suri wrote:

im sorry i meant i *could not* find the file

suri wrote: I do know the series expansion of sine i was just interested to know how

its implemented in the ansi C library. like how many terms of the

infinite series are included.

I have linux and use glibc. so i could find the file in the path u

mentioned

I stopped using Linux shortly after growing out of puberty. I developed more

sophisticated tastes in life... but I digress...

As someone else pointed out, there is no canonical ANSI C implementation.

There are various and sundry different ways of computing transcendental

functions with various accuracies and efficiencies.

The FreeBSD code mentions "a special Remez algorithm", but it boils down to

a Horner method polynomial computation (and if you don't know what the

Horner method is, google it):

----------------------------------------------------------------------------

/*

* Copyright (c) 1987, 1993

* The Regents of the University of California. 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.

* 3. All advertising materials mentioning features or use of this software

* must display the following acknowledgement :

* This product includes software developed by the University of

* California, Berkeley and its contributors.

* 4. Neither the name of the University nor the names of its contributors

* may be used to endorse or promote products derived from this software

* without specific prior written permission.

*

* THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.

*

* @(#)trig.h 8.1 (Berkeley) 6/4/93

*/

#include "mathimpl.h "

vc(thresh, 2.6117239648121 182150E-1 ,b863,3f85,6ea0 ,6b02,

-1, .85B8636B026EA0 )

vc(PIo4, 7.8539816339744 830676E-1 ,0fda,4049,68c2 ,a221,

0, .C90FDAA22168C2 )

vc(PIo2, 1.5707963267948 966135E0 ,0fda,40c9,68c2 ,a221,

1, .C90FDAA22168C2 )

vc(PI3o4, 2.3561944901923 449203E0 ,cbe3,4116,0e92 ,f999,

2, .96CBE3F9990E92 )

vc(PI, 3.1415926535897 932270E0 ,0fda,4149,68c2 ,a221,

2, .C90FDAA22168C2 )

vc(PI2, 6.2831853071795 864540E0 ,0fda,41c9,68c2 ,a221,

3, .C90FDAA22168C2 )

ic(thresh, 2.6117239648121 182150E-1 , -2, 1.0B70C6D604DD4 )

ic(PIo4, 7.8539816339744 827900E-1 , -1, 1.921FB54442D18 )

ic(PIo2, 1.5707963267948 965580E0 , 0, 1.921FB54442D18 )

ic(PI3o4, 2.3561944901923 448370E0 , 1, 1.2D97C7F3321D2 )

ic(PI, 3.1415926535897 931160E0 , 1, 1.921FB54442D18 )

ic(PI2, 6.2831853071795 862320E0 , 2, 1.921FB54442D18 )

#ifdef vccast

#define thresh vccast(thresh)

#define PIo4 vccast(PIo4)

#define PIo2 vccast(PIo2)

#define PI3o4 vccast(PI3o4)

#define PI vccast(PI)

#define PI2 vccast(PI2)

#endif

#ifdef national

static long fmaxx[] = { 0xffffffff, 0x7fefffff};

#define fmax (*(double*)fmax x)

#endif /* national */

static const double

zero = 0,

one = 1,

negone = -1,

half = 1.0/2.0,

small = 1E-10, /* 1+small**2 == 1; better values for small:

* small = 1.5E-9 for VAX D

* = 1.2E-8 for IEEE Double

* = 2.8E-10 for IEEE Extended

*/

big = 1E20; /* big := 1/(small**2) */

/* sin__S(x*x) ... re-implemented as a macro

* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)

* STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)

* CODED IN C BY K.C. NG, 1/21/85;

* REVISED BY K.C. NG on 8/13/85.

*

* sin(x*k) - x

* RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the

rounded

* x

* value of pi in machine precision:

*

* Decimal:

* pi = 3.1415926535897 93 23846264338327 .....

* 53 bits PI = 3.1415926535897 93 115997963 ..... ,

* 56 bits PI = 3.1415926535897 93 227020265 ..... ,

*

* Hexadecimal:

* pi = 3.243F6A8885A30 8D313198A2E....

* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18

* 56 bits PI = 3.243F6A8885A30 8 = 4 * .C90FDAA22168C2

*

* Method:

* 1. Let z=x*x. Create a polynomial approximation to

* (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5).

* Then

* sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5)

*

* The coefficient S's are obtained by a special Remez algorithm.

*

* Accuracy:

* In the absence of rounding error, the approximation has absolute error

* less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE.

*

* Constants:

* The hexadecimal values are the intended ones for the following constants.

* The decimal values may be used, provided that the compiler will convert

* from decimal to binary accurately enough to produce the hexadecimal

values

* shown.

*

*/

vc(S0, -1.6666666666666 646660E-1 ,aaaa,bf2a,aa71 ,aaaa, -2,

-.AAAAAAAAAAAA71 )

vc(S1, 8.3333333333297 230413E-3 ,8888,3d08,477f ,8888,

-6, .8888888888477F )

vc(S2, -1.9841269838362 403710E-4 ,0d00,ba50,1057 ,cf8a, -12,

-.D00D00CF8A1057 )

vc(S3, 2.7557318019967 078930E-6 ,ef1c,3738,bedc ,a326,

-18, .B8EF1CA326BEDC )

vc(S4, -2.5051841873876 551398E-8 ,3195,b3d7,e1d3 ,374c, -25,

-.D73195374CE1D3 )

vc(S5, 1.6028995389845 827653E-10 ,3d9c,3030,cccc ,6d26,

-32, .B03D9C6D26CCCC )

vc(S6, -6.2723499671769 283121E-13 ,8d0b,ac30,ea82 ,7561, -40,

-.B08D0B7561EA82 )

ic(S0, -1.6666666666666 463126E-1 , -3, -1.555555555550C )

ic(S1, 8.3333333332992 771264E-3 , -7, 1.111111110C461 )

ic(S2, -1.9841269816180 999116E-4 , -13, -1.A01A019746345 )

ic(S3, 2.7557309793219 876880E-6 , -19, 1.71DE3209CDCD9 )

ic(S4, -2.5050225177523 807003E-8 , -26, -1.AE5C0E319A4EF )

ic(S5, 1.5868926979889 205164E-10 , -33, 1.5CF61DF672B13 )

#ifdef vccast

#define S0 vccast(S0)

#define S1 vccast(S1)

#define S2 vccast(S2)

#define S3 vccast(S3)

#define S4 vccast(S4)

#define S5 vccast(S5)

#define S6 vccast(S6)

#endif

#if defined(vax)||d efined(tahoe)

# define sin__S(z) (z*(S0+z*(S1+z* (S2+z*(S3+z*(S4 +z*(S5+z*S6)))) )))

#else /* defined(vax)||d efined(tahoe) */

# define sin__S(z) (z*(S0+z*(S1+z* (S2+z*(S3+z*(S4 +z*S5))))))

#endif /* defined(vax)||d efined(tahoe) */

/* cos__C(x*x) ... re-implemented as a macro

* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)

* STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)

* CODED IN C BY K.C. NG, 1/21/85;

* REVISED BY K.C. NG on 8/13/85.

*

* x*x

* RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI,

* 2

* PI is the rounded value of pi in machine precision :

*

* Decimal:

* pi = 3.1415926535897 93 23846264338327 .....

* 53 bits PI = 3.1415926535897 93 115997963 ..... ,

* 56 bits PI = 3.1415926535897 93 227020265 ..... ,

*

* Hexadecimal:

* pi = 3.243F6A8885A30 8D313198A2E....

* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18

* 56 bits PI = 3.243F6A8885A30 8 = 4 * .C90FDAA22168C2

*

*

* Method:

* 1. Let z=x*x. Create a polynomial approximation to

* cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5)

* then

* cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5)

*

* The coefficient C's are obtained by a special Remez algorithm.

*

* Accuracy:

* In the absence of rounding error, the approximation has absolute error

* less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE.

*

*

* Constants:

* The hexadecimal values are the intended ones for the following constants.

* The decimal values may be used, provided that the compiler will convert

* from decimal to binary accurately enough to produce the hexadecimal

values

* shown.

*/

vc(C0, 4.1666666666666 504759E-2 ,aaaa,3e2a,a9f0 ,aaaa,

-4, .AAAAAAAAAAA9F0 )

vc(C1, -1.3888888888865 302059E-3 ,0b60,bbb6,0cca ,b60a, -9,

-.B60B60B60A0CCA )

vc(C2, 2.4801587285601 038265E-5 ,0d00,38d0,098f ,cdcd,

-15, .D00D00CDCD098F )

vc(C3, -2.7557313470902 390219E-7 ,f27b,b593,e805 ,b593, -21,

-.93F27BB593E805 )

vc(C4, 2.0875623401082 232009E-9 ,74c8,320f,3ff0 ,fa1e,

-28, .8F74C8FA1E3FF0 )

vc(C5, -1.1355178117642 986178E-11 ,c32d,ae47,5a63 ,0a5c, -36,

-.C7C32D0A5C5A63 )

ic(C0, 4.1666666666666 504759E-2 , -5, 1.555555555553E )

ic(C1, -1.3888888888865 301516E-3 , -10, -1.6C16C16C14199 )

ic(C2, 2.4801587269650 015769E-5 , -16, 1.A01A01971CAEB )

ic(C3, -2.7557304623183 959811E-7 , -22, -1.27E4F1314AD1A )

ic(C4, 2.0873958177697 780076E-9 , -29, 1.1EE3B60DDDC8C )

ic(C5, -1.1250289076471 311557E-11 , -37, -1.8BD5986B2A52E )

#ifdef vccast

#define C0 vccast(C0)

#define C1 vccast(C1)

#define C2 vccast(C2)

#define C3 vccast(C3)

#define C4 vccast(C4)

#define C5 vccast(C5)

#endif

#define cos__C(z) (z*z*(C0+z*(C1+ z*(C2+z*(C3+z*( C4+z*C5))))))

----------------------------------------------------------------------------