| /*- |
| * 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]))))))))))); |
| } |