214 lines
8.4 KiB
C
214 lines
8.4 KiB
C
/*
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* Copyright (c) 1987, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* @(#)trig.h 8.1 (Berkeley) 6/4/93
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*/
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vc(thresh, 2.6117239648121182150E-1 ,b863,3f85,6ea0,6b02, -1, .85B8636B026EA0)
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vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2)
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vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2)
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vc(PI3o4, 2.3561944901923449203E0 ,cbe3,4116,0e92,f999, 2, .96CBE3F9990E92)
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vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2)
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vc(PI2, 6.2831853071795864540E0 ,0fda,41c9,68c2,a221, 3, .C90FDAA22168C2)
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ic(thresh, 2.6117239648121182150E-1 , -2, 1.0B70C6D604DD4)
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ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18)
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ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18)
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ic(PI3o4, 2.3561944901923448370E0 , 1, 1.2D97C7F3321D2)
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ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18)
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ic(PI2, 6.2831853071795862320E0 , 2, 1.921FB54442D18)
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#ifdef vccast
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#define thresh vccast(thresh)
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#define PIo4 vccast(PIo4)
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#define PIo2 vccast(PIo2)
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#define PI3o4 vccast(PI3o4)
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#define PI vccast(PI)
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#define PI2 vccast(PI2)
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#endif
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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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static const 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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vc(S0, -1.6666666666666646660E-1 ,aaaa,bf2a,aa71,aaaa, -2, -.AAAAAAAAAAAA71)
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vc(S1, 8.3333333333297230413E-3 ,8888,3d08,477f,8888, -6, .8888888888477F)
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vc(S2, -1.9841269838362403710E-4 ,0d00,ba50,1057,cf8a, -12, -.D00D00CF8A1057)
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vc(S3, 2.7557318019967078930E-6 ,ef1c,3738,bedc,a326, -18, .B8EF1CA326BEDC)
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vc(S4, -2.5051841873876551398E-8 ,3195,b3d7,e1d3,374c, -25, -.D73195374CE1D3)
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vc(S5, 1.6028995389845827653E-10 ,3d9c,3030,cccc,6d26, -32, .B03D9C6D26CCCC)
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vc(S6, -6.2723499671769283121E-13 ,8d0b,ac30,ea82,7561, -40, -.B08D0B7561EA82)
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ic(S0, -1.6666666666666463126E-1 , -3, -1.555555555550C)
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ic(S1, 8.3333333332992771264E-3 , -7, 1.111111110C461)
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ic(S2, -1.9841269816180999116E-4 , -13, -1.A01A019746345)
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ic(S3, 2.7557309793219876880E-6 , -19, 1.71DE3209CDCD9)
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ic(S4, -2.5050225177523807003E-8 , -26, -1.AE5C0E319A4EF)
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ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13)
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#ifdef vccast
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#define S0 vccast(S0)
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#define S1 vccast(S1)
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#define S2 vccast(S2)
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#define S3 vccast(S3)
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#define S4 vccast(S4)
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#define S5 vccast(S5)
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#define S6 vccast(S6)
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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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vc(C0, 4.1666666666666504759E-2 ,aaaa,3e2a,a9f0,aaaa, -4, .AAAAAAAAAAA9F0)
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vc(C1, -1.3888888888865302059E-3 ,0b60,bbb6,0cca,b60a, -9, -.B60B60B60A0CCA)
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vc(C2, 2.4801587285601038265E-5 ,0d00,38d0,098f,cdcd, -15, .D00D00CDCD098F)
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vc(C3, -2.7557313470902390219E-7 ,f27b,b593,e805,b593, -21, -.93F27BB593E805)
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vc(C4, 2.0875623401082232009E-9 ,74c8,320f,3ff0,fa1e, -28, .8F74C8FA1E3FF0)
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vc(C5, -1.1355178117642986178E-11 ,c32d,ae47,5a63,0a5c, -36, -.C7C32D0A5C5A63)
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ic(C0, 4.1666666666666504759E-2 , -5, 1.555555555553E)
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ic(C1, -1.3888888888865301516E-3 , -10, -1.6C16C16C14199)
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ic(C2, 2.4801587269650015769E-5 , -16, 1.A01A01971CAEB)
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ic(C3, -2.7557304623183959811E-7 , -22, -1.27E4F1314AD1A)
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ic(C4, 2.0873958177697780076E-9 , -29, 1.1EE3B60DDDC8C)
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ic(C5, -1.1250289076471311557E-11 , -37, -1.8BD5986B2A52E)
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#ifdef vccast
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#define C0 vccast(C0)
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#define C1 vccast(C1)
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#define C2 vccast(C2)
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#define C3 vccast(C3)
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#define C4 vccast(C4)
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#define C5 vccast(C5)
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#endif
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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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