newlib/libm/ld128/invtrig.h

   1 /*-
   2  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
   3  *
   4  * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
   5  * All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice, this list of conditions and the following disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  17  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  18  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  19  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  20  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  21  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  22  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  23  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  24  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  25  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  26  * SUCH DAMAGE.
  27  *
  28  * $FreeBSD$
  29  */
  30
  31 #include <float.h>
  32
  33 #include "../ld/fpmath.h"
  34
  35 #define BIAS            (LDBL_MAX_EXP - 1)
  36 #define MANH_SIZE       (LDBL_MANH_SIZE + 1)
  37
  38 /* Approximation thresholds. */
  39 #define ASIN_LINEAR     (BIAS - 56)     /* 2**-56 */
  40 #define ACOS_CONST      (BIAS - 113)    /* 2**-113 */
  41 #define ATAN_CONST      (BIAS + 113)    /* 2**113 */
  42 #define ATAN_LINEAR     (BIAS - 56)     /* 2**-56 */
  43
  44 /* 0.95 */
  45 #define THRESH  ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
  46
  47 /* Constants shared by the long double inverse trig functions. */
  48 #define pS0     _ItL_pS0
  49 #define pS1     _ItL_pS1
  50 #define pS2     _ItL_pS2
  51 #define pS3     _ItL_pS3
  52 #define pS4     _ItL_pS4
  53 #define pS5     _ItL_pS5
  54 #define pS6     _ItL_pS6
  55 #define pS7     _ItL_pS7
  56 #define pS8     _ItL_pS8
  57 #define pS9     _ItL_pS9
  58 #define qS1     _ItL_qS1
  59 #define qS2     _ItL_qS2
  60 #define qS3     _ItL_qS3
  61 #define qS4     _ItL_qS4
  62 #define qS5     _ItL_qS5
  63 #define qS6     _ItL_qS6
  64 #define qS7     _ItL_qS7
  65 #define qS8     _ItL_qS8
  66 #define qS9     _ItL_qS9
  67 #define atanhi  _ItL_atanhi
  68 #define atanlo  _ItL_atanlo
  69 #define aT      _ItL_aT
  70 #define pi_lo   _ItL_pi_lo
  71
  72 #define pio2_hi atanhi[3]
  73 #define pio2_lo atanlo[3]
  74 #define pio4_hi atanhi[1]
  75
  76 /* Constants shared by the long double inverse trig functions. */
  77 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
  78 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
  79 extern const long double atanhi[], atanlo[], aT[];
  80 extern const long double pi_lo;
  81
  82 static inline long double
  83 P(long double x)
  84 {
  85
  86         return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
  87                 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
  88                 pS9))))))))));
  89 }
  90
  91 static inline long double
  92 Q(long double x)
  93 {
  94
  95         return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
  96                 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
  97 }
  98
  99 static inline long double
 100 T_even(long double x)
 101 {
 102
 103         return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
 104                 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
 105                 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
 106 }
 107
 108 static inline long double
 109 T_odd(long double x)
 110 {
 111
 112         return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
 113                 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
 114                 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
 115 }