172 lines
4.0 KiB
C
172 lines
4.0 KiB
C
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/* @(#)z_sineh.c 1.0 98/08/13 */
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/******************************************************************
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* The following routines are coded directly from the algorithms
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* and coefficients given in "Software Manual for the Elementary
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Hall, 1980.
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******************************************************************/
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/*
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FUNCTION
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<<sinh>>, <<sinhf>>, <<cosh>>, <<coshf>>, <<sineh>>---hyperbolic sine or cosine
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INDEX
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sinh
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INDEX
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sinhf
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INDEX
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cosh
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INDEX
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coshf
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SYNOPSIS
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#include <math.h>
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double sinh(double <[x]>);
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float sinhf(float <[x]>);
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double cosh(double <[x]>);
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float coshf(float <[x]>);
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DESCRIPTION
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<<sinh>> and <<cosh>> compute the hyperbolic sine or cosine
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of the argument <[x]>.
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Angles are specified in radians. <<sinh>>(<[x]>) is defined as
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@ifnottex
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. (exp(<[x]>) - exp(-<[x]>))/2
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@end ifnottex
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@tex
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$${e^x - e^{-x}}\over 2$$
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@end tex
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<<cosh>> is defined as
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@ifnottex
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. (exp(<[x]>) - exp(-<[x]>))/2
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@end ifnottex
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@tex
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$${e^x + e^{-x}}\over 2$$
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@end tex
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<<sinhf>> and <<coshf>> are identical, save that they take
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and returns <<float>> values.
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RETURNS
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The hyperbolic sine or cosine of <[x]> is returned.
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When the correct result is too large to be representable (an
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overflow), the functions return <<HUGE_VAL>> with the
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appropriate sign, and sets the global value <<errno>> to
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<<ERANGE>>.
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PORTABILITY
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<<sinh>> is ANSI C.
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<<sinhf>> is an extension.
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<<cosh>> is ANSI C.
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<<coshf>> is an extension.
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*/
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/******************************************************************
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* Hyperbolic Sine
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*
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* Input:
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* x - floating point value
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*
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* Output:
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* hyperbolic sine of x
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*
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* Description:
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* This routine calculates hyperbolic sines.
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*
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*****************************************************************/
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#include <float.h>
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#include "fdlibm.h"
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#include "zmath.h"
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static const double q[] = { -0.21108770058106271242e+7,
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0.36162723109421836460e+5,
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-0.27773523119650701667e+3 };
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static const double p[] = { -0.35181283430177117881e+6,
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-0.11563521196851768270e+5,
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-0.16375798202630751372e+3,
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-0.78966127417357099479 };
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static const double LNV = 0.6931610107421875000;
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static const double INV_V2 = 0.24999308500451499336;
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static const double V_OVER2_MINUS1 = 0.13830277879601902638e-4;
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double
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sineh (double x,
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int cosineh)
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{
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double y, f, P, Q, R, res, z, w;
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int sgn = 1;
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double WBAR = 18.55;
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/* Check for special values. */
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switch (numtest (x))
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{
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case NAN:
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errno = EDOM;
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return (x);
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case INF:
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errno = ERANGE;
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return (ispos (x) ? z_infinity.d : -z_infinity.d);
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}
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y = fabs (x);
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if (!cosineh && x < 0.0)
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sgn = -1;
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if ((y > 1.0 && !cosineh) || cosineh)
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{
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if (y > BIGX)
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{
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w = y - LNV;
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/* Check for w > maximum here. */
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if (w > BIGX)
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{
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errno = ERANGE;
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return (x);
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}
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z = exp (w);
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if (w > WBAR)
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res = z * (V_OVER2_MINUS1 + 1.0);
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}
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else
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{
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z = exp (y);
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if (cosineh)
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res = (z + 1 / z) / 2.0;
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else
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res = (z - 1 / z) / 2.0;
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}
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if (sgn < 0)
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res = -res;
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}
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else
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{
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/* Check for y being too small. */
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if (y < z_rooteps)
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{
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res = x;
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}
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/* Calculate the Taylor series. */
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else
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{
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f = x * x;
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Q = ((f + q[2]) * f + q[1]) * f + q[0];
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P = ((p[3] * f + p[2]) * f + p[1]) * f + p[0];
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R = f * (P / Q);
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res = x + x * R;
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}
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}
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return (res);
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}
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