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Diffstat (limited to 'libm/ldouble/asinl.c')
| -rw-r--r-- | libm/ldouble/asinl.c | 249 |
1 files changed, 0 insertions, 249 deletions
diff --git a/libm/ldouble/asinl.c b/libm/ldouble/asinl.c deleted file mode 100644 index 163f01055..000000000 --- a/libm/ldouble/asinl.c +++ /dev/null @@ -1,249 +0,0 @@ -/* asinl.c - * - * Inverse circular sine, long double precision - * - * - * - * SYNOPSIS: - * - * double x, y, asinl(); - * - * y = asinl( x ); - * - * - * - * DESCRIPTION: - * - * Returns radian angle between -pi/2 and +pi/2 whose sine is x. - * - * A rational function of the form x + x**3 P(x**2)/Q(x**2) - * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is - * transformed by the identity - * - * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -1, 1 30000 2.7e-19 4.8e-20 - * - * - * ERROR MESSAGES: - * - * message condition value returned - * asinl domain |x| > 1 NANL - * - */ - /* acosl() - * - * Inverse circular cosine, long double precision - * - * - * - * SYNOPSIS: - * - * double x, y, acosl(); - * - * y = acosl( x ); - * - * - * - * DESCRIPTION: - * - * Returns radian angle between -pi/2 and +pi/2 whose cosine - * is x. - * - * Analytically, acos(x) = pi/2 - asin(x). However if |x| is - * near 1, there is cancellation error in subtracting asin(x) - * from pi/2. Hence if x < -0.5, - * - * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) ); - * - * or if x > +0.5, - * - * acos(x) = 2.0 * asin( sqrt((1-x)/2) ). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -1, 1 30000 1.4e-19 3.5e-20 - * - * - * ERROR MESSAGES: - * - * message condition value returned - * acosl domain |x| > 1 NANL - */ - -/* asin.c */ - -/* -Cephes Math Library Release 2.7: May, 1998 -Copyright 1984, 1990, 1998 by Stephen L. Moshier -*/ - -#include <math.h> - -#ifdef UNK -static long double P[] = { - 3.7769340062433674871612E-3L, --6.1212919176969202969441E-1L, - 5.9303993515791417710775E0L, --1.8631697621590161441592E1L, - 2.3314603132141795720634E1L, --1.0087146579384916260197E1L, -}; -static long double Q[] = { -/* 1.0000000000000000000000E0L,*/ --1.5684335624873146511217E1L, - 7.8702951549021104258866E1L, --1.7078401170625864261444E2L, - 1.6712291455718995937376E2L, --6.0522879476309497128868E1L, -}; -#endif - -#ifdef IBMPC -static short P[] = { -0x59d1,0x3509,0x7009,0xf786,0x3ff6, XPD -0xbe97,0x93e6,0x7fab,0x9cb4,0xbffe, XPD -0x8bf5,0x6810,0xd4dc,0xbdc5,0x4001, XPD -0x9bd4,0x8d86,0xb77b,0x950d,0xc003, XPD -0x3b0f,0x9e25,0x4ea5,0xba84,0x4003, XPD -0xea38,0xc6a9,0xf3cf,0xa164,0xc002, XPD -}; -static short Q[] = { -/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/ -0x1229,0x8516,0x09e9,0xfaf3,0xc002, XPD -0xb5c3,0xf36f,0xe943,0x9d67,0x4005, XPD -0xe11a,0xbe0f,0xb4fd,0xaac8,0xc006, XPD -0x4c69,0x1355,0x7754,0xa71f,0x4006, XPD -0xded7,0xa9fe,0x6db7,0xf217,0xc004, XPD -}; -#endif - -#ifdef MIEEE -static long P[] = { -0x3ff60000,0xf7867009,0x350959d1, -0xbffe0000,0x9cb47fab,0x93e6be97, -0x40010000,0xbdc5d4dc,0x68108bf5, -0xc0030000,0x950db77b,0x8d869bd4, -0x40030000,0xba844ea5,0x9e253b0f, -0xc0020000,0xa164f3cf,0xc6a9ea38, -}; -static long Q[] = { -/*0x3fff0000,0x80000000,0x00000000,*/ -0xc0020000,0xfaf309e9,0x85161229, -0x40050000,0x9d67e943,0xf36fb5c3, -0xc0060000,0xaac8b4fd,0xbe0fe11a, -0x40060000,0xa71f7754,0x13554c69, -0xc0040000,0xf2176db7,0xa9feded7, -}; -#endif -#ifdef NANS -extern long double NANL; -#endif -#ifdef ANSIPROT -extern long double ldexpl ( long double, int ); -extern long double sqrtl ( long double ); -extern long double polevll ( long double, void *, int ); -extern long double p1evll ( long double, void *, int ); -long double asinl ( long double ); -#else -long double ldexpl(), sqrtl(), polevll(), p1evll(); -long double asinl(); -#endif - -long double asinl(x) -long double x; -{ -long double a, p, z, zz; -short sign, flag; -extern long double PIO2L; - -if( x > 0 ) - { - sign = 1; - a = x; - } -else - { - sign = -1; - a = -x; - } - -if( a > 1.0L ) - { - mtherr( "asinl", DOMAIN ); -#ifdef NANS - return( NANL ); -#else - return( 0.0L ); -#endif - } - -if( a < 1.0e-8L ) - { - z = a; - goto done; - } - -if( a > 0.5L ) - { - zz = 0.5L -a; - zz = ldexpl( zz + 0.5L, -1 ); - z = sqrtl( zz ); - flag = 1; - } -else - { - z = a; - zz = z * z; - flag = 0; - } - -p = zz * polevll( zz, P, 5)/p1evll( zz, Q, 5); -z = z * p + z; -if( flag != 0 ) - { - z = z + z; - z = PIO2L - z; - } -done: -if( sign < 0 ) - z = -z; -return(z); -} - - -extern long double PIO2L, PIL; - -long double acosl(x) -long double x; -{ - -if( x < -1.0L ) - goto domerr; - -if( x < -0.5L) - return( PIL - 2.0L * asinl( sqrtl(0.5L*(1.0L+x)) ) ); - -if( x > 1.0L ) - { -domerr: mtherr( "acosl", DOMAIN ); -#ifdef NANS - return( NANL ); -#else - return( 0.0L ); -#endif - } - -if( x > 0.5L ) - return( 2.0L * asinl( sqrtl(0.5L*(1.0L-x) ) ) ); - -return( PIO2L - asinl(x) ); -} |