fd(), basic_string< _CharT, _Traits, _Alloc >::_M_assign(), _Rope_RopeRep< _CharT, _Alloc >::_M_free_tree(), vector< _Tp, >::_M_set(), _Rope_fill(), _S_apply_to_pieces(), rope< _CharT, _Alloc >::_S_fetch(), rope< _CharT, _Alloc >::_S_flatten(), rope< _CharT, _Alloc >::_S_new_RopeFunction(), rope< _CharT, _Alloc >::_S_substring(), valarray< _Tp >::apply(), num_put< _CharT, _OutputIter >::do_put(), time_put< _Ch, _OutIt >::do_put(), unordered_map< _Key, _Tp,,, >::erase(), unordered_multimap< _Key, _Tp,,, >::erase(), unordered_set< _Value,,, >::erase(), unordered_multiset< _Value,,, >::erase(), hash_map< _Key, _Tp,,, >::erase(), hash_multimap< _Key, _Tp,,, >::erase(), hash_set< _Value,,, >::erase(), hash_multiset< _Value,,, >::erase(), for_each(), hash_map< _Key, _Tp,,, >::hash_map(), hash_multimap< _Key, _Tp,,, >::hash_multimap(), hash_multiset< _Value,,, >::hash_multiset(), hash_set< _Value,,, >::hash_set(), hash_map< _Key, _Tp,,, >::insert(), hash_multimap< _Key, _Tp,,, >::insert(), hash_multiset< _Value,,, >::insert(), unordered_map< _Key, _Tp,,, >::insert(), unordered_multimap< _Key, _Tp,,, >::insert(), unordered_multiset< _Value,,, >::insert(), hash_set< _Value,,, >::insert(), unordered_set< _Value,,, >::insert(), hashtable< _Val, _Key, _HF, _Traits, _ExK, _EqK, _All >::insert_equal(), hashtable< _Val, _Key, _HF, _Traits, _ExK, _EqK, _All >::insert_unique(), locale::locale(), mem_fun(), mem_fun1(), mem_fun1_ref(), mem_fun_ref(), basic_ostream< _CharT, _Traits >::operator<<(), operator<<(), basic_istream< _CharT, _Traits >::operator>>(), operator>>(), ptr_fun(), time_put< _Ch, _OutIt >::put(), num_put< _CharT, _OutputIter >::put(), __malloc_alloc::set_malloc_handler(), setprecision(), setw(), unordered_map< _Key, _Tp,,, >::unordered_map(), unordered_multimap< _Key, _Tp,,, >::unordered_multimap(), unordered_multiset< _Value,,, >::unordered_multiset(), and unordered_set< _Value,,, >::unordered_set().
◆ __i
Definition at line 269 of file math.h.
Referenced by __advance(), __DOUBLE_BITS(), __FLOAT_BITS(), __insertion_sort(), __match(), __money_do_get(), __money_do_put(), __mutable_reference_at(), __next_permutation(), __partial_sort(), __prev_permutation(), __rotate_aux(), __search_n(), __stl_string_hash(), __stlp_string_fill(), __unguarded_insertion_sort_aux(), _CArray< _Tp, _Nb >::_CArray(), _Bit_iterator_base::_M_advance(), bitset< _Nb >::_M_copy_from_string(), bitset< _Nb >::_M_copy_to_string(), _Base_bitset< _Nw >::_M_do_and(), _Base_bitset< _Nw >::_M_do_find_first(), _Base_bitset< _Nw >::_M_do_find_next(), _Base_bitset< _Nw >::_M_do_flip(), _Base_bitset< _Nw >::_M_do_or(), _Base_bitset< _Nw >::_M_do_set(), _Base_bitset< _Nw >::_M_do_to_ulong(), _Base_bitset< _Nw >::_M_do_xor(), vector< _Tp, >::_M_erase(), list< _Tp, >::_M_fill_assign(), deque< wstring >::_M_fill_insert(), __BVECTOR_QUALIFIED::_M_fill_insert(), subtractive_rng::_M_initialize(), slist< _Tp, >::_M_insert_after_fill(), __BVECTOR_QUALIFIED::_M_insert_aux(), _Base_bitset< _Nw >::_M_is_any(), _Base_bitset< _Nw >::_M_is_equal(), deque< _Tp, >::_M_new_elements_at_front(), mask_array< _Tp >::_M_num_true(), _Rope_fill(), rope< _CharT, _Alloc >::_S_add_leaf_to_forest(), rope< _CharT, _Alloc >::_S_balance(), __node_alloc_impl::_S_chunk_alloc(), rope< _CharT, _Alloc >::_S_fetch(), rope< _CharT, _Alloc >::_S_fetch_ptr(), _Rope_iterator_base< _CharT, _Alloc >::_S_setcache(), _Rope_iterator_base< _CharT, _Alloc >::_S_setcache_for_incr(), _Slist_sort(), abs(), acos(), advance(), sequence_buffer< _Sequence, _Buf_sz >::append(), asin(), __char_traits_base< _CharT, _IntT >::assign(), atan(), atan2(), binary_search(), __char_traits_base< _CharT, _IntT >::compare(), cos(), cosh(), istreambuf_iterator< _CharT, _Traits >::equal(), _Rb_tree< _Key, _Compare, _Value, _KeyOfValue, _Traits, >::erase_unique(), exp(), __BVECTOR_QUALIFIED::insert(), rope< _CharT, _Alloc >::insert(), inserter(), __char_traits_base< _CharT, _IntT >::length(), log(), log10(), modfl(), valarray< _Tp >::operator!(), operator!=(), operator%(), slice_array< _Tp >::operator%=(), gslice_array< _Tp >::operator%=(), mask_array< _Tp >::operator%=(), indirect_array< _Tp >::operator%=(), valarray< _Tp >::operator%=(), operator&(), operator&&(), slice_array< _Tp >::operator&=(), gslice_array< _Tp >::operator&=(), mask_array< _Tp >::operator&=(), indirect_array< _Tp >::operator&=(), valarray< _Tp >::operator&=(), _Rope_find_char_char_consumer< _CharT >::operator()(), _Rope_insert_char_consumer< _CharT, _Traits >::operator()(), operator*(), complex< _Tp >::operator*=(), complex< float >::operator*=(), complex< double >::operator*=(), complex< long double >::operator*=(), slice_array< _Tp >::operator*=(), gslice_array< _Tp >::operator*=(), mask_array< _Tp >::operator*=(), indirect_array< _Tp >::operator*=(), valarray< _Tp >::operator*=(), operator+(), _Bit_iter< _Ref, _Ptr >::operator+(), slice_array< _Tp >::operator+=(), gslice_array< _Tp >::operator+=(), mask_array< _Tp >::operator+=(), indirect_array< _Tp >::operator+=(), valarray< _Tp >::operator+=(), _Bit_iter< _Ref, _Ptr >::operator+=(), valarray< _Tp >::operator-(), operator-(), _Bit_iter< _Ref, _Ptr >::operator-(), slice_array< _Tp >::operator-=(), gslice_array< _Tp >::operator-=(), mask_array< _Tp >::operator-=(), indirect_array< _Tp >::operator-=(), valarray< _Tp >::operator-=(), _Bit_iter< _Ref, _Ptr >::operator-=(), operator/(), complex< _Tp >::operator/=(), complex< float >::operator/=(), complex< double >::operator/=(), complex< long double >::operator/=(), slice_array< _Tp >::operator/=(), gslice_array< _Tp >::operator/=(), mask_array< _Tp >::operator/=(), indirect_array< _Tp >::operator/=(), valarray< _Tp >::operator/=(), operator<(), operator<<(), slice_array< _Tp >::operator<<=(), gslice_array< _Tp >::operator<<=(), mask_array< _Tp >::operator<<=(), indirect_array< _Tp >::operator<<=(), valarray< _Tp >::operator<<=(), operator<=(), vector< _Tp, >::operator=(), valarray< _Tp >::operator=(), slice_array< _Tp >::operator=(), gslice_array< _Tp >::operator=(), mask_array< _Tp >::operator=(), indirect_array< _Tp >::operator=(), iostream_withassign::operator=(), operator==(), operator>(), operator>=(), operator>>(), slice_array< _Tp >::operator>>=(), gslice_array< _Tp >::operator>>=(), mask_array< _Tp >::operator>>=(), indirect_array< _Tp >::operator>>=(), valarray< _Tp >::operator>>=(), map< _Key, _Tp,, >::operator[](), _Bit_iter< _Ref, _Ptr >::operator[](), _CArray< _Tp, _Nb >::operator[](), valarray< _Tp >::operator[](), operator^(), slice_array< _Tp >::operator^=(), gslice_array< _Tp >::operator^=(), mask_array< _Tp >::operator^=(), indirect_array< _Tp >::operator^=(), valarray< _Tp >::operator^=(), operator|(), slice_array< _Tp >::operator|=(), gslice_array< _Tp >::operator|=(), mask_array< _Tp >::operator|=(), indirect_array< _Tp >::operator|=(), operator||(), valarray< _Tp >::operator~(), pow(), random_shuffle(), rope< _CharT, _Alloc >::replace(), list< _Tp, >::resize(), sin(), sinh(), list< _Tp, >::splice(), slist< _Tp, >::splice(), sqrt(), tan(), and tanh().
◆
| const union { ... } __inff |
◆
| const union { ... } __nanf |
