271 lines
10 KiB
C
271 lines
10 KiB
C
/* trigP.h - trigonometric definitions for Berkeley math package */
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/* Copyright 1994 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01e,14oct94,ism fixed syntax error per SPR#3718
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01d,22sep92,rrr added support for c++
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01c,01jul92,smb added to clib library.
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01b,04oct91,rrr passed through the ansification filter
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-fixed #else and #endif
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-changed copyright notice
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01a,14sep90,mcl adapted from Berkeley.
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*/
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#ifndef __INCtrigPh
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#define __INCtrigPh
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#ifdef __cplusplus
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extern "C" {
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#endif
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/*
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* Copyright (c) 1987 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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* @(#)trig.h 5.3 (Berkeley) 6/30/88
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*/
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#if defined(vax)||defined(tahoe)
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/*thresh = 2.6117239648121182150E-1 , Hex 2^ -1 * .85B8636B026EA0 */
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/*PIo4 = 7.8539816339744830676E-1 , Hex 2^ 0 * .C90FDAA22168C2 */
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/*PIo2 = 1.5707963267948966135E0 , Hex 2^ 1 * .C90FDAA22168C2 */
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/*PI3o4 = 2.3561944901923449203E0 , Hex 2^ 2 * .96CBE3F9990E92 */
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/*PI = 3.1415926535897932270E0 , Hex 2^ 2 * .C90FDAA22168C2 */
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/*PI2 = 6.2831853071795864540E0 ; Hex 2^ 3 * .C90FDAA22168C2 */
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static long threshx[] = { _0x(b863,3f85), _0x(6ea0,6b02)};
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static long PIo4x[] = { _0x(0fda,4049), _0x(68c2,a221)};
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static long PIo2x[] = { _0x(0fda,40c9), _0x(68c2,a221)};
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static long PI3o4x[] = { _0x(cbe3,4116), _0x(0e92,f999)};
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static long PIx[] = { _0x(0fda,4149), _0x(68c2,a221)};
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static long PI2x[] = { _0x(0fda,41c9), _0x(68c2,a221)};
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#define thresh (*(double*)threshx)
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#define PIo4 (*(double*)PIo4x)
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#define PIo2 (*(double*)PIo2x)
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#define PI3o4 (*(double*)PI3o4x)
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#define PI (*(double*)PIx)
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#define PI2 (*(double*)PI2x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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thresh = 2.6117239648121182150E-1 , /*Hex 2^ -2 * 1.0B70C6D604DD4 */
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PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */
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PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */
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PI3o4 = 2.3561944901923448370E0 , /*Hex 2^ 1 * 1.2D97C7F3321D2 */
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PI = 3.1415926535897931160E0 , /*Hex 2^ 1 * 1.921FB54442D18 */
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PI2 = 6.2831853071795862320E0 ; /*Hex 2^ 2 * 1.921FB54442D18 */
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#ifdef national
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static long fmaxx[] = { 0xffffffff, 0x7fefffff};
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#define fmax (*(double*)fmaxx)
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#endif /* national */
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#endif /* defined(vax)||defined(tahoe) */
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static double
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zero = 0,
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one = 1,
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negone = -1,
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half = 1.0/2.0,
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small = 1E-10, /* 1+small**2 == 1; better values for small:
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* small = 1.5E-9 for VAX D
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* = 1.2E-8 for IEEE Double
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* = 2.8E-10 for IEEE Extended
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*/
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big = 1E20; /* big := 1/(small**2) */
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/* sin__S(x*x) ... re-implemented as a macro
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)
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* CODED IN C BY K.C. NG, 1/21/85;
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* REVISED BY K.C. NG on 8/13/85.
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*
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* sin(x*k) - x
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* RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded
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* x
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* value of pi in machine precision:
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*
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* Decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* Hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
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*
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* Method:
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* 1. Let z=x*x. Create a polynomial approximation to
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* (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5).
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* Then
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* sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5)
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*
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* The coefficient S's are obtained by a special Remez algorithm.
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*
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* Accuracy:
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* In the absence of rounding error, the approximation has absolute error
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* less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*
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*/
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#if defined(vax)||defined(tahoe)
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/*S0 = -1.6666666666666646660E-1 , Hex 2^ -2 * -.AAAAAAAAAAAA71 */
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/*S1 = 8.3333333333297230413E-3 , Hex 2^ -6 * .8888888888477F */
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/*S2 = -1.9841269838362403710E-4 , Hex 2^-12 * -.D00D00CF8A1057 */
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/*S3 = 2.7557318019967078930E-6 , Hex 2^-18 * .B8EF1CA326BEDC */
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/*S4 = -2.5051841873876551398E-8 , Hex 2^-25 * -.D73195374CE1D3 */
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/*S5 = 1.6028995389845827653E-10 , Hex 2^-32 * .B03D9C6D26CCCC */
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/*S6 = -6.2723499671769283121E-13 ; Hex 2^-40 * -.B08D0B7561EA82 */
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static long S0x[] = { _0x(aaaa,bf2a), _0x(aa71,aaaa)};
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static long S1x[] = { _0x(8888,3d08), _0x(477f,8888)};
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static long S2x[] = { _0x(0d00,ba50), _0x(1057,cf8a)};
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static long S3x[] = { _0x(ef1c,3738), _0x(bedc,a326)};
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static long S4x[] = { _0x(3195,b3d7), _0x(e1d3,374c)};
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static long S5x[] = { _0x(3d9c,3030), _0x(cccc,6d26)};
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static long S6x[] = { _0x(8d0b,ac30), _0x(ea82,7561)};
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#define S0 (*(double*)S0x)
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#define S1 (*(double*)S1x)
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#define S2 (*(double*)S2x)
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#define S3 (*(double*)S3x)
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#define S4 (*(double*)S4x)
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#define S5 (*(double*)S5x)
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#define S6 (*(double*)S6x)
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#else /* IEEE double */
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static double
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S0 = -1.6666666666666463126E-1 , /*Hex 2^ -3 * -1.555555555550C */
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S1 = 8.3333333332992771264E-3 , /*Hex 2^ -7 * 1.111111110C461 */
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S2 = -1.9841269816180999116E-4 , /*Hex 2^-13 * -1.A01A019746345 */
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S3 = 2.7557309793219876880E-6 , /*Hex 2^-19 * 1.71DE3209CDCD9 */
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S4 = -2.5050225177523807003E-8 , /*Hex 2^-26 * -1.AE5C0E319A4EF */
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S5 = 1.5868926979889205164E-10 ; /*Hex 2^-33 * 1.5CF61DF672B13 */
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#endif
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#if defined(vax)||defined(tahoe)
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#define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6)))))))
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#else /* defined(vax)||defined(tahoe) */
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#define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5))))))
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#endif /* defined(vax)||defined(tahoe) */
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/* cos__C(x*x) ... re-implemented as a macro
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* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
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* STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)
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* CODED IN C BY K.C. NG, 1/21/85;
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* REVISED BY K.C. NG on 8/13/85.
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*
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* x*x
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* RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI,
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* 2
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* PI is the rounded value of pi in machine precision :
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*
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* Decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* Hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
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*
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*
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* Method:
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* 1. Let z=x*x. Create a polynomial approximation to
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* cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5)
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* then
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* cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5)
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*
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* The coefficient C's are obtained by a special Remez algorithm.
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*
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* Accuracy:
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* In the absence of rounding error, the approximation has absolute error
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* less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE.
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*
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*
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*/
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#if defined(vax)||defined(tahoe)
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/*C0 = 4.1666666666666504759E-2 , Hex 2^ -4 * .AAAAAAAAAAA9F0 */
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/*C1 = -1.3888888888865302059E-3 , Hex 2^ -9 * -.B60B60B60A0CCA */
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/*C2 = 2.4801587285601038265E-5 , Hex 2^-15 * .D00D00CDCD098F */
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/*C3 = -2.7557313470902390219E-7 , Hex 2^-21 * -.93F27BB593E805 */
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/*C4 = 2.0875623401082232009E-9 , Hex 2^-28 * .8F74C8FA1E3FF0 */
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/*C5 = -1.1355178117642986178E-11 ; Hex 2^-36 * -.C7C32D0A5C5A63 */
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static long C0x[] = { _0x(aaaa,3e2a), _0x(a9f0,aaaa)};
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static long C1x[] = { _0x(0b60,bbb6), _0x(0cca,b60a)};
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static long C2x[] = { _0x(0d00,38d0), _0x(098f,cdcd)};
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static long C3x[] = { _0x(f27b,b593), _0x(e805,b593)};
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static long C4x[] = { _0x(74c8,320f), _0x(3ff0,fa1e)};
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static long C5x[] = { _0x(c32d,ae47), _0x(5a63,0a5c)};
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#define C0 (*(double*)C0x)
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#define C1 (*(double*)C1x)
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#define C2 (*(double*)C2x)
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#define C3 (*(double*)C3x)
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#define C4 (*(double*)C4x)
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#define C5 (*(double*)C5x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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C0 = 4.1666666666666504759E-2 , /*Hex 2^ -5 * 1.555555555553E */
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C1 = -1.3888888888865301516E-3 , /*Hex 2^-10 * -1.6C16C16C14199 */
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C2 = 2.4801587269650015769E-5 , /*Hex 2^-16 * 1.A01A01971CAEB */
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C3 = -2.7557304623183959811E-7 , /*Hex 2^-22 * -1.27E4F1314AD1A */
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C4 = 2.0873958177697780076E-9 , /*Hex 2^-29 * 1.1EE3B60DDDC8C */
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C5 = -1.1250289076471311557E-11 ; /*Hex 2^-37 * -1.8BD5986B2A52E */
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#endif /* defined(vax)||defined(tahoe) */
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#define cos__C(z) (z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5))))))
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/* function declarations */
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#if defined(__STDC__) || defined(__cplusplus)
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extern int finite(double x);
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extern double copysign(double x, double y);
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extern double drem(double x, double p);
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#else /* __STDC__ */
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extern int finite();
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extern double copysign();
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extern double drem();
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#endif /* __STDC__ */
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#ifdef __cplusplus
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}
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#endif
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#endif /* __INCtrigPh */
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