From 45ff9d8eb6f43b8f612d1b01ada627f5b4447c45 Mon Sep 17 00:00:00 2001 From: Szabolcs Nagy Date: Wed, 14 Nov 2012 01:01:38 +0100 Subject: math: ld80 invtrig cleanups keeping only commonly used data in invtrigl --- src/math/__invtrigl.c | 42 +++++----------------------------- src/math/__invtrigl.h | 63 +++++++++------------------------------------------ src/math/acos.c | 1 + src/math/acosl.c | 9 ++++---- src/math/asinl.c | 4 ++++ src/math/atan2.c | 1 + src/math/atan2l.c | 32 ++++++++++++-------------- src/math/atanl.c | 45 ++++++++++++++++++++++++++++++++++++ 8 files changed, 87 insertions(+), 110 deletions(-) (limited to 'src') 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; -- cgit v1.2.1