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Diffstat (limited to 'newlib/libm/ld128/invtrig.h')
| -rw-r--r-- | newlib/libm/ld128/invtrig.h | 115 |
1 files changed, 115 insertions, 0 deletions
diff --git a/newlib/libm/ld128/invtrig.h b/newlib/libm/ld128/invtrig.h new file mode 100644 index 000000000..423b56847 --- /dev/null +++ b/newlib/libm/ld128/invtrig.h @@ -0,0 +1,115 @@ +/*- + * SPDX-License-Identifier: BSD-2-Clause-FreeBSD + * + * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#include <float.h> + +#include "fpmath.h" + +#define BIAS (LDBL_MAX_EXP - 1) +#define MANH_SIZE (LDBL_MANH_SIZE + 1) + +/* Approximation thresholds. */ +#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ +#define ACOS_CONST (BIAS - 113) /* 2**-113 */ +#define ATAN_CONST (BIAS + 113) /* 2**113 */ +#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ + +/* 0.95 */ +#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) + +/* Constants shared by the long double inverse trig functions. */ +#define pS0 _ItL_pS0 +#define pS1 _ItL_pS1 +#define pS2 _ItL_pS2 +#define pS3 _ItL_pS3 +#define pS4 _ItL_pS4 +#define pS5 _ItL_pS5 +#define pS6 _ItL_pS6 +#define pS7 _ItL_pS7 +#define pS8 _ItL_pS8 +#define pS9 _ItL_pS9 +#define qS1 _ItL_qS1 +#define qS2 _ItL_qS2 +#define qS3 _ItL_qS3 +#define qS4 _ItL_qS4 +#define qS5 _ItL_qS5 +#define qS6 _ItL_qS6 +#define qS7 _ItL_qS7 +#define qS8 _ItL_qS8 +#define qS9 _ItL_qS9 +#define atanhi _ItL_atanhi +#define atanlo _ItL_atanlo +#define aT _ItL_aT +#define pi_lo _ItL_pi_lo + +#define pio2_hi atanhi[3] +#define pio2_lo atanlo[3] +#define pio4_hi atanhi[1] + +/* Constants shared by the long double inverse trig functions. */ +extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; +extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; +extern const long double atanhi[], atanlo[], aT[]; +extern const long double pi_lo; + +static inline long double +P(long double x) +{ + + return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ + (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ + pS9)))))))))); +} + +static inline long double +Q(long double x) +{ + + return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ + (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); +} + +static inline 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] + x * (aT[14] + x * \ + (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); +} + +static inline 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] + x * (aT[13] + x * (aT[15] + x * \ + (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); +} |