riscv
/
musl
mirror of https://git.musl-libc.org/git/musl
1
0
Fork 0
Code Issues Projects Releases Wiki Activity
Browse Source

math: ld80 invtrig cleanups 

keeping only commonly used data in invtrigl
rs-1.0
Szabolcs Nagy 14 years ago
parent
529a8de46c
commit
45ff9d8eb6
8 changed files with 87 additions and 110 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 42
      src/math/__invtrigl.c
  2. 63
      src/math/__invtrigl.h
  3. 1
      src/math/acos.c
  4. 9
      src/math/acosl.c
  5. 4
      src/math/asinl.c
  6. 1
      src/math/atan2.c
  7. 22
      src/math/atan2l.c
  8. 45
      src/math/atanl.c

42
src/math/__invtrigl.c
View File

@ -28,9 +28,8 @@
#include "__invtrigl.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
/*
* asinl() and acosl()
*/
/* coefficients used in asinl() and acosl() */
const long double
pS0 = 1.66666666666666666631e-01L,
pS1 = -4.16313987993683104320e-01L,
@ -45,38 +44,9 @@ qS3 = -1.68285799854822427013e+00L,
qS4 = 3.90699412641738801874e-01L,
qS5 = -3.14365703596053263322e-02L;
/*
* atanl()
*/
const long double atanhi[] = {
4.63647609000806116202e-01L,
7.85398163397448309628e-01L,
9.82793723247329067960e-01L,
1.57079632679489661926e+00L,
};
const long double atanlo[] = {
1.18469937025062860669e-20L,
-1.25413940316708300586e-20L,
2.55232234165405176172e-20L,
-2.50827880633416601173e-20L,
};
const long double aT[] = {
3.33333333333333333017e-01L,
-1.99999999999999632011e-01L,
1.42857142857046531280e-01L,
-1.11111111100562372733e-01L,
9.09090902935647302252e-02L,
-7.69230552476207730353e-02L,
6.66661718042406260546e-02L,
-5.88158892835030888692e-02L,
5.25499891539726639379e-02L,
-4.70119845393155721494e-02L,
4.03539201366454414072e-02L,
-2.91303858419364158725e-02L,
1.24822046299269234080e-02L,
};
const long double pi_hi = 3.1415926535897932384626433832795L;
const long double pi_lo = -5.01655761266833202345e-20L;
const long double pio2_hi = 1.57079632679489661926L;
const long double pio2_lo = -2.50827880633416601173e-20L;
#endif

63
src/math/__invtrigl.h
View File

@ -32,15 +32,6 @@
#define BIAS (LDBL_MAX_EXP - 1)
#define MANH_SIZE LDBL_MANH_SIZE
/* Approximation thresholds. */
#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
#define ACOS_CONST (BIAS - 65) /* 2**-65 */
#define ATAN_CONST (BIAS + 65) /* 2**65 */
#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
/* 0.95 */
#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
/* Constants shared by the long double inverse trig functions. */
#define pS0 __pS0
#define pS1 __pS1
@ -54,56 +45,24 @@
#define qS3 __qS3
#define qS4 __qS4
#define qS5 __qS5
#define atanhi __atanhi
#define atanlo __atanlo
#define aT __aT
#define pi_hi __pi_hi
#define pi_lo __pi_lo
#define pio2_hi __pio2_hi
#define pio2_lo __pio2_lo
#define pio2_hi atanhi[3]
#define pio2_lo atanlo[3]
#define pio4_hi atanhi[1]
#ifdef STRUCT_DECLS
typedef struct longdouble {
uint64_t mant;
uint16_t expsign;
} LONGDOUBLE;
#else
typedef long double LONGDOUBLE;
#endif
extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
extern const LONGDOUBLE atanhi[], atanlo[], aT[];
extern const LONGDOUBLE pi_lo;
#ifndef STRUCT_DECLS
static inline long double
P(long double x)
{
return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
(pS4 + x * (pS5 + x * pS6)))))));
}
static inline long double
Q(long double x)
{
return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
}
extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6;
extern const long double qS1, qS2, qS3, qS4, qS5;
extern const long double pi_hi, pi_lo, pio2_hi, pio2_lo;
static inline long double
T_even(long double x)
static long double P(long double x)
{
return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
(aT[8] + x * (aT[10] + x * aT[12]))))));
return x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 +
x * (pS4 + x * (pS5 + x * pS6))))));
}
static inline long double
T_odd(long double x)
static long double Q(long double x)
{
return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
(aT[9] + x * aT[11])))));
return 1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))));
}
#endif
#endif

1
src/math/acos.c
View File

@ -38,6 +38,7 @@
static const double
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
// FIXME
static const volatile double
pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
static const double

9
src/math/acosl.c
View File

@ -23,9 +23,7 @@ long double acosl(long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const long double
pi = 3.14159265358979323846264338327950280e+00L;
#define ACOS_CONST (BIAS - 65) /* 2**-65 */
long double acosl(long double x)
{
@ -41,7 +39,8 @@ long double acosl(long double x)
if (expsign > 0)
return 0.0; /* acos(1) = 0 */
else
return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
// FIXME
return pi_hi + 2.0 * pio2_lo; /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
}
@ -60,7 +59,7 @@ long double acosl(long double x)
s = sqrtl(z);
r = p / q;
w = r * s - pio2_lo;
return pi - 2.0 * (s + w);
return pi_hi - 2.0 * (s + w);
} else { /* x > 0.5 */
z = (1.0 - x) * 0.5;
s = sqrtl(z);

4
src/math/asinl.c
View File

@ -24,6 +24,10 @@ long double asinl(long double x)
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const long double huge = 1.000e+300;
static const long double pio4_hi = 7.85398163397448309628e-01L;
#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
/* 0.95 */
#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
long double asinl(long double x)
{

1
src/math/atan2.c
View File

@ -39,6 +39,7 @@
#include "libm.h"
// FIXME
static const volatile double
tiny = 1.0e-300;
static const double

22
src/math/atan2l.c
View File

@ -24,10 +24,8 @@ long double atan2l(long double y, long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const volatile long double
tiny = 1.0e-300;
static const long double
pi = 3.14159265358979323846264338327950280e+00L;
// FIXME:
static const volatile long double tiny = 1.0e-300;
long double atan2l(long double y, long double x)
{
@ -56,8 +54,8 @@ long double atan2l(long double y, long double x)
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny; /* atan(+0,-anything) = pi */
case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
case 2: return pi_hi+tiny; /* atan(+0,-anything) = pi */
case 3: return -pi_hi-tiny; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
@ -69,15 +67,15 @@ long double atan2l(long double y, long double x)
switch(m) {
case 0: return pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+tiny; /*atan(+INF,-INF)*/
case 3: return -1.5*pio2_hi-tiny; /*atan(-INF,-INF)*/
case 2: return 1.5*pio2_hi+tiny; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi-tiny; /* atan(-INF,-INF) */
}
} else {
switch(m) {
case 0: return 0.0; /* atan(+...,+INF) */
case 1: return -0.0; /* atan(-...,+INF) */
case 2: return pi+tiny; /* atan(+...,-INF) */
case 3: return -pi-tiny; /* atan(-...,-INF) */
case 2: return pi_hi+tiny; /* atan(+...,-INF) */
case 3: return -pi_hi-tiny; /* atan(-...,-INF) */
}
}
}
@ -97,9 +95,9 @@ long double atan2l(long double y, long double x)
switch (m) {
case 0: return z; /* atan(+,+) */
case 1: return -z; /* atan(-,+) */
case 2: return pi - (z-pi_lo); /* atan(+,-) */
case 2: return pi_hi-(z-pi_lo); /* atan(+,-) */
default: /* case 3 */
return (z-pi_lo) - pi; /* atan(-,-) */
return (z-pi_lo)-pi_hi; /* atan(-,-) */
}
}
#endif

45
src/math/atanl.c
View File

@ -23,8 +23,53 @@ long double atanl(long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
#define ATAN_CONST (BIAS + 65) /* 2**65 */
#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
static const long double huge = 1.0e300;
static const long double atanhi[] = {
4.63647609000806116202e-01L,
7.85398163397448309628e-01L,
9.82793723247329067960e-01L,
1.57079632679489661926e+00L,
};
static const long double atanlo[] = {
1.18469937025062860669e-20L,
-1.25413940316708300586e-20L,
2.55232234165405176172e-20L,
-2.50827880633416601173e-20L,
};
static const long double aT[] = {
3.33333333333333333017e-01L,
-1.99999999999999632011e-01L,
1.42857142857046531280e-01L,
-1.11111111100562372733e-01L,
9.09090902935647302252e-02L,
-7.69230552476207730353e-02L,
6.66661718042406260546e-02L,
-5.88158892835030888692e-02L,
5.25499891539726639379e-02L,
-4.70119845393155721494e-02L,
4.03539201366454414072e-02L,
-2.91303858419364158725e-02L,
1.24822046299269234080e-02L,
};
static long double T_even(long double x)
{
return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
x * (aT[8] + x * (aT[10] + x * aT[12])))));
}
static long double T_odd(long double x)
{
return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
x * (aT[9] + x * aT[11]))));
}
long double atanl(long double x)
{
union IEEEl2bits u;

Write Preview
Loading…
Cancel
Save