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-rw-r--r--src/math/__invtrigl.c42
-rw-r--r--src/math/__invtrigl.h63
-rw-r--r--src/math/acos.c1
-rw-r--r--src/math/acosl.c9
-rw-r--r--src/math/asinl.c4
-rw-r--r--src/math/atan2.c1
-rw-r--r--src/math/atan2l.c32
-rw-r--r--src/math/atanl.c45
8 files changed, 87 insertions, 110 deletions
diff --git a/src/math/__invtrigl.c b/src/math/__invtrigl.c
index a821842c..a51330e2 100644
--- a/src/math/__invtrigl.c
+++ b/src/math/__invtrigl.c
@@ -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
diff --git a/src/math/__invtrigl.h b/src/math/__invtrigl.h
index c3ad3c49..22748b68 100644
--- a/src/math/__invtrigl.h
+++ b/src/math/__invtrigl.h
@@ -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
diff --git a/src/math/acos.c b/src/math/acos.c
index 54d266ee..0eb15bed 100644
--- a/src/math/acos.c
+++ b/src/math/acos.c
@@ -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
diff --git a/src/math/acosl.c b/src/math/acosl.c
index cc565336..83857d49 100644
--- a/src/math/acosl.c
+++ b/src/math/acosl.c
@@ -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);
diff --git a/src/math/asinl.c b/src/math/asinl.c
index ddd807e2..7572767c 100644
--- a/src/math/asinl.c
+++ b/src/math/asinl.c
@@ -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)
{
diff --git a/src/math/atan2.c b/src/math/atan2.c
index 143c3834..825a38fe 100644
--- a/src/math/atan2.c
+++ b/src/math/atan2.c
@@ -39,6 +39,7 @@
#include "libm.h"
+// FIXME
static const volatile double
tiny = 1.0e-300;
static const double
diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index 0fc901c8..45cbfcc1 100644
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -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)
{
@@ -55,9 +53,9 @@ long double atan2l(long double y, long double x)
if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
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 1: return y; /* atan(+-0,+anything)=+-0 */
+ 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 0: return 0.0; /* atan(+...,+INF) */
+ case 1: return -0.0; /* atan(-...,+INF) */
+ case 2: return pi_hi+tiny; /* atan(+...,-INF) */
+ case 3: return -pi_hi-tiny; /* atan(-...,-INF) */
}
}
}
@@ -95,11 +93,11 @@ long double atan2l(long double y, long double x)
else /* safe to do y/x */
z = atanl(fabsl(y/x));
switch (m) {
- case 0: return z; /* atan(+,+) */
- case 1: return -z; /* atan(-,+) */
- case 2: return pi - (z-pi_lo); /* atan(+,-) */
+ case 0: return z; /* atan(+,+) */
+ case 1: return -z; /* 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
diff --git a/src/math/atanl.c b/src/math/atanl.c
index 36072c17..33ecff0d 100644
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -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;
generated by cgit v1.2.3-70-g09d2 (git 2.46.0) at 2024-11-10 18:43:59 +0000