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add JavaScript Interpreter

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geniusgogo
2014-02-25 01:47:49 +08:00
parent 7255137b0a
commit 121bb5fcdf
115 changed files with 29947 additions and 13 deletions
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233
components/external/espruino/libs/jswrap_math.c vendored Normal file
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/*
* This file is part of Espruino, a JavaScript interpreter for Microcontrollers
*
* Copyright (C) 2013 Gordon Williams <gw@pur3.co.uk>
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* ----------------------------------------------------------------------------
* This file is designed to be parsed during the build process
*
* Contains built-in functions for Maths
* ----------------------------------------------------------------------------
*/
#include "jswrap_math.h"
/*JSON{ "type":"class",
"class" : "Math",
"description" : "This is a standard JavaScript class that contains useful Maths routines"
}*/
// -------------------------------------------------------------------- Integer
/*JSON{ "type":"staticmethod",
"class" : "Integer", "name" : "valueOf",
"generate" : "jswrap_integer_valueOf",
"description" : "Given a string containing a single character, return the numeric value of it",
"params" : [ [ "character" ,"JsVar", "A string containing a single character"] ],
"return" : ["int", "The integer value of char"]
}*/
JsVarInt jswrap_integer_valueOf(JsVar *v) {
if (!jsvIsString(v) || jsvGetStringLength(v)!=1)
return 0;
return (int)v->varData.str[0];
}
/*JSON{ "type":"variable", "name" : "NaN",
"generate_full" : "NAN",
"return" : ["float", "Not a Number"]
}*/
// -------------------------------------------------------------------- Double
/*JSON{ "type":"staticmethod",
"class" : "Double", "name" : "doubleToIntBits",
"generate_full" : "*(JsVarInt*)&x",
"description" : " Convert the floating point value given into an integer representing the bits contained in it",
"params" : [ [ "x", "float", "A floating point number"] ],
"return" : ["int", "The integer representation of x"]
}*/
// -------------------------------------------------------------------- Math
/*JSON{ "type":"staticproperty",
"class" : "Math", "name" : "E",
"generate_full" : "2.71828182846",
"return" : ["float", "The value of E - 2.71828182846"]
}*/
/*JSON{ "type":"staticproperty",
"class" : "Math", "name" : "PI",
"generate_full" : "3.14159265359",
"return" : ["float", "The value of PI - 3.14159265359"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "abs",
"generate" : "jswrap_math_abs",
"params" : [ [ "x", "float", "A floating point value"] ],
"return" : ["float", "The absolute value of x (eg, ```Math.abs(2)==2```, but also ```Math.abs(-2)==2```)"]
}*/
JsVarFloat jswrap_math_abs(JsVarFloat x) {
return (x<0)?-x:x;
}
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "acos",
"generate" : "acos",
"params" : [ [ "x", "float", "The value to get the arc cosine of"] ],
"return" : ["float", "The arc cosine of x, between 0 and PI"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "asin",
"generate" : "asin",
"params" : [ [ "x", "float", "The value to get the arc sine of"] ],
"return" : ["float", "The arc sine of x, between -PI/2 and PI/2"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "atan",
"generate" : "atan",
"params" : [ [ "x", "float", "The value to get the arc tangent of"] ],
"return" : ["float", "The arc tangent of x, between -PI/2 and PI/2"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "atan2",
"generate" : "atan2",
"params" : [ [ "y", "float", "The Y-part of the angle to get the arc tangent of"],
[ "x", "float", "The X-part of the angle to get the arc tangent of"] ],
"return" : ["float", "The arctangent of Y/X, between -PI and PI"]
}*/
/* we use sin here, not cos, to try and save a bit of code space */
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "cos",
"generate_full" : "sin(jsvGetFloat(theta) + (3.14159265359/2.0))",
"params" : [ [ "theta", "float", "The angle to get the cosine of"] ],
"return" : ["float", "The cosine of theta"]
}*/
#define DBL_MAX 1.7976931348623157E+308
double fs_fmod(double x, double y)
{
double a, b;
const double c = x;
if (0 > c) {
x = -x;
}
if (0 > y) {
y = -y;
}
if (y != 0 && DBL_MAX >= y && DBL_MAX >= x) {
while (x >= y) {
a = x / 2;
b = y;
while (a >= b) {
b *= 2;
}
x -= b;
}
} else {
x = 0;
}
return 0 > c ? -x : x;
}
double jswrap_math_pow(double x, double y)
{
double p;
if (0 > x && fs_fmod(y, 1) == 0) {
if (fs_fmod(y, 2) == 0) {
p = exp(log(-x) * y);
} else {
p = -exp(log(-x) * y);
}
} else {
if (x != 0 || 0 >= y) {
p = exp(log( x) * y);
} else {
p = 0;
}
}
return p;
}
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "pow",
"generate" : "jswrap_math_pow",
"params" : [ [ "x", "float", "The value to raise to the power"],
[ "y", "float", "The power x should be raised to"] ],
"return" : ["float", "x raised to the power y (x^y)"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "random",
"generate_full" : "(JsVarFloat)rand() / (JsVarFloat)RAND_MAX",
"return" : ["float", "A random number between 0 and 1"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "round",
"generate" : "(JsVarInt)round",
"params" : [ [ "x", "float", "The value to round"] ],
"return" : ["int", "x, rounded to the nearest integer"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "sin",
"generate" : "sin",
"params" : [ [ "theta", "float", "The angle to get the sine of"] ],
"return" : ["float", "The sine of theta"]
}*/
/* we could use the real sqrt - but re-use pow to save on code space */
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "sqrt",
"generate_full" : "jswrap_math_pow(jsvGetFloat(x),0.5)",
"params" : [ [ "x", "float", "The value to take the square root of"] ],
"return" : ["float", "The square root of x"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "ceil",
"generate" : "ceil",
"params" : [ [ "x", "float", "The value to round up"] ],
"return" : ["float", "x, rounded upwards to the nearest integer"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "floor",
"generate" : "floor",
"params" : [ [ "x", "float", "The value to round down"] ],
"return" : ["float", "x, rounded downwards to the nearest integer"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "exp",
"generate" : "exp",
"params" : [ [ "x", "float", "The value raise E to the power of"] ],
"return" : ["float", "E^x"]
}*/
/*JSON{ "type":"staticmethod",
"class" : "Math", "name" : "log",
"generate" : "log",
"params" : [ [ "x", "float", "The value to take the logarithm (base E) root of"] ],
"return" : ["float", "The log (base E) of x"]
}*/
/*JSON{ "type":"staticmethod", "ifndef" : "SAVE_ON_FLASH",
"class" : "Math", "name" : "clip",
"generate" : "jswrap_math_clip",
"description" : "Clip a number to be between min and max (inclusive)",
"params" : [ [ "x", "float", "A floating point value to clip"],
[ "min", "float", "The smallest the value should be"],
[ "max", "float", "The largest the value should be"] ],
"return" : ["float", "The value of x, clipped so as not to be below min or above max."]
}*/
JsVarFloat jswrap_math_clip(JsVarFloat x, JsVarFloat min, JsVarFloat max) {
if (x<min) x=min;
if (x>max) x=max;
return x;
}
/*JSON{ "type":"staticmethod", "ifndef" : "SAVE_ON_FLASH",
"class" : "Math", "name" : "wrap",
"generate" : "wrapAround",
"description" : "Wrap a number around if it is less than 0 or greater than or equal to max. For instance you might do: ```Math.wrap(angleInDegrees, 360)```",
"params" : [ [ "x", "float", "A floating point value to wrap"],
[ "max", "float", "The largest the value should be"] ],
"return" : ["float", "The value of x, wrapped so as not to be below min or above max."]
}*/

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components/external/espruino/libs/jswrap_math.h vendored Normal file
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/*
* This file is part of Espruino, a JavaScript interpreter for Microcontrollers
*
* Copyright (C) 2013 Gordon Williams <gw@pur3.co.uk>
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* ----------------------------------------------------------------------------
* Contains built-in functions for Maths
* ----------------------------------------------------------------------------
*/
#include "jsutils.h"
#include "jsvar.h"
#ifdef ARM
#include "mconf.h"
#include "protos.h"
#else
#include <math.h>
#endif
JsVarInt jswrap_integer_valueOf(JsVar *v);
JsVarFloat jswrap_math_abs(JsVarFloat x);
double jswrap_math_pow(double x, double y);
JsVarFloat jswrap_math_clip(JsVarFloat x, JsVarFloat min, JsVarFloat max);

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This suite of C language elementary functions offers support for
not-a-number (NaN) and infinity rules, subnormal numbers, and minus
zero as described by IEEE standard 754 and the Numerical C Extensions
Group (NCEG). For a variety of reasons, many computers cannot take
advantage of these features. You can disable any or all of them by
removing the corresponding preprocessor macros. Check the files
mconf.h and const.c carefully to be sure they are appropriate for your
system.
------------------------------------------
http://www.netlib.org/cephes/readme
Some software in this archive may be from the book _Methods and
Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
International, 1989) or from the Cephes Mathematical Library, a
commercial product. In either event, it is copyrighted by the author.
What you see here may be used freely but it comes with no support or
guarantee.
The two known misprints in the book are repaired here in the
source listings for the gamma function and the incomplete beta
integral.
Stephen L. Moshier
moshier@na-net.ornl.gov

167
components/external/espruino/libs/math/acosh.c vendored Normal file
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/* acosh.c
*
* Inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* double x, y, acosh();
*
* y = acosh( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic cosine of argument.
*
* If 1 <= x < 1.5, a rational approximation
*
* sqrt(z) * P(z)/Q(z)
*
* where z = x-1, is used. Otherwise,
*
* acosh(x) = log( x + sqrt( (x-1)(x+1) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 1,3 30000 4.2e-17 1.1e-17
* IEEE 1,3 30000 4.6e-16 8.7e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* acosh domain |x| < 1 NAN
*
*/
/* acosh.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
#include "mconf.h"
#ifdef UNK
const static double P[] = {
1.18801130533544501356E2,
3.94726656571334401102E3,
3.43989375926195455866E4,
1.08102874834699867335E5,
1.10855947270161294369E5
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
1.86145380837903397292E2,
4.15352677227719831579E3,
2.97683430363289370382E4,
8.29725251988426222434E4,
7.83869920495893927727E4
};
#endif
#ifdef DEC
static unsigned short P[] = {
0041755,0115055,0144002,0146444,
0043166,0132103,0155150,0150302,
0044006,0057360,0003021,0162753,
0044323,0021557,0175225,0056253,
0044330,0101771,0040046,0006636
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0042072,0022467,0126670,0041232,
0043201,0146066,0152142,0034015,
0043750,0110257,0121165,0026100,
0044242,0007103,0034667,0033173,
0044231,0014576,0175573,0017472
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x59a4,0xb900,0xb345,0x405d,
0x1a18,0x7b4d,0xd688,0x40ae,
0x3cbd,0x00c2,0xcbde,0x40e0,
0xab95,0xff52,0x646d,0x40fa,
0xc1b4,0x2804,0x107f,0x40fb
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x0853,0xf5b7,0x44a6,0x4067,
0x4702,0xda8c,0x3986,0x40b0,
0xa588,0xf44e,0x1215,0x40dd,
0xe6cf,0x6736,0x41c8,0x40f4,
0x63e7,0xdf6f,0x232f,0x40f3
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x405d,0xb345,0xb900,0x59a4,
0x40ae,0xd688,0x7b4d,0x1a18,
0x40e0,0xcbde,0x00c2,0x3cbd,
0x40fa,0x646d,0xff52,0xab95,
0x40fb,0x107f,0x2804,0xc1b4
};
static unsigned short Q[] = {
0x4067,0x44a6,0xf5b7,0x0853,
0x40b0,0x3986,0xda8c,0x4702,
0x40dd,0x1215,0xf44e,0xa588,
0x40f4,0x41c8,0x6736,0xe6cf,
0x40f3,0x232f,0xdf6f,0x63e7,
};
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double log ( double );
extern double sqrt ( double );
#else
double log(), sqrt(), polevl(), p1evl();
#endif
extern double LOGE2, INFINITY, NAN;
double acosh(x)
double x;
{
double a, z;
if( x < 1.0 )
{
mtherr( "acosh", DOMAIN );
return(NAN);
}
if( x > 1.0e8 )
{
#ifdef INFINITIES
if( x == INFINITY )
return( INFINITY );
#endif
return( log(x) + LOGE2 );
}
z = x - 1.0;
if( z < 0.5 )
{
a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
return( a );
}
a = sqrt( z*(x+1.0) );
return( log(x + a) );
}

324
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/* asin.c
*
* Inverse circular sine
*
*
*
* SYNOPSIS:
*
* double x, y, asin();
*
* y = asin( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose sine is x.
*
* A rational function of the form x + x**3 P(x**2)/Q(x**2)
* is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
* transformed by the identity
*
* asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -1, 1 40000 2.6e-17 7.1e-18
* IEEE -1, 1 10^6 1.9e-16 5.4e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* asin domain |x| > 1 NAN
*
*/
/* acos()
*
* Inverse circular cosine
*
*
*
* SYNOPSIS:
*
* double x, y, acos();
*
* y = acos( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between 0 and pi whose cosine
* is x.
*
* Analytically, acos(x) = pi/2 - asin(x). However if |x| is
* near 1, there is cancellation error in subtracting asin(x)
* from pi/2. Hence if x < -0.5,
*
* acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
*
* or if x > +0.5,
*
* acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -1, 1 50000 3.3e-17 8.2e-18
* IEEE -1, 1 10^6 2.2e-16 6.5e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* asin domain |x| > 1 NAN
*/
/* asin.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
/* arcsin(x) = x + x^3 P(x^2)/Q(x^2)
0 <= x <= 0.625
Peak relative error = 1.2e-18 */
#if UNK
const static double P[6] = {
4.253011369004428248960E-3,
-6.019598008014123785661E-1,
5.444622390564711410273E0,
-1.626247967210700244449E1,
1.956261983317594739197E1,
-8.198089802484824371615E0,
};
const static double Q[5] = {
/* 1.000000000000000000000E0, */
-1.474091372988853791896E1,
7.049610280856842141659E1,
-1.471791292232726029859E2,
1.395105614657485689735E2,
-4.918853881490881290097E1,
};
#endif
#if DEC
static short P[24] = {
0036213,0056330,0057244,0053234,
0140032,0015011,0114762,0160255,
0040656,0035130,0136121,0067313,
0141202,0014616,0170474,0101731,
0041234,0100076,0151674,0111310,
0141003,0025540,0033165,0077246,
};
static short Q[20] = {
/* 0040200,0000000,0000000,0000000, */
0141153,0155310,0055360,0072530,
0041614,0177001,0027764,0101237,
0142023,0026733,0064653,0133266,
0042013,0101264,0023775,0176351,
0141504,0140420,0050660,0036543,
};
#endif
#if IBMPC
static short P[24] = {
0x8ad3,0x0bd4,0x6b9b,0x3f71,
0x5c16,0x333e,0x4341,0xbfe3,
0x2dd9,0x178a,0xc74b,0x4015,
0x907b,0xde27,0x4331,0xc030,
0x9259,0xda77,0x9007,0x4033,
0xafd5,0x06ce,0x656c,0xc020,
};
static short Q[20] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x0eab,0x0b5e,0x7b59,0xc02d,
0x9054,0x25fe,0x9fc0,0x4051,
0x76d7,0x6d35,0x65bb,0xc062,
0xbf9d,0x84ff,0x7056,0x4061,
0x07ac,0x0a36,0x9822,0xc048,
};
#endif
#if MIEEE
static short P[24] = {
0x3f71,0x6b9b,0x0bd4,0x8ad3,
0xbfe3,0x4341,0x333e,0x5c16,
0x4015,0xc74b,0x178a,0x2dd9,
0xc030,0x4331,0xde27,0x907b,
0x4033,0x9007,0xda77,0x9259,
0xc020,0x656c,0x06ce,0xafd5,
};
static short Q[20] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc02d,0x7b59,0x0b5e,0x0eab,
0x4051,0x9fc0,0x25fe,0x9054,
0xc062,0x65bb,0x6d35,0x76d7,
0x4061,0x7056,0x84ff,0xbf9d,
0xc048,0x9822,0x0a36,0x07ac,
};
#endif
/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
0 <= x <= 0.5
Peak relative error = 4.2e-18 */
#if UNK
const static double R[5] = {
2.967721961301243206100E-3,
-5.634242780008963776856E-1,
6.968710824104713396794E0,
-2.556901049652824852289E1,
2.853665548261061424989E1,
};
const static double S[4] = {
/* 1.000000000000000000000E0, */
-2.194779531642920639778E1,
1.470656354026814941758E2,
-3.838770957603691357202E2,
3.424398657913078477438E2,
};
#endif
#if DEC
static short R[20] = {
0036102,0077034,0142164,0174103,
0140020,0036222,0147711,0044173,
0040736,0177655,0153631,0171523,
0141314,0106525,0060015,0055474,
0041344,0045422,0003630,0040344,
};
static short S[16] = {
/* 0040200,0000000,0000000,0000000, */
0141257,0112425,0132772,0166136,
0042023,0010315,0075523,0175020,
0142277,0170104,0126203,0017563,
0042253,0034115,0102662,0022757,
};
#endif
#if IBMPC
static short R[20] = {
0x9f08,0x988e,0x4fc3,0x3f68,
0x290f,0x59f9,0x0792,0xbfe2,
0x3e6a,0xbaf3,0xdff5,0x401b,
0xab68,0xac01,0x91aa,0xc039,
0x081d,0x40f3,0x8962,0x403c,
};
static short S[16] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x5d8c,0xb6bf,0xf2a2,0xc035,
0x7f42,0xaf6a,0x6219,0x4062,
0x63ee,0x9590,0xfe08,0xc077,
0x44be,0xb0b6,0x6709,0x4075,
};
#endif
#if MIEEE
static short R[20] = {
0x3f68,0x4fc3,0x988e,0x9f08,
0xbfe2,0x0792,0x59f9,0x290f,
0x401b,0xdff5,0xbaf3,0x3e6a,
0xc039,0x91aa,0xac01,0xab68,
0x403c,0x8962,0x40f3,0x081d,
};
static short S[16] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc035,0xf2a2,0xb6bf,0x5d8c,
0x4062,0x6219,0xaf6a,0x7f42,
0xc077,0xfe08,0x9590,0x63ee,
0x4075,0x6709,0xb0b6,0x44be,
};
#endif
/* pi/2 = PIO2 + MOREBITS. */
#ifdef DEC
#define MOREBITS 5.721188726109831840122E-18
#else
#define MOREBITS 6.123233995736765886130E-17
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double sqrt ( double );
double asin ( double );
#else
double sqrt(), polevl(), p1evl();
double asin();
#endif
extern double PIO2, PIO4, NAN;
double asin(x)
double x;
{
double a, p, z, zz;
short sign;
if( x > 0 )
{
sign = 1;
a = x;
}
else
{
sign = -1;
a = -x;
}
if( a > 1.0 )
{
mtherr( "asin", DOMAIN );
return( NAN );
}
if( a > 0.625 )
{
/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x)) */
zz = 1.0 - a;
p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
zz = sqrt(zz+zz);
z = PIO4 - zz;
zz = zz * p - MOREBITS;
z = z - zz;
z = z + PIO4;
}
else
{
if( a < 1.0e-8 )
{
return(x);
}
zz = a * a;
z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
z = a * z + a;
}
if( sign < 0 )
z = -z;
return(z);
}
double acos(x)
double x;
{
double z;
if( (x < -1.0) || (x > 1.0) )
{
mtherr( "acos", DOMAIN );
return( NAN );
}
if( x > 0.5 )
{
return( 2.0 * asin( sqrt(0.5 - 0.5*x) ) );
}
z = PIO4 - asin(x);
z = z + MOREBITS;
z = z + PIO4;
return( z );
}

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/* asinh.c
*
* Inverse hyperbolic sine
*
*
*
* SYNOPSIS:
*
* double x, y, asinh();
*
* y = asinh( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic sine of argument.
*
* If |x| < 0.5, the function is approximated by a rational
* form x + x**3 P(x)/Q(x). Otherwise,
*
* asinh(x) = log( x + sqrt(1 + x*x) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -3,3 75000 4.6e-17 1.1e-17
* IEEE -1,1 30000 3.7e-16 7.8e-17
* IEEE 1,3 30000 2.5e-16 6.7e-17
*
*/
/* asinh.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-4.33231683752342103572E-3,
-5.91750212056387121207E-1,
-4.37390226194356683570E0,
-9.09030533308377316566E0,
-5.56682227230859640450E0
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
1.28757002067426453537E1,
4.86042483805291788324E1,
6.95722521337257608734E1,
3.34009336338516356383E1
};
#endif
#ifdef DEC
static unsigned short P[] = {
0136215,0173033,0110410,0105475,
0140027,0076361,0020056,0164520,
0140613,0173401,0160136,0053142,
0141021,0070744,0000503,0176261,
0140662,0021550,0073106,0133351
};
static unsigned short Q[] = {
/* 0040200,0000000,0000000,0000000,*/
0041116,0001336,0034120,0173054,
0041502,0065300,0013144,0021231,
0041613,0022376,0035516,0153063,
0041405,0115216,0054265,0004557
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x1168,0x7221,0xbec3,0xbf71,
0xdd2a,0x2405,0xef9e,0xbfe2,
0xcacc,0x3c0b,0x7ee0,0xc011,
0x7f96,0x8028,0x2e3c,0xc022,
0xd6dd,0x0ec8,0x446d,0xc016
};
static unsigned short Q[] = {
/* 0x0000,0x0000,0x0000,0x3ff0,*/
0x1ec5,0xc70a,0xc05b,0x4029,
0x8453,0x02cc,0x4d58,0x4048,
0xdac6,0xc769,0x649f,0x4051,
0xa12e,0xcb16,0xb351,0x4040
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xbf71,0xbec3,0x7221,0x1168,
0xbfe2,0xef9e,0x2405,0xdd2a,
0xc011,0x7ee0,0x3c0b,0xcacc,
0xc022,0x2e3c,0x8028,0x7f96,
0xc016,0x446d,0x0ec8,0xd6dd
};
static unsigned short Q[] = {
0x4029,0xc05b,0xc70a,0x1ec5,
0x4048,0x4d58,0x02cc,0x8453,
0x4051,0x649f,0xc769,0xdac6,
0x4040,0xb351,0xcb16,0xa12e
};
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double sqrt ( double );
extern double log ( double );
#else
double log(), sqrt(), polevl(), p1evl();
#endif
extern double LOGE2, INFINITY;
double asinh(xx)
double xx;
{
double a, z, x;
int sign;
#ifdef MINUSZERO
if( xx == 0.0 )
return(xx);
#endif
if( xx < 0.0 )
{
sign = -1;
x = -xx;
}
else
{
sign = 1;
x = xx;
}
if( x > 1.0e8 )
{
#ifdef INFINITIES
if( x == INFINITY )
return(xx);
#endif
return( sign * (log(x) + LOGE2) );
}
z = x * x;
if( x < 0.5 )
{
a = ( polevl(z, P, 4)/p1evl(z, Q, 4) ) * z;
a = a * x + x;
if( sign < 0 )
a = -a;
return(a);
}
a = sqrt( z + 1.0 );
return( sign * log(x + a) );
}

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/* atan.c
*
* Inverse circular tangent
* (arctangent)
*
*
*
* SYNOPSIS:
*
* double x, y, atan();
*
* y = atan( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose tangent
* is x.
*
* Range reduction is from three intervals into the interval
* from zero to 0.66. The approximant uses a rational
* function of degree 4/5 of the form x + x**3 P(x)/Q(x).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10, 10 50000 2.4e-17 8.3e-18
* IEEE -10, 10 10^6 1.8e-16 5.0e-17
*
*/
/* atan2()
*
* Quadrant correct inverse circular tangent
*
*
*
* SYNOPSIS:
*
* double x, y, z, atan2();
*
* z = atan2( y, x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle whose tangent is y/x.
* Define compile time symbol ANSIC = 1 for ANSI standard,
* range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
* 0 to 2PI, args (x,y).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10, 10 10^6 2.5e-16 6.9e-17
* See atan.c.
*
*/
/* atan.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
/* arctan(x) = x + x^3 P(x^2)/Q(x^2)
0 <= x <= 0.66
Peak relative error = 2.6e-18 */
#ifdef UNK
const static double P[5] = {
-8.750608600031904122785E-1,
-1.615753718733365076637E1,
-7.500855792314704667340E1,
-1.228866684490136173410E2,
-6.485021904942025371773E1,
};
const static double Q[5] = {
/* 1.000000000000000000000E0, */
2.485846490142306297962E1,
1.650270098316988542046E2,
4.328810604912902668951E2,
4.853903996359136964868E2,
1.945506571482613964425E2,
};
/* tan( 3*pi/8 ) */
const static double T3P8 = 2.41421356237309504880;
#endif
#ifdef DEC
static short P[20] = {
0140140,0001775,0007671,0026242,
0141201,0041242,0155534,0001715,
0141626,0002141,0132100,0011625,
0141765,0142771,0064055,0150453,
0141601,0131517,0164507,0062164,
};
static short Q[20] = {
/* 0040200,0000000,0000000,0000000, */
0041306,0157042,0154243,0000742,
0042045,0003352,0016707,0150452,
0042330,0070306,0113425,0170730,
0042362,0130770,0116602,0047520,
0042102,0106367,0156753,0013541,
};
/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
#define T3P8 *(double *)T3P8A
#endif
#ifdef IBMPC
static short P[20] = {
0x2594,0xa1f7,0x007f,0xbfec,
0x807a,0x5b6b,0x2854,0xc030,
0x0273,0x3688,0xc08c,0xc052,
0xba25,0x2d05,0xb8bf,0xc05e,
0xec8e,0xfd28,0x3669,0xc050,
};
static short Q[20] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x603c,0x5b14,0xdbc4,0x4038,
0xfa25,0x43b8,0xa0dd,0x4064,
0xbe3b,0xd2e2,0x0e18,0x407b,
0x49ea,0x13b0,0x563f,0x407e,
0x62ec,0xfbbd,0x519e,0x4068,
};
/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
#define T3P8 *(double *)T3P8A
#endif
#ifdef MIEEE
static short P[20] = {
0xbfec,0x007f,0xa1f7,0x2594,
0xc030,0x2854,0x5b6b,0x807a,
0xc052,0xc08c,0x3688,0x0273,
0xc05e,0xb8bf,0x2d05,0xba25,
0xc050,0x3669,0xfd28,0xec8e,
};
static short Q[20] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0x4038,0xdbc4,0x5b14,0x603c,
0x4064,0xa0dd,0x43b8,0xfa25,
0x407b,0x0e18,0xd2e2,0xbe3b,
0x407e,0x563f,0x13b0,0x49ea,
0x4068,0x519e,0xfbbd,0x62ec,
};
/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {
0x4003,0x504f,0x333f,0x9de6
};
#define T3P8 *(double *)T3P8A
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double atan ( double );
extern double fabs ( double );
extern int signbit ( double );
extern int isnan ( double );
#else
double polevl(), p1evl(), atan(), fabs();
int signbit(), isnan();
#endif
extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;
/* pi/2 = PIO2 + MOREBITS. */
#ifdef DEC
#define MOREBITS 5.721188726109831840122E-18
#else
#define MOREBITS 6.123233995736765886130E-17
#endif
double atan(x)
double x;
{
double y, z;
short sign, flag;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
#ifdef INFINITIES
if(x == INFINITY)
return(PIO2);
if(x == -INFINITY)
return(-PIO2);
#endif
/* make argument positive and save the sign */
sign = 1;
if( x < 0.0 )
{
sign = -1;
x = -x;
}
/* range reduction */
flag = 0;
if( x > T3P8 )
{
y = PIO2;
flag = 1;
x = -( 1.0/x );
}
else if( x <= 0.66 )
{
y = 0.0;
}
else
{
y = PIO4;
flag = 2;
x = (x-1.0)/(x+1.0);
}
z = x * x;
z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
z = x * z + x;
if( flag == 2 )
z += 0.5 * MOREBITS;
else if( flag == 1 )
z += MOREBITS;
y = y + z;
if( sign < 0 )
y = -y;
return(y);
}
/* atan2 */
#ifdef ANSIC
double atan2( y, x )
#else
double atan2( x, y )
#endif
double x, y;
{
double z, w;
short code;
code = 0;
#ifdef NANS
if( isnan(x) )
return(x);
if( isnan(y) )
return(y);
#endif
#ifdef MINUSZERO
if( y == 0.0 )
{
if( signbit(y) )
{
if( x > 0.0 )
z = y;
else if( x < 0.0 )
z = -PI;
else
{
if( signbit(x) )
z = -PI;
else
z = y;
}
}
else /* y is +0 */
{
if( x == 0.0 )
{
if( signbit(x) )
z = PI;
else
z = 0.0;
}
else if( x > 0.0 )
z = 0.0;
else
z = PI;
}
return z;
}
if( x == 0.0 )
{
if( y > 0.0 )
z = PIO2;
else
z = -PIO2;
return z;
}
#endif /* MINUSZERO */
#ifdef INFINITIES
if( x == INFINITY )
{
if( y == INFINITY )
z = 0.25 * PI;
else if( y == -INFINITY )
z = -0.25 * PI;
else if( y < 0.0 )
z = NEGZERO;
else
z = 0.0;
return z;
}
if( x == -INFINITY )
{
if( y == INFINITY )
z = 0.75 * PI;
else if( y <= -INFINITY )
z = -0.75 * PI;
else if( y >= 0.0 )
z = PI;
else
z = -PI;
return z;
}
if( y == INFINITY )
return( PIO2 );
if( y == -INFINITY )
return( -PIO2 );
#endif
if( x < 0.0 )
code = 2;
if( y < 0.0 )
code |= 1;
#ifdef INFINITIES
if( x == 0.0 )
#else
if( fabs(x) <= (fabs(y) / MAXNUM) )
#endif
{
if( code & 1 )
{
#if ANSIC
return( -PIO2 );
#else
return( 3.0*PIO2 );
#endif
}
if( y == 0.0 )
return( 0.0 );
return( PIO2 );
}
if( y == 0.0 )
{
if( code & 2 )
return( PI );
return( 0.0 );
}
switch( code )
{
#if ANSIC
default:
case 0:
case 1: w = 0.0; break;
case 2: w = PI; break;
case 3: w = -PI; break;
#else
default:
case 0: w = 0.0; break;
case 1: w = 2.0 * PI; break;
case 2:
case 3: w = PI; break;
#endif
}
z = w + atan( y/x );
#ifdef MINUSZERO
if( z == 0.0 && y < 0 )
z = NEGZERO;
#endif
return( z );
}

156
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/* atanh.c
*
* Inverse hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* double x, y, atanh();
*
* y = atanh( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic tangent of argument in the range
* MINLOG to MAXLOG.
*
* If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
* employed. Otherwise,
* atanh(x) = 0.5 * log( (1+x)/(1-x) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -1,1 50000 2.4e-17 6.4e-18
* IEEE -1,1 30000 1.9e-16 5.2e-17
*
*/
/* atanh.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-8.54074331929669305196E-1,
1.20426861384072379242E1,
-4.61252884198732692637E1,
6.54566728676544377376E1,
-3.09092539379866942570E1
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
-1.95638849376911654834E1,
1.08938092147140262656E2,
-2.49839401325893582852E2,
2.52006675691344555838E2,
-9.27277618139601130017E1
};
#endif
#ifdef DEC
static unsigned short P[] = {
0140132,0122235,0105775,0130300,
0041100,0127327,0124407,0034722,
0141470,0100113,0115607,0130535,
0041602,0164721,0003257,0013673,
0141367,0043046,0166673,0045750
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0141234,0101326,0015460,0134564,
0041731,0160115,0116451,0032045,
0142171,0153343,0000532,0167226,
0042174,0000665,0077604,0000310,
0141671,0072235,0031114,0074377
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0xb618,0xb17f,0x5493,0xbfeb,
0xe73a,0xf520,0x15da,0x4028,
0xf62c,0x7370,0x1009,0xc047,
0xe2f7,0x20d5,0x5d3a,0x4050,
0x697d,0xddb7,0xe8c4,0xc03e
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x172f,0xc366,0x905a,0xc033,
0x2685,0xb3a5,0x3c09,0x405b,
0x5dd3,0x602b,0x3adc,0xc06f,
0x8019,0xaff0,0x8036,0x406f,
0x8f20,0xa649,0x2e93,0xc057
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xbfeb,0x5493,0xb17f,0xb618,
0x4028,0x15da,0xf520,0xe73a,
0xc047,0x1009,0x7370,0xf62c,
0x4050,0x5d3a,0x20d5,0xe2f7,
0xc03e,0xe8c4,0xddb7,0x697d
};
static unsigned short Q[] = {
0xc033,0x905a,0xc366,0x172f,
0x405b,0x3c09,0xb3a5,0x2685,
0xc06f,0x3adc,0x602b,0x5dd3,
0x406f,0x8036,0xaff0,0x8019,
0xc057,0x2e93,0xa649,0x8f20
};
#endif
#ifdef ANSIPROT
extern double fabs ( double );
extern double log ( double x );
extern double polevl ( double x, void *P, int N );
extern double p1evl ( double x, void *P, int N );
#else
double fabs(), log(), polevl(), p1evl();
#endif
extern double INFINITY, NAN;
double atanh(x)
double x;
{
double s, z;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
z = fabs(x);
if( z >= 1.0 )
{
if( x == 1.0 )
return( INFINITY );
if( x == -1.0 )
return( -INFINITY );
mtherr( "atanh", DOMAIN );
return( NAN );
}
if( z < 1.0e-7 )
return(x);
if( z < 0.5 )
{
z = x * x;
s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
return(s);
}
return( 0.5 * log((1.0+x)/(1.0-x)) );
}

142
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/* cbrt.c
*
* Cube root
*
*
*
* SYNOPSIS:
*
* double x, y, cbrt();
*
* y = cbrt( x );
*
*
*
* DESCRIPTION:
*
* Returns the cube root of the argument, which may be negative.
*
* Range reduction involves determining the power of 2 of
* the argument. A polynomial of degree 2 applied to the
* mantissa, and multiplication by the cube root of 1, 2, or 4
* approximates the root to within about 0.1%. Then Newton's
* iteration is used three times to converge to an accurate
* result.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,10 200000 1.8e-17 6.2e-18
* IEEE 0,1e308 30000 1.5e-16 5.0e-17
*
*/
/* cbrt.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1991, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
const static double CBRT2 = 1.2599210498948731647672;
const static double CBRT4 = 1.5874010519681994747517;
const static double CBRT2I = 0.79370052598409973737585;
const static double CBRT4I = 0.62996052494743658238361;
#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double frexp(), ldexp();
int isnan(), isfinite();
#endif
double cbrt(x)
double x;
{
int e, rem, sign;
double z;
#ifdef NANS
if( isnan(x) )
return x;
#endif
#ifdef INFINITIES
if( !isfinite(x) )
return x;
#endif
if( x == 0 )
return( x );
if( x > 0 )
sign = 1;
else
{
sign = -1;
x = -x;
}
z = x;
/* extract power of 2, leaving
* mantissa between 0.5 and 1
*/
x = frexp( x, &e );
/* Approximate cube root of number between .5 and 1,
* peak relative error = 9.2e-6
*/
x = (((-1.3466110473359520655053e-1 * x
+ 5.4664601366395524503440e-1) * x
- 9.5438224771509446525043e-1) * x
+ 1.1399983354717293273738e0 ) * x
+ 4.0238979564544752126924e-1;
/* exponent divided by 3 */
if( e >= 0 )
{
rem = e;
e /= 3;
rem -= 3*e;
if( rem == 1 )
x *= CBRT2;
else if( rem == 2 )
x *= CBRT4;
}
/* argument less than 1 */
else
{
e = -e;
rem = e;
e /= 3;
rem -= 3*e;
if( rem == 1 )
x *= CBRT2I;
else if( rem == 2 )
x *= CBRT4I;
e = -e;
}
/* multiply by power of 2 */
x = ldexp( x, e );
/* Newton iteration */
x -= ( x - (z/(x*x)) )*0.33333333333333333333;
#ifdef DEC
x -= ( x - (z/(x*x)) )/3.0;
#else
x -= ( x - (z/(x*x)) )*0.33333333333333333333;
#endif
if( sign < 0 )
x = -x;
return(x);
}

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/* chbevl.c
*
* Evaluate Chebyshev series
*
*
*
* SYNOPSIS:
*
* int N;
* double x, y, coef[N], chebevl();
*
* y = chbevl( x, coef, N );
*
*
*
* DESCRIPTION:
*
* Evaluates the series
*
* N-1
* - '
* y = > coef[i] T (x/2)
* - i
* i=0
*
* of Chebyshev polynomials Ti at argument x/2.
*
* Coefficients are stored in reverse order, i.e. the zero
* order term is last in the array. Note N is the number of
* coefficients, not the order.
*
* If coefficients are for the interval a to b, x must
* have been transformed to x -> 2(2x - b - a)/(b-a) before
* entering the routine. This maps x from (a, b) to (-1, 1),
* over which the Chebyshev polynomials are defined.
*
* If the coefficients are for the inverted interval, in
* which (a, b) is mapped to (1/b, 1/a), the transformation
* required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
* this becomes x -> 4a/x - 1.
*
*
*
* SPEED:
*
* Taking advantage of the recurrence properties of the
* Chebyshev polynomials, the routine requires one more
* addition per loop than evaluating a nested polynomial of
* the same degree.
*
*/
/* chbevl.c */
/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1985, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
double chbevl( x, array, n )
double x;
double array[];
int n;
{
double b0, b1, b2, *p;
int i;
p = array;
b0 = *p++;
b1 = 0.0;
i = n - 1;
do
{
b2 = b1;
b1 = b0;
b0 = x * b1 - b2 + *p++;
}
while( --i );
return( 0.5*(b0-b2) );
}

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/* cmplx.c
*
* Complex number arithmetic
*
*
*
* SYNOPSIS:
*
* typedef struct {
* double r; real part
* double i; imaginary part
* }cmplx;
*
* cmplx *a, *b, *c;
*
* cadd( a, b, c ); c = b + a
* csub( a, b, c ); c = b - a
* cmul( a, b, c ); c = b * a
* cdiv( a, b, c ); c = b / a
* cneg( c ); c = -c
* cmov( b, c ); c = b
*
*
*
* DESCRIPTION:
*
* Addition:
* c.r = b.r + a.r
* c.i = b.i + a.i
*
* Subtraction:
* c.r = b.r - a.r
* c.i = b.i - a.i
*
* Multiplication:
* c.r = b.r * a.r - b.i * a.i
* c.i = b.r * a.i + b.i * a.r
*
* Division:
* d = a.r * a.r + a.i * a.i
* c.r = (b.r * a.r + b.i * a.i)/d
* c.i = (b.i * a.r - b.r * a.i)/d
* ACCURACY:
*
* In DEC arithmetic, the test (1/z) * z = 1 had peak relative
* error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
* peak relative error 8.3e-17, rms 2.1e-17.
*
* Tests in the rectangle {-10,+10}:
* Relative error:
* arithmetic function # trials peak rms
* DEC cadd 10000 1.4e-17 3.4e-18
* IEEE cadd 100000 1.1e-16 2.7e-17
* DEC csub 10000 1.4e-17 4.5e-18
* IEEE csub 100000 1.1e-16 3.4e-17
* DEC cmul 3000 2.3e-17 8.7e-18
* IEEE cmul 100000 2.1e-16 6.9e-17
* DEC cdiv 18000 4.9e-17 1.3e-17
* IEEE cdiv 100000 3.7e-16 1.1e-16
*/
/* cmplx.c
* complex number arithmetic
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double fabs ( double );
extern double cabs ( cmplx * );
extern double sqrt ( double );
extern double atan2 ( double, double );
extern double cos ( double );
extern double sin ( double );
extern double sqrt ( double );
extern double frexp ( double, int * );
extern double ldexp ( double, int );
int isnan ( double );
void cdiv ( cmplx *, cmplx *, cmplx * );
void cadd ( cmplx *, cmplx *, cmplx * );
#else
double fabs(), cabs(), sqrt(), atan2(), cos(), sin();
double sqrt(), frexp(), ldexp();
int isnan();
void cdiv(), cadd();
#endif
extern double MAXNUM, MACHEP, PI, PIO2, INFINITY, NAN;
/*
typedef struct
{
double r;
double i;
}cmplx;
*/
cmplx czero = {0.0, 0.0};
extern cmplx czero;
cmplx cone = {1.0, 0.0};
extern cmplx cone;
/* c = b + a */
void cadd( a, b, c )
register cmplx *a, *b;
cmplx *c;
{
c->r = b->r + a->r;
c->i = b->i + a->i;
}
/* c = b - a */
void csub( a, b, c )
register cmplx *a, *b;
cmplx *c;
{
c->r = b->r - a->r;
c->i = b->i - a->i;
}
/* c = b * a */
void cmul( a, b, c )
register cmplx *a, *b;
cmplx *c;
{
double y;
y = b->r * a->r - b->i * a->i;
c->i = b->r * a->i + b->i * a->r;
c->r = y;
}
/* c = b / a */
void cdiv( a, b, c )
register cmplx *a, *b;
cmplx *c;
{
double y, p, q, w;
y = a->r * a->r + a->i * a->i;
p = b->r * a->r + b->i * a->i;
q = b->i * a->r - b->r * a->i;
if( y < 1.0 )
{
w = MAXNUM * y;
if( (fabs(p) > w) || (fabs(q) > w) || (y == 0.0) )
{
c->r = MAXNUM;
c->i = MAXNUM;
mtherr( "cdiv", OVERFLOW );
return;
}
}
c->r = p/y;
c->i = q/y;
}
/* b = a
Caution, a `short' is assumed to be 16 bits wide. */
void cmov( a, b )
void *a, *b;
{
register short *pa, *pb;
int i;
pa = (short *) a;
pb = (short *) b;
i = 8;
do
*pb++ = *pa++;
while( --i );
}
void cneg( a )
register cmplx *a;
{
a->r = -a->r;
a->i = -a->i;
}
/* cabs()
*
* Complex absolute value
*
*
*
* SYNOPSIS:
*
* double cabs();
* cmplx z;
* double a;
*
* a = cabs( &z );
*
*
*
* DESCRIPTION:
*
*
* If z = x + iy
*
* then
*
* a = sqrt( x**2 + y**2 ).
*
* Overflow and underflow are avoided by testing the magnitudes
* of x and y before squaring. If either is outside half of
* the floating point full scale range, both are rescaled.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -30,+30 30000 3.2e-17 9.2e-18
* IEEE -10,+10 100000 2.7e-16 6.9e-17
*/
/*
Cephes Math Library Release 2.1: January, 1989
Copyright 1984, 1987, 1989 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/*
typedef struct
{
double r;
double i;
}cmplx;
*/
#ifdef UNK
#define PREC 27
#define MAXEXP 1024
#define MINEXP -1077
#endif
#ifdef DEC
#define PREC 29
#define MAXEXP 128
#define MINEXP -128
#endif
#ifdef IBMPC
#define PREC 27
#define MAXEXP 1024
#define MINEXP -1077
#endif
#ifdef MIEEE
#define PREC 27
#define MAXEXP 1024
#define MINEXP -1077
#endif
double cabs( z )
register cmplx *z;
{
double x, y, b, re, im;
int ex, ey, e;
#ifdef INFINITIES
/* Note, cabs(INFINITY,NAN) = INFINITY. */
if( z->r == INFINITY || z->i == INFINITY
|| z->r == -INFINITY || z->i == -INFINITY )
return( INFINITY );
#endif
#ifdef NANS
if( isnan(z->r) )
return(z->r);
if( isnan(z->i) )
return(z->i);
#endif
re = fabs( z->r );
im = fabs( z->i );
if( re == 0.0 )
return( im );
if( im == 0.0 )
return( re );
/* Get the exponents of the numbers */
x = frexp( re, &ex );
y = frexp( im, &ey );
/* Check if one number is tiny compared to the other */
e = ex - ey;
if( e > PREC )
return( re );
if( e < -PREC )
return( im );
/* Find approximate exponent e of the geometric mean. */
e = (ex + ey) >> 1;
/* Rescale so mean is about 1 */
x = ldexp( re, -e );
y = ldexp( im, -e );
/* Hypotenuse of the right triangle */
b = sqrt( x * x + y * y );
/* Compute the exponent of the answer. */
y = frexp( b, &ey );
ey = e + ey;
/* Check it for overflow and underflow. */
if( ey > MAXEXP )
{
mtherr( "cabs", OVERFLOW );
return( INFINITY );
}
if( ey < MINEXP )
return(0.0);
/* Undo the scaling */
b = ldexp( b, e );
return( b );
}
/* csqrt()
*
* Complex square root
*
*
*
* SYNOPSIS:
*
* void csqrt();
* cmplx z, w;
*
* csqrt( &z, &w );
*
*
*
* DESCRIPTION:
*
*
* If z = x + iy, r = |z|, then
*
* 1/2
* Im w = [ (r - x)/2 ] ,
*
* Re w = y / 2 Im w.
*
*
* Note that -w is also a square root of z. The root chosen
* is always in the upper half plane.
*
* Because of the potential for cancellation error in r - x,
* the result is sharpened by doing a Heron iteration
* (see sqrt.c) in complex arithmetic.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 25000 3.2e-17 9.6e-18
* IEEE -10,+10 100000 3.2e-16 7.7e-17
*
* 2
* Also tested by csqrt( z ) = z, and tested by arguments
* close to the real axis.
*/
void csqrt( z, w )
cmplx *z, *w;
{
cmplx q, s;
double x, y, r, t;
x = z->r;
y = z->i;
if( y == 0.0 )
{
if( x < 0.0 )
{
w->r = 0.0;
w->i = sqrt(-x);
return;
}
else
{
w->r = sqrt(x);
w->i = 0.0;
return;
}
}
if( x == 0.0 )
{
r = fabs(y);
r = sqrt(0.5*r);
if( y > 0 )
w->r = r;
else
w->r = -r;
w->i = r;
return;
}
/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
* The relative error in the first term is approximately y^2/12x^2 .
*/
if( (fabs(y) < 2.e-4 * fabs(x))
&& (x > 0) )
{
t = 0.25*y*(y/x);
}
else
{
r = cabs(z);
t = 0.5*(r - x);
}
r = sqrt(t);
q.i = r;
q.r = y/(2.0*r);
/* Heron iteration in complex arithmetic */
cdiv( &q, z, &s );
cadd( &q, &s, w );
w->r *= 0.5;
w->i *= 0.5;
}
double hypot( x, y )
double x, y;
{
cmplx z;
z.r = x;
z.i = y;
return( cabs(&z) );
}

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/* const.c
*
* Globally declared constants
*
*
*
* SYNOPSIS:
*
* extern const double nameofconstant;
*
*
*
*
* DESCRIPTION:
*
* This file contains a number of mathematical constants and
* also some needed size parameters of the computer arithmetic.
* The values are supplied as arrays of hexadecimal integers
* for IEEE arithmetic; arrays of octal constants for DEC
* arithmetic; and in a normal decimal scientific notation for
* other machines. The particular notation used is determined
* by a symbol (DEC, IBMPC, or UNK) defined in the include file
* mconf.h.
*
* The default size parameters are as follows.
*
* For DEC and UNK modes:
* MACHEP = 1.38777878078144567553E-17 2**-56
* MAXLOG = 8.8029691931113054295988E1 log(2**127)
* MINLOG = -8.872283911167299960540E1 log(2**-128)
* MAXNUM = 1.701411834604692317316873e38 2**127
*
* For IEEE arithmetic (IBMPC):
* MACHEP = 1.11022302462515654042E-16 2**-53
* MAXLOG = 7.09782712893383996843E2 log(2**1024)
* MINLOG = -7.08396418532264106224E2 log(2**-1022)
* MAXNUM = 1.7976931348623158E308 2**1024
*
* The global symbols for mathematical constants are
* PI = 3.14159265358979323846 pi
* PIO2 = 1.57079632679489661923 pi/2
* PIO4 = 7.85398163397448309616E-1 pi/4
* SQRT2 = 1.41421356237309504880 sqrt(2)
* SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
* LOG2E = 1.4426950408889634073599 1/log(2)
* SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
* LOGE2 = 6.93147180559945309417E-1 log(2)
* LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
* THPIO4 = 2.35619449019234492885 3*pi/4
* TWOOPI = 6.36619772367581343075535E-1 2/pi
*
* These lists are subject to change.
*/
/* const.c */
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
#if 1
const double MACHEP = 1.11022302462515654042E-16; /* 2**-53 */
#else
const double MACHEP = 1.38777878078144567553E-17; /* 2**-56 */
#endif
const double UFLOWTHRESH = 2.22507385850720138309E-308; /* 2**-1022 */
#ifdef DENORMAL
const double MAXLOG = 7.09782712893383996732E2; /* log(MAXNUM) */
/* const double MINLOG = -7.44440071921381262314E2; */ /* log(2**-1074) */
const double MINLOG = -7.451332191019412076235E2; /* log(2**-1075) */
#else
const double MAXLOG = 7.08396418532264106224E2; /* log 2**1022 */
const double MINLOG = -7.08396418532264106224E2; /* log 2**-1022 */
#endif
const double MAXNUM = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
const double PI = 3.14159265358979323846; /* pi */
const double PIO2 = 1.57079632679489661923; /* pi/2 */
const double PIO4 = 7.85398163397448309616E-1; /* pi/4 */
const double SQRT2 = 1.41421356237309504880; /* sqrt(2) */
const double SQRTH = 7.07106781186547524401E-1; /* sqrt(2)/2 */
const double LOG2E = 1.4426950408889634073599; /* 1/log(2) */
const double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */
const double LOGE2 = 6.93147180559945309417E-1; /* log(2) */
const double LOGSQ2 = 3.46573590279972654709E-1; /* log(2)/2 */
const double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */
const double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */
#ifdef INFINITIES
const double INFINITY = 1.0/0.0; /* 99e999; */
#else
const double INFINITY = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
#endif
#ifdef NANS
const double NAN = 1.0/0.0 - 1.0/0.0;
#else
const double NAN = 0.0;
#endif
#ifdef MINUSZERO
const double NEGZERO = -0.0;
#else
const double NEGZERO = 0.0;
#endif
#endif
#ifdef IBMPC
/* 2**-53 = 1.11022302462515654042E-16 */
const unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
const unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
#ifdef DENORMAL
/* log(MAXNUM) = 7.09782712893383996732224E2 */
const unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
/* log(2**-1074) = - -7.44440071921381262314E2 */
/*const unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
const unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
#else
/* log(2**1022) = 7.08396418532264106224E2 */
const unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
/* log(2**-1022) = - 7.08396418532264106224E2 */
const unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
#endif
/* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
const unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
const unsigned short PI[4] = {0x2d18,0x5444,0x21fb,0x4009};
const unsigned short PIO2[4] = {0x2d18,0x5444,0x21fb,0x3ff9};
const unsigned short PIO4[4] = {0x2d18,0x5444,0x21fb,0x3fe9};
const unsigned short SQRT2[4] = {0x3bcd,0x667f,0xa09e,0x3ff6};
const unsigned short SQRTH[4] = {0x3bcd,0x667f,0xa09e,0x3fe6};
const unsigned short LOG2E[4] = {0x82fe,0x652b,0x1547,0x3ff7};
const unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
const unsigned short LOGE2[4] = {0x39ef,0xfefa,0x2e42,0x3fe6};
const unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
const unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
const unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
#ifdef INFINITIES
const unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
#else
const unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
#endif
#ifdef NANS
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
#else
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
#else
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#endif
#ifdef MIEEE
/* 2**-53 = 1.11022302462515654042E-16 */
const unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
const unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
#ifdef DENORMAL
/* log(2**1024) = 7.09782712893383996843E2 */
const unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
/* log(2**-1074) = - -7.44440071921381262314E2 */
/* const unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
const unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
#else
/* log(2**1022) = 7.08396418532264106224E2 */
const unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
/* log(2**-1022) = - 7.08396418532264106224E2 */
const unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
#endif
/* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
const unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
const unsigned short PI[4] = {0x4009,0x21fb,0x5444,0x2d18};
const unsigned short PIO2[4] = {0x3ff9,0x21fb,0x5444,0x2d18};
const unsigned short PIO4[4] = {0x3fe9,0x21fb,0x5444,0x2d18};
const unsigned short SQRT2[4] = {0x3ff6,0xa09e,0x667f,0x3bcd};
const unsigned short SQRTH[4] = {0x3fe6,0xa09e,0x667f,0x3bcd};
const unsigned short LOG2E[4] = {0x3ff7,0x1547,0x652b,0x82fe};
const unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
const unsigned short LOGE2[4] = {0x3fe6,0x2e42,0xfefa,0x39ef};
const unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
const unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
const unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
#ifdef INFINITIES
const unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
#else
const unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
#endif
#ifdef NANS
const unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
#else
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
#else
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#endif
#ifdef DEC
/* 2**-56 = 1.38777878078144567553E-17 */
const unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
const unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
/* log 2**127 = 88.029691931113054295988 */
const unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
/* log 2**-128 = -88.72283911167299960540 */
const unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
/* 2**127 = 1.701411834604692317316873e38 */
const unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
const unsigned short PI[4] = {040511,007732,0121041,064302,};
const unsigned short PIO2[4] = {040311,007732,0121041,064302,};
const unsigned short PIO4[4] = {040111,007732,0121041,064302,};
const unsigned short SQRT2[4] = {040265,002363,031771,0157145,};
const unsigned short SQRTH[4] = {040065,002363,031771,0157144,};
const unsigned short LOG2E[4] = {040270,0125073,024534,013761,};
const unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
const unsigned short LOGE2[4] = {040061,071027,0173721,0147572,};
const unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
const unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
const unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
/* Approximate infinity by MAXNUM. */
const unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
const unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
#else
const unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
#endif
#endif
#ifndef UNK
extern const unsigned short MACHEP[];
extern const unsigned short UFLOWTHRESH[];
extern const unsigned short MAXLOG[];
extern const unsigned short UNDLOG[];
extern const unsigned short MINLOG[];
extern const unsigned short MAXNUM[];
extern const unsigned short PI[];
extern const unsigned short PIO2[];
extern const unsigned short PIO4[];
extern const unsigned short SQRT2[];
extern const unsigned short SQRTH[];
extern const unsigned short LOG2E[];
extern const unsigned short SQ2OPI[];
extern const unsigned short LOGE2[];
extern const unsigned short LOGSQ2[];
extern const unsigned short THPIO4[];
extern const unsigned short TWOOPI[];
extern const unsigned short INFINITY[];
extern const unsigned short NAN[];
extern const unsigned short NEGZERO[];
#endif

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/* cosh.c
*
* Hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* double x, y, cosh();
*
* y = cosh( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic cosine of argument in the range MINLOG to
* MAXLOG.
*
* cosh(x) = ( exp(x) + exp(-x) )/2.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +- 88 50000 4.0e-17 7.7e-18
* IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* cosh overflow |x| > MAXLOG MAXNUM
*
*
*/
/* cosh.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1985, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double exp ( double );
extern int isnan ( double );
extern int isfinite ( double );
#else
double exp();
int isnan(), isfinite();
#endif
extern double MAXLOG, INFINITY, LOGE2;
double cosh(x)
double x;
{
double y;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
if( x < 0 )
x = -x;
if( x > (MAXLOG + LOGE2) )
{
mtherr( "cosh", OVERFLOW );
return( INFINITY );
}
if( x >= (MAXLOG - LOGE2) )
{
y = exp(0.5 * x);
y = (0.5 * y) * y;
return(y);
}
y = exp(x);
y = 0.5 * (y + 1.0 / y);
return( y );
}

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CFLAGS= /DEBUG/NOLIST
hfiles= mconf.h-
ofiles= acosh.obj-
asin.obj-
asinh.obj-
atan.obj-
atanh.obj-
cbrt.obj-
chbevl.obj-
const.obj-
cosh.obj-
drand.obj-
exp.obj-
exp10.obj-
fabs.obj-
floor.obj-
log.obj-
log10.obj-
polevl.obj-
pow.obj-
powi.obj-
round.obj-
sin.obj-
sinh.obj-
tan.obj-
tanh.obj-
unity.obj-
sqrt.obj-
floor.obj-
polevl.obj-
mtherr.obj
mtst.exe : $(ofiles)
LINK mtst/option
acosh.obj : acosh.c,$(HFILES)
CC $(CFLAGS) acosh
asin.obj : asin.c,$(HFILES)
CC $(CFLAGS) asin
asinh.obj : asinh.c,$(HFILES)
CC $(CFLAGS) asinh
atan.obj : atan.c,$(HFILES)
CC $(CFLAGS) atan
atan.obj : atan.c,$(HFILES)
CC $(CFLAGS) atan
atanh.obj : atanh.c,$(HFILES)
CC $(CFLAGS) atanh
cbrt.obj : cbrt.c,$(HFILES)
CC $(CFLAGS) cbrt
chbevl.obj : chbevl.c,$(HFILES)
CC $(CFLAGS) chbevl
const.obj : const.c,$(HFILES)
CC $(CFLAGS) const
cosh.obj : cosh.c,$(HFILES)
CC $(CFLAGS) cosh
drand.obj : drand.c,$(HFILES)
CC $(CFLAGS) drand
exp.obj : exp.c,$(HFILES)
CC $(CFLAGS) exp
exp10.obj : exp10.c,$(HFILES)
CC $(CFLAGS) exp10
fabs.obj : fabs.c,$(HFILES)
CC $(CFLAGS) fabs
floor.obj : floor.c,$(HFILES)
CC $(CFLAGS) floor
log.obj : log.c,$(HFILES)
CC $(CFLAGS) log
log10.obj : log10.c,$(HFILES)
CC $(CFLAGS) log10
polevl.obj : polevl.c,$(HFILES)
CC $(CFLAGS) polevl
pow.obj : pow.c,$(HFILES)
CC $(CFLAGS) pow
powi.obj : powi.c,$(HFILES)
CC $(CFLAGS) powi
round.obj : round.c,$(HFILES)
CC $(CFLAGS) round
sin.obj : sin.c,$(HFILES)
CC $(CFLAGS) sin
sinh.obj : sinh.c,$(HFILES)
CC $(CFLAGS) sinh
tan.obj : tan.c,$(HFILES)
CC $(CFLAGS) tan
tanh.obj : tanh.c,$(HFILES)
CC $(CFLAGS) tanh
unity.obj : unity.c,$(HFILES)
CC $(CFLAGS) unity
sqrt.obj : sqrt.c,$(HFILES)
CC $(CFLAGS) sqrt
mtherr.obj : mtherr.c,$(HFILES)
CC $(CFLAGS) mtherr

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/* drand.c
*
* Pseudorandom number generator
*
*
*
* SYNOPSIS:
*
* double y, drand();
*
* drand( &y );
*
*
*
* DESCRIPTION:
*
* Yields a random number 1.0 <= y < 2.0.
*
* The three-generator congruential algorithm by Brian
* Wichmann and David Hill (BYTE magazine, March, 1987,
* pp 127-8) is used. The period, given by them, is
* 6953607871644.
*
* Versions invoked by the different arithmetic compile
* time options DEC, IBMPC, and MIEEE, produce
* approximately the same sequences, differing only in the
* least significant bits of the numbers. The UNK option
* implements the algorithm as recommended in the BYTE
* article. It may be used on all computers. However,
* the low order bits of a double precision number may
* not be adequately random, and may vary due to arithmetic
* implementation details on different computers.
*
* The other compile options generate an additional random
* integer that overwrites the low order bits of the double
* precision number. This reduces the period by a factor of
* two but tends to overcome the problems mentioned.
*
*/
/* Three-generator random number algorithm
* of Brian Wichmann and David Hill
* BYTE magazine, March, 1987 pp 127-8
*
* The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
*/
#include "mconf.h"
#ifdef ANSIPROT
static int ranwh ( void );
#else
static int ranwh();
#endif
static int sx = 1;
static int sy = 10000;
static int sz = 3000;
static union {
double d;
unsigned short s[4];
} unkans;
/* This function implements the three
* congruential generators.
*/
static int ranwh()
{
int r, s;
/* sx = sx * 171 mod 30269 */
r = sx/177;
s = sx - 177 * r;
sx = 171 * s - 2 * r;
if( sx < 0 )
sx += 30269;
/* sy = sy * 172 mod 30307 */
r = sy/176;
s = sy - 176 * r;
sy = 172 * s - 35 * r;
if( sy < 0 )
sy += 30307;
/* sz = 170 * sz mod 30323 */
r = sz/178;
s = sz - 178 * r;
sz = 170 * s - 63 * r;
if( sz < 0 )
sz += 30323;
/* The results are in static sx, sy, sz. */
return 0;
}
/* drand.c
*
* Random double precision floating point number between 1 and 2.
*
* C callable:
* drand( &x );
*/
int drand( a )
double *a;
{
unsigned short r;
#ifdef DEC
unsigned short s, t;
#endif
/* This algorithm of Wichmann and Hill computes a floating point
* result:
*/
ranwh();
unkans.d = sx/30269.0 + sy/30307.0 + sz/30323.0;
r = unkans.d;
unkans.d -= r;
unkans.d += 1.0;
/* if UNK option, do nothing further.
* Otherwise, make a random 16 bit integer
* to overwrite the least significant word
* of unkans.
*/
#ifdef UNK
/* do nothing */
#else
ranwh();
r = sx * sy + sz;
#endif
#ifdef DEC
/* To make the numbers as similar as possible
* in all arithmetics, the random integer has
* to be inserted 3 bits higher up in a DEC number.
* An alternative would be put it 3 bits lower down
* in all the other number types.
*/
s = unkans.s[2];
t = s & 07; /* save these bits to put in at the bottom */
s &= 0177770;
s |= (r >> 13) & 07;
unkans.s[2] = s;
t |= r << 3;
unkans.s[3] = t;
#endif
#ifdef IBMPC
unkans.s[0] = r;
#endif
#ifdef MIEEE
unkans.s[3] = r;
#endif
*a = unkans.d;
return 0;
}

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/* Test vectors for math functions.
See C9X section F.9. */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1998, 2000 by Stephen L. Moshier
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int isfinite (double);
/* C9X spells lgam lgamma. */
#define GLIBC2 0
extern double PI;
const static double MPI, PIO2, MPIO2, PIO4, MPIO4, THPIO4, MTHPIO4;
#if 0
#define PI 3.141592653589793238463E0
#define PIO2 1.570796326794896619231E0
#define PIO4 7.853981633974483096157E-1
#define THPIO4 2.35619449019234492884698
#define SQRT2 1.414213562373095048802E0
#define SQRTH 7.071067811865475244008E-1
#define INF (1.0/0.0)
#define MINF (-1.0/0.0)
#endif
extern double MACHEP, SQRTH, SQRT2;
extern double NAN, INFINITY, NEGZERO;
const static double INF, MINF;
const static double ZERO, MZERO, HALF, MHALF, ONE, MONE, TWO, MTWO, THREE, MTHREE;
/* #define NAN (1.0/0.0 - 1.0/0.0) */
/* Functions of one variable. */
double log (double);
double exp ( double);
double atan (double);
double sin (double);
double cos (double);
double tan (double);
double acos (double);
double asin (double);
double acosh (double);
double asinh (double);
double atanh (double);
double sinh (double);
double cosh (double);
double tanh (double);
double exp2 (double);
double expm1 (double);
double log10 (double);
double log1p (double);
double log2 (double);
double fabs (double);
double erf (double);
double erfc (double);
double gamma (double);
double floor (double);
double ceil (double);
double cbrt (double);
#if GLIBC2
double lgamma (double);
#else
double lgam (double);
#endif
struct oneargument
{
char *name; /* Name of the function. */
double (*func) (double);
double *arg1;
double *answer;
int thresh; /* Error report threshold. */
};
struct oneargument test1[] =
{
{"atan", atan, &ONE, &PIO4, 0},
{"sin", sin, &PIO2, &ONE, 0},
#if 0
{"cos", cos, &PIO4, &SQRTH, 0},
{"sin", sin, 32767., 1.8750655394138942394239E-1, 0},
{"cos", cos, 32767., 9.8226335176928229845654E-1, 0},
{"tan", tan, 32767., 1.9089234430221485740826E-1, 0},
{"sin", sin, 8388607., 9.9234509376961249835628E-1, 0},
{"cos", cos, 8388607., -1.2349580912475928183718E-1, 0},
{"tan", tan, 8388607., -8.0354556223613614748329E0, 0},
/*
{"sin", sin, 2147483647., -7.2491655514455639054829E-1, 0},
{"cos", cos, 2147483647., -6.8883669187794383467976E-1, 0},
{"tan", tan, 2147483647., 1.0523779637351339136698E0, 0},
*/
{"cos", cos, &PIO2, 6.1232339957367574e-17, 1},
{"sin", sin, &PIO4, &SQRTH, 1},
#endif
{"acos", acos, &NAN, &NAN, 0},
{"acos", acos, &ONE, &ZERO, 0},
{"acos", acos, &TWO, &NAN, 0},
{"acos", acos, &MTWO, &NAN, 0},
{"asin", asin, &NAN, &NAN, 0},
{"asin", asin, &ZERO, &ZERO, 0},
{"asin", asin, &MZERO, &MZERO, 0},
{"asin", asin, &TWO, &NAN, 0},
{"asin", asin, &MTWO, &NAN, 0},
{"atan", atan, &NAN, &NAN, 0},
{"atan", atan, &ZERO, &ZERO, 0},
{"atan", atan, &MZERO, &MZERO, 0},
{"atan", atan, &INF, &PIO2, 0},
{"atan", atan, &MINF, &MPIO2, 0},
{"cos", cos, &NAN, &NAN, 0},
{"cos", cos, &ZERO, &ONE, 0},
{"cos", cos, &MZERO, &ONE, 0},
{"cos", cos, &INF, &NAN, 0},
{"cos", cos, &MINF, &NAN, 0},
{"sin", sin, &NAN, &NAN, 0},
{"sin", sin, &MZERO, &MZERO, 0},
{"sin", sin, &ZERO, &ZERO, 0},
{"sin", sin, &INF, &NAN, 0},
{"sin", sin, &MINF, &NAN, 0},
{"tan", tan, &NAN, &NAN, 0},
{"tan", tan, &ZERO, &ZERO, 0},
{"tan", tan, &MZERO, &MZERO, 0},
{"tan", tan, &INF, &NAN, 0},
{"tan", tan, &MINF, &NAN, 0},
{"acosh", acosh, &NAN, &NAN, 0},
{"acosh", acosh, &ONE, &ZERO, 0},
{"acosh", acosh, &INF, &INF, 0},
{"acosh", acosh, &HALF, &NAN, 0},
{"acosh", acosh, &MONE, &NAN, 0},
{"asinh", asinh, &NAN, &NAN, 0},
{"asinh", asinh, &ZERO, &ZERO, 0},
{"asinh", asinh, &MZERO, &MZERO, 0},
{"asinh", asinh, &INF, &INF, 0},
{"asinh", asinh, &MINF, &MINF, 0},
{"atanh", atanh, &NAN, &NAN, 0},
{"atanh", atanh, &ZERO, &ZERO, 0},
{"atanh", atanh, &MZERO, &MZERO, 0},
{"atanh", atanh, &ONE, &INF, 0},
{"atanh", atanh, &MONE, &MINF, 0},
{"atanh", atanh, &TWO, &NAN, 0},
{"atanh", atanh, &MTWO, &NAN, 0},
{"cosh", cosh, &NAN, &NAN, 0},
{"cosh", cosh, &ZERO, &ONE, 0},
{"cosh", cosh, &MZERO, &ONE, 0},
{"cosh", cosh, &INF, &INF, 0},
{"cosh", cosh, &MINF, &INF, 0},
{"sinh", sinh, &NAN, &NAN, 0},
{"sinh", sinh, &ZERO, &ZERO, 0},
{"sinh", sinh, &MZERO, &MZERO, 0},
{"sinh", sinh, &INF, &INF, 0},
{"sinh", sinh, &MINF, &MINF, 0},
{"tanh", tanh, &NAN, &NAN, 0},
{"tanh", tanh, &ZERO, &ZERO, 0},
{"tanh", tanh, &MZERO, &MZERO, 0},
{"tanh", tanh, &INF, &ONE, 0},
{"tanh", tanh, &MINF, &MONE, 0},
{"exp", exp, &NAN, &NAN, 0},
{"exp", exp, &ZERO, &ONE, 0},
{"exp", exp, &MZERO, &ONE, 0},
{"exp", exp, &INF, &INF, 0},
{"exp", exp, &MINF, &ZERO, 0},
#if !GLIBC2
{"exp2", exp2, &NAN, &NAN, 0},
{"exp2", exp2, &ZERO, &ONE, 0},
{"exp2", exp2, &MZERO, &ONE, 0},
{"exp2", exp2, &INF, &INF, 0},
{"exp2", exp2, &MINF, &ZERO, 0},
#endif
{"expm1", expm1, &NAN, &NAN, 0},
{"expm1", expm1, &ZERO, &ZERO, 0},
{"expm1", expm1, &MZERO, &MZERO, 0},
{"expm1", expm1, &INF, &INF, 0},
{"expm1", expm1, &MINF, &MONE, 0},
{"log", log, &NAN, &NAN, 0},
{"log", log, &ZERO, &MINF, 0},
{"log", log, &MZERO, &MINF, 0},
{"log", log, &ONE, &ZERO, 0},
{"log", log, &MONE, &NAN, 0},
{"log", log, &INF, &INF, 0},
{"log10", log10, &NAN, &NAN, 0},
{"log10", log10, &ZERO, &MINF, 0},
{"log10", log10, &MZERO, &MINF, 0},
{"log10", log10, &ONE, &ZERO, 0},
{"log10", log10, &MONE, &NAN, 0},
{"log10", log10, &INF, &INF, 0},
{"log1p", log1p, &NAN, &NAN, 0},
{"log1p", log1p, &ZERO, &ZERO, 0},
{"log1p", log1p, &MZERO, &MZERO, 0},
{"log1p", log1p, &MONE, &MINF, 0},
{"log1p", log1p, &MTWO, &NAN, 0},
{"log1p", log1p, &INF, &INF, 0},
#if !GLIBC2
{"log2", log2, &NAN, &NAN, 0},
{"log2", log2, &ZERO, &MINF, 0},
{"log2", log2, &MZERO, &MINF, 0},
{"log2", log2, &MONE, &NAN, 0},
{"log2", log2, &INF, &INF, 0},
#endif
/* {"fabs", fabs, NAN, NAN, 0}, */
{"fabs", fabs, &ONE, &ONE, 0},
{"fabs", fabs, &MONE, &ONE, 0},
{"fabs", fabs, &ZERO, &ZERO, 0},
{"fabs", fabs, &MZERO, &ZERO, 0},
{"fabs", fabs, &INF, &INF, 0},
{"fabs", fabs, &MINF, &INF, 0},
{"cbrt", cbrt, &NAN, &NAN, 0},
{"cbrt", cbrt, &ZERO, &ZERO, 0},
{"cbrt", cbrt, &MZERO, &MZERO, 0},
{"cbrt", cbrt, &INF, &INF, 0},
{"cbrt", cbrt, &MINF, &MINF, 0},
{"erf", erf, &NAN, &NAN, 0},
{"erf", erf, &ZERO, &ZERO, 0},
{"erf", erf, &MZERO, &MZERO, 0},
{"erf", erf, &INF, &ONE, 0},
{"erf", erf, &MINF, &MONE, 0},
{"erfc", erfc, &NAN, &NAN, 0},
{"erfc", erfc, &INF, &ZERO, 0},
{"erfc", erfc, &MINF, &TWO, 0},
{"gamma", gamma, &NAN, &NAN, 0},
{"gamma", gamma, &INF, &INF, 0},
{"gamma", gamma, &MONE, &NAN, 0},
{"gamma", gamma, &ZERO, &NAN, 0},
{"gamma", gamma, &MINF, &NAN, 0},
#if GLIBC2
{"lgamma", lgamma, &NAN, &NAN, 0},
{"lgamma", lgamma, &INF, &INF, 0},
{"lgamma", lgamma, &MONE, &INF, 0},
{"lgamma", lgamma, &ZERO, &INF, 0},
{"lgamma", lgamma, &MINF, &INF, 0},
#else
{"lgam", lgam, &NAN, &NAN, 0},
{"lgam", lgam, &INF, &INF, 0},
{"lgam", lgam, &MONE, &INF, 0},
{"lgam", lgam, &ZERO, &INF, 0},
{"lgam", lgam, &MINF, &INF, 0},
#endif
{"ceil", ceil, &NAN, &NAN, 0},
{"ceil", ceil, &ZERO, &ZERO, 0},
{"ceil", ceil, &MZERO, &MZERO, 0},
{"ceil", ceil, &INF, &INF, 0},
{"ceil", ceil, &MINF, &MINF, 0},
{"floor", floor, &NAN, &NAN, 0},
{"floor", floor, &ZERO, &ZERO, 0},
{"floor", floor, &MZERO, &MZERO, 0},
{"floor", floor, &INF, &INF, 0},
{"floor", floor, &MINF, &MINF, 0},
{"null", NULL, &ZERO, &ZERO, 0},
};
/* Functions of two variables. */
double atan2 (double, double);
double pow (double, double);
struct twoarguments
{
char *name; /* Name of the function. */
double (*func) (double, double);
double *arg1;
double *arg2;
double *answer;
int thresh;
};
struct twoarguments test2[] =
{
{"atan2", atan2, &ZERO, &ONE, &ZERO, 0},
{"atan2", atan2, &MZERO, &ONE, &MZERO, 0},
{"atan2", atan2, &ZERO, &ZERO, &ZERO, 0},
{"atan2", atan2, &MZERO, &ZERO, &MZERO, 0},
{"atan2", atan2, &ZERO, &MONE, &PI, 0},
{"atan2", atan2, &MZERO, &MONE, &MPI, 0},
{"atan2", atan2, &ZERO, &MZERO, &PI, 0},
{"atan2", atan2, &MZERO, &MZERO, &MPI, 0},
{"atan2", atan2, &ONE, &ZERO, &PIO2, 0},
{"atan2", atan2, &ONE, &MZERO, &PIO2, 0},
{"atan2", atan2, &MONE, &ZERO, &MPIO2, 0},
{"atan2", atan2, &MONE, &MZERO, &MPIO2, 0},
{"atan2", atan2, &ONE, &INF, &ZERO, 0},
{"atan2", atan2, &MONE, &INF, &MZERO, 0},
{"atan2", atan2, &INF, &ONE, &PIO2, 0},
{"atan2", atan2, &INF, &MONE, &PIO2, 0},
{"atan2", atan2, &MINF, &ONE, &MPIO2, 0},
{"atan2", atan2, &MINF, &MONE, &MPIO2, 0},
{"atan2", atan2, &ONE, &MINF, &PI, 0},
{"atan2", atan2, &MONE, &MINF, &MPI, 0},
{"atan2", atan2, &INF, &INF, &PIO4, 0},
{"atan2", atan2, &MINF, &INF, &MPIO4, 0},
{"atan2", atan2, &INF, &MINF, &THPIO4, 0},
{"atan2", atan2, &MINF, &MINF, &MTHPIO4, 0},
{"atan2", atan2, &ONE, &ONE, &PIO4, 0},
{"atan2", atan2, &NAN, &ONE, &NAN, 0},
{"atan2", atan2, &ONE, &NAN, &NAN, 0},
{"atan2", atan2, &NAN, &NAN, &NAN, 0},
{"pow", pow, &ONE, &ZERO, &ONE, 0},
{"pow", pow, &ONE, &MZERO, &ONE, 0},
{"pow", pow, &MONE, &ZERO, &ONE, 0},
{"pow", pow, &MONE, &MZERO, &ONE, 0},
{"pow", pow, &INF, &ZERO, &ONE, 0},
{"pow", pow, &INF, &MZERO, &ONE, 0},
{"pow", pow, &NAN, &ZERO, &ONE, 0},
{"pow", pow, &NAN, &MZERO, &ONE, 0},
{"pow", pow, &TWO, &INF, &INF, 0},
{"pow", pow, &MTWO, &INF, &INF, 0},
{"pow", pow, &HALF, &INF, &ZERO, 0},
{"pow", pow, &MHALF, &INF, &ZERO, 0},
{"pow", pow, &TWO, &MINF, &ZERO, 0},
{"pow", pow, &MTWO, &MINF, &ZERO, 0},
{"pow", pow, &HALF, &MINF, &INF, 0},
{"pow", pow, &MHALF, &MINF, &INF, 0},
{"pow", pow, &INF, &HALF, &INF, 0},
{"pow", pow, &INF, &TWO, &INF, 0},
{"pow", pow, &INF, &MHALF, &ZERO, 0},
{"pow", pow, &INF, &MTWO, &ZERO, 0},
{"pow", pow, &MINF, &THREE, &MINF, 0},
{"pow", pow, &MINF, &TWO, &INF, 0},
{"pow", pow, &MINF, &MTHREE, &MZERO, 0},
{"pow", pow, &MINF, &MTWO, &ZERO, 0},
{"pow", pow, &NAN, &ONE, &NAN, 0},
{"pow", pow, &ONE, &NAN, &NAN, 0},
{"pow", pow, &NAN, &NAN, &NAN, 0},
{"pow", pow, &ONE, &INF, &NAN, 0},
{"pow", pow, &MONE, &INF, &NAN, 0},
{"pow", pow, &ONE, &MINF, &NAN, 0},
{"pow", pow, &MONE, &MINF, &NAN, 0},
{"pow", pow, &MTWO, &HALF, &NAN, 0},
{"pow", pow, &ZERO, &MTHREE, &INF, 0},
{"pow", pow, &MZERO, &MTHREE, &MINF, 0},
{"pow", pow, &ZERO, &MHALF, &INF, 0},
{"pow", pow, &MZERO, &MHALF, &INF, 0},
{"pow", pow, &ZERO, &THREE, &ZERO, 0},
{"pow", pow, &MZERO, &THREE, &MZERO, 0},
{"pow", pow, &ZERO, &HALF, &ZERO, 0},
{"pow", pow, &MZERO, &HALF, &ZERO, 0},
{"null", NULL, &ZERO, &ZERO, &ZERO, 0},
};
/* Integer functions of one variable. */
int isnan (double);
int signbit (double);
struct intans
{
char *name; /* Name of the function. */
int (*func) (double);
double *arg1;
int ianswer;
};
struct intans test3[] =
{
{"isfinite", isfinite, &ZERO, 1},
{"isfinite", isfinite, &INF, 0},
{"isfinite", isfinite, &MINF, 0},
{"isnan", isnan, &NAN, 1},
{"isnan", isnan, &INF, 0},
{"isnan", isnan, &ZERO, 0},
{"isnan", isnan, &MZERO, 0},
{"signbit", signbit, &MZERO, 1},
{"signbit", signbit, &MONE, 1},
{"signbit", signbit, &ZERO, 0},
{"signbit", signbit, &ONE, 0},
{"signbit", signbit, &MINF, 1},
{"signbit", signbit, &INF, 0},
{"null", NULL, &ZERO, 0},
};
static volatile double x1;
static volatile double x2;
static volatile double y;
static volatile double answer;
void
pvec(x)
double x;
{
union
{
double d;
unsigned short s[4];
} u;
int i;
u.d = x;
for (i = 0; i < 4; i++)
printf ("0x%04x ", u.s[i]);
printf ("\n");
}
int
main ()
{
int i, nerrors, k, ianswer, ntests;
double (*fun1) (double);
double (*fun2) (double, double);
int (*fun3) (double);
double e;
union
{
double d;
char c[8];
} u, v;
ZERO = 0.0;
MZERO = NEGZERO;
HALF = 0.5;
MHALF = -HALF;
ONE = 1.0;
MONE = -ONE;
TWO = 2.0;
MTWO = -TWO;
THREE = 3.0;
MTHREE = -THREE;
INF = INFINITY;
MINF = -INFINITY;
MPI = -PI;
PIO2 = 0.5 * PI;
MPIO2 = -PIO2;
PIO4 = 0.5 * PIO2;
MPIO4 = -PIO4;
THPIO4 = 3.0 * PIO4;
MTHPIO4 = -THPIO4;
nerrors = 0;
ntests = 0;
i = 0;
for (;;)
{
fun1 = test1[i].func;
if (fun1 == NULL)
break;
x1 = *(test1[i].arg1);
y = (*(fun1)) (x1);
answer = *(test1[i].answer);
if (test1[i].thresh == 0)
{
v.d = answer;
u.d = y;
if (memcmp(u.c, v.c, 8) != 0)
{
if( isnan(v.d) && isnan(u.d) )
goto nxttest1;
goto wrongone;
}
else
goto nxttest1;
}
if (y != answer)
{
e = y - answer;
if (answer != 0.0)
e = e / answer;
if (e < 0)
e = -e;
if (e > test1[i].thresh * MACHEP)
{
wrongone:
printf ("%s (%.16e) = %.16e\n should be %.16e\n",
test1[i].name, x1, y, answer);
nerrors += 1;
}
}
nxttest1:
ntests += 1;
i += 1;
}
i = 0;
for (;;)
{
fun2 = test2[i].func;
if (fun2 == NULL)
break;
x1 = *(test2[i].arg1);
x2 = *(test2[i].arg2);
y = (*(fun2)) (x1, x2);
answer = *(test2[i].answer);
if (test2[i].thresh == 0)
{
v.d = answer;
u.d = y;
if (memcmp(u.c, v.c, 8) != 0)
{
if( isnan(v.d) && isnan(u.d) )
goto nxttest2;
#if 0
if( isnan(v.d) )
pvec(v.d);
if( isnan(u.d) )
pvec(u.d);
#endif
goto wrongtwo;
}
else
goto nxttest2;
}
if (y != answer)
{
e = y - answer;
if (answer != 0.0)
e = e / answer;
if (e < 0)
e = -e;
if (e > test2[i].thresh * MACHEP)
{
wrongtwo:
printf ("%s (%.16e, %.16e) = %.16e\n should be %.16e\n",
test2[i].name, x1, x2, y, answer);
nerrors += 1;
}
}
nxttest2:
ntests += 1;
i += 1;
}
i = 0;
for (;;)
{
fun3 = test3[i].func;
if (fun3 == NULL)
break;
x1 = *(test3[i].arg1);
k = (*(fun3)) (x1);
ianswer = test3[i].ianswer;
if (k != ianswer)
{
printf ("%s (%.16e) = %d\n should be. %d\n",
test3[i].name, x1, k, ianswer);
nerrors += 1;
}
ntests += 1;
i += 1;
}
printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
exit (0);
}

203
components/external/espruino/libs/math/exp.c vendored Normal file
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/* exp.c
*
* Exponential function
*
*
*
* SYNOPSIS:
*
* double x, y, exp();
*
* y = exp( x );
*
*
*
* DESCRIPTION:
*
* Returns e (2.71828...) raised to the x power.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
*
* x k f
* e = 2 e.
*
* A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
* of degree 2/3 is used to approximate exp(f) in the basic
* interval [-0.5, 0.5].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +- 88 50000 2.8e-17 7.0e-18
* IEEE +- 708 40000 2.0e-16 5.6e-17
*
*
* Error amplification in the exponential function can be
* a serious matter. The error propagation involves
* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
* which shows that a 1 lsb error in representing X produces
* a relative error of X times 1 lsb in the function.
* While the routine gives an accurate result for arguments
* that are exactly represented by a double precision
* computer number, the result contains amplified roundoff
* error for large arguments not exactly represented.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp underflow x < MINLOG 0.0
* exp overflow x > MAXLOG INFINITY
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
/* Exponential function */
#include "mconf.h"
#ifdef UNK
const static double P[] = {
1.26177193074810590878E-4,
3.02994407707441961300E-2,
9.99999999999999999910E-1,
};
const static double Q[] = {
3.00198505138664455042E-6,
2.52448340349684104192E-3,
2.27265548208155028766E-1,
2.00000000000000000009E0,
};
const static double C1 = 6.93145751953125E-1;
const static double C2 = 1.42860682030941723212E-6;
#endif
#ifdef DEC
static unsigned short P[] = {
0035004,0047156,0127442,0057502,
0036770,0033210,0063121,0061764,
0040200,0000000,0000000,0000000,
};
static unsigned short Q[] = {
0033511,0072665,0160662,0176377,
0036045,0070715,0124105,0132777,
0037550,0134114,0142077,0001637,
0040400,0000000,0000000,0000000,
};
static unsigned short sc1[] = {0040061,0071000,0000000,0000000};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0033277,0137216,0075715,0057117};
#define C2 (*(double *)sc2)
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x4be8,0xd5e4,0x89cd,0x3f20,
0x2c7e,0x0cca,0x06d1,0x3f9f,
0x0000,0x0000,0x0000,0x3ff0,
};
static unsigned short Q[] = {
0x5fa0,0xbc36,0x2eb6,0x3ec9,
0xb6c0,0xb508,0xae39,0x3f64,
0xe074,0x9887,0x1709,0x3fcd,
0x0000,0x0000,0x0000,0x4000,
};
static unsigned short sc1[] = {0x0000,0x0000,0x2e40,0x3fe6};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0xabca,0xcf79,0xf7d1,0x3eb7};
#define C2 (*(double *)sc2)
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f20,0x89cd,0xd5e4,0x4be8,
0x3f9f,0x06d1,0x0cca,0x2c7e,
0x3ff0,0x0000,0x0000,0x0000,
};
static unsigned short Q[] = {
0x3ec9,0x2eb6,0xbc36,0x5fa0,
0x3f64,0xae39,0xb508,0xb6c0,
0x3fcd,0x1709,0x9887,0xe074,
0x4000,0x0000,0x0000,0x0000,
};
static unsigned short sc1[] = {0x3fe6,0x2e40,0x0000,0x0000};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0x3eb7,0xf7d1,0xcf79,0xabca};
#define C2 (*(double *)sc2)
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double polevl(), p1evl(), floor(), ldexp();
int isnan(), isfinite();
#endif
extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
#ifdef INFINITIES
extern double INFINITY;
#endif
double exp(x)
double x;
{
double px, xx;
int n;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
if( x > MAXLOG)
{
#ifdef INFINITIES
return( INFINITY );
#else
mtherr( "exp", OVERFLOW );
return( MAXNUM );
#endif
}
if( x < MINLOG )
{
#ifndef INFINITIES
mtherr( "exp", UNDERFLOW );
#endif
return(0.0);
}
/* Express e**x = e**g 2**n
* = e**g e**( n loge(2) )
* = e**( g + n loge(2) )
*/
px = floor( LOG2E * x + 0.5 ); /* floor() truncates toward -infinity. */
n = px;
x -= px * C1;
x -= px * C2;
/* rational approximation for exponential
* of the fractional part:
* e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
*/
xx = x * x;
px = x * polevl( xx, P, 2 );
x = px/( polevl( xx, Q, 3 ) - px );
x = 1.0 + 2.0 * x;
/* multiply by power of 2 */
x = ldexp( x, n );
return(x);
}

223
components/external/espruino/libs/math/exp10.c vendored Normal file
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/* exp10.c
*
* Base 10 exponential function
* (Common antilogarithm)
*
*
*
* SYNOPSIS:
*
* double x, y, exp10();
*
* y = exp10( x );
*
*
*
* DESCRIPTION:
*
* Returns 10 raised to the x power.
*
* Range reduction is accomplished by expressing the argument
* as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
* The Pade' form
*
* 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
*
* is used to approximate 10**f.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -307,+307 30000 2.2e-16 5.5e-17
* Test result from an earlier version (2.1):
* DEC -38,+38 70000 3.1e-17 7.0e-18
*
* ERROR MESSAGES:
*
* message condition value returned
* exp10 underflow x < -MAXL10 0.0
* exp10 overflow x > MAXL10 MAXNUM
*
* DEC arithmetic: MAXL10 = 38.230809449325611792.
* IEEE arithmetic: MAXL10 = 308.2547155599167.
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1991, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
4.09962519798587023075E-2,
1.17452732554344059015E1,
4.06717289936872725516E2,
2.39423741207388267439E3,
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
8.50936160849306532625E1,
1.27209271178345121210E3,
2.07960819286001865907E3,
};
/* const static double LOG102 = 3.01029995663981195214e-1; */
const static double LOG210 = 3.32192809488736234787e0;
const static double LG102A = 3.01025390625000000000E-1;
const static double LG102B = 4.60503898119521373889E-6;
/* const static double MAXL10 = 38.230809449325611792; */
const static double MAXL10 = 308.2547155599167;
#endif
#ifdef DEC
static unsigned short P[] = {
0037047,0165657,0114061,0067234,
0041073,0166243,0123052,0144643,
0042313,0055720,0024032,0047443,
0043025,0121714,0070232,0050007,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041652,0027756,0071216,0050075,
0042637,0001367,0077263,0136017,
0043001,0174673,0024157,0133416,
};
/*
static unsigned short L102[] = {0037632,0020232,0102373,0147770};
#define LOG102 *(double *)L102
*/
static unsigned short L210[] = {0040524,0115170,0045715,0015613};
#define LOG210 *(double *)L210
static unsigned short L102A[] = {0037632,0020000,0000000,0000000,};
#define LG102A *(double *)L102A
static unsigned short L102B[] = {0033632,0102373,0147767,0114220,};
#define LG102B *(double *)L102B
static unsigned short MXL[] = {0041430,0166131,0047761,0154130,};
#define MAXL10 ( *(double *)MXL )
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x2dd4,0xf306,0xfd75,0x3fa4,
0x5934,0x74c5,0x7d94,0x4027,
0x49e4,0x0503,0x6b7a,0x4079,
0x4a01,0x8e13,0xb479,0x40a2,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xca08,0xce51,0x45fd,0x4055,
0x7782,0xefd6,0xe05e,0x4093,
0xf6e2,0x650d,0x3f37,0x40a0,
};
/*
static unsigned short L102[] = {0x79ff,0x509f,0x4413,0x3fd3};
#define LOG102 *(double *)L102
*/
static unsigned short L210[] = {0xa371,0x0979,0x934f,0x400a};
#define LOG210 *(double *)L210
static unsigned short L102A[] = {0x0000,0x0000,0x4400,0x3fd3,};
#define LG102A *(double *)L102A
static unsigned short L102B[] = {0xf312,0x79fe,0x509f,0x3ed3,};
#define LG102B *(double *)L102B
const static double MAXL10 = 308.2547155599167;
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3fa4,0xfd75,0xf306,0x2dd4,
0x4027,0x7d94,0x74c5,0x5934,
0x4079,0x6b7a,0x0503,0x49e4,
0x40a2,0xb479,0x8e13,0x4a01,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x4055,0x45fd,0xce51,0xca08,
0x4093,0xe05e,0xefd6,0x7782,
0x40a0,0x3f37,0x650d,0xf6e2,
};
/*
static unsigned short L102[] = {0x3fd3,0x4413,0x509f,0x79ff};
#define LOG102 *(double *)L102
*/
static unsigned short L210[] = {0x400a,0x934f,0x0979,0xa371};
#define LOG210 *(double *)L210
static unsigned short L102A[] = {0x3fd3,0x4400,0x0000,0x0000,};
#define LG102A *(double *)L102A
static unsigned short L102B[] = {0x3ed3,0x509f,0x79fe,0xf312,};
#define LG102B *(double *)L102B
const static double MAXL10 = 308.2547155599167;
#endif
#ifdef ANSIPROT
extern double floor ( double );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double floor(), ldexp(), polevl(), p1evl();
int isnan(), isfinite();
#endif
extern double MAXNUM;
#ifdef INFINITIES
extern double INFINITY;
#endif
double exp10(x)
double x;
{
double px, xx;
short n;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
if( x > MAXL10 )
{
#ifdef INFINITIES
return( INFINITY );
#else
mtherr( "exp10", OVERFLOW );
return( MAXNUM );
#endif
}
if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
{
#ifndef INFINITIES
mtherr( "exp10", UNDERFLOW );
#endif
return(0.0);
}
/* Express 10**x = 10**g 2**n
* = 10**g 10**( n log10(2) )
* = 10**( g + n log10(2) )
*/
px = floor( LOG210 * x + 0.5 );
n = px;
x -= px * LG102A;
x -= px * LG102B;
/* rational approximation for exponential
* of the fractional part:
* 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
*/
xx = x * x;
px = x * polevl( xx, P, 3 );
x = px/( p1evl( xx, Q, 3 ) - px );
x = 1.0 + ldexp( x, 1 );
/* multiply by power of 2 */
x = ldexp( x, n );
return(x);
}

183
components/external/espruino/libs/math/exp2.c vendored Normal file
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/* exp2.c
*
* Base 2 exponential function
*
*
*
* SYNOPSIS:
*
* double x, y, exp2();
*
* y = exp2( x );
*
*
*
* DESCRIPTION:
*
* Returns 2 raised to the x power.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
* x k f
* 2 = 2 2.
*
* A Pade' form
*
* 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
*
* approximates 2**x in the basic range [-0.5, 0.5].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1022,+1024 30000 1.8e-16 5.4e-17
*
*
* See exp.c for comments on error amplification.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp underflow x < -MAXL2 0.0
* exp overflow x > MAXL2 MAXNUM
*
* For DEC arithmetic, MAXL2 = 127.
* For IEEE arithmetic, MAXL2 = 1024.
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
2.30933477057345225087E-2,
2.02020656693165307700E1,
1.51390680115615096133E3,
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
2.33184211722314911771E2,
4.36821166879210612817E3,
};
#define MAXL2 1024.0
#define MINL2 -1024.0
#endif
#ifdef DEC
static unsigned short P[] = {
0036675,0027102,0122327,0053227,
0041241,0116724,0115412,0157355,
0042675,0036404,0101733,0132226,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0042151,0027450,0077732,0160744,
0043210,0100661,0077550,0056560,
};
#define MAXL2 127.0
#define MINL2 -127.0
#endif
#ifdef IBMPC
static unsigned short P[] = {
0xead3,0x549a,0xa5c8,0x3f97,
0x5bde,0x9361,0x33ba,0x4034,
0x7693,0x907b,0xa7a0,0x4097,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x5c3c,0x0ffb,0x25e5,0x406d,
0x0bae,0x2fed,0x1036,0x40b1,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f97,0xa5c8,0x549a,0xead3,
0x4034,0x33ba,0x9361,0x5bde,
0x4097,0xa7a0,0x907b,0x7693,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x406d,0x25e5,0x0ffb,0x5c3c,
0x40b1,0x1036,0x2fed,0x0bae,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double polevl(), p1evl(), floor(), ldexp();
int isnan(), isfinite();
#endif
#ifdef INFINITIES
extern double INFINITY;
#endif
extern double MAXNUM;
double exp2(x)
double x;
{
double px, xx;
short n;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
if( x > MAXL2)
{
#ifdef INFINITIES
return( INFINITY );
#else
mtherr( "exp2", OVERFLOW );
return( MAXNUM );
#endif
}
if( x < MINL2 )
{
#ifndef INFINITIES
mtherr( "exp2", UNDERFLOW );
#endif
return(0.0);
}
xx = x; /* save x */
/* separate into integer and fractional parts */
px = floor(x+0.5);
n = px;
x = x - px;
/* rational approximation
* exp2(x) = 1 + 2xP(xx)/(Q(xx) - P(xx))
* where xx = x**2
*/
xx = x * x;
px = x * polevl( xx, P, 2 );
x = px / ( p1evl( xx, Q, 2 ) - px );
x = 1.0 + ldexp( x, 1 );
/* scale by power of 2 */
x = ldexp( x, n );
return(x);
}

56
components/external/espruino/libs/math/fabs.c vendored Normal file
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/* fabs.c
*
* Absolute value
*
*
*
* SYNOPSIS:
*
* double x, y;
*
* y = fabs( x );
*
*
*
* DESCRIPTION:
*
* Returns the absolute value of the argument.
*
*/
#include "mconf.h"
/* Avoid using UNK if possible. */
#ifdef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#endif
double fabs(x)
double x;
{
union
{
double d;
short i[4];
} u;
u.d = x;
#ifdef IBMPC
u.i[3] &= 0x7fff;
#endif
#ifdef MIEEE
u.i[0] &= 0x7fff;
#endif
#ifdef DEC
u.i[3] &= 0x7fff;
#endif
#ifdef UNK
if( u.d < 0 )
u.d = -u.d;
#endif
return( u.d );
}

453
components/external/espruino/libs/math/floor.c vendored Normal file
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@@ -0,0 +1,453 @@
/* ceil()
* floor()
* frexp()
* ldexp()
* signbit()
* isnan()
* isfinite()
*
* Floating point numeric utilities
*
*
*
* SYNOPSIS:
*
* double ceil(), floor(), frexp(), ldexp();
* int signbit(), isnan(), isfinite();
* double x, y;
* int expnt, n;
*
* y = floor(x);
* y = ceil(x);
* y = frexp( x, &expnt );
* y = ldexp( x, n );
* n = signbit(x);
* n = isnan(x);
* n = isfinite(x);
*
*
*
* DESCRIPTION:
*
* All four routines return a double precision floating point
* result.
*
* floor() returns the largest integer less than or equal to x.
* It truncates toward minus infinity.
*
* ceil() returns the smallest integer greater than or equal
* to x. It truncates toward plus infinity.
*
* frexp() extracts the exponent from x. It returns an integer
* power of two to expnt and the significand between 0.5 and 1
* to y. Thus x = y * 2**expn.
*
* ldexp() multiplies x by 2**n.
*
* signbit(x) returns 1 if the sign bit of x is 1, else 0.
*
* These functions are part of the standard C run time library
* for many but not all C compilers. The ones supplied are
* written in C for either DEC or IEEE arithmetic. They should
* be used only if your compiler library does not already have
* them.
*
* The IEEE versions assume that denormal numbers are implemented
* in the arithmetic. Some modifications will be required if
* the arithmetic has abrupt rather than gradual underflow.
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
#undef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#endif
#ifdef DEC
#define EXPMSK 0x807f
#define MEXP 255
#define NBITS 56
#endif
#ifdef IBMPC
#define EXPMSK 0x800f
#define MEXP 0x7ff
#define NBITS 53
#endif
#ifdef MIEEE
#define EXPMSK 0x800f
#define MEXP 0x7ff
#define NBITS 53
#endif
extern double MAXNUM, NEGZERO;
#ifdef ANSIPROT
double floor ( double );
int isnan ( double );
int isfinite ( double );
double ldexp ( double, int );
#else
double floor();
int isnan(), isfinite();
double ldexp();
#endif
double ceil(x)
double x;
{
double y;
#ifdef UNK
mtherr( "ceil", DOMAIN );
return(0.0);
#endif
#ifdef NANS
if( isnan(x) )
return( x );
#endif
#ifdef INFINITIES
if(!isfinite(x))
return(x);
#endif
y = floor(x);
if( y < x )
y += 1.0;
#ifdef MINUSZERO
if( y == 0.0 && x < 0.0 )
return( NEGZERO );
#endif
return(y);
}
/* Bit clearing masks: */
static unsigned short bmask[] = {
0xffff,
0xfffe,
0xfffc,
0xfff8,
0xfff0,
0xffe0,
0xffc0,
0xff80,
0xff00,
0xfe00,
0xfc00,
0xf800,
0xf000,
0xe000,
0xc000,
0x8000,
0x0000,
};
double floor(x)
double x;
{
union
{
double y;
unsigned short sh[4];
} u;
unsigned short *p;
int e;
#ifdef UNK
mtherr( "floor", DOMAIN );
return(0.0);
#endif
#ifdef NANS
if( isnan(x) )
return( x );
#endif
#ifdef INFINITIES
if(!isfinite(x))
return(x);
#endif
#ifdef MINUSZERO
if(x == 0.0L)
return(x);
#endif
u.y = x;
/* find the exponent (power of 2) */
#ifdef DEC
p = (unsigned short *)&u.sh[0];
e = (( *p >> 7) & 0377) - 0201;
p += 3;
#endif
#ifdef IBMPC
p = (unsigned short *)&u.sh[3];
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p -= 3;
#endif
#ifdef MIEEE
p = (unsigned short *)&u.sh[0];
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p += 3;
#endif
if( e < 0 )
{
if( u.y < 0.0 )
return( -1.0 );
else
return( 0.0 );
}
e = (NBITS -1) - e;
/* clean out 16 bits at a time */
while( e >= 16 )
{
#ifdef IBMPC
*p++ = 0;
#endif
#ifdef DEC
*p-- = 0;
#endif
#ifdef MIEEE
*p-- = 0;
#endif
e -= 16;
}
/* clear the remaining bits */
if( e > 0 )
*p &= bmask[e];
if( (x < 0) && (u.y != x) )
u.y -= 1.0;
return(u.y);
}
double frexp( x, pw2 )
double x;
int *pw2;
{
union
{
double y;
unsigned short sh[4];
} u;
int i;
#ifdef DENORMAL
int k;
#endif
short *q;
u.y = x;
#ifdef UNK
mtherr( "frexp", DOMAIN );
return(0.0);
#endif
#ifdef IBMPC
q = (short *)&u.sh[3];
#endif
#ifdef DEC
q = (short *)&u.sh[0];
#endif
#ifdef MIEEE
q = (short *)&u.sh[0];
#endif
/* find the exponent (power of 2) */
#ifdef DEC
i = ( *q >> 7) & 0377;
if( i == 0 )
{
*pw2 = 0;
return(0.0);
}
i -= 0200;
*pw2 = i;
*q &= 0x807f; /* strip all exponent bits */
*q |= 040000; /* mantissa between 0.5 and 1 */
return(u.y);
#endif
#ifdef IBMPC
i = ( *q >> 4) & 0x7ff;
if( i != 0 )
goto ieeedon;
#endif
#ifdef MIEEE
i = *q >> 4;
i &= 0x7ff;
if( i != 0 )
goto ieeedon;
#ifdef DENORMAL
#else
*pw2 = 0;
return(0.0);
#endif
#endif
#ifndef DEC
/* Number is denormal or zero */
#ifdef DENORMAL
if( u.y == 0.0 )
{
*pw2 = 0;
return( 0.0 );
}
/* Handle denormal number. */
do
{
u.y *= 2.0;
i -= 1;
k = ( *q >> 4) & 0x7ff;
}
while( k == 0 );
i = i + k;
#endif /* DENORMAL */
ieeedon:
i -= 0x3fe;
*pw2 = i;
*q &= 0x800f;
*q |= 0x3fe0;
return( u.y );
#endif
}
double ldexp( x, pw2 )
double x;
int pw2;
{
union
{
double y;
unsigned short sh[4];
} u;
short *q;
int e;
#ifdef UNK
mtherr( "ldexp", DOMAIN );
return(0.0);
#endif
u.y = x;
#ifdef DEC
q = (short *)&u.sh[0];
e = ( *q >> 7) & 0377;
if( e == 0 )
return(0.0);
#else
#ifdef IBMPC
q = (short *)&u.sh[3];
#endif
#ifdef MIEEE
q = (short *)&u.sh[0];
#endif
while( (e = (*q & 0x7ff0) >> 4) == 0 )
{
if( u.y == 0.0 )
{
return( 0.0 );
}
/* Input is denormal. */
if( pw2 > 0 )
{
u.y *= 2.0;
pw2 -= 1;
}
if( pw2 < 0 )
{
if( pw2 < -53 )
return(0.0);
u.y /= 2.0;
pw2 += 1;
}
if( pw2 == 0 )
return(u.y);
}
#endif /* not DEC */
e += pw2;
/* Handle overflow */
#ifdef DEC
if( e > MEXP )
return( MAXNUM );
#else
if( e >= MEXP )
return( 2.0*MAXNUM );
#endif
/* Handle denormalized results */
if( e < 1 )
{
#ifdef DENORMAL
if( e < -53 )
return(0.0);
*q &= 0x800f;
*q |= 0x10;
/* For denormals, significant bits may be lost even
when dividing by 2. Construct 2^-(1-e) so the result
is obtained with only one multiplication. */
u.y *= ldexp(1.0, e-1);
return(u.y);
#else
return(0.0);
#endif
}
else
{
#ifdef DEC
*q &= 0x807f; /* strip all exponent bits */
*q |= (e & 0xff) << 7;
#else
*q &= 0x800f;
*q |= (e & 0x7ff) << 4;
#endif
return(u.y);
}
}

289
components/external/espruino/libs/math/ftilib.mak vendored Normal file
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# MSDOS Microsoft C makefile for Cephes library
CFLAGS=/c
# For large memory model:
#CFLAGS=/c /AL
# Add /FPa to the CFLAGS if you want to use the fast software FPa arithmetic.
#
# Use the following with /FPa if you do not want to use the 80x87 coprocessor
# or software emulator.
#polevl.obj: polevl.c mconf.h
# cl /c /Ox polevl.c
#
# Use the following instead if you want to use an 80x87 chip or
# software emulator for maximum accuracy computation of the
# polynomial expansions:
polevl.obj: polevl.asm mconf.h
masm polevl.asm/r;
floor.obj: floor.asm
masm floor.asm;
#floor.obj: floor.c mconf.h
# cl $(CFLAGS) floor.c
acosh.obj: acosh.c mconf.h
cl $(CFLAGS) acosh.c
airy.obj: airy.c mconf.h
cl $(CFLAGS) airy.c
asin.obj: asin.c mconf.h
cl $(CFLAGS) asin.c
asinh.obj: asinh.c mconf.h
cl $(CFLAGS) asinh.c
atan.obj: atan.c mconf.h
cl $(CFLAGS) atan.c
atanh.obj: atanh.c mconf.h
cl $(CFLAGS) atanh.c
asinh.obj: asinh.c mconf.h
cl $(CFLAGS) asinh.c
bdtr.obj: bdtr.c mconf.h
cl $(CFLAGS) bdtr.c
beta.obj: beta.c mconf.h
cl $(CFLAGS) beta.c
btdtr.obj: btdtr.c mconf.h
cl $(CFLAGS) btdtr.c
cbrt.obj: cbrt.c mconf.h
cl $(CFLAGS) cbrt.c
chbevl.obj: chbevl.c mconf.h
cl $(CFLAGS) chbevl.c
chdtr.obj: chdtr.c mconf.h
cl $(CFLAGS) chdtr.c
clog.obj: clog.c mconf.h
cl $(CFLAGS) clog.c
cmplx.obj: cmplx.c mconf.h
cl $(CFLAGS) cmplx.c
const.obj: const.c mconf.h
cl $(CFLAGS) const.c
cosh.obj: cosh.c mconf.h
cl $(CFLAGS) cosh.c
dawsn.obj: dawsn.c mconf.h
cl $(CFLAGS) dawsn.c
drand.obj: drand.c mconf.h
cl $(CFLAGS) drand.c
ellie.obj: ellie.c mconf.h
cl $(CFLAGS) ellie.c
ellik.obj: ellik.c mconf.h
cl $(CFLAGS) ellik.c
ellpe.obj: ellpe.c mconf.h
cl $(CFLAGS) ellpe.c
ellpj.obj: ellpj.c mconf.h
cl $(CFLAGS) ellpj.c
ellpk.obj: ellpk.c mconf.h
cl $(CFLAGS) ellpk.c
exp.obj: exp.c mconf.h
cl $(CFLAGS) exp.c
exp10.obj: exp10.c mconf.h
cl $(CFLAGS) exp10.c
exp2.obj: exp2.c mconf.h
cl $(CFLAGS) exp2.c
expn.obj: expn.c mconf.h
cl $(CFLAGS) expn.c
fabs.obj: fabs.c mconf.h
cl $(CFLAGS) fabs.c
fac.obj: fac.c mconf.h
cl $(CFLAGS) fac.c
fdtr.obj: fdtr.c mconf.h
cl $(CFLAGS) fdtr.c
fresnl.obj: fresnl.c mconf.h
cl $(CFLAGS) fresnl.c
gamma.obj: gamma.c mconf.h
cl $(CFLAGS) gamma.c
gdtr.obj: gdtr.c mconf.h
cl $(CFLAGS) gdtr.c
hyp2f1.obj: hyp2f1.c mconf.h
cl $(CFLAGS) hyp2f1.c
hyperg.obj: hyperg.c mconf.h
cl $(CFLAGS) hyperg.c
i0.obj: i0.c mconf.h
cl $(CFLAGS) i0.c
i1.obj: i1.c mconf.h
cl $(CFLAGS) i1.c
igam.obj: igam.c mconf.h
cl $(CFLAGS) igam.c
igami.obj: igami.c mconf.h
cl $(CFLAGS) igami.c
incbet.obj: incbet.c mconf.h
cl $(CFLAGS) incbet.c
incbi.obj: incbi.c mconf.h
cl $(CFLAGS) incbi.c
isnan.obj: isnan.c mconf.h
cl $(CFLAGS) isnan.c
iv.obj: iv.c mconf.h
cl $(CFLAGS) iv.c
j0.obj: j0.c mconf.h
cl $(CFLAGS) j0.c
j1.obj: j1.c mconf.h
cl $(CFLAGS) j1.c
jn.obj: jn.c mconf.h
cl $(CFLAGS) jn.c
jv.obj: jv.c mconf.h
cl $(CFLAGS) jv.c
k0.obj: k0.c mconf.h
cl $(CFLAGS) k0.c
k1.obj: k1.c mconf.h
cl $(CFLAGS) k1.c
kn.obj: kn.c mconf.h
cl $(CFLAGS) kn.c
log.obj: log.c mconf.h
cl $(CFLAGS) log.c
log2.obj: log2.c mconf.h
cl $(CFLAGS) log2.c
log10.obj: log10.c mconf.h
cl $(CFLAGS) log10.c
mtherr.obj: mtherr.c mconf.h
cl $(CFLAGS) mtherr.c
nbdtr.obj: nbdtr.c mconf.h
cl $(CFLAGS) nbdtr.c
ndtr.obj: ndtr.c mconf.h
cl $(CFLAGS) ndtr.c
ndtri.obj: ndtri.c mconf.h
cl $(CFLAGS) ndtri.c
pdtr.obj: pdtr.c mconf.h
cl $(CFLAGS) pdtr.c
pow.obj: pow.c mconf.h
cl $(CFLAGS) pow.c
powi.obj: powi.c mconf.h
cl $(CFLAGS) powi.c
psi.obj: psi.c mconf.h
cl $(CFLAGS) psi.c
rgamma.obj: rgamma.c mconf.h
cl $(CFLAGS) rgamma.c
round.obj: round.c mconf.h
cl $(CFLAGS) round.c
setprec.obj: setprec.87
masm setprec.87;
shichi.obj: shichi.c mconf.h
cl $(CFLAGS) shichi.c
sici.obj: sici.c mconf.h
cl $(CFLAGS) sici.c
sin.obj: sin.c mconf.h
cl $(CFLAGS) sin.c
sindg.obj: sindg.c mconf.h
cl $(CFLAGS) sindg.c
sinh.obj: sinh.c mconf.h
cl $(CFLAGS) sinh.c
spence.obj: spence.c mconf.h
cl $(CFLAGS) spence.c
sqrt.obj: sqrt.87
masm sqrt.87;
#sqrt.obj: sqrt.c
# cl $(CFLAGS) sqrt.c
stdtr.obj: stdtr.c mconf.h
cl $(CFLAGS) stdtr.c
struve.obj: struve.c mconf.h
cl $(CFLAGS) struve.c
tan.obj: tan.c mconf.h
cl $(CFLAGS) tan.c
tandg.obj: tandg.c mconf.h
cl $(CFLAGS) tandg.c
tanh.obj: tanh.c mconf.h
cl $(CFLAGS) tanh.c
yn.obj: yn.c mconf.h
cl $(CFLAGS) yn.c
zeta.obj: zeta.c mconf.h
cl $(CFLAGS) zeta.c
zetac.obj: zetac.c mconf.h
cl $(CFLAGS) zetac.c
polyn.obj: polyn.c mconf.h
cl $(CFLAGS) polyn.c
polmisc.obj: polmisc.c mconf.h
cl $(CFLAGS) polmisc.c
unity.obj: unity.c mconf.h
cl $(CFLAGS) unity.c
fti.lib: acosh.obj airy.obj asin.obj asinh.obj atan.obj atanh.obj bdtr.obj \
beta.obj btdtr.obj cbrt.obj chbevl.obj chdtr.obj clog.obj \
cmplx.obj const.obj cosh.obj dawsn.obj drand.obj ellie.obj ellik.obj \
ellpe.obj ellpj.obj ellpk.obj exp.obj exp10.obj \
exp2.obj expn.obj fabs.obj fac.obj fdtr.obj floor.obj fresnl.obj gamma.obj \
gdtr.obj hyp2f1.obj hyperg.obj i0.c i1.c igam.c igami.obj incbet.obj \
incbi.obj isnan.obj iv.obj j0.obj j1.obj jn.obj jv.obj k0.obj k1.obj \
kn.obj log.obj log2.obj log10.obj mtherr.obj nbdtr.obj ndtr.obj ndtri.obj \
pdtr.obj polevl.obj polmisc.obj polyn.obj pow.obj powi.obj psi.obj \
rgamma.obj round.obj shichi.obj sici.obj sin.obj sindg.obj sinh.obj \
spence.obj sqrt.obj stdtr.obj setprec.obj struve.obj tan.obj \
tandg.obj tanh.obj unity.obj yn.obj zeta.obj zetac.obj \
mconf.h
lib @ftilib.rsp

17
components/external/espruino/libs/math/ftilib.rsp vendored Normal file
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fti
y
acosh airy asin asinh atan &
atanh bdtr beta btdtr cbrt chbevl &
chdtr clog cmplx const &
cosh dawsn drand ellie ellik ellpe ellpk &
ellpj exp exp2 exp10 expn fac &
fdtr fresnl gamma gdtr &
hyperg hyp2f1 incbet incbi igam igami isnan &
iv i0 i1 jn jv j0 j1 k0 k1 kn log log2 log10 &
mtherr nbdtr ndtr ndtri pdtr &
polmisc polyn pow powi psi &
rgamma round shichi sici sin sindg &
sinh spence sqrt stdtr struve tan tandg &
tanh unity yn zeta zetac floor fabs polevl
fti.lst
fti

237
components/external/espruino/libs/math/isnan.c vendored Normal file
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/* isnan()
* signbit()
* isfinite()
*
* Floating point numeric utilities
*
*
*
* SYNOPSIS:
*
* double ceil(), floor(), frexp(), ldexp();
* int signbit(), isnan(), isfinite();
* double x, y;
* int expnt, n;
*
* y = floor(x);
* y = ceil(x);
* y = frexp( x, &expnt );
* y = ldexp( x, n );
* n = signbit(x);
* n = isnan(x);
* n = isfinite(x);
*
*
*
* DESCRIPTION:
*
* All four routines return a double precision floating point
* result.
*
* floor() returns the largest integer less than or equal to x.
* It truncates toward minus infinity.
*
* ceil() returns the smallest integer greater than or equal
* to x. It truncates toward plus infinity.
*
* frexp() extracts the exponent from x. It returns an integer
* power of two to expnt and the significand between 0.5 and 1
* to y. Thus x = y * 2**expn.
*
* ldexp() multiplies x by 2**n.
*
* signbit(x) returns 1 if the sign bit of x is 1, else 0.
*
* These functions are part of the standard C run time library
* for many but not all C compilers. The ones supplied are
* written in C for either DEC or IEEE arithmetic. They should
* be used only if your compiler library does not already have
* them.
*
* The IEEE versions assume that denormal numbers are implemented
* in the arithmetic. Some modifications will be required if
* the arithmetic has abrupt rather than gradual underflow.
*/
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
#undef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#endif
/* Return 1 if the sign bit of x is 1, else 0. */
int signbit(x)
double x;
{
union
{
double d;
short s[4];
int i[2];
} u;
u.d = x;
if( sizeof(int) == 4 )
{
#ifdef IBMPC
return( u.i[1] < 0 );
#endif
#ifdef DEC
return( u.s[3] < 0 );
#endif
#ifdef MIEEE
return( u.i[0] < 0 );
#endif
}
else
{
#ifdef IBMPC
return( u.s[3] < 0 );
#endif
#ifdef DEC
return( u.s[3] < 0 );
#endif
#ifdef MIEEE
return( u.s[0] < 0 );
#endif
}
}
/* Return 1 if x is a number that is Not a Number, else return 0. */
int isnan(x)
double x;
{
#ifdef NANS
union
{
double d;
unsigned short s[4];
unsigned int i[2];
} u;
u.d = x;
if( sizeof(int) == 4 )
{
#ifdef IBMPC
if( ((u.i[1] & 0x7ff00000) == 0x7ff00000)
&& (((u.i[1] & 0x000fffff) != 0) || (u.i[0] != 0)))
return 1;
#endif
#ifdef DEC
if( (u.s[1] & 0x7fff) == 0)
{
if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
return(1);
}
#endif
#ifdef MIEEE
if( ((u.i[0] & 0x7ff00000) == 0x7ff00000)
&& (((u.i[0] & 0x000fffff) != 0) || (u.i[1] != 0)))
return 1;
#endif
return(0);
}
else
{ /* size int not 4 */
#ifdef IBMPC
if( (u.s[3] & 0x7ff0) == 0x7ff0)
{
if( ((u.s[3] & 0x000f) | u.s[2] | u.s[1] | u.s[0]) != 0 )
return(1);
}
#endif
#ifdef DEC
if( (u.s[3] & 0x7fff) == 0)
{
if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
return(1);
}
#endif
#ifdef MIEEE
if( (u.s[0] & 0x7ff0) == 0x7ff0)
{
if( ((u.s[0] & 0x000f) | u.s[1] | u.s[2] | u.s[3]) != 0 )
return(1);
}
#endif
return(0);
} /* size int not 4 */
#else
/* No NANS. */
return(0);
#endif
}
/* Return 1 if x is not infinite and is not a NaN. */
int isfinite(x)
double x;
{
#ifdef INFINITIES
union
{
double d;
unsigned short s[4];
unsigned int i[2];
} u;
u.d = x;
if( sizeof(int) == 4 )
{
#ifdef IBMPC
if( (u.i[1] & 0x7ff00000) != 0x7ff00000)
return 1;
#endif
#ifdef DEC
if( (u.s[3] & 0x7fff) != 0)
return 1;
#endif
#ifdef MIEEE
if( (u.i[0] & 0x7ff00000) != 0x7ff00000)
return 1;
#endif
return(0);
}
else
{
#ifdef IBMPC
if( (u.s[3] & 0x7ff0) != 0x7ff0)
return 1;
#endif
#ifdef DEC
if( (u.s[3] & 0x7fff) != 0)
return 1;
#endif
#ifdef MIEEE
if( (u.s[0] & 0x7ff0) != 0x7ff0)
return 1;
#endif
return(0);
}
#else
/* No INFINITY. */
return(1);
#endif
}

341
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/* log.c
*
* Natural logarithm
*
*
*
* SYNOPSIS:
*
* double x, y, log();
*
* y = log( x );
*
*
*
* DESCRIPTION:
*
* Returns the base e (2.718...) logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the logarithm
* of the fraction is approximated by
*
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z**3 P(z)/Q(z).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
* IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
* DEC 0, 10 170000 1.8e-17 6.3e-18
*
* In the tests over the interval [+-MAXNUM], the logarithms
* of the random arguments were uniformly distributed over
* [0, MAXLOG].
*
* ERROR MESSAGES:
*
* log singularity: x = 0; returns -INFINITY
* log domain: x < 0; returns NAN
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
static char fname[] = {"log"};
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
*/
#ifdef UNK
const static double P[] = {
1.01875663804580931796E-4,
4.97494994976747001425E-1,
4.70579119878881725854E0,
1.44989225341610930846E1,
1.79368678507819816313E1,
7.70838733755885391666E0,
};
const static double Q[] = {
/* 1.00000000000000000000E0, */
1.12873587189167450590E1,
4.52279145837532221105E1,
8.29875266912776603211E1,
7.11544750618563894466E1,
2.31251620126765340583E1,
};
#endif
#ifdef DEC
static unsigned short P[] = {
0037777,0127270,0162547,0057274,
0041001,0054665,0164317,0005341,
0041451,0034104,0031640,0105773,
0041677,0011276,0123617,0160135,
0041701,0126603,0053215,0117250,
0041420,0115777,0135206,0030232,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041220,0144332,0045272,0174241,
0041742,0164566,0035720,0130431,
0042246,0126327,0166065,0116357,
0042372,0033420,0157525,0124560,
0042271,0167002,0066537,0172303,
0041730,0164777,0113711,0044407,
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x1bb0,0x93c3,0xb4c2,0x3f1a,
0x52f2,0x3f56,0xd6f5,0x3fdf,
0x6911,0xed92,0xd2ba,0x4012,
0xeb2e,0xc63e,0xff72,0x402c,
0xc84d,0x924b,0xefd6,0x4031,
0xdcf8,0x7d7e,0xd563,0x401e,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xef8e,0xae97,0x9320,0x4026,
0xc033,0x4e19,0x9d2c,0x4046,
0xbdbd,0xa326,0xbf33,0x4054,
0xae21,0xeb5e,0xc9e2,0x4051,
0x25b2,0x9e1f,0x200a,0x4037,
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f1a,0xb4c2,0x93c3,0x1bb0,
0x3fdf,0xd6f5,0x3f56,0x52f2,
0x4012,0xd2ba,0xed92,0x6911,
0x402c,0xff72,0xc63e,0xeb2e,
0x4031,0xefd6,0x924b,0xc84d,
0x401e,0xd563,0x7d7e,0xdcf8,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x4026,0x9320,0xae97,0xef8e,
0x4046,0x9d2c,0x4e19,0xc033,
0x4054,0xbf33,0xa326,0xbdbd,
0x4051,0xc9e2,0xeb5e,0xae21,
0x4037,0x200a,0x9e1f,0x25b2,
};
#endif
/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
*/
#ifdef UNK
const static double R[3] = {
-7.89580278884799154124E-1,
1.63866645699558079767E1,
-6.41409952958715622951E1,
};
const static double S[3] = {
/* 1.00000000000000000000E0,*/
-3.56722798256324312549E1,
3.12093766372244180303E2,
-7.69691943550460008604E2,
};
#endif
#ifdef DEC
static unsigned short R[12] = {
0140112,0020756,0161540,0072035,
0041203,0013743,0114023,0155527,
0141600,0044060,0104421,0050400,
};
static unsigned short S[12] = {
/*0040200,0000000,0000000,0000000,*/
0141416,0130152,0017543,0064122,
0042234,0006000,0104527,0020155,
0142500,0066110,0146631,0174731,
};
#endif
#ifdef IBMPC
static unsigned short R[12] = {
0x0e84,0xdc6c,0x443d,0xbfe9,
0x7b6b,0x7302,0x62fc,0x4030,
0x2a20,0x1122,0x0906,0xc050,
};
static unsigned short S[12] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6d0a,0x43ec,0xd60d,0xc041,
0xe40e,0x112a,0x8180,0x4073,
0x3f3b,0x19b3,0x0d89,0xc088,
};
#endif
#ifdef MIEEE
static unsigned short R[12] = {
0xbfe9,0x443d,0xdc6c,0x0e84,
0x4030,0x62fc,0x7302,0x7b6b,
0xc050,0x0906,0x1122,0x2a20,
};
static unsigned short S[12] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0xc041,0xd60d,0x43ec,0x6d0a,
0x4073,0x8180,0x112a,0xe40e,
0xc088,0x0d89,0x19b3,0x3f3b,
};
#endif
#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double frexp(), ldexp(), polevl(), p1evl();
int isnan(), isfinite();
#endif
#define SQRTH 0.70710678118654752440
extern double INFINITY, NAN;
double log(x)
double x;
{
int e;
#ifdef DEC
short *q;
#endif
double y, z;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
if( x == INFINITY )
return(x);
#endif
/* Test for domain */
if( x <= 0.0 )
{
if( x == 0.0 )
{
mtherr( fname, SING );
return( -INFINITY );
}
else
{
mtherr( fname, DOMAIN );
return( NAN );
}
}
/* separate mantissa from exponent */
#ifdef DEC
q = (short *)&x;
e = *q; /* short containing exponent */
e = ((e >> 7) & 0377) - 0200; /* the exponent */
*q &= 0177; /* strip exponent from x */
*q |= 040000; /* x now between 0.5 and 1 */
#endif
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
#ifdef IBMPC
x = frexp( x, &e );
/*
q = (short *)&x;
q += 3;
e = *q;
e = ((e >> 4) & 0x0fff) - 0x3fe;
*q &= 0x0f;
*q |= 0x3fe0;
*/
#endif
/* Equivalent C language standard library function: */
#ifdef UNK
x = frexp( x, &e );
#endif
#ifdef MIEEE
x = frexp( x, &e );
#endif
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if( (e > 2) || (e < -2) )
{
if( x < SQRTH )
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5;
y = 0.5 * z + 0.5;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5;
z -= 0.5;
y = 0.5 * x + 0.5;
}
x = z / y;
/* rational form */
z = x*x;
z = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
y = e;
z = z - y * 2.121944400546905827679e-4;
z = z + x;
z = z + e * 0.693359375;
goto ldone;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if( x < SQRTH )
{
e -= 1;
x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
}
else
{
x = x - 1.0;
}
/* rational form */
z = x*x;
#if DEC
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) );
#else
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
#endif
if( e )
y = y - e * 2.121944400546905827679e-4;
y = y - ldexp( z, -1 ); /* y - 0.5 * z */
z = x + y;
if( e )
z = z + e * 0.693359375;
ldone:
return( z );
}

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/* log10.c
*
* Common logarithm
*
*
*
* SYNOPSIS:
*
* double x, y, log10();
*
* y = log10( x );
*
*
*
* DESCRIPTION:
*
* Returns logarithm to the base 10 of x.
*
* The argument is separated into its exponent and fractional
* parts. The logarithm of the fraction is approximated by
*
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
* IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
* DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
*
* In the tests over the interval [1, MAXNUM], the logarithms
* of the random arguments were uniformly distributed over
* [0, MAXLOG].
*
* ERROR MESSAGES:
*
* log10 singularity: x = 0; returns -INFINITY
* log10 domain: x < 0; returns NAN
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
static char fname[] = {"log10"};
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
*/
#ifdef UNK
const static double P[] = {
4.58482948458143443514E-5,
4.98531067254050724270E-1,
6.56312093769992875930E0,
2.97877425097986925891E1,
6.06127134467767258030E1,
5.67349287391754285487E1,
1.98892446572874072159E1
};
const static double Q[] = {
/* 1.00000000000000000000E0, */
1.50314182634250003249E1,
8.27410449222435217021E1,
2.20664384982121929218E2,
3.07254189979530058263E2,
2.14955586696422947765E2,
5.96677339718622216300E1
};
#endif
#ifdef DEC
static unsigned short P[] = {
0034500,0046473,0051374,0135174,
0037777,0037566,0145712,0150321,
0040722,0002426,0031543,0123107,
0041356,0046513,0170752,0004346,
0041562,0071553,0023536,0163343,
0041542,0170221,0024316,0114216,
0041237,0016454,0046611,0104602
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041160,0100260,0067736,0102424,
0041645,0075552,0036563,0147072,
0042134,0125025,0021132,0025320,
0042231,0120211,0046030,0103271,
0042126,0172241,0052151,0120426,
0041556,0125702,0072116,0047103
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x974f,0x6a5f,0x09a7,0x3f08,
0x5a1a,0xd979,0xe7ee,0x3fdf,
0x74c9,0xc66c,0x40a2,0x401a,
0x411d,0x7e3d,0xc9a9,0x403d,
0xdcdc,0x64eb,0x4e6d,0x404e,
0xd312,0x2519,0x5e12,0x404c,
0x3130,0x89b1,0xe3a5,0x4033
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xd0a2,0x0dfb,0x1016,0x402e,
0x79c7,0x47ae,0xaf6d,0x4054,
0x455a,0xa44b,0x9542,0x406b,
0x10d7,0x2983,0x3411,0x4073,
0x3423,0x2a8d,0xde94,0x406a,
0xc9c8,0x4e89,0xd578,0x404d
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f08,0x09a7,0x6a5f,0x974f,
0x3fdf,0xe7ee,0xd979,0x5a1a,
0x401a,0x40a2,0xc66c,0x74c9,
0x403d,0xc9a9,0x7e3d,0x411d,
0x404e,0x4e6d,0x64eb,0xdcdc,
0x404c,0x5e12,0x2519,0xd312,
0x4033,0xe3a5,0x89b1,0x3130
};
static unsigned short Q[] = {
0x402e,0x1016,0x0dfb,0xd0a2,
0x4054,0xaf6d,0x47ae,0x79c7,
0x406b,0x9542,0xa44b,0x455a,
0x4073,0x3411,0x2983,0x10d7,
0x406a,0xde94,0x2a8d,0x3423,
0x404d,0xd578,0x4e89,0xc9c8
};
#endif
#define SQRTH 0.70710678118654752440
#define L102A 3.0078125E-1
#define L102B 2.48745663981195213739E-4
#define L10EA 4.3359375E-1
#define L10EB 7.00731903251827651129E-4
#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double frexp(), ldexp(), polevl(), p1evl();
int isnan(), isfinite();
#endif
extern double LOGE2, SQRT2, INFINITY, NAN;
double log10(x)
double x;
{
VOLATILE double z;
double y;
#ifdef DEC
short *q;
#endif
int e;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
if( x == INFINITY )
return(x);
#endif
/* Test for domain */
if( x <= 0.0 )
{
if( x == 0.0 )
{
mtherr( fname, SING );
return( -INFINITY );
}
else
{
mtherr( fname, DOMAIN );
return( NAN );
}
}
/* separate mantissa from exponent */
#ifdef DEC
q = (short *)&x;
e = *q; /* short containing exponent */
e = ((e >> 7) & 0377) - 0200; /* the exponent */
*q &= 0177; /* strip exponent from x */
*q |= 040000; /* x now between 0.5 and 1 */
#endif
#ifdef IBMPC
x = frexp( x, &e );
/*
q = (short *)&x;
q += 3;
e = *q;
e = ((e >> 4) & 0x0fff) - 0x3fe;
*q &= 0x0f;
*q |= 0x3fe0;
*/
#endif
/* Equivalent C language standard library function: */
#ifdef UNK
x = frexp( x, &e );
#endif
#ifdef MIEEE
x = frexp( x, &e );
#endif
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if( x < SQRTH )
{
e -= 1;
x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
}
else
{
x = x - 1.0;
}
/* rational form */
z = x*x;
y = x * ( z * polevl( x, P, 6 ) / p1evl( x, Q, 6 ) );
y = y - ldexp( z, -1 ); /* y - 0.5 * x**2 */
/* multiply log of fraction by log10(e)
* and base 2 exponent by log10(2)
*/
z = (x + y) * L10EB; /* accumulate terms in order of size */
z += y * L10EA;
z += x * L10EA;
z += e * L102B;
z += e * L102A;
return( z );
}

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/* log2.c
*
* Base 2 logarithm
*
*
*
* SYNOPSIS:
*
* double x, y, log2();
*
* y = log2( x );
*
*
*
* DESCRIPTION:
*
* Returns the base 2 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the base e
* logarithm of the fraction is approximated by
*
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z**3 P(z)/Q(z).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 30000 2.0e-16 5.5e-17
* IEEE exp(+-700) 40000 1.3e-16 4.6e-17
*
* In the tests over the interval [exp(+-700)], the logarithms
* of the random arguments were uniformly distributed.
*
* ERROR MESSAGES:
*
* log2 singularity: x = 0; returns -INFINITY
* log2 domain: x < 0; returns NAN
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
static char fname[] = {"log2"};
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
*/
#ifdef UNK
const static double P[] = {
1.01875663804580931796E-4,
4.97494994976747001425E-1,
4.70579119878881725854E0,
1.44989225341610930846E1,
1.79368678507819816313E1,
7.70838733755885391666E0,
};
const static double Q[] = {
/* 1.00000000000000000000E0, */
1.12873587189167450590E1,
4.52279145837532221105E1,
8.29875266912776603211E1,
7.11544750618563894466E1,
2.31251620126765340583E1,
};
#define LOG2EA 0.44269504088896340735992
#endif
#ifdef DEC
static unsigned short P[] = {
0037777,0127270,0162547,0057274,
0041001,0054665,0164317,0005341,
0041451,0034104,0031640,0105773,
0041677,0011276,0123617,0160135,
0041701,0126603,0053215,0117250,
0041420,0115777,0135206,0030232,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041220,0144332,0045272,0174241,
0041742,0164566,0035720,0130431,
0042246,0126327,0166065,0116357,
0042372,0033420,0157525,0124560,
0042271,0167002,0066537,0172303,
0041730,0164777,0113711,0044407,
};
static unsigned short L[5] = {0037742,0124354,0122560,0057703};
#define LOG2EA (*(double *)(&L[0]))
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x1bb0,0x93c3,0xb4c2,0x3f1a,
0x52f2,0x3f56,0xd6f5,0x3fdf,
0x6911,0xed92,0xd2ba,0x4012,
0xeb2e,0xc63e,0xff72,0x402c,
0xc84d,0x924b,0xefd6,0x4031,
0xdcf8,0x7d7e,0xd563,0x401e,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xef8e,0xae97,0x9320,0x4026,
0xc033,0x4e19,0x9d2c,0x4046,
0xbdbd,0xa326,0xbf33,0x4054,
0xae21,0xeb5e,0xc9e2,0x4051,
0x25b2,0x9e1f,0x200a,0x4037,
};
static unsigned short L[5] = {0x0bf8,0x94ae,0x551d,0x3fdc};
#define LOG2EA (*(double *)(&L[0]))
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f1a,0xb4c2,0x93c3,0x1bb0,
0x3fdf,0xd6f5,0x3f56,0x52f2,
0x4012,0xd2ba,0xed92,0x6911,
0x402c,0xff72,0xc63e,0xeb2e,
0x4031,0xefd6,0x924b,0xc84d,
0x401e,0xd563,0x7d7e,0xdcf8,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x4026,0x9320,0xae97,0xef8e,
0x4046,0x9d2c,0x4e19,0xc033,
0x4054,0xbf33,0xa326,0xbdbd,
0x4051,0xc9e2,0xeb5e,0xae21,
0x4037,0x200a,0x9e1f,0x25b2,
};
static unsigned short L[5] = {0x3fdc,0x551d,0x94ae,0x0bf8};
#define LOG2EA (*(double *)(&L[0]))
#endif
/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
*/
#ifdef UNK
const static double R[3] = {
-7.89580278884799154124E-1,
1.63866645699558079767E1,
-6.41409952958715622951E1,
};
const static double S[3] = {
/* 1.00000000000000000000E0,*/
-3.56722798256324312549E1,
3.12093766372244180303E2,
-7.69691943550460008604E2,
};
/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340735992
#endif
#ifdef DEC
static unsigned short R[12] = {
0140112,0020756,0161540,0072035,
0041203,0013743,0114023,0155527,
0141600,0044060,0104421,0050400,
};
static unsigned short S[12] = {
/*0040200,0000000,0000000,0000000,*/
0141416,0130152,0017543,0064122,
0042234,0006000,0104527,0020155,
0142500,0066110,0146631,0174731,
};
/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340735992L
#endif
#ifdef IBMPC
static unsigned short R[12] = {
0x0e84,0xdc6c,0x443d,0xbfe9,
0x7b6b,0x7302,0x62fc,0x4030,
0x2a20,0x1122,0x0906,0xc050,
};
static unsigned short S[12] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6d0a,0x43ec,0xd60d,0xc041,
0xe40e,0x112a,0x8180,0x4073,
0x3f3b,0x19b3,0x0d89,0xc088,
};
#endif
#ifdef MIEEE
static unsigned short R[12] = {
0xbfe9,0x443d,0xdc6c,0x0e84,
0x4030,0x62fc,0x7302,0x7b6b,
0xc050,0x0906,0x1122,0x2a20,
};
static unsigned short S[12] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0xc041,0xd60d,0x43ec,0x6d0a,
0x4073,0x8180,0x112a,0xe40e,
0xc088,0x0d89,0x19b3,0x3f3b,
};
#endif
#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double frexp(), ldexp(), polevl(), p1evl();
int isnan(), isfinite();
#endif
#define SQRTH 0.70710678118654752440
extern double LOGE2, INFINITY, NAN;
double log2(x)
double x;
{
int e;
double y;
VOLATILE double z;
#ifdef DEC
short *q;
#endif
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
if( x == INFINITY )
return(x);
#endif
/* Test for domain */
if( x <= 0.0 )
{
if( x == 0.0 )
{
mtherr( fname, SING );
return( -INFINITY );
}
else
{
mtherr( fname, DOMAIN );
return( NAN );
}
}
/* separate mantissa from exponent */
#ifdef DEC
q = (short *)&x;
e = *q; /* short containing exponent */
e = ((e >> 7) & 0377) - 0200; /* the exponent */
*q &= 0177; /* strip exponent from x */
*q |= 040000; /* x now between 0.5 and 1 */
#endif
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
#ifdef IBMPC
x = frexp( x, &e );
/*
q = (short *)&x;
q += 3;
e = *q;
e = ((e >> 4) & 0x0fff) - 0x3fe;
*q &= 0x0f;
*q |= 0x3fe0;
*/
#endif
/* Equivalent C language standard library function: */
#ifdef UNK
x = frexp( x, &e );
#endif
#ifdef MIEEE
x = frexp( x, &e );
#endif
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if( (e > 2) || (e < -2) )
{
if( x < SQRTH )
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5;
y = 0.5 * z + 0.5;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5;
z -= 0.5;
y = 0.5 * x + 0.5;
}
x = z / y;
z = x*x;
y = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
goto ldone;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if( x < SQRTH )
{
e -= 1;
x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
}
else
{
x = x - 1.0;
}
z = x*x;
#if DEC
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) ) - ldexp( z, -1 );
#else
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) ) - ldexp( z, -1 );
#endif
ldone:
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*
* ***CAUTION***
*
* This sequence of operations is critical and it may
* be horribly defeated by some compiler optimizers.
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += e;
return( z );
}

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/* mconf.h
*
* Common include file for math routines
*
*
*
* SYNOPSIS:
*
* #include "mconf.h"
*
*
*
* DESCRIPTION:
*
* This file contains definitions for error codes that are
* passed to the common error handling routine mtherr()
* (which see).
*
* The file also includes a conditional assembly definition
* for the type of computer arithmetic (IEEE, DEC, Motorola
* IEEE, or UNKnown).
*
* For Digital Equipment PDP-11 and VAX computers, certain
* IBM systems, and others that use numbers with a 56-bit
* significand, the symbol DEC should be defined. In this
* mode, most floating point constants are given as arrays
* of octal integers to eliminate decimal to binary conversion
* errors that might be introduced by the compiler.
*
* For little-endian computers, such as IBM PC, that follow the
* IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE
* Std 754-1985), the symbol IBMPC should be defined. These
* numbers have 53-bit significands. In this mode, constants
* are provided as arrays of hexadecimal 16 bit integers.
*
* Big-endian IEEE format is denoted MIEEE. On some RISC
* systems such as Sun SPARC, double precision constants
* must be stored on 8-byte address boundaries. Since integer
* arrays may be aligned differently, the MIEEE configuration
* may fail on such machines.
*
* To accommodate other types of computer arithmetic, all
* constants are also provided in a normal decimal radix
* which one can hope are correctly converted to a suitable
* format by the available C language compiler. To invoke
* this mode, define the symbol UNK.
*
* An important difference among these modes is a predefined
* set of machine arithmetic constants for each. The numbers
* MACHEP (the machine roundoff error), MAXNUM (largest number
* represented), and several other parameters are preset by
* the configuration symbol. Check the file const.c to
* ensure that these values are correct for your computer.
*
* Configurations NANS, INFINITIES, MINUSZERO, and DENORMAL
* may fail on many systems. Verify that they are supposed
* to work on your computer.
*/
/*
Cephes Math Library Release 2.3: June, 1995
Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
*/
/* Define if the `long double' type works. */
#define HAVE_LONG_DOUBLE 1
/* Define as the return type of signal handlers (int or void). */
#define RETSIGTYPE void
/* Define if you have the ANSI C header files. */
#define STDC_HEADERS 1
/* Define if your processor stores words with the most significant
byte first (like Motorola and SPARC, unlike Intel and VAX). */
/* #undef WORDS_BIGENDIAN */
/* Define if floating point words are bigendian. */
/* #undef FLOAT_WORDS_BIGENDIAN */
/* The number of bytes in a int. */
#define SIZEOF_INT 4
/* Define if you have the <string.h> header file. */
#define HAVE_STRING_H 1
/* Name of package */
#define PACKAGE "cephes"
/* Version number of package */
#define VERSION "2.7"
/* Constant definitions for math error conditions
*/
#define DOMAIN 1 /* argument domain error */
#define SING 2 /* argument singularity */
#define OVERFLOW 3 /* overflow range error */
#define UNDERFLOW 4 /* underflow range error */
#define TLOSS 5 /* total loss of precision */
#define PLOSS 6 /* partial loss of precision */
#define EDOM 33
#define ERANGE 34
/* Complex numeral. */
typedef struct
{
double r;
double i;
} cmplx;
#ifdef HAVE_LONG_DOUBLE
/* Long double complex numeral. */
typedef struct
{
long double r;
long double i;
} cmplxl;
#endif
/* Type of computer arithmetic */
/* PDP-11, Pro350, VAX:
*/
/* #define DEC 1 */
/* Intel IEEE, low order words come first:
*/
/* #define IBMPC 1 */
/* Motorola IEEE, high order words come first
* (Sun 680x0 workstation):
*/
/* #define MIEEE 1 */
/* UNKnown arithmetic, invokes coefficients given in
* normal decimal format. Beware of range boundary
* problems (MACHEP, MAXLOG, etc. in const.c) and
* roundoff problems in pow.c:
* (Sun SPARCstation)
*/
#define UNK 1
/* If you define UNK, then be sure to set BIGENDIAN properly. */
#ifdef FLOAT_WORDS_BIGENDIAN
#define BIGENDIAN 1
#else
#define BIGENDIAN 0
#endif
/* Define this `volatile' if your compiler thinks
* that floating point arithmetic obeys the associative
* and distributive laws. It will defeat some optimizations
* (but probably not enough of them).
*
* #define VOLATILE volatile
*/
#define VOLATILE
/* For 12-byte long doubles on an i386, pad a 16-bit short 0
* to the end of real constants initialized by integer arrays.
*
* #define XPD 0,
*
* Otherwise, the type is 10 bytes long and XPD should be
* defined blank (e.g., Microsoft C).
*
* #define XPD
*/
#define XPD 0,
/* Define to support tiny denormal numbers, else undefine. */
#define DENORMAL 1
/* Define to ask for infinity support, else undefine. */
#define INFINITIES 1
/* Define to ask for support of numbers that are Not-a-Number,
else undefine. This may automatically define INFINITIES in some files. */
#define NANS 1
/* Define to distinguish between -0.0 and +0.0. */
#define MINUSZERO 1
/* Define 1 for ANSI C atan2() function
See atan.c and clog.c. */
#define ANSIC 1
/* Get ANSI function prototypes, if you want them. */
#if 1
/* #ifdef __STDC__ */
#define ANSIPROT 1
int mtherr ( char *, int );
#else
int mtherr();
#endif
/* Variable for error reporting. See mtherr.c. */
extern int merror;

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/* Program to test range reduction of trigonometry functions
*
* -- Steve Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double floor ( double );
extern double ldexp ( double, int );
extern double sin ( double );
#else
double floor(), ldexp(), sin();
#endif
#define TPI 6.283185307179586476925
main()
{
char s[40];
double a, n, t, x, y, z;
int lflg;
x = TPI/4.0;
t = 1.0;
loop:
t = 2.0 * t;
/* Stop testing at a point beyond which the integer part of
* x/2pi cannot be represented exactly by a double precision number.
* The library trigonometry functions will probably give up long before
* this point is reached.
*/
if( t > 1.0e16 )
exit(0);
/* Adjust the following to choose a nontrivial x
* where test function(x) has a slope of about 1 or more.
*/
x = TPI * t + 0.5;
z = x;
lflg = 0;
inlup:
/* floor() returns the largest integer less than its argument.
* If you do not have this, or AINT(), then you may convert x/TPI
* to a long integer and then back to double; but in that case
* x will be limited to the largest value that will fit into a
* long integer.
*/
n = floor( z/TPI );
/* Carefully subtract 2 pi n from x.
* This is done by subtracting n * 2**k in such a way that there
* is no arithmetic cancellation error at any step. The k are the
* bits in the number 2 pi.
*
* If you do not have ldexp(), then you may multiply or
* divide n by an appropriate power of 2 after each step.
* For example:
* a = z - 4*n;
* a -= 2*n;
* n /= 4;
* a -= n; n/4
* n /= 8;
* a -= n; n/32
* etc.
* This will only work if division by a power of 2 is exact.
*/
a = z - ldexp(n, 2); /* 4n */
a -= ldexp( n, 1); /* 2n */
a -= ldexp( n, -2 ); /* n/4 */
a -= ldexp( n, -5 ); /* n/32 */
a -= ldexp( n, -9 ); /* n/512 */
a += ldexp( n, -15 ); /* add n/32768 */
a -= ldexp( n, -17 ); /* n/131072 */
a -= ldexp( n, -18 );
a -= ldexp( n, -20 );
a -= ldexp( n, -22 );
a -= ldexp( n, -24 );
a -= ldexp( n, -28 );
a -= ldexp( n, -32 );
a -= ldexp( n, -37 );
a -= ldexp( n, -39 );
a -= ldexp( n, -40 );
a -= ldexp( n, -42 );
a -= ldexp( n, -46 );
a -= ldexp( n, -47 );
/* Subtract what is left of 2 pi n after all the above reductions.
*/
a -= 2.44929359829470635445e-16 * n;
/* If the test is extended too far, it is possible
* to have chosen the wrong value of n. The following
* will fix that, but at some reduction in accuracy.
*/
if( (a > TPI) || (a < -1e-11) )
{
z = a;
lflg += 1;
printf( "Warning! Reduction failed on first try.\n" );
goto inlup;
}
if( a < 0.0 )
{
printf( "Warning! Reduced value < 0\n" );
a += TPI;
}
/* Compute the test function at x and at a = x mod 2 pi.
*/
y = sin(x);
z = sin(a);
printf( "sin(%.15e) error = %.3e\n", x, y-z );
goto loop;
}

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/* mtherr.c
*
* Library common error handling routine
*
*
*
* SYNOPSIS:
*
* char *fctnam;
* int code;
* int mtherr();
*
* mtherr( fctnam, code );
*
*
*
* DESCRIPTION:
*
* This routine may be called to report one of the following
* error conditions (in the include file mconf.h).
*
* Mnemonic Value Significance
*
* DOMAIN 1 argument domain error
* SING 2 function singularity
* OVERFLOW 3 overflow range error
* UNDERFLOW 4 underflow range error
* TLOSS 5 total loss of precision
* PLOSS 6 partial loss of precision
* EDOM 33 Unix domain error code
* ERANGE 34 Unix range error code
*
* The default version of the file prints the function name,
* passed to it by the pointer fctnam, followed by the
* error condition. The display is directed to the standard
* output device. The routine then returns to the calling
* program. Users may wish to modify the program to abort by
* calling exit() under severe error conditions such as domain
* errors.
*
* Since all error conditions pass control to this function,
* the display may be easily changed, eliminated, or directed
* to an error logging device.
*
* SEE ALSO:
*
* mconf.h
*
*/
/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#if 0
#include <stdio.h>
#endif
#include "mconf.h"
int merror = 0;
/* Notice: the order of appearance of the following
* messages is bound to the error codes defined
* in mconf.h.
*/
static char *ermsg[7] = {
"unknown", /* error code 0 */
"domain", /* error code 1 */
"singularity", /* et seq. */
"overflow",
"underflow",
"total loss of precision",
"partial loss of precision"
};
int mtherr( name, code )
char *name;
int code;
{
#if 0
/* Display string passed by calling program,
* which is supposed to be the name of the
* function in which the error occurred:
*/
printf( "\n%s ", name );
/* Set global error message word */
merror = code;
/* Display error message defined
* by the code argument.
*/
if( (code <= 0) || (code >= 7) )
code = 0;
printf( "%s error\n", ermsg[code] );
#endif
/* Return to calling
* program
*/
return( 0 );
}

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/* mtst.c
Consistency tests for math functions.
To get strict rounding rules on a 386 or 68000 computer,
define SETPREC to 1.
With NTRIALS=10000, the following are typical results for
IEEE double precision arithmetic.
Consistency test of math functions.
Max and rms relative errors for 10000 random arguments.
x = cbrt( cube(x) ): max = 0.00E+00 rms = 0.00E+00
x = atan( tan(x) ): max = 2.21E-16 rms = 3.27E-17
x = sin( asin(x) ): max = 2.13E-16 rms = 2.95E-17
x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
x = log( exp(x) ): max = 1.11E-16 A rms = 4.35E-18 A
x = tanh( atanh(x) ): max = 2.22E-16 rms = 2.43E-17
x = asinh( sinh(x) ): max = 2.05E-16 rms = 3.49E-18
x = acosh( cosh(x) ): max = 1.43E-15 A rms = 1.54E-17 A
x = log10( exp10(x) ): max = 5.55E-17 A rms = 1.27E-18 A
x = pow( pow(x,a),1/a ): max = 7.60E-14 rms = 1.05E-15
x = cos( acos(x) ): max = 2.22E-16 A rms = 6.90E-17 A
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
*/
#include <stdio.h>
#include <stdlib.h>
#include "mconf.h"
#ifndef NTRIALS
#define NTRIALS 10000
#endif
/* C9X spells lgam lgamma. */
#define GLIBC2 0
#define GLIBC2r1 0
#define SETPREC 1
#define STRTST 0
#define WTRIALS (NTRIALS/5)
#if GLIBC2
double PI = 3.141592653589793238462643;
double PIO2 = 3.141592653589793238462643 * 0.5;
double MAXLOG = 7.09782712893383996732224E2;
#else
extern double PI;
extern double PIO2;
extern double MAXLOG;
#endif
extern double MINLOG;
/*
define MINLOG -170.0
define MAXLOG +170.0
define PI 3.14159265358979323846
define PIO2 1.570796326794896619
*/
#ifdef ANSIPROT
extern double fabs ( double );
extern double sqrt ( double );
extern double cbrt ( double );
extern double exp ( double );
extern double log ( double );
extern double exp10 ( double );
extern double log10 ( double );
extern double tan ( double );
extern double atan ( double );
extern double sin ( double );
extern double asin ( double );
extern double cos ( double );
extern double acos ( double );
extern double pow ( double, double );
extern double tanh ( double );
extern double atanh ( double );
extern double sinh ( double );
extern double asinh ( double x );
extern double cosh ( double );
extern double acosh ( double );
extern double gamma ( double );
extern double lgam ( double );
extern double jn ( int, double );
extern double yn ( int, double );
extern double ndtr ( double );
extern double ndtri ( double );
extern double stdtr ( int, double );
extern double stdtri ( int, double );
extern double ellpe ( double );
extern double ellpk ( double );
#else
double fabs(), sqrt(), cbrt(), exp(), log();
double exp10(), log10(), tan(), atan();
double sin(), asin(), cos(), acos(), pow();
double tanh(), atanh(), sinh(), asinh(), cosh(), acosh();
double gamma(), lgam(), jn(), yn(), ndtrl(), ndtril();
double stdtrl(), stdtril(), ellpel(), ellpkl();
#endif
#if GLIBC2
extern double lgamma (double);
extern double tgamma ( double );
#endif
#if SETPREC
int dprec();
#endif
int drand();
/* void exit(); */
/* int printf(); */
/* Provide inverses for square root and cube root: */
double square(x)
double x;
{
return( x * x );
}
double cube(x)
double x;
{
return( x * x * x );
}
/* lookup table for each function */
struct fundef
{
char *nam1; /* the function */
double (*name )();
char *nam2; /* its inverse */
double (*inv )();
int nargs; /* number of function arguments */
int tstyp; /* type code of the function */
long ctrl; /* relative error flag */
double arg1w; /* width of domain for 1st arg */
double arg1l; /* lower bound domain 1st arg */
long arg1f; /* flags, e.g. integer arg */
double arg2w; /* same info for args 2, 3, 4 */
double arg2l;
long arg2f;
/*
double arg3w;
double arg3l;
long arg3f;
double arg4w;
double arg4l;
long arg4f;
*/
};
/* fundef.ctrl bits: */
#define RELERR 1
/* fundef.tstyp test types: */
#define POWER 1
#define ELLIP 2
#define GAMMA 3
#define WRONK1 4
#define WRONK2 5
#define WRONK3 6
#define STDTR 7
/* fundef.argNf argument flag bits: */
#define INT 2
#define EXPSCAL 4
#if GLIBC2r1
#define NTESTS 12
#else
#if GLIBC2
#define NTESTS 13
#else
#define NTESTS 17
#endif
#endif
struct fundef defs[NTESTS] = {
{" cube", cube, " cbrt", cbrt, 1, 0, 1, 2002.0, -1001.0, 0,
0.0, 0.0, 0},
{" tan", tan, " atan", atan, 1, 0, 1, 0.0, 0.0, 0,
0.0, 0.0, 0},
{" asin", asin, " sin", sin, 1, 0, 1, 2.0, -1.0, 0,
0.0, 0.0, 0},
{"square", square, " sqrt", sqrt, 1, 0, 1, 170.0, -85.0, EXPSCAL,
0.0, 0.0, 0},
{" exp", exp, " log", log, 1, 0, 0, 340.0, -170.0, 0,
0.0, 0.0, 0},
{" atanh", atanh, " tanh", tanh, 1, 0, 1, 2.0, -1.0, 0,
0.0, 0.0, 0},
{" sinh", sinh, " asinh", asinh, 1, 0, 1, 340.0, 0.0, 0,
0.0, 0.0, 0},
{" cosh", cosh, " acosh", acosh, 1, 0, 0, 340.0, 0.0, 0,
0.0, 0.0, 0},
#if !GLIBC2r1
{" exp10", exp10, " log10", log10, 1, 0, 0, 340.0, -170.0, 0,
0.0, 0.0, 0},
#endif
{"pow", pow, "pow", pow, 2, POWER, 1, 21.0, 0.0, 0,
42.0, -21.0, 0},
{" acos", acos, " cos", cos, 1, 0, 0, 2.0, -1.0, 0,
0.0, 0.0, 0},
#if GLIBC2
#if !GLIBC2r1
{ "tgamma", tgamma, "lgamma", lgamma, 1, GAMMA, 0, 34.0, 0.0, 0,
0.0, 0.0, 0},
#endif
#else
{ "gamma", gamma, "lgam", lgam, 1, GAMMA, 0, 34.0, 0.0, 0,
0.0, 0.0, 0},
#endif
{ " Jn", jn, " Yn", yn, 2, WRONK1, 0, 30.0, 0.1, 0,
40.0, -20.0, INT},
#if !GLIBC2
{ " ndtr", ndtr, " ndtri", ndtri, 1, 0, 1, 10.0L, -10.0L, 0,
0.0, 0.0, 0},
{ " ndtri", ndtri, " ndtr", ndtr, 1, 0, 1, 1.0L, 0.0L, 0,
0.0, 0.0, 0},
{" ellpe", ellpe, " ellpk", ellpk, 1, ELLIP, 0, 1.0L, 0.0L, 0,
0.0, 0.0, 0},
{ "stdtr", stdtr, "stdtri", stdtri, 2, STDTR, 1, 4.0L, -2.0L, 0,
30.0, 1.0, INT},
#endif
};
static char *headrs[] = {
"x = %s( %s(x) ): ",
"x = %s( %s(x,a),1/a ): ", /* power */
"Legendre %s, %s: ", /* ellip */
"%s(x) = log(%s(x)): ", /* gamma */
"Wronksian of %s, %s: ",
"Wronksian of %s, %s: ",
"Wronksian of %s, %s: ",
"x = %s(%s(k,x) ): ", /* stdtr */
};
const static double yy1 = 0.0;
const static double y2 = 0.0;
const static double y3 = 0.0;
const static double y4 = 0.0;
const static double a = 0.0;
const static double x = 0.0;
const static double y = 0.0;
const static double z = 0.0;
const static double e = 0.0;
const static double max = 0.0;
const static double rmsa = 0.0;
const static double rms = 0.0;
const static double ave = 0.0;
int main()
{
double (*fun )();
double (*ifun )();
struct fundef *d;
int i, k, itst;
int m, ntr;
#if SETPREC
dprec(); /* set coprocessor precision */
#endif
ntr = NTRIALS;
printf( "Consistency test of math functions.\n" );
printf( "Max and rms relative errors for %d random arguments.\n",
ntr );
/* Initialize machine dependent parameters: */
defs[1].arg1w = PI;
defs[1].arg1l = -PI/2.0;
/* Microsoft C has trouble with denormal numbers. */
#if 0
defs[3].arg1w = MAXLOG;
defs[3].arg1l = -MAXLOG/2.0;
defs[4].arg1w = 2*MAXLOG;
defs[4].arg1l = -MAXLOG;
#endif
defs[6].arg1w = 2.0*MAXLOG;
defs[6].arg1l = -MAXLOG;
defs[7].arg1w = MAXLOG;
defs[7].arg1l = 0.0;
/* Outer loop, on the test number: */
for( itst=STRTST; itst<NTESTS; itst++ )
{
d = &defs[itst];
k = 0;
m = 0;
max = 0.0;
rmsa = 0.0;
ave = 0.0;
fun = d->name;
ifun = d->inv;
/* Absolute error criterion starts with gamma function
* (put all such at end of table)
*/
#if 0
if( d->tstyp == GAMMA )
printf( "Absolute error criterion (but relative if >1):\n" );
#endif
/* Smaller number of trials for Wronksians
* (put them at end of list)
*/
#if 0
if( d->tstyp == WRONK1 )
{
ntr = WTRIALS;
printf( "Absolute error and only %d trials:\n", ntr );
}
#endif
if( d->tstyp == STDTR )
{
ntr = NTRIALS/10;
printf( "Relative error and only %d trials:\n", ntr );
}
printf( headrs[d->tstyp], d->nam2, d->nam1 );
for( i=0; i<ntr; i++ )
{
m++;
/* make random number(s) in desired range(s) */
switch( d->nargs )
{
default:
goto illegn;
case 2:
drand( &a );
a = d->arg2w * ( a - 1.0 ) + d->arg2l;
if( d->arg2f & EXPSCAL )
{
a = exp(a);
drand( &y2 );
a -= 1.0e-13 * a * y2;
}
if( d->arg2f & INT )
{
k = a + 0.25;
a = k;
}
case 1:
drand( &x );
x = d->arg1w * ( x - 1.0 ) + d->arg1l;
if( d->arg1f & EXPSCAL )
{
x = exp(x);
drand( &a );
x += 1.0e-13 * x * a;
}
}
/* compute function under test */
switch( d->nargs )
{
case 1:
switch( d->tstyp )
{
case ELLIP:
yy1 = ( *(fun) )(x);
y2 = ( *(fun) )(1.0-x);
y3 = ( *(ifun) )(x);
y4 = ( *(ifun) )(1.0-x);
break;
case GAMMA:
#if GLIBC2
y = lgamma(x);
x = log( tgamma(x) );
#else
y = lgam(x);
x = log( gamma(x) );
#endif
break;
default:
z = ( *(fun) )(x);
y = ( *(ifun) )(z);
}
break;
case 2:
if( d->arg2f & INT )
{
switch( d->tstyp )
{
case WRONK1:
yy1 = (*fun)( k, x ); /* jn */
y2 = (*fun)( k+1, x );
y3 = (*ifun)( k, x ); /* yn */
y4 = (*ifun)( k+1, x );
break;
case WRONK2:
yy1 = (*fun)( a, x ); /* iv */
y2 = (*fun)( a+1.0, x );
y3 = (*ifun)( k, x ); /* kn */
y4 = (*ifun)( k+1, x );
break;
default:
z = (*fun)( k, x );
y = (*ifun)( k, z );
}
}
else
{
if( d->tstyp == POWER )
{
z = (*fun)( x, a );
y = (*ifun)( z, 1.0/a );
}
else
{
z = (*fun)( a, x );
y = (*ifun)( a, z );
}
}
break;
default:
illegn:
printf( "Illegal nargs= %d", d->nargs );
exit(1);
}
switch( d->tstyp )
{
case WRONK1:
e = (y2*y3 - yy1*y4) - 2.0/(PI*x); /* Jn, Yn */
break;
case WRONK2:
e = (y2*y3 + yy1*y4) - 1.0/x; /* In, Kn */
break;
case ELLIP:
e = (yy1-y3)*y4 + y3*y2 - PIO2;
break;
default:
e = y - x;
break;
}
if( d->ctrl & RELERR )
e /= x;
else
{
if( fabs(x) > 1.0 )
e /= x;
}
ave += e;
/* absolute value of error */
if( e < 0 )
e = -e;
/* peak detect the error */
if( e > max )
{
max = e;
if( e > 1.0e-10 )
{
printf("x %.6E z %.6E y %.6E max %.4E\n",
x, z, y, max);
if( d->tstyp == POWER )
{
printf( "a %.6E\n", a );
}
if( d->tstyp >= WRONK1 )
{
printf( "yy1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
yy1, y2, y3, y4, k, x );
}
}
/*
printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
a, b, c, x, y, max, n);
*/
}
/* accumulate rms error */
e *= 1.0e16; /* adjust range */
rmsa += e * e; /* accumulate the square of the error */
}
/* report after NTRIALS trials */
rms = 1.0e-16 * sqrt( rmsa/m );
if(d->ctrl & RELERR)
printf(" max = %.2E rms = %.2E\n", max, rms );
else
printf(" max = %.2E A rms = %.2E A\n", max, rms );
} /* loop on itst */
exit(0);
}

30
components/external/espruino/libs/math/mtst.opt vendored Normal file
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@@ -0,0 +1,30 @@
acosh.obj,-
asin.obj,-
asinh.obj,-
atan.obj,-
atanh.obj,-
cbrt.obj,-
chbevl.obj,-
const.obj,-
cosh.obj,-
drand.obj,-
exp.obj,-
exp10.obj,-
fabs.obj,-
floor.obj,-
log.obj,-
log10.obj,-
polevl.obj,-
pow.obj,-
powi.obj,-
round.obj,-
sin.obj,-
sinh.obj,-
tan.obj,-
tanh.obj,-
unity.obj,-
sqrt.obj,-
floor.obj,-
polevl.obj,-
mtherr.obj,-
sys$library:vaxcrtl/lib

116
components/external/espruino/libs/math/polevl.asm vendored Normal file
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@@ -0,0 +1,116 @@
; Static Name Aliases
;
TITLE polevl
_TEXT SEGMENT BYTE PUBLIC 'CODE'
_TEXT ENDS
CONST SEGMENT WORD PUBLIC 'CONST'
CONST ENDS
_BSS SEGMENT WORD PUBLIC 'BSS'
_BSS ENDS
_DATA SEGMENT WORD PUBLIC 'DATA'
_DATA ENDS
DGROUP GROUP CONST, _BSS, _DATA
ASSUME CS: _TEXT, DS: DGROUP, SS: DGROUP, ES: DGROUP
PUBLIC _polevl
PUBLIC _p1evl
_DATA SEGMENT
EXTRN __chkstk:NEAR
EXTRN __fac:NEAR
EXTRN __fltused:NEAR
$T20001 DQ 0000000000H ; .0000000000000000
ans DQ 0
ctrlw DW 0
_DATA ENDS
_TEXT SEGMENT
PUBLIC _polevl
_polevl PROC NEAR
push bp
mov bp,sp
mov ax,12
call __chkstk
push si
mov si,[bp+12]
; fstcw ctrlw
; fwait
; mov ax,ctrlw
; or ax,00100h
; mov ctrlw,ax
; fldcw ctrlw
fldz
fwait
mov ax,[bp+14]
inc ax
mov [bp-12],ax
$D15:
fmul QWORD PTR [bp+4]
add si,8
fwait
fadd QWORD PTR [si-8]
fwait
dec WORD PTR [bp-12]
jne $D15
fstp ans
; fstcw ctrlw
; fwait
; mov ax,ctrlw
; and ax,0feffh
; mov ctrlw,ax
; fldcw ctrlw
lea ax, ans
fwait
pop si
mov sp,bp
pop bp
ret
_polevl ENDP
PUBLIC _p1evl
_p1evl PROC NEAR
push bp
mov bp,sp
mov ax,12
call __chkstk
push si
; fstcw ctrlw
; fwait
; mov ax,ctrlw
; or ax,00100h
; mov ctrlw,ax
; fldcw ctrlw
mov si,[bp+12]
fld QWORD PTR [bp+4]
add si,8
fadd QWORD PTR [si-8]
fwait
mov ax,[bp+14]
dec ax
mov [bp-12],ax
$D26:
fmul QWORD PTR [bp+4]
add si,8
fadd QWORD PTR [si-8]
fwait
dec WORD PTR [bp-12]
jne $D26
fstp ans
lea ax, ans
; fstcw ctrlw
; fwait
; mov ax,ctrlw
; and ax,0feffh
; mov ctrlw,ax
; fldcw ctrlw
fwait
pop si
mov sp,bp
pop bp
ret
_p1evl ENDP
_TEXT ENDS
END

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components/external/espruino/libs/math/polevl.c vendored Normal file
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/* polevl.c
* p1evl.c
*
* Evaluate polynomial
*
*
*
* SYNOPSIS:
*
* int N;
* double x, y, coef[N+1], polevl[];
*
* y = polevl( x, coef, N );
*
*
*
* DESCRIPTION:
*
* Evaluates polynomial of degree N:
*
* 2 N
* y = C + C x + C x +...+ C x
* 0 1 2 N
*
* Coefficients are stored in reverse order:
*
* coef[0] = C , ..., coef[N] = C .
* N 0
*
* The function p1evl() assumes that coef[N] = 1.0 and is
* omitted from the array. Its calling arguments are
* otherwise the same as polevl().
*
*
* SPEED:
*
* In the interest of speed, there are no checks for out
* of bounds arithmetic. This routine is used by most of
* the functions in the library. Depending on available
* equipment features, the user may wish to rewrite the
* program in microcode or assembly language.
*
*/
/*
Cephes Math Library Release 2.1: December, 1988
Copyright 1984, 1987, 1988 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
double polevl( x, coef, N )
double x;
double coef[];
int N;
{
double ans;
int i;
double *p;
p = coef;
ans = *p++;
i = N;
do
ans = ans * x + *p++;
while( --i );
return( ans );
}
/* p1evl() */
/* N
* Evaluate polynomial when coefficient of x is 1.0.
* Otherwise same as polevl.
*/
double p1evl( x, coef, N )
double x;
double coef[];
int N;
{
double ans;
double *p;
int i;
p = coef;
ans = x + *p++;
i = N-1;
do
ans = ans * x + *p++;
while( --i );
return( ans );
}

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components/external/espruino/libs/math/pow.c vendored Normal file
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/* pow.c
*
* Power function
*
*
*
* SYNOPSIS:
*
* double x, y, z, pow();
*
* z = pow( x, y );
*
*
*
* DESCRIPTION:
*
* Computes x raised to the yth power. Analytically,
*
* x**y = exp( y log(x) ).
*
* Following Cody and Waite, this program uses a lookup table
* of 2**-i/16 and pseudo extended precision arithmetic to
* obtain an extra three bits of accuracy in both the logarithm
* and the exponential.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -26,26 30000 4.2e-16 7.7e-17
* DEC -26,26 60000 4.8e-17 9.1e-18
* 1/26 < x < 26, with log(x) uniformly distributed.
* -26 < y < 26, y uniformly distributed.
* IEEE 0,8700 30000 1.5e-14 2.1e-15
* 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* pow overflow x**y > MAXNUM INFINITY
* pow underflow x**y < 1/MAXNUM 0.0
* pow domain x<0 and y noninteger 0.0
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
static char fname[] = {"pow"};
#define SQRTH 0.70710678118654752440
#ifdef UNK
const static double P[] = {
4.97778295871696322025E-1,
3.73336776063286838734E0,
7.69994162726912503298E0,
4.66651806774358464979E0
};
const static double Q[] = {
/* 1.00000000000000000000E0, */
9.33340916416696166113E0,
2.79999886606328401649E1,
3.35994905342304405431E1,
1.39995542032307539578E1
};
/* 2^(-i/16), IEEE precision */
const static double A[] = {
1.00000000000000000000E0,
9.57603280698573700036E-1,
9.17004043204671215328E-1,
8.78126080186649726755E-1,
8.40896415253714502036E-1,
8.05245165974627141736E-1,
7.71105412703970372057E-1,
7.38413072969749673113E-1,
7.07106781186547572737E-1,
6.77127773468446325644E-1,
6.48419777325504820276E-1,
6.20928906036742001007E-1,
5.94603557501360513449E-1,
5.69394317378345782288E-1,
5.45253866332628844837E-1,
5.22136891213706877402E-1,
5.00000000000000000000E-1
};
const static double B[] = {
0.00000000000000000000E0,
1.64155361212281360176E-17,
4.09950501029074826006E-17,
3.97491740484881042808E-17,
-4.83364665672645672553E-17,
1.26912513974441574796E-17,
1.99100761573282305549E-17,
-1.52339103990623557348E-17,
0.00000000000000000000E0
};
const static double R[] = {
1.49664108433729301083E-5,
1.54010762792771901396E-4,
1.33335476964097721140E-3,
9.61812908476554225149E-3,
5.55041086645832347466E-2,
2.40226506959099779976E-1,
6.93147180559945308821E-1
};
#define douba(k) A[k]
#define doubb(k) B[k]
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif
#ifdef DEC
static unsigned short P[] = {
0037776,0156313,0175332,0163602,
0040556,0167577,0052366,0174245,
0040766,0062753,0175707,0055564,
0040625,0052035,0131344,0155636,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041025,0052644,0154404,0105155,
0041337,0177772,0007016,0047646,
0041406,0062740,0154273,0020020,
0041137,0177054,0106127,0044555,
};
static unsigned short A[] = {
0040200,0000000,0000000,0000000,
0040165,0022575,0012444,0103314,
0040152,0140306,0163735,0022071,
0040140,0146336,0166052,0112341,
0040127,0042374,0145326,0116553,
0040116,0022214,0012437,0102201,
0040105,0063452,0010525,0003333,
0040075,0004243,0117530,0006067,
0040065,0002363,0031771,0157145,
0040055,0054076,0165102,0120513,
0040045,0177326,0124661,0050471,
0040036,0172462,0060221,0120422,
0040030,0033760,0050615,0134251,
0040021,0141723,0071653,0010703,
0040013,0112701,0161752,0105727,
0040005,0125303,0063714,0044173,
0040000,0000000,0000000,0000000
};
static unsigned short B[] = {
0000000,0000000,0000000,0000000,
0021473,0040265,0153315,0140671,
0121074,0062627,0042146,0176454,
0121413,0003524,0136332,0066212,
0121767,0046404,0166231,0012553,
0121257,0015024,0002357,0043574,
0021736,0106532,0043060,0056206,
0121310,0020334,0165705,0035326,
0000000,0000000,0000000,0000000
};
static unsigned short R[] = {
0034173,0014076,0137624,0115771,
0035041,0076763,0003744,0111311,
0035656,0141766,0041127,0074351,
0036435,0112533,0073611,0116664,
0037143,0054106,0134040,0152223,
0037565,0176757,0176026,0025551,
0040061,0071027,0173721,0147572
};
/*
const static double R[] = {
0.14928852680595608186e-4,
0.15400290440989764601e-3,
0.13333541313585784703e-2,
0.96181290595172416964e-2,
0.55504108664085595326e-1,
0.24022650695909537056e0,
0.69314718055994529629e0
};
*/
#define douba(k) (*(double *)&A[(k)<<2])
#define doubb(k) (*(double *)&B[(k)<<2])
#define MEXP 2031.0
#define MNEXP -2031.0
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x5cf0,0x7f5b,0xdb99,0x3fdf,
0xdf15,0xea9e,0xddef,0x400d,
0xeb6f,0x7f78,0xccbd,0x401e,
0x9b74,0xb65c,0xaa83,0x4012,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x914e,0x9b20,0xaab4,0x4022,
0xc9f5,0x41c1,0xffff,0x403b,
0x6402,0x1b17,0xccbc,0x4040,
0xe92e,0x918a,0xffc5,0x402b,
};
static unsigned short A[] = {
0x0000,0x0000,0x0000,0x3ff0,
0x90da,0xa2a4,0xa4af,0x3fee,
0xa487,0xdcfb,0x5818,0x3fed,
0x529c,0xdd85,0x199b,0x3fec,
0xd3ad,0x995a,0xe89f,0x3fea,
0xf090,0x82a3,0xc491,0x3fe9,
0xa0db,0x422a,0xace5,0x3fe8,
0x0187,0x73eb,0xa114,0x3fe7,
0x3bcd,0x667f,0xa09e,0x3fe6,
0x5429,0xdd48,0xab07,0x3fe5,
0x2a27,0xd536,0xbfda,0x3fe4,
0x3422,0x4c12,0xdea6,0x3fe3,
0xb715,0x0a31,0x06fe,0x3fe3,
0x6238,0x6e75,0x387a,0x3fe2,
0x517b,0x3c7d,0x72b8,0x3fe1,
0x890f,0x6cf9,0xb558,0x3fe0,
0x0000,0x0000,0x0000,0x3fe0
};
static unsigned short B[] = {
0x0000,0x0000,0x0000,0x0000,
0x3707,0xd75b,0xed02,0x3c72,
0xcc81,0x345d,0xa1cd,0x3c87,
0x4b27,0x5686,0xe9f1,0x3c86,
0x6456,0x13b2,0xdd34,0xbc8b,
0x42e2,0xafec,0x4397,0x3c6d,
0x82e4,0xd231,0xf46a,0x3c76,
0x8a76,0xb9d7,0x9041,0xbc71,
0x0000,0x0000,0x0000,0x0000
};
static unsigned short R[] = {
0x937f,0xd7f2,0x6307,0x3eef,
0x9259,0x60fc,0x2fbe,0x3f24,
0xef1d,0xc84a,0xd87e,0x3f55,
0x33b7,0x6ef1,0xb2ab,0x3f83,
0x1a92,0xd704,0x6b08,0x3fac,
0xc56d,0xff82,0xbfbd,0x3fce,
0x39ef,0xfefa,0x2e42,0x3fe6
};
#define douba(k) (*(double *)&A[(k)<<2])
#define doubb(k) (*(double *)&B[(k)<<2])
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3fdf,0xdb99,0x7f5b,0x5cf0,
0x400d,0xddef,0xea9e,0xdf15,
0x401e,0xccbd,0x7f78,0xeb6f,
0x4012,0xaa83,0xb65c,0x9b74
};
static unsigned short Q[] = {
0x4022,0xaab4,0x9b20,0x914e,
0x403b,0xffff,0x41c1,0xc9f5,
0x4040,0xccbc,0x1b17,0x6402,
0x402b,0xffc5,0x918a,0xe92e
};
static unsigned short A[] = {
0x3ff0,0x0000,0x0000,0x0000,
0x3fee,0xa4af,0xa2a4,0x90da,
0x3fed,0x5818,0xdcfb,0xa487,
0x3fec,0x199b,0xdd85,0x529c,
0x3fea,0xe89f,0x995a,0xd3ad,
0x3fe9,0xc491,0x82a3,0xf090,
0x3fe8,0xace5,0x422a,0xa0db,
0x3fe7,0xa114,0x73eb,0x0187,
0x3fe6,0xa09e,0x667f,0x3bcd,
0x3fe5,0xab07,0xdd48,0x5429,
0x3fe4,0xbfda,0xd536,0x2a27,
0x3fe3,0xdea6,0x4c12,0x3422,
0x3fe3,0x06fe,0x0a31,0xb715,
0x3fe2,0x387a,0x6e75,0x6238,
0x3fe1,0x72b8,0x3c7d,0x517b,
0x3fe0,0xb558,0x6cf9,0x890f,
0x3fe0,0x0000,0x0000,0x0000
};
static unsigned short B[] = {
0x0000,0x0000,0x0000,0x0000,
0x3c72,0xed02,0xd75b,0x3707,
0x3c87,0xa1cd,0x345d,0xcc81,
0x3c86,0xe9f1,0x5686,0x4b27,
0xbc8b,0xdd34,0x13b2,0x6456,
0x3c6d,0x4397,0xafec,0x42e2,
0x3c76,0xf46a,0xd231,0x82e4,
0xbc71,0x9041,0xb9d7,0x8a76,
0x0000,0x0000,0x0000,0x0000
};
static unsigned short R[] = {
0x3eef,0x6307,0xd7f2,0x937f,
0x3f24,0x2fbe,0x60fc,0x9259,
0x3f55,0xd87e,0xc84a,0xef1d,
0x3f83,0xb2ab,0x6ef1,0x33b7,
0x3fac,0x6b08,0xd704,0x1a92,
0x3fce,0xbfbd,0xff82,0xc56d,
0x3fe6,0x2e42,0xfefa,0x39ef
};
#define douba(k) (*(double *)&A[(k)<<2])
#define doubb(k) (*(double *)&B[(k)<<2])
#define MEXP 16383.0
#ifdef DENORMAL
#define MNEXP -17183.0
#else
#define MNEXP -16383.0
#endif
#endif
/* log2(e) - 1 */
#define LOG2EA 0.44269504088896340736
#define F W
#define Fa Wa
#define Fb Wb
#define G W
#define Ga Wa
#define Gb u
#define H W
#define Ha Wb
#define Hb Wb
#ifdef ANSIPROT
extern double floor ( double );
extern double fabs ( double );
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double powi ( double, int );
extern int signbit ( double );
extern int isnan ( double );
extern int isfinite ( double );
const static double reduc ( double );
#else
double floor(), fabs(), frexp(), ldexp();
double polevl(), p1evl(), powi();
int signbit(), isnan(), isfinite();
const static double reduc();
#endif
extern double MAXNUM;
#ifdef INFINITIES
extern double INFINITY;
#endif
#ifdef NANS
extern double NAN;
#endif
#ifdef MINUSZERO
extern double NEGZERO;
#endif
double pow( x, y )
double x, y;
{
double w, z, W, Wa, Wb, ya, yb, u;
/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
double aw, ay, wy;
int e, i, nflg, iyflg, yoddint;
if( y == 0.0 )
return( 1.0 );
#ifdef NANS
if( isnan(x) )
return( x );
if( isnan(y) )
return( y );
#endif
if( y == 1.0 )
return( x );
#ifdef INFINITIES
if( !isfinite(y) && (x == 1.0 || x == -1.0) )
{
mtherr( "pow", DOMAIN );
#ifdef NANS
return( NAN );
#else
return( INFINITY );
#endif
}
#endif
if( x == 1.0 )
return( 1.0 );
if( y >= MAXNUM )
{
#ifdef INFINITIES
if( x > 1.0 )
return( INFINITY );
#else
if( x > 1.0 )
return( MAXNUM );
#endif
if( x > 0.0 && x < 1.0 )
return( 0.0);
if( x < -1.0 )
{
#ifdef INFINITIES
return( INFINITY );
#else
return( MAXNUM );
#endif
}
if( x > -1.0 && x < 0.0 )
return( 0.0 );
}
if( y <= -MAXNUM )
{
if( x > 1.0 )
return( 0.0 );
#ifdef INFINITIES
if( x > 0.0 && x < 1.0 )
return( INFINITY );
#else
if( x > 0.0 && x < 1.0 )
return( MAXNUM );
#endif
if( x < -1.0 )
return( 0.0 );
#ifdef INFINITIES
if( x > -1.0 && x < 0.0 )
return( INFINITY );
#else
if( x > -1.0 && x < 0.0 )
return( MAXNUM );
#endif
}
if( x >= MAXNUM )
{
#if INFINITIES
if( y > 0.0 )
return( INFINITY );
#else
if( y > 0.0 )
return( MAXNUM );
#endif
return(0.0);
}
/* Set iyflg to 1 if y is an integer. */
iyflg = 0;
w = floor(y);
if( w == y )
iyflg = 1;
/* Test for odd integer y. */
yoddint = 0;
if( iyflg )
{
ya = fabs(y);
ya = floor(0.5 * ya);
yb = 0.5 * fabs(w);
if( ya != yb )
yoddint = 1;
}
if( x <= -MAXNUM )
{
if( y > 0.0 )
{
#ifdef INFINITIES
if( yoddint )
return( -INFINITY );
return( INFINITY );
#else
if( yoddint )
return( -MAXNUM );
return( MAXNUM );
#endif
}
if( y < 0.0 )
{
#ifdef MINUSZERO
if( yoddint )
return( NEGZERO );
#endif
return( 0.0 );
}
}
nflg = 0; /* flag = 1 if x<0 raised to integer power */
if( x <= 0.0 )
{
if( x == 0.0 )
{
if( y < 0.0 )
{
#ifdef MINUSZERO
if( signbit(x) && yoddint )
return( -INFINITY );
#endif
#ifdef INFINITIES
return( INFINITY );
#else
return( MAXNUM );
#endif
}
if( y > 0.0 )
{
#ifdef MINUSZERO
if( signbit(x) && yoddint )
return( NEGZERO );
#endif
return( 0.0 );
}
return( 1.0 );
}
else
{
if( iyflg == 0 )
{ /* noninteger power of negative number */
mtherr( fname, DOMAIN );
#ifdef NANS
return(NAN);
#else
return(0.0L);
#endif
}
nflg = 1;
}
}
/* Integer power of an integer. */
if( iyflg )
{
i = w;
w = floor(x);
if( (w == x) && (fabs(y) < 32768.0) )
{
w = powi( x, (int) y );
return( w );
}
}
if( nflg )
x = fabs(x);
/* For results close to 1, use a series expansion. */
w = x - 1.0;
aw = fabs(w);
ay = fabs(y);
wy = w * y;
ya = fabs(wy);
if((aw <= 1.0e-3 && ay <= 1.0)
|| (ya <= 1.0e-3 && ay >= 1.0))
{
z = (((((w*(y-5.)/720. + 1./120.)*w*(y-4.) + 1./24.)*w*(y-3.)
+ 1./6.)*w*(y-2.) + 0.5)*w*(y-1.) )*wy + wy + 1.;
goto done;
}
/* These are probably too much trouble. */
#if 0
w = y * log(x);
if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
{
z = ((((((
w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
goto done;
}
if(ya <= 1.0e-3 && aw <= 1.0e-4)
{
z = (((((
wy*1./720.
+ (-w*1./48. + 1./120.) )*wy
+ ((w*17./144. - 1./12.)*w + 1./24.) )*wy
+ (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
+ ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
+ (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
+ wy + 1.0;
goto done;
}
#endif
/* separate significand from exponent */
x = frexp( x, &e );
#if 0
/* For debugging, check for gross overflow. */
if( (e * y) > (MEXP + 1024) )
goto overflow;
#endif
/* Find significand of x in antilog table A[]. */
i = 1;
if( x <= douba(9) )
i = 9;
if( x <= douba(i+4) )
i += 4;
if( x <= douba(i+2) )
i += 2;
if( x >= douba(1) )
i = -1;
i += 1;
/* Find (x - A[i])/A[i]
* in order to compute log(x/A[i]):
*
* log(x) = log( a x/a ) = log(a) + log(x/a)
*
* log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
*/
x -= douba(i);
x -= doubb(i/2);
x /= douba(i);
/* rational approximation for log(1+v):
*
* log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
*/
z = x*x;
w = x * ( z * polevl( x, P, 3 ) / p1evl( x, Q, 4 ) );
w = w - ldexp( z, -1 ); /* w - 0.5 * z */
/* Convert to base 2 logarithm:
* multiply by log2(e)
*/
w = w + LOG2EA * w;
/* Note x was not yet added in
* to above rational approximation,
* so do it now, while multiplying
* by log2(e).
*/
z = w + LOG2EA * x;
z = z + x;
/* Compute exponent term of the base 2 logarithm. */
w = -i;
w = ldexp( w, -4 ); /* divide by 16 */
w += e;
/* Now base 2 log of x is w + z. */
/* Multiply base 2 log by y, in extended precision. */
/* separate y into large part ya
* and small part yb less than 1/16
*/
ya = reduc(y);
yb = y - ya;
F = z * y + w * yb;
Fa = reduc(F);
Fb = F - Fa;
G = Fa + w * ya;
Ga = reduc(G);
Gb = G - Ga;
H = Fb + Gb;
Ha = reduc(H);
w = ldexp( Ga+Ha, 4 );
/* Test the power of 2 for overflow */
if( w > MEXP )
{
#ifndef INFINITIES
mtherr( fname, OVERFLOW );
#endif
#ifdef INFINITIES
if( nflg && yoddint )
return( -INFINITY );
return( INFINITY );
#else
if( nflg && yoddint )
return( -MAXNUM );
return( MAXNUM );
#endif
}
if( w < (MNEXP - 1) )
{
#ifndef DENORMAL
mtherr( fname, UNDERFLOW );
#endif
#ifdef MINUSZERO
if( nflg && yoddint )
return( NEGZERO );
#endif
return( 0.0 );
}
e = w;
Hb = H - Ha;
if( Hb > 0.0 )
{
e += 1;
Hb -= 0.0625;
}
/* Now the product y * log2(x) = Hb + e/16.0.
*
* Compute base 2 exponential of Hb,
* where -0.0625 <= Hb <= 0.
*/
z = Hb * polevl( Hb, R, 6 ); /* z = 2**Hb - 1 */
/* Express e/16 as an integer plus a negative number of 16ths.
* Find lookup table entry for the fractional power of 2.
*/
if( e < 0 )
i = 0;
else
i = 1;
i = e/16 + i;
e = 16*i - e;
w = douba( e );
z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
z = ldexp( z, i ); /* multiply by integer power of 2 */
done:
/* Negate if odd integer power of negative number */
if( nflg && yoddint )
{
#ifdef MINUSZERO
if( z == 0.0 )
z = NEGZERO;
else
#endif
z = -z;
}
return( z );
}
/* Find a multiple of 1/16 that is within 1/16 of x. */
const static double reduc(x)
double x;
{
double t;
t = ldexp( x, 4 );
t = floor( t );
t = ldexp( t, -4 );
return(t);
}

186
components/external/espruino/libs/math/powi.c vendored Normal file
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/* powi.c
*
* Real raised to integer power
*
*
*
* SYNOPSIS:
*
* double x, y, powi();
* int n;
*
* y = powi( x, n );
*
*
*
* DESCRIPTION:
*
* Returns argument x raised to the nth power.
* The routine efficiently decomposes n as a sum of powers of
* two. The desired power is a product of two-to-the-kth
* powers of x. Thus to compute the 32767 power of x requires
* 28 multiplications instead of 32767 multiplications.
*
*
*
* ACCURACY:
*
*
* Relative error:
* arithmetic x domain n domain # trials peak rms
* DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
* IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
* IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
*
* Returns MAXNUM on overflow, zero on underflow.
*
*/
/* powi.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double log ( double );
extern double frexp ( double, int * );
extern int signbit ( double );
#else
double log(), frexp();
int signbit();
#endif
extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;
double powi( x, nn )
double x;
int nn;
{
int n, e, sign, asign, lx;
double w, y, s;
/* See pow.c for these tests. */
if( x == 0.0 )
{
if( nn == 0 )
return( 1.0 );
else if( nn < 0 )
return( INFINITY );
else
{
if( nn & 1 )
return( x );
else
return( 0.0 );
}
}
if( nn == 0 )
return( 1.0 );
if( nn == -1 )
return( 1.0/x );
if( x < 0.0 )
{
asign = -1;
x = -x;
}
else
asign = 0;
if( nn < 0 )
{
sign = -1;
n = -nn;
}
else
{
sign = 1;
n = nn;
}
/* Even power will be positive. */
if( (n & 1) == 0 )
asign = 0;
/* Overflow detection */
/* Calculate approximate logarithm of answer */
s = frexp( x, &lx );
e = (lx - 1)*n;
if( (e == 0) || (e > 64) || (e < -64) )
{
s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
}
else
{
s = LOGE2 * e;
}
if( s > MAXLOG )
{
mtherr( "powi", OVERFLOW );
y = INFINITY;
goto done;
}
#if DENORMAL
if( s < MINLOG )
{
y = 0.0;
goto done;
}
/* Handle tiny denormal answer, but with less accuracy
* since roundoff error in 1.0/x will be amplified.
* The precise demarcation should be the gradual underflow threshold.
*/
if( (s < (-MAXLOG+2.0)) && (sign < 0) )
{
x = 1.0/x;
sign = -sign;
}
#else
/* do not produce denormal answer */
if( s < -MAXLOG )
return(0.0);
#endif
/* First bit of the power */
if( n & 1 )
y = x;
else
y = 1.0;
w = x;
n >>= 1;
while( n )
{
w = w * w; /* arg to the 2-to-the-kth power */
if( n & 1 ) /* if that bit is set, then include in product */
y *= w;
n >>= 1;
}
if( sign < 0 )
y = 1.0/y;
done:
if( asign )
{
/* odd power of negative number */
if( y == 0.0 )
y = NEGZERO;
else
y = -y;
}
return(y);
}

184
components/external/espruino/libs/math/protos.h vendored Normal file
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@@ -0,0 +1,184 @@
/*
* This file was automatically generated by version 1.7 of cextract.
* Manual editing not recommended.
*
* Created: Fri Mar 31 19:17:33 1995
*/
extern double acosh ( double x );
extern int airy ( double, double *, double *, double *, double * );
extern double asin ( double );
extern double acos ( double );
extern double asinh ( double x );
extern double atan ( double );
extern double atan2 ( double y, double x );
extern double atanh ( double );
extern double bdtrc ( int k, int n, double p );
extern double bdtr ( int k, int n, double p );
extern double bdtri ( int k, int n, double y );
extern double beta ( double a, double b );
extern double lbeta ( double a, double b );
extern double btdtr ( double a, double b, double x );
extern double cbrt ( double );
extern double chbevl ( double, void *, int );
extern double chdtrc ( double df, double x );
extern double chdtr ( double df, double x );
extern double chdtri ( double df, double y );
//extern void clog ( cmplx *z, cmplx *w );
//extern void cexp ( cmplx *z, cmplx *w );
//extern void csin ( cmplx *z, cmplx *w );
//extern void ccos ( cmplx *z, cmplx *w );
//extern void ctan ( cmplx *z, cmplx *w );
extern void ccot ( cmplx *z, cmplx *w );
//extern void casin ( cmplx *z, cmplx *w );
//extern void cacos ( cmplx *z, cmplx *w );
//extern void catan ( cmplx *z, cmplx *w );
extern void cadd ( cmplx *a, cmplx *b, cmplx *c );
extern void csub ( cmplx *a, cmplx *b, cmplx *c );
extern void cmul ( cmplx *a, cmplx *b, cmplx *c );
extern void cdiv ( cmplx *a, cmplx *b, cmplx *c );
extern void cmov ( void *a, void *b );
extern void cneg ( cmplx *a );
//extern double cabs ( cmplx *z );
//extern void csqrt ( cmplx *z, cmplx *w );
extern double hypot ( double, double );
extern double cosh ( double );
extern double dawsn ( double xx );
extern void eigens ( double A[], double RR[], double E[], int N );
extern double ellie ( double, double );
extern double ellik ( double, double );
extern double ellpe ( double );
extern int ellpj ( double u, double m, double *sn, double *cn, double *dn, double *ph );
extern double ellpk ( double );
extern double exp10 ( double );
extern double exp1m ( double );
extern double exp2 ( double );
extern double expn ( int n, double x );
extern double fac ( int i );
extern double fdtrc ( int ia, int ib, double x );
extern double fdtr ( int ia, int ib, double x );
extern double fdtri ( int ia, int ib, double y );
extern int fftr ( double x[], int m0, double sine[] );
extern double ceil ( double x );
extern double fabs ( double );
extern double floor ( double );
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern int signbit ( double );
extern int isnan ( double );
extern int isfinite ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double exp ( double );
extern double log ( double );
extern double sin ( double );
extern double cos ( double );
extern double sqrt ( double );
extern int fresnl ( double xxa, double *ssa, double *cca );
extern double gamma ( double );
extern double lgam ( double );
extern double gdtr ( double a, double b, double x );
extern double gdtrc ( double a, double b, double x );
extern int gels ( double A[], double R[], int M, double EPS, double AUX[] );
extern double hyp2f1 ( double a, double b, double c, double x );
extern double hyperg ( double, double, double );
extern double hyp2f0 ( double a, double b, double x, int type, double *err );
extern double i0 ( double );
extern double i0e ( double x );
extern double i1 ( double );
extern double i1e ( double x );
extern double igamc ( double, double );
extern double igam ( double, double );
extern double igami ( double, double );
extern double incbet ( double, double, double );
extern double incbi ( double, double, double );
extern double iv ( double v, double x );
extern double j0 ( double );
extern double y0 ( double );
extern double j1 ( double );
extern double y1 ( double );
extern double jn ( int n, double x );
extern double jv ( double, double );
extern double k0 ( double x );
extern double k0e ( double x );
extern double k1 ( double x );
extern double k1e ( double x );
extern double kn ( int nn, double x );
extern int levnsn ( int n, double r[], double a[], double e[], double refl[] );
extern double log10 ( double );
extern double log2 ( double );
extern long lrand ( void );
extern long lsqrt ( long x );
extern int minv ( double A[], double X[], int n, double B[], int IPS[] );
extern int mmmpy ( int r, int c, double *A, double *B, double *Y );
extern int mtherr ( char *name, int code );
extern int mtransp ( int n, double *A, double *T );
extern int mvmpy ( int r, int c, double *A, double *V, double *Y );
extern double nbdtrc ( int k, int n, double p );
extern double nbdtr ( int k, int n, double p );
extern double nbdtri ( int k, int n, double p );
extern double ndtr ( double a );
extern double erfc ( double );
extern double erf ( double );
extern double ndtri ( double );
extern double pdtrc ( int k, double m );
extern double pdtr ( int k, double m );
extern double pdtri ( int k, double y );
extern double pow ( double, double );
extern double powi ( double, int );
extern double psi ( double );
extern void revers ( double y[], double x[], int n );
extern double rgamma ( double x );
extern double round ( double );
extern int sprec ( void );
extern int dprec ( void );
extern int ldprec ( void );
extern int shichi ( double x, double *si, double *ci );
extern int sici ( double x, double *si, double *ci );
extern double simpsn ( double f[], double delta );
extern int simq ( double A[], double B[], double X[], int n, int flag, int IPS[] );
extern double radian ( double d, double m, double s );
/*
extern int sincos ( double x, double *s, double *c, int flg );
*/
extern double sindg ( double x );
extern double cosdg ( double x );
extern double sinh ( double );
extern double spence ( double );
extern double stdtr ( int k, double t );
extern double stdtri ( int k, double p );
extern double onef2 ( double a, double b, double c, double x, double *err );
extern double threef0 ( double a, double b, double c, double x, double *err );
extern double struve ( double v, double x );
extern double tan ( double );
extern double cot ( double );
extern double tandg ( double x );
extern double cotdg ( double x );
extern double tanh ( double );
extern double log1p ( double );
extern double exmp1 ( double );
extern double cosm1 ( double x );
extern double yn ( int, double );
extern double zeta ( double x, double q );
extern double zetac ( double );
extern int drand ( double *a );
double smirnov ( int, double );
double smirnovi ( int, double );
double kolmogorov ( double );
double kolmogi ( double );
/* polyn.c */
extern void polini ( int maxdeg );
extern void polprt ( double a[], int na, int d );
extern void polclr ( double *a, int n );
extern void polmov ( double *a, int na, double *b );
extern void polmul ( double a[], int na, double b[], int nb, double c[] );
extern void poladd ( double a[], int na, double b[], int nb, double c[] );
extern void polsub ( double a[], int na, double b[], int nb, double c[] );
extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
extern double poleva ( double a[], int na, double x );
/* polmisc.c */
extern void polatn ( double num[], double den[], double ans[], int nn );
extern void polsqt ( double pol[], double ans[], int nn );
extern void polsin ( double x[], double y[], int nn );
extern void polcos ( double x[], double y[], int nn );

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/* round.c
*
* Round double to nearest or even integer valued double
*
*
*
* SYNOPSIS:
*
* double x, y, round();
*
* y = round(x);
*
*
*
* DESCRIPTION:
*
* Returns the nearest integer to x as a double precision
* floating point result. If x ends in 0.5 exactly, the
* nearest even integer is chosen.
*
*
*
* ACCURACY:
*
* If x is greater than 1/(2*MACHEP), its closest machine
* representation is already an integer, so rounding does
* not change it.
*/
/*
Cephes Math Library Release 2.1: January, 1989
Copyright 1984, 1987, 1989 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include "mconf.h"
#ifdef ANSIPROT
double floor ( double );
#else
double floor();
#endif
double round(x)
double x;
{
double y, r;
/* Largest integer <= x */
y = floor(x);
/* Fractional part */
r = x - y;
/* Round up to nearest. */
if( r > 0.5 )
goto rndup;
/* Round to even */
if( r == 0.5 )
{
r = y - 2.0 * floor( 0.5 * y );
if( r == 1.0 )
{
rndup:
y += 1.0;
}
}
/* Else round down. */
return(y);
}

207
components/external/espruino/libs/math/setprbor.asm vendored Normal file
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;
; Borland assembler header
;
; Microsoft MASM subroutines for setting coprocessor precision
;
.286
.287
PREC_TEXT SEGMENT BYTE PUBLIC 'CODE'
PREC_TEXT ENDS
DGROUP group _DATA,_BSS
assume cs:PREC_TEXT,ds:DGROUP
_DATA segment word public 'DATA'
d@ label byte
d@w label word
_DATA ends
_BSS segment word public 'BSS'
b@ label byte
b@w label word
_BSS ends
; exception masks (1 = masked)
; 1 invalid operation
; 2 denormalized operand
; 4 zero divide
; 8 overflow
; 10 underflow
; 20 precision
_DATA SEGMENT
; double precision setting
;;ctlwrd dw 01230h ; note this traps on denormal operands!
;;ctld dw 0133fh ; this doesn't trap
ctld dw 01230h
; single precision
ctls dw 01030h
; long double precision
ctlld dw 01320h
_DATA ENDS
PREC_TEXT segment byte public 'CODE'
assume cs:PREC_TEXT,ds:DGROUP
; Set coprocessor to single precision float
PUBLIC _sprec
_sprec PROC FAR
fclex
fwait
finit
fwait
fldcw word ptr ctls
fwait
ret
_sprec ENDP
; set coprocessor to long double precision
PUBLIC _ldprec
_ldprec PROC far
fclex
fwait
finit
fwait
fldcw word ptr ctlld
fwait
ret
_ldprec ENDP
; set coprocessor to double precision
PUBLIC _dprec
_dprec PROC far
fclex
fwait
finit
fwait
fldcw word ptr ctld
fwait
ret
_dprec ENDP
; get a double promoted to long double size
; getld( &doub, &ldoub );
PUBLIC _getld
_getld PROC far
push bp
mov bp,sp
push bx
mov bx, word ptr [bp+4]
; fld st(0)
fld qword ptr [bx]
mov bx, word ptr [bp+6]
fstp tbyte ptr [bx]
mov bx, word ptr [bp+4]
fld qword ptr [bx]
mov bx, word ptr [bp+8]
fstp qword ptr [bx]
pop bx
pop bp
ret
_getld ENDP
PUBLIC _getprec
_getprec PROC far
push bp
mov bp,sp
sub sp,4
fstcw [bp-4]
fwait
mov ax,[bp-4]
add sp,4
pop bp
ret
_getprec ENDP
PUBLIC _fpclear
_fpclear PROC far
push bp
mov bp,sp
fnclex
fwait
pop bp
ret
_fpclear ENDP
PUBLIC _noexcept
_noexcept PROC far
push bp
mov bp,sp
push ax
sub sp,4
fnclex
fwait
fstcw [bp-4]
fwait
mov ax,[bp-4]
and ax,0FFC0h
or ax,003fh
mov [bp-4],ax
fldcw [bp-4]
add sp,4
pop ax
pop bp
ret
_noexcept ENDP
; single precision square root
; assumes coprocessor precision already set up
; return value in static __fac
PUBLIC _sqrtf
_sqrtf PROC FAR
push bp
mov bp,sp
fld DWORD PTR [bp+6]
fsqrt
fwait
mov sp,bp
pop bp
ret
_sqrtf ENDP
; double precision square root
; assumes coprocessor precision already set up
; return value in static __fac
PUBLIC _sqrt
_sqrt PROC FAR
push bp
mov bp,sp
fld QWORD PTR [bp+6]
fsqrt
fwait
mov sp,bp
pop bp
ret
_sqrt ENDP
; long double precision square root
; assumes coprocessor precision already set up
; return value in fp register
PUBLIC _sqrtl
_sqrtl PROC FAR
push bp
mov bp,sp
fld tbyte ptr [bp+6]
fsqrt
fwait
mov sp,bp
pop bp
ret
_sqrtl ENDP
PREC_TEXT ends
_DATA segment word public 'DATA'
s@ label byte
_DATA ends
PREC_TEXT segment byte public 'CODE'
PREC_TEXT ends
_s@ equ s@
public _sprec
public _dprec
public _ldprec
end

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components/external/espruino/libs/math/setprec.387 vendored Normal file
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/* Set 80387 floating point hardware rounding precision */
.file "setprec.387"
.text
.align 2
.globl _sprec
_sprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
andl $0xfcff,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.align 2
.globl _dprec
_dprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
/* andl $0xfcff,%eax */
/* exception on overflow */
andl $0xfcf7,%eax
orl $0x200,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.align 2
.globl _ldprec
_ldprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
orl $0x300,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.globl _getprec
_getprec:
pushl %ebp
movl %esp,%ebp
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
leave
ret
.globl _setfpu
_setfpu:
pushl %ebp
movl %esp,%ebp
movl 8(%ebp),%eax
pushl %eax
fldcw (%esp)
fwait
movl %ebp,%esp
popl %ebp
ret

35
components/external/espruino/libs/math/setprec.688 vendored Normal file
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/* Set 68881/2 floating point rounding precision */
/* Reference: MC68881/MC68882 Floating-Point Coprocessor */
/* User's Manual, Motorola, Prentice-Hall, 1987 (First Edition) */
/* Pages 1-14, 2-3, 4-68. */
/* FPcr code $80 sets the 68882 coprocessor to */
/* rounding precision = 53 bits */
/* rounding mode = nearest or even */
/* all exceptions (bits 8-15) disabled */
/* The instruction is */
/* FMOVE.L #$80,Fcr */
/* if the assembler will understand it. */
.align 2
.text
/* set to single precision */
.globl _sprec
_sprec
.word 0xf23c,0x9000,0x0000,0x0040
rts
/* set to double precision */
.globl _dprec
_dprec:
.word 0xf23c,0x9000,0x0000,0x0080
rts
/* set to extended (long double) precision */
.globl _ldprec
_ldprec:
.word 0xf23c,0x9000,0x0000,0x0000
rts

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components/external/espruino/libs/math/setprec.87 vendored Normal file
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;
; Microsoft MASM subroutines for setting coprocessor precision
;
.286
.287
_TEXT SEGMENT BYTE PUBLIC 'CODE'
_TEXT ENDS
CONST SEGMENT WORD PUBLIC 'CONST'
CONST ENDS
_BSS SEGMENT WORD PUBLIC 'BSS'
_BSS ENDS
_DATA SEGMENT WORD PUBLIC 'DATA'
_DATA ENDS
DGROUP GROUP CONST, _BSS, _DATA
ASSUME CS: _TEXT, DS: DGROUP, SS: DGROUP, ES: DGROUP
EXTRN __fac:QWORD
_BSS SEGMENT
EXTRN __fltused:NEAR
_BSS ENDS
; exception masks (1 = masked)
; 1 invalid operation
; 2 denormalized operand
; 4 zero divide
; 8 overflow
; 10 underflow
; 20 precision
_DATA SEGMENT
; double precision setting
;;ctlwrd dw 01230h ; note this traps on denormal operands!
;;ctld dw 0133fh ; this doesn't trap
ctld dw 01230h
; single precision
ctls dw 01030h
; long double precision
ctlld dw 01320h
_DATA ENDS
ASSUME CS: _TEXT
_TEXT SEGMENT
; Set coprocessor to single precision float
PUBLIC _sprec
_sprec PROC NEAR
fclex
fwait
finit
fwait
fldcw word ptr ctls
fwait
ret
_sprec ENDP
; set coprocessor to long double precision
PUBLIC _ldprec
_ldprec PROC NEAR
fclex
fwait
finit
fwait
fldcw word ptr ctlld
fwait
ret
_ldprec ENDP
; set coprocessor to double precision
PUBLIC _dprec
_dprec PROC NEAR
fclex
fwait
finit
fwait
fldcw word ptr ctld
fwait
ret
_dprec ENDP
; get a double promoted to long double size
; getld( &doub, &ldoub );
PUBLIC _getld
_getld PROC NEAR
push bp
mov bp,sp
push bx
mov bx, word ptr [bp+4]
; fld st(0)
fld qword ptr [bx]
mov bx, word ptr [bp+6]
fstp tbyte ptr [bx]
mov bx, word ptr [bp+4]
fld qword ptr [bx]
mov bx, word ptr [bp+8]
fstp qword ptr [bx]
pop bx
pop bp
ret
_getld ENDP
PUBLIC _getprec
_getprec PROC NEAR
push bp
mov bp,sp
sub sp,4
fstcw [bp-4]
fwait
mov ax,[bp-4]
add sp,4
pop bp
ret
_getprec ENDP
PUBLIC _fpclear
_fpclear PROC NEAR
push bp
mov bp,sp
fnclex
fwait
pop bp
ret
_fpclear ENDP
PUBLIC _noexcept
_noexcept PROC NEAR
push bp
mov bp,sp
push ax
sub sp,4
fnclex
fwait
fstcw [bp-4]
fwait
mov ax,[bp-4]
and ax,0FFC0h
or ax,003fh
mov [bp-4],ax
fldcw [bp-4]
add sp,4
pop ax
pop bp
ret
_noexcept ENDP
;; single precision square root
;; assumes coprocessor precision already set up
;; return value in static __fac
; PUBLIC _sqrtf
;_sqrtf PROC NEAR
; push bp
; mov bp,sp
; fld DWORD PTR [bp+4]
; fsqrt
; fwait
; fstp DWORD PTR __fac
; mov ax,OFFSET __fac
; mov sp,bp
; pop bp
; ret
;_sqrtf ENDP
;
;
;; double precision square root
;; assumes coprocessor precision already set up
;; return value in static __fac
; PUBLIC _sqrt
;_sqrt PROC NEAR
; push bp
; mov bp,sp
; fld QWORD PTR [bp+4]
; fsqrt
; fwait
; fstp QWORD PTR __fac
; mov ax,OFFSET __fac
; mov sp,bp
; pop bp
; ret
;_sqrt ENDP
;
;
;; long double precision square root
;; assumes coprocessor precision already set up
;; return value in fp register
; PUBLIC _sqrtl
;_sqrtl PROC NEAR
; push bp
; mov bp,sp
; fld tbyte ptr [bp+4]
; fsqrt
; fwait
; mov sp,bp
; pop bp
; ret
;_sqrtl ENDP
;
_TEXT ENDS
END

10
components/external/espruino/libs/math/setprec.c vendored Normal file
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/* Null stubs for coprocessor precision settings */
int
sprec() {return 0; }
int
dprec() {return 0; }
int
ldprec() {return 0; }

83
components/external/espruino/libs/math/setprelf.387 vendored Normal file
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/* Set 80387 floating point hardware rounding precision */
.file "setprec.387"
.version "01.01"
.text
.align 16
.globl sprec
sprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
andl $0xfcff,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.Lfe1:
.size sprec,.Lfe1-sprec
.align 16
.globl dprec
dprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
andl $0xfcff,%eax
/* trap on overflow */
/* andl $0xfcf7,%eax */
orl $0x200,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.Lfe2:
.size dprec,.Lfe2-dprec
.align 16
.globl ldprec
ldprec:
pushl %ebp
movl %esp,%ebp
pushl %eax
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
orl $0x300,%eax
movl %eax,(%esp)
fldcw (%esp)
popl %eax
popl %eax
leave
ret
.Lfe3:
.size ldprec,.Lfe3-ldprec
.align 16
.globl getprec
getprec:
pushl %ebp
movl %esp,%ebp
subl $4,%esp
fstcw (%esp)
fwait
movl (%esp),%eax
leave
ret
.Lfe4:
.size getprec,.Lfe4-getprec

387
components/external/espruino/libs/math/sin.c vendored Normal file
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/* sin.c
*
* Circular sine
*
*
*
* SYNOPSIS:
*
* double x, y, sin();
*
* y = sin( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of pi/4. The reduction
* error is nearly eliminated by contriving an extended precision
* modular arithmetic.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the sine is approximated by
* x + x**3 P(x**2).
* Between pi/4 and pi/2 the cosine is represented as
* 1 - x**2 Q(x**2).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0, 10 150000 3.0e-17 7.8e-18
* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* sin total loss x > 1.073741824e9 0.0
*
* Partial loss of accuracy begins to occur at x = 2**30
* = 1.074e9. The loss is not gradual, but jumps suddenly to
* about 1 part in 10e7. Results may be meaningless for
* x > 2**49 = 5.6e14. The routine as implemented flags a
* TLOSS error for x > 2**30 and returns 0.0.
*/
/* cos.c
*
* Circular cosine
*
*
*
* SYNOPSIS:
*
* double x, y, cos();
*
* y = cos( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of pi/4. The reduction
* error is nearly eliminated by contriving an extended precision
* modular arithmetic.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the cosine is approximated by
* 1 - x**2 Q(x**2).
* Between pi/4 and pi/2 the sine is represented as
* x + x**3 P(x**2).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
* DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
*/
/* sin.c */
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1985, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double sincof[] = {
1.58962301576546568060E-10,
-2.50507477628578072866E-8,
2.75573136213857245213E-6,
-1.98412698295895385996E-4,
8.33333333332211858878E-3,
-1.66666666666666307295E-1,
};
const static double coscof[6] = {
-1.13585365213876817300E-11,
2.08757008419747316778E-9,
-2.75573141792967388112E-7,
2.48015872888517045348E-5,
-1.38888888888730564116E-3,
4.16666666666665929218E-2,
};
const static double DP1 = 7.85398125648498535156E-1;
const static double DP2 = 3.77489470793079817668E-8;
const static double DP3 = 2.69515142907905952645E-15;
/* const static double lossth = 1.073741824e9; */
#endif
#ifdef DEC
static unsigned short sincof[] = {
0030056,0143750,0177214,0163153,
0131727,0027455,0044510,0175352,
0033470,0167432,0131752,0042414,
0135120,0006400,0146776,0174027,
0036410,0104210,0104207,0137202,
0137452,0125252,0125252,0125103,
};
static unsigned short coscof[24] = {
0127107,0151115,0002060,0152325,
0031017,0072353,0155161,0174053,
0132623,0171173,0172542,0057056,
0034320,0006400,0147102,0023652,
0135666,0005540,0133012,0076213,
0037052,0125252,0125252,0125126,
};
/* 7.853981629014015197753906250000E-1 */
static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
/* 4.960467869796758577649598009884E-10 */
static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
/* 2.860594363054915898381331279295E-18 */
static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
#endif
#ifdef IBMPC
static unsigned short sincof[] = {
0x9ccd,0x1fd1,0xd8fd,0x3de5,
0x1f5d,0xa929,0xe5e5,0xbe5a,
0x48a1,0x567d,0x1de3,0x3ec7,
0xdf03,0x19bf,0x01a0,0xbf2a,
0xf7d0,0x1110,0x1111,0x3f81,
0x5548,0x5555,0x5555,0xbfc5,
};
static unsigned short coscof[24] = {
0x1a9b,0xa086,0xfa49,0xbda8,
0x3f05,0x7b4e,0xee9d,0x3e21,
0x4bc6,0x7eac,0x7e4f,0xbe92,
0x44f5,0x19c8,0x01a0,0x3efa,
0x4f91,0x16c1,0xc16c,0xbf56,
0x554b,0x5555,0x5555,0x3fa5,
};
/*
7.85398125648498535156E-1,
3.77489470793079817668E-8,
2.69515142907905952645E-15,
*/
static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
#endif
#ifdef MIEEE
static unsigned short sincof[] = {
0x3de5,0xd8fd,0x1fd1,0x9ccd,
0xbe5a,0xe5e5,0xa929,0x1f5d,
0x3ec7,0x1de3,0x567d,0x48a1,
0xbf2a,0x01a0,0x19bf,0xdf03,
0x3f81,0x1111,0x1110,0xf7d0,
0xbfc5,0x5555,0x5555,0x5548,
};
static unsigned short coscof[24] = {
0xbda8,0xfa49,0xa086,0x1a9b,
0x3e21,0xee9d,0x7b4e,0x3f05,
0xbe92,0x7e4f,0x7eac,0x4bc6,
0x3efa,0x01a0,0x19c8,0x44f5,
0xbf56,0xc16c,0x16c1,0x4f91,
0x3fa5,0x5555,0x5555,0x554b,
};
static unsigned short P1[] = {0x3fe9,0x21fb,0x4000,0x0000};
static unsigned short P2[] = {0x3e64,0x442d,0x0000,0x0000};
static unsigned short P3[] = {0x3ce8,0x4698,0x98cc,0x5170};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double polevl(), floor(), ldexp();
int isnan(), isfinite();
#endif
extern double PIO4;
const static double lossth = 1.073741824e9;
#ifdef NANS
extern double NAN;
#endif
#ifdef INFINITIES
extern double INFINITY;
#endif
double sin(x)
double x;
{
double y, z, zz;
int j, sign;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
#ifdef NANS
if( isnan(x) )
return(x);
if( !isfinite(x) )
{
mtherr( "sin", DOMAIN );
return(NAN);
}
#endif
/* make argument positive but save the sign */
sign = 1;
if( x < 0 )
{
x = -x;
sign = -1;
}
if( x > lossth )
{
mtherr( "sin", TLOSS );
return(0.0);
}
y = floor( x/PIO4 ); /* integer part of x/PIO4 */
/* strip high bits of integer part to prevent integer overflow */
z = ldexp( y, -4 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
j = z; /* convert to integer for tests on the phase angle */
/* map zeros to origin */
if( j & 1 )
{
j += 1;
y += 1.0;
}
j = j & 07; /* octant modulo 360 degrees */
/* reflect in x axis */
if( j > 3)
{
sign = -sign;
j -= 4;
}
/* Extended precision modular arithmetic */
z = ((x - y * DP1) - y * DP2) - y * DP3;
zz = z * z;
if( (j==1) || (j==2) )
{
y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
}
else
{
/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
y = z + z * z * z * polevl( zz, sincof, 5 );
}
if(sign < 0)
y = -y;
return(y);
}
double cos(x)
double x;
{
double y, z, zz;
long i;
int j, sign;
#ifdef NANS
if( isnan(x) )
return(x);
if( !isfinite(x) )
{
mtherr( "cos", DOMAIN );
return(NAN);
}
#endif
/* make argument positive */
sign = 1;
if( x < 0 )
x = -x;
if( x > lossth )
{
mtherr( "cos", TLOSS );
return(0.0);
}
y = floor( x/PIO4 );
z = ldexp( y, -4 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
i = z;
if( i & 1 ) /* map zeros to origin */
{
i += 1;
y += 1.0;
}
j = i & 07;
if( j > 3)
{
j -=4;
sign = -sign;
}
if( j > 1 )
sign = -sign;
/* Extended precision modular arithmetic */
z = ((x - y * DP1) - y * DP2) - y * DP3;
zz = z * z;
if( (j==1) || (j==2) )
{
/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
y = z + z * z * z * polevl( zz, sincof, 5 );
}
else
{
y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
}
if(sign < 0)
y = -y;
return(y);
}
/* Degrees, minutes, seconds to radians: */
/* 1 arc second, in radians = 4.8481368110953599358991410e-5 */
#ifdef DEC
static unsigned short P648[] = {034513,054170,0176773,0116043,};
#define P64800 *(double *)P648
#else
const static double P64800 = 4.8481368110953599358991410e-5;
#endif
double radian(d,m,s)
double d,m,s;
{
return( ((d*60.0 + m)*60.0 + s)*P64800 );
}

358
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/* sincos.c
*
* Circular sine and cosine of argument in degrees
* Table lookup and interpolation algorithm
*
*
*
* SYNOPSIS:
*
* double x, sine, cosine, flg, sincos();
*
* sincos( x, &sine, &cosine, flg );
*
*
*
* DESCRIPTION:
*
* Returns both the sine and the cosine of the argument x.
* Several different compile time options and minimax
* approximations are supplied to permit tailoring the
* tradeoff between computation speed and accuracy.
*
* Since range reduction is time consuming, the reduction
* of x modulo 360 degrees is also made optional.
*
* sin(i) is internally tabulated for 0 <= i <= 90 degrees.
* Approximation polynomials, ranging from linear interpolation
* to cubics in (x-i)**2, compute the sine and cosine
* of the residual x-i which is between -0.5 and +0.5 degree.
* In the case of the high accuracy options, the residual
* and the tabulated values are combined using the trigonometry
* formulas for sin(A+B) and cos(A+B).
*
* Compile time options are supplied for 5, 11, or 17 decimal
* relative accuracy (ACC5, ACC11, ACC17 respectively).
* A subroutine flag argument "flg" chooses betwen this
* accuracy and table lookup only (peak absolute error
* = 0.0087).
*
* If the argument flg = 1, then the tabulated value is
* returned for the nearest whole number of degrees. The
* approximation polynomials are not computed. At
* x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
*
* An intermediate speed and precision can be obtained using
* the compile time option LINTERP and flg = 1. This yields
* a linear interpolation using a slope estimated from the sine
* or cosine at the nearest integer argument. The peak absolute
* error with this option is 3.8e-5. Relative error at small
* angles is about 1e-5.
*
* If flg = 0, then the approximation polynomials are computed
* and applied.
*
*
*
* SPEED:
*
* Relative speed comparisons follow for 6MHz IBM AT clone
* and Microsoft C version 4.0. These figures include
* software overhead of do loop and function calls.
* Since system hardware and software vary widely, the
* numbers should be taken as representative only.
*
* flg=0 flg=0 flg=1 flg=1
* ACC11 ACC5 LINTERP Lookup only
* In-line 8087 (/FPi)
* sin(), cos() 1.0 1.0 1.0 1.0
*
* In-line 8087 (/FPi)
* sincos() 1.1 1.4 1.9 3.0
*
* Software (/FPa)
* sin(), cos() 0.19 0.19 0.19 0.19
*
* Software (/FPa)
* sincos() 0.39 0.50 0.73 1.7
*
*
*
* ACCURACY:
*
* The accurate approximations are designed with a relative error
* criterion. The absolute error is greatest at x = 0.5 degree.
* It decreases from a local maximum at i+0.5 degrees to full
* machine precision at each integer i degrees. With the
* ACC5 option, the relative error of 6.3e-6 is equivalent to
* an absolute angular error of 0.01 arc second in the argument
* at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5
* accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
* error decreases in proportion to the argument. This is true
* for both the sine and cosine approximations, since the latter
* is for the function 1 - cos(x).
*
* If absolute error is of most concern, use the compile time
* option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
* precision. This is about half the absolute error of the
* relative precision option. In this case the relative error
* for small angles will increase to 9.5e-6 -- a reasonable
* tradeoff.
*/
#include "mconf.h"
/* Define one of the following to be 1:
*/
#define ACC5 1
#define ACC11 0
#define ACC17 0
/* Option for linear interpolation when flg = 1
*/
#define LINTERP 1
/* Option for absolute error criterion
*/
#define ABSERR 1
/* Option to include modulo 360 function:
*/
#define MOD360 1
/*
Cephes Math Library Release 2.1
Copyright 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Table of sin(i degrees)
* for 0 <= i <= 90
*/
const static double sintbl[92] = {
0.00000000000000000000E0,
1.74524064372835128194E-2,
3.48994967025009716460E-2,
5.23359562429438327221E-2,
6.97564737441253007760E-2,
8.71557427476581735581E-2,
1.04528463267653471400E-1,
1.21869343405147481113E-1,
1.39173100960065444112E-1,
1.56434465040230869010E-1,
1.73648177666930348852E-1,
1.90808995376544812405E-1,
2.07911690817759337102E-1,
2.24951054343864998051E-1,
2.41921895599667722560E-1,
2.58819045102520762349E-1,
2.75637355816999185650E-1,
2.92371704722736728097E-1,
3.09016994374947424102E-1,
3.25568154457156668714E-1,
3.42020143325668733044E-1,
3.58367949545300273484E-1,
3.74606593415912035415E-1,
3.90731128489273755062E-1,
4.06736643075800207754E-1,
4.22618261740699436187E-1,
4.38371146789077417453E-1,
4.53990499739546791560E-1,
4.69471562785890775959E-1,
4.84809620246337029075E-1,
5.00000000000000000000E-1,
5.15038074910054210082E-1,
5.29919264233204954047E-1,
5.44639035015027082224E-1,
5.59192903470746830160E-1,
5.73576436351046096108E-1,
5.87785252292473129169E-1,
6.01815023152048279918E-1,
6.15661475325658279669E-1,
6.29320391049837452706E-1,
6.42787609686539326323E-1,
6.56059028990507284782E-1,
6.69130606358858213826E-1,
6.81998360062498500442E-1,
6.94658370458997286656E-1,
7.07106781186547524401E-1,
7.19339800338651139356E-1,
7.31353701619170483288E-1,
7.43144825477394235015E-1,
7.54709580222771997943E-1,
7.66044443118978035202E-1,
7.77145961456970879980E-1,
7.88010753606721956694E-1,
7.98635510047292846284E-1,
8.09016994374947424102E-1,
8.19152044288991789684E-1,
8.29037572555041692006E-1,
8.38670567945424029638E-1,
8.48048096156425970386E-1,
8.57167300702112287465E-1,
8.66025403784438646764E-1,
8.74619707139395800285E-1,
8.82947592858926942032E-1,
8.91006524188367862360E-1,
8.98794046299166992782E-1,
9.06307787036649963243E-1,
9.13545457642600895502E-1,
9.20504853452440327397E-1,
9.27183854566787400806E-1,
9.33580426497201748990E-1,
9.39692620785908384054E-1,
9.45518575599316810348E-1,
9.51056516295153572116E-1,
9.56304755963035481339E-1,
9.61261695938318861916E-1,
9.65925826289068286750E-1,
9.70295726275996472306E-1,
9.74370064785235228540E-1,
9.78147600733805637929E-1,
9.81627183447663953497E-1,
9.84807753012208059367E-1,
9.87688340595137726190E-1,
9.90268068741570315084E-1,
9.92546151641322034980E-1,
9.94521895368273336923E-1,
9.96194698091745532295E-1,
9.97564050259824247613E-1,
9.98629534754573873784E-1,
9.99390827019095730006E-1,
9.99847695156391239157E-1,
1.00000000000000000000E0,
9.99847695156391239157E-1,
};
#ifdef ANSIPROT
double floor ( double );
#else
double floor();
#endif
int sincos(x, s, c, flg)
double x;
double *s, *c;
int flg;
{
int ix, ssign, csign, xsign;
double y, z, sx, sz, cx, cz;
/* Make argument nonnegative.
*/
xsign = 1;
if( x < 0.0 )
{
xsign = -1;
x = -x;
}
#if MOD360
x = x - 360.0 * floor( x/360.0 );
#endif
/* Find nearest integer to x.
* Note there should be a domain error test here,
* but this is omitted to gain speed.
*/
ix = x + 0.5;
z = x - ix; /* the residual */
/* Look up the sine and cosine of the integer.
*/
if( ix <= 180 )
{
ssign = 1;
csign = 1;
}
else
{
ssign = -1;
csign = -1;
ix -= 180;
}
if( ix > 90 )
{
csign = -csign;
ix = 180 - ix;
}
sx = sintbl[ix];
if( ssign < 0 )
sx = -sx;
cx = sintbl[ 90-ix ];
if( csign < 0 )
cx = -cx;
/* If the flag argument is set, then just return
* the tabulated values for arg to the nearest whole degree.
*/
if( flg )
{
#if LINTERP
y = sx + 1.74531263774940077459e-2 * z * cx;
cx -= 1.74531263774940077459e-2 * z * sx;
sx = y;
#endif
if( xsign < 0 )
sx = -sx;
*s = sx; /* sine */
*c = cx; /* cosine */
return 0;
}
/* Find sine and cosine
* of the residual angle between -0.5 and +0.5 degree.
*/
#if ACC5
#if ABSERR
/* absolute error = 2.769e-8: */
sz = 1.74531263774940077459e-2 * z;
/* absolute error = 4.146e-11: */
cz = 1.0 - 1.52307909153324666207e-4 * z * z;
#else
/* relative error = 6.346e-6: */
sz = 1.74531817576426662296e-2 * z;
/* relative error = 3.173e-6: */
cz = 1.0 - 1.52308226602566149927e-4 * z * z;
#endif
#else
y = z * z;
#endif
#if ACC11
sz = ( -8.86092781698004819918e-7 * y
+ 1.74532925198378577601e-2 ) * z;
cz = 1.0 - ( -3.86631403698859047896e-9 * y
+ 1.52308709893047593702e-4 ) * y;
#endif
#if ACC17
sz = (( 1.34959795251974073996e-11 * y
- 8.86096155697856783296e-7 ) * y
+ 1.74532925199432957214e-2 ) * z;
cz = 1.0 - (( 3.92582397764340914444e-14 * y
- 3.86632385155548605680e-9 ) * y
+ 1.52308709893354299569e-4 ) * y;
#endif
/* Combine the tabulated part and the calculated part
* by trigonometry.
*/
y = sx * cz + cx * sz;
if( xsign < 0 )
y = - y;
*s = y; /* sine */
*c = cx * cz - sx * sz; /* cosine */
return 0;
}

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/* sindg.c
*
* Circular sine of angle in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, sindg();
*
* y = sindg( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the sine is approximated by
* x + x**3 P(x**2).
* Between pi/4 and pi/2 the cosine is represented as
* 1 - x**2 P(x**2).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +-1000 3100 3.3e-17 9.0e-18
* IEEE +-1000 30000 2.3e-16 5.6e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* sindg total loss x > 8.0e14 (DEC) 0.0
* x > 1.0e14 (IEEE)
*
*/
/* cosdg.c
*
* Circular cosine of angle in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, cosdg();
*
* y = cosdg( x );
*
*
*
* DESCRIPTION:
*
* Range reduction is into intervals of 45 degrees.
*
* Two polynomial approximating functions are employed.
* Between 0 and pi/4 the cosine is approximated by
* 1 - x**2 P(x**2).
* Between pi/4 and pi/2 the sine is represented as
* x + x**3 P(x**2).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +-1000 3400 3.5e-17 9.1e-18
* IEEE +-1000 30000 2.1e-16 5.7e-17
* See also sin().
*
*/
/* Cephes Math Library Release 2.0: April, 1987
* Copyright 1985, 1987 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
#include "mconf.h"
#ifdef UNK
const static double sincof[] = {
1.58962301572218447952E-10,
-2.50507477628503540135E-8,
2.75573136213856773549E-6,
-1.98412698295895384658E-4,
8.33333333332211858862E-3,
-1.66666666666666307295E-1
};
const static double coscof[] = {
1.13678171382044553091E-11,
-2.08758833757683644217E-9,
2.75573155429816611547E-7,
-2.48015872936186303776E-5,
1.38888888888806666760E-3,
-4.16666666666666348141E-2,
4.99999999999999999798E-1
};
const static double PI180 = 1.74532925199432957692E-2; /* pi/180 */
const static double lossth = 1.0e14;
#endif
#ifdef DEC
static unsigned short sincof[] = {
0030056,0143750,0177170,0073013,
0131727,0027455,0044510,0132205,
0033470,0167432,0131752,0042263,
0135120,0006400,0146776,0174027,
0036410,0104210,0104207,0137202,
0137452,0125252,0125252,0125103
};
static unsigned short coscof[] = {
0027107,0176030,0153315,0110312,
0131017,0072476,0007450,0123243,
0032623,0171174,0070066,0146445,
0134320,0006400,0147355,0163313,
0035666,0005540,0133012,0165067,
0137052,0125252,0125252,0125206,
0040000,0000000,0000000,0000000
};
static unsigned short P1[] = {0036616,0175065,0011224,0164711};
#define PI180 *(double *)P1
const static double lossth = 8.0e14;
#endif
#ifdef IBMPC
static unsigned short sincof[] = {
0x0ec1,0x1fcf,0xd8fd,0x3de5,
0x1691,0xa929,0xe5e5,0xbe5a,
0x4896,0x567d,0x1de3,0x3ec7,
0xdf03,0x19bf,0x01a0,0xbf2a,
0xf7d0,0x1110,0x1111,0x3f81,
0x5548,0x5555,0x5555,0xbfc5
};
static unsigned short coscof[] = {
0xb219,0x1ad9,0xff83,0x3da8,
0x14d4,0xc1e5,0xeea7,0xbe21,
0xd9a5,0x8e06,0x7e4f,0x3e92,
0xbcd9,0x19dd,0x01a0,0xbefa,
0x5d47,0x16c1,0xc16c,0x3f56,
0x5551,0x5555,0x5555,0xbfa5,
0x0000,0x0000,0x0000,0x3fe0
};
static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
#define PI180 *(double *)P1
const static double lossth = 1.0e14;
#endif
#ifdef MIEEE
static unsigned short sincof[] = {
0x3de5,0xd8fd,0x1fcf,0x0ec1,
0xbe5a,0xe5e5,0xa929,0x1691,
0x3ec7,0x1de3,0x567d,0x4896,
0xbf2a,0x01a0,0x19bf,0xdf03,
0x3f81,0x1111,0x1110,0xf7d0,
0xbfc5,0x5555,0x5555,0x5548
};
static unsigned short coscof[] = {
0x3da8,0xff83,0x1ad9,0xb219,
0xbe21,0xeea7,0xc1e5,0x14d4,
0x3e92,0x7e4f,0x8e06,0xd9a5,
0xbefa,0x01a0,0x19dd,0xbcd9,
0x3f56,0xc16c,0x16c1,0x5d47,
0xbfa5,0x5555,0x5555,0x5551,
0x3fe0,0x0000,0x0000,0x0000
};
static unsigned short P1[] = {
0x3f91,0xdf46,0xa252,0x9d39
};
#define PI180 *(double *)P1
const static double lossth = 1.0e14;
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
#else
double polevl(), floor(), ldexp();
#endif
extern double PIO4;
double sindg(x)
double x;
{
double y, z, zz;
int j, sign;
/* make argument positive but save the sign */
sign = 1;
if( x < 0 )
{
x = -x;
sign = -1;
}
if( x > lossth )
{
mtherr( "sindg", TLOSS );
return(0.0);
}
y = floor( x/45.0 ); /* integer part of x/PIO4 */
/* strip high bits of integer part to prevent integer overflow */
z = ldexp( y, -4 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
j = z; /* convert to integer for tests on the phase angle */
/* map zeros to origin */
if( j & 1 )
{
j += 1;
y += 1.0;
}
j = j & 07; /* octant modulo 360 degrees */
/* reflect in x axis */
if( j > 3)
{
sign = -sign;
j -= 4;
}
z = x - y * 45.0; /* x mod 45 degrees */
z *= PI180; /* multiply by pi/180 to convert to radians */
zz = z * z;
if( (j==1) || (j==2) )
{
y = 1.0 - zz * polevl( zz, coscof, 6 );
}
else
{
y = z + z * (zz * polevl( zz, sincof, 5 ));
}
if(sign < 0)
y = -y;
return(y);
}
double cosdg(x)
double x;
{
double y, z, zz;
int j, sign;
/* make argument positive */
sign = 1;
if( x < 0 )
x = -x;
if( x > lossth )
{
mtherr( "cosdg", TLOSS );
return(0.0);
}
y = floor( x/45.0 );
z = ldexp( y, -4 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
j = z;
if( j & 1 ) /* map zeros to origin */
{
j += 1;
y += 1.0;
}
j = j & 07;
if( j > 3)
{
j -=4;
sign = -sign;
}
if( j > 1 )
sign = -sign;
z = x - y * 45.0; /* x mod 45 degrees */
z *= PI180; /* multiply by pi/180 to convert to radians */
zz = z * z;
if( (j==1) || (j==2) )
{
y = z + z * (zz * polevl( zz, sincof, 5 ));
}
else
{
y = 1.0 - zz * polevl( zz, coscof, 6 );
}
if(sign < 0)
y = -y;
return(y);
}

148
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/* sinh.c
*
* Hyperbolic sine
*
*
*
* SYNOPSIS:
*
* double x, y, sinh();
*
* y = sinh( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic sine of argument in the range MINLOG to
* MAXLOG.
*
* The range is partitioned into two segments. If |x| <= 1, a
* rational function of the form x + x**3 P(x)/Q(x) is employed.
* Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +- 88 50000 4.0e-17 7.7e-18
* IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-7.89474443963537015605E-1,
-1.63725857525983828727E2,
-1.15614435765005216044E4,
-3.51754964808151394800E5
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
-2.77711081420602794433E2,
3.61578279834431989373E4,
-2.11052978884890840399E6
};
#endif
#ifdef DEC
static unsigned short P[] = {
0140112,0015377,0042731,0163255,
0142043,0134721,0146177,0123761,
0143464,0122706,0034353,0006017,
0144653,0140536,0157665,0054045
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0142212,0155404,0133513,0022040,
0044015,0036723,0173271,0011053,
0145400,0150407,0023710,0001034
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x3cd6,0xe8bb,0x435f,0xbfe9,
0xf4fe,0x398f,0x773a,0xc064,
0x6182,0xc71d,0x94b8,0xc0c6,
0xab05,0xdbf6,0x782b,0xc115
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6484,0x96e9,0x5b60,0xc071,
0x2245,0x7ed7,0xa7ba,0x40e1,
0x0044,0xe4f9,0x1a20,0xc140
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xbfe9,0x435f,0xe8bb,0x3cd6,
0xc064,0x773a,0x398f,0xf4fe,
0xc0c6,0x94b8,0xc71d,0x6182,
0xc115,0x782b,0xdbf6,0xab05
};
static unsigned short Q[] = {
0xc071,0x5b60,0x96e9,0x6484,
0x40e1,0xa7ba,0x7ed7,0x2245,
0xc140,0x1a20,0xe4f9,0x0044
};
#endif
#ifdef ANSIPROT
extern double fabs ( double );
extern double exp ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
#else
double fabs(), exp(), polevl(), p1evl();
#endif
extern double INFINITY, MINLOG, MAXLOG, LOGE2;
double sinh(x)
double x;
{
double a;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
a = fabs(x);
if( (x > (MAXLOG + LOGE2)) || (x > -(MINLOG-LOGE2) ) )
{
mtherr( "sinh", DOMAIN );
if( x > 0 )
return( INFINITY );
else
return( -INFINITY );
}
if( a > 1.0 )
{
if( a >= (MAXLOG - LOGE2) )
{
a = exp(0.5*a);
a = (0.5 * a) * a;
if( x < 0 )
a = -a;
return(a);
}
a = exp(a);
a = 0.5*a - (0.5/a);
if( x < 0 )
a = -a;
return(a);
}
a *= a;
return( x + x * a * (polevl(a,P,3)/p1evl(a,Q,3)) );
}

178
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/* sqrt.c
*
* Square root
*
*
*
* SYNOPSIS:
*
* double x, y, sqrt();
*
* y = sqrt( x );
*
*
*
* DESCRIPTION:
*
* Returns the square root of x.
*
* Range reduction involves isolating the power of two of the
* argument and using a polynomial approximation to obtain
* a rough value for the square root. Then Heron's iteration
* is used three times to converge to an accurate value.
*
*
*
* ACCURACY:
*
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0, 10 60000 2.1e-17 7.9e-18
* IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* sqrt domain x < 0 0.0
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
#else
double frexp(), ldexp();
#endif
extern double SQRT2; /* SQRT2 = 1.41421356237309504880 */
double sqrt(x)
double x;
{
int e;
#ifndef UNK
short *q;
#endif
double z, w;
if( x <= 0.0 )
{
if( x < 0.0 )
mtherr( "sqrt", DOMAIN );
return( 0.0 );
}
w = x;
/* separate exponent and significand */
#ifdef UNK
z = frexp( x, &e );
#endif
#ifdef DEC
q = (short *)&x;
e = ((*q >> 7) & 0377) - 0200;
*q &= 0177;
*q |= 040000;
z = x;
#endif
/* Note, frexp and ldexp are used in order to
* handle denormal numbers properly.
*/
#ifdef IBMPC
z = frexp( x, &e );
q = (short *)&x;
q += 3;
/*
e = ((*q >> 4) & 0x0fff) - 0x3fe;
*q &= 0x000f;
*q |= 0x3fe0;
z = x;
*/
#endif
#ifdef MIEEE
z = frexp( x, &e );
q = (short *)&x;
/*
e = ((*q >> 4) & 0x0fff) - 0x3fe;
*q &= 0x000f;
*q |= 0x3fe0;
z = x;
*/
#endif
/* approximate square root of number between 0.5 and 1
* relative error of approximation = 7.47e-3
*/
x = 4.173075996388649989089E-1 + 5.9016206709064458299663E-1 * z;
/* adjust for odd powers of 2 */
if( (e & 1) != 0 )
x *= SQRT2;
/* re-insert exponent */
#ifdef UNK
x = ldexp( x, (e >> 1) );
#endif
#ifdef DEC
*q += ((e >> 1) & 0377) << 7;
*q &= 077777;
#endif
#ifdef IBMPC
x = ldexp( x, (e >> 1) );
/*
*q += ((e >>1) & 0x7ff) << 4;
*q &= 077777;
*/
#endif
#ifdef MIEEE
x = ldexp( x, (e >> 1) );
/*
*q += ((e >>1) & 0x7ff) << 4;
*q &= 077777;
*/
#endif
/* Newton iterations: */
#ifdef UNK
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
#endif
/* Note, assume the square root cannot be denormal,
* so it is safe to use integer exponent operations here.
*/
#ifdef DEC
x += w/x;
*q -= 0200;
x += w/x;
*q -= 0200;
x += w/x;
*q -= 0200;
#endif
#ifdef IBMPC
x += w/x;
*q -= 0x10;
x += w/x;
*q -= 0x10;
x += w/x;
*q -= 0x10;
#endif
#ifdef MIEEE
x += w/x;
*q -= 0x10;
x += w/x;
*q -= 0x10;
x += w/x;
*q -= 0x10;
#endif
return(x);
}

304
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/* tan.c
*
* Circular tangent
*
*
*
* SYNOPSIS:
*
* double x, y, tan();
*
* y = tan( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular tangent of the radian argument x.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +-1.07e9 44000 4.1e-17 1.0e-17
* IEEE +-1.07e9 30000 2.9e-16 8.1e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* tan total loss x > 1.073741824e9 0.0
*
*/
/* cot.c
*
* Circular cotangent
*
*
*
* SYNOPSIS:
*
* double x, y, cot();
*
* y = cot( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular cotangent of the radian argument x.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-1.07e9 30000 2.9e-16 8.2e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* cot total loss x > 1.073741824e9 0.0
* cot singularity x = 0 INFINITY
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
yright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-1.30936939181383777646E4,
1.15351664838587416140E6,
-1.79565251976484877988E7
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
1.36812963470692954678E4,
-1.32089234440210967447E6,
2.50083801823357915839E7,
-5.38695755929454629881E7
};
const static double DP1 = 7.853981554508209228515625E-1;
const static double DP2 = 7.94662735614792836714E-9;
const static double DP3 = 3.06161699786838294307E-17;
const static double lossth = 1.073741824e9;
#endif
#ifdef DEC
static unsigned short P[] = {
0143514,0113306,0111171,0174674,
0045214,0147545,0027744,0167346,
0146210,0177526,0114514,0105660
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0043525,0142457,0072633,0025617,
0145241,0036742,0140525,0162256,
0046276,0146176,0013526,0143573,
0146515,0077401,0162762,0150607
};
/* 7.853981629014015197753906250000E-1 */
static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
/* 4.960467869796758577649598009884E-10 */
static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
/* 2.860594363054915898381331279295E-18 */
static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
const static double lossth = 1.073741824e9;
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x3f38,0xd24f,0x92d8,0xc0c9,
0x9ddd,0xa5fc,0x99ec,0x4131,
0x9176,0xd329,0x1fea,0xc171
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6572,0xeeb3,0xb8a5,0x40ca,
0xbc96,0x582a,0x27bc,0xc134,
0xd8ef,0xc2ea,0xd98f,0x4177,
0x5a31,0x3cbe,0xafe0,0xc189
};
/*
7.85398125648498535156E-1,
3.77489470793079817668E-8,
2.69515142907905952645E-15,
*/
static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
const static double lossth = 1.073741824e9;
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xc0c9,0x92d8,0xd24f,0x3f38,
0x4131,0x99ec,0xa5fc,0x9ddd,
0xc171,0x1fea,0xd329,0x9176
};
static unsigned short Q[] = {
0x40ca,0xb8a5,0xeeb3,0x6572,
0xc134,0x27bc,0x582a,0xbc96,
0x4177,0xd98f,0xc2ea,0xd8ef,
0xc189,0xafe0,0x3cbe,0x5a31
};
static unsigned short P1[] = {
0x3fe9,0x21fb,0x4000,0x0000
};
static unsigned short P2[] = {
0x3e64,0x442d,0x0000,0x0000
};
static unsigned short P3[] = {
0x3ce8,0x4698,0x98cc,0x5170,
};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
const static double lossth = 1.073741824e9;
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
const static double tancot(double, int);
#else
double polevl(), p1evl(), floor(), ldexp();
const static double tancot();
int isnan(), isfinite();
#endif
extern double PIO4;
extern double INFINITY;
extern double NAN;
double tan(x)
double x;
{
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
#ifdef NANS
if( isnan(x) )
return(x);
if( !isfinite(x) )
{
mtherr( "tan", DOMAIN );
return(NAN);
}
#endif
return( tancot(x,0) );
}
double cot(x)
double x;
{
if( x == 0.0 )
{
mtherr( "cot", SING );
return( INFINITY );
}
return( tancot(x,1) );
}
const static double tancot( xx, cotflg )
double xx;
int cotflg;
{
double x, y, z, zz;
int j, sign;
/* make argument positive but save the sign */
if( xx < 0 )
{
x = -xx;
sign = -1;
}
else
{
x = xx;
sign = 1;
}
if( x > lossth )
{
if( cotflg )
mtherr( "cot", TLOSS );
else
mtherr( "tan", TLOSS );
return(0.0);
}
/* compute x mod PIO4 */
y = floor( x/PIO4 );
/* strip high bits of integer part */
z = ldexp( y, -3 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
j = z;
/* map zeros and singularities to origin */
if( j & 1 )
{
j += 1;
y += 1.0;
}
z = ((x - y * DP1) - y * DP2) - y * DP3;
zz = z * z;
if( zz > 1.0e-14 )
y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
else
y = z;
if( j & 2 )
{
if( cotflg )
y = -y;
else
y = -1.0/y;
}
else
{
if( cotflg )
y = 1.0/y;
}
if( sign < 0 )
y = -y;
return( y );
}

267
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/* tandg.c
*
* Circular tangent of argument in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, tandg();
*
* y = tandg( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular tangent of the argument x in degrees.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,10 8000 3.4e-17 1.2e-17
* IEEE 0,10 30000 3.2e-16 8.4e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* tandg total loss x > 8.0e14 (DEC) 0.0
* x > 1.0e14 (IEEE)
* tandg singularity x = 180 k + 90 MAXNUM
*/
/* cotdg.c
*
* Circular cotangent of argument in degrees
*
*
*
* SYNOPSIS:
*
* double x, y, cotdg();
*
* y = cotdg( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular cotangent of the argument x in degrees.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
* ERROR MESSAGES:
*
* message condition value returned
* cotdg total loss x > 8.0e14 (DEC) 0.0
* x > 1.0e14 (IEEE)
* cotdg singularity x = 180 k MAXNUM
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-1.30936939181383777646E4,
1.15351664838587416140E6,
-1.79565251976484877988E7
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
1.36812963470692954678E4,
-1.32089234440210967447E6,
2.50083801823357915839E7,
-5.38695755929454629881E7
};
const static double PI180 = 1.74532925199432957692E-2;
const static double lossth = 1.0e14;
#endif
#ifdef DEC
static unsigned short P[] = {
0143514,0113306,0111171,0174674,
0045214,0147545,0027744,0167346,
0146210,0177526,0114514,0105660
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0043525,0142457,0072633,0025617,
0145241,0036742,0140525,0162256,
0046276,0146176,0013526,0143573,
0146515,0077401,0162762,0150607
};
static unsigned short P1[] = {0036616,0175065,0011224,0164711};
#define PI180 *(double *)P1
const static double lossth = 8.0e14;
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x3f38,0xd24f,0x92d8,0xc0c9,
0x9ddd,0xa5fc,0x99ec,0x4131,
0x9176,0xd329,0x1fea,0xc171
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6572,0xeeb3,0xb8a5,0x40ca,
0xbc96,0x582a,0x27bc,0xc134,
0xd8ef,0xc2ea,0xd98f,0x4177,
0x5a31,0x3cbe,0xafe0,0xc189
};
static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
#define PI180 *(double *)P1
const static double lossth = 1.0e14;
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xc0c9,0x92d8,0xd24f,0x3f38,
0x4131,0x99ec,0xa5fc,0x9ddd,
0xc171,0x1fea,0xd329,0x9176
};
static unsigned short Q[] = {
0x40ca,0xb8a5,0xeeb3,0x6572,
0xc134,0x27bc,0x582a,0xbc96,
0x4177,0xd98f,0xc2ea,0xd8ef,
0xc189,0xafe0,0x3cbe,0x5a31
};
static unsigned short P1[] = {
0x3f91,0xdf46,0xa252,0x9d39
};
#define PI180 *(double *)P1
const static double lossth = 1.0e14;
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
const static double tancot( double, int );
#else
double polevl(), p1evl(), floor(), ldexp();
const static double tancot();
#endif
extern double MAXNUM;
extern double PIO4;
double tandg(x)
double x;
{
return( tancot(x,0) );
}
double cotdg(x)
double x;
{
return( tancot(x,1) );
}
const static double tancot( xx, cotflg )
double xx;
int cotflg;
{
double x, y, z, zz;
int j, sign;
/* make argument positive but save the sign */
if( xx < 0 )
{
x = -xx;
sign = -1;
}
else
{
x = xx;
sign = 1;
}
if( x > lossth )
{
mtherr( "tandg", TLOSS );
return(0.0);
}
/* compute x mod PIO4 */
y = floor( x/45.0 );
/* strip high bits of integer part */
z = ldexp( y, -3 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
j = z;
/* map zeros and singularities to origin */
if( j & 1 )
{
j += 1;
y += 1.0;
}
z = x - y * 45.0;
z *= PI180;
zz = z * z;
if( zz > 1.0e-14 )
y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
else
y = z;
if( j & 2 )
{
if( cotflg )
y = -y;
else
{
if( y != 0.0 )
{
y = -1.0/y;
}
else
{
mtherr( "tandg", SING );
y = MAXNUM;
}
}
}
else
{
if( cotflg )
{
if( y != 0.0 )
y = 1.0/y;
else
{
mtherr( "cotdg", SING );
y = MAXNUM;
}
}
}
if( sign < 0 )
y = -y;
return( y );
}

141
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/* tanh.c
*
* Hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* double x, y, tanh();
*
* y = tanh( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic tangent of argument in the range MINLOG to
* MAXLOG.
*
* A rational function is used for |x| < 0.625. The form
* x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
* Otherwise,
* tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -2,2 50000 3.3e-17 6.4e-18
* IEEE -2,2 30000 2.5e-16 5.8e-17
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
const static double P[] = {
-9.64399179425052238628E-1,
-9.92877231001918586564E1,
-1.61468768441708447952E3
};
const static double Q[] = {
/* 1.00000000000000000000E0,*/
1.12811678491632931402E2,
2.23548839060100448583E3,
4.84406305325125486048E3
};
#endif
#ifdef DEC
static unsigned short P[] = {
0140166,0161335,0053753,0075126,
0141706,0111520,0070463,0040552,
0142711,0153001,0101300,0025430
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041741,0117624,0051300,0156060,
0043013,0133720,0071251,0127717,
0043227,0060201,0021020,0020136
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x6f4b,0xaafd,0xdc5b,0xbfee,
0x682d,0x0e26,0xd26a,0xc058,
0x0563,0x3058,0x3ac0,0xc099
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x1b86,0x8a58,0x33f2,0x405c,
0x35fa,0x0e55,0x76fa,0x40a1,
0x040c,0x2442,0xec10,0x40b2
};
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xbfee,0xdc5b,0xaafd,0x6f4b,
0xc058,0xd26a,0x0e26,0x682d,
0xc099,0x3ac0,0x3058,0x0563
};
static unsigned short Q[] = {
0x405c,0x33f2,0x8a58,0x1b86,
0x40a1,0x76fa,0x0e55,0x35fa,
0x40b2,0xec10,0x2442,0x040c
};
#endif
#ifdef ANSIPROT
extern double fabs ( double );
extern double exp ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
#else
double fabs(), exp(), polevl(), p1evl();
#endif
extern double MAXLOG;
double tanh(x)
double x;
{
double s, z;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
z = fabs(x);
if( z > 0.5 * MAXLOG )
{
if( x > 0 )
return( 1.0 );
else
return( -1.0 );
}
if( z >= 0.625 )
{
s = exp(2.0*z);
z = 1.0 - 2.0/(s + 1.0);
if( x < 0 )
z = -z;
}
else
{
if( x == 0.0 )
return(x);
s = x * x;
z = polevl( s, P, 2 )/p1evl(s, Q, 3);
z = x * s * z;
z = x + z;
}
return( z );
}

138
components/external/espruino/libs/math/unity.c vendored Normal file
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/* unity.c
*
* Relative error approximations for function arguments near
* unity.
*
* log1p(x) = log(1+x)
* expm1(x) = exp(x) - 1
* cosm1(x) = cos(x) - 1
*
*/
#include "mconf.h"
#ifdef ANSIPROT
extern int isnan (double);
extern int isfinite (double);
extern double log ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double exp ( double );
extern double cos ( double );
#else
double log(), polevl(), p1evl(), exp(), cos();
int isnan(), isfinite();
#endif
extern double INFINITY;
/* log1p(x) = log(1 + x) */
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 2.32e-20
*/
const static double LP[] = {
4.5270000862445199635215E-5,
4.9854102823193375972212E-1,
6.5787325942061044846969E0,
2.9911919328553073277375E1,
6.0949667980987787057556E1,
5.7112963590585538103336E1,
2.0039553499201281259648E1,
};
const static double LQ[] = {
/* 1.0000000000000000000000E0,*/
1.5062909083469192043167E1,
8.3047565967967209469434E1,
2.2176239823732856465394E2,
3.0909872225312059774938E2,
2.1642788614495947685003E2,
6.0118660497603843919306E1,
};
#define SQRTH 0.70710678118654752440
#define SQRT2 1.41421356237309504880
double log1p(x)
double x;
{
double z;
z = 1.0 + x;
if( (z < SQRTH) || (z > SQRT2) )
return( log(z) );
z = x*x;
z = -0.5 * z + x * ( z * polevl( x, LP, 6 ) / p1evl( x, LQ, 6 ) );
return (x + z);
}
/* expm1(x) = exp(x) - 1 */
/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
* -0.5 <= x <= 0.5
*/
const static double EP[3] = {
1.2617719307481059087798E-4,
3.0299440770744196129956E-2,
9.9999999999999999991025E-1,
};
const static double EQ[4] = {
3.0019850513866445504159E-6,
2.5244834034968410419224E-3,
2.2726554820815502876593E-1,
2.0000000000000000000897E0,
};
double expm1(x)
double x;
{
double r, xx;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
if( x == INFINITY )
return(INFINITY);
if( x == -INFINITY )
return(-1.0);
#endif
if( (x < -0.5) || (x > 0.5) )
return( exp(x) - 1.0 );
xx = x * x;
r = x * polevl( xx, EP, 2 );
r = r/( polevl( xx, EQ, 3 ) - r );
return (r + r);
}
/* cosm1(x) = cos(x) - 1 */
const static double coscof[7] = {
4.7377507964246204691685E-14,
-1.1470284843425359765671E-11,
2.0876754287081521758361E-9,
-2.7557319214999787979814E-7,
2.4801587301570552304991E-5,
-1.3888888888888872993737E-3,
4.1666666666666666609054E-2,
};
extern double PIO4;
double cosm1(x)
double x;
{
double xx;
if( (x < -PIO4) || (x > PIO4) )
return( cos(x) - 1.0 );
xx = x * x;
xx = -0.5*xx + xx * xx * polevl( xx, coscof, 6 );
return xx;
}

109
components/external/espruino/libs/math/unix.mak vendored Normal file
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# Double precision Cephes library
# Makefile for unix or GCC
CC = gcc
CFLAGS = -g -O2 -Wall -fno-builtin
AR = ar
RANLIB = ranlib
INCS = mconf.h
AS = as
OBJS = acosh.o airy.o asin.o asinh.o atan.o atanh.o bdtr.o beta.o \
btdtr.o cbrt.o chbevl.o chdtr.o clog.o cmplx.o const.o \
cosh.o dawsn.o drand.o ellie.o ellik.o ellpe.o ellpj.o ellpk.o \
exp.o exp10.o exp2.o expn.o fabs.o fac.o fdtr.o \
fresnl.o gamma.o gdtr.o hyp2f1.o hyperg.o i0.o i1.o igami.o \
incbet.o incbi.o igam.o isnan.o iv.o j0.o j1.o jn.o jv.o k0.o k1.o \
kn.o log.o log2.o log10.o lrand.o nbdtr.o ndtr.o ndtri.o pdtr.o \
polevl.o polmisc.o polyn.o pow.o powi.o psi.o rgamma.o round.o \
shichi.o sici.o sin.o sindg.o sinh.o spence.o stdtr.o struve.o \
tan.o tandg.o tanh.o unity.o yn.o zeta.o zetac.o \
sqrt.o floor.o setprec.o mtherr.o
all: libmd.a mtst dtestvec dcalc paranoia # stamp-timing
stamp-timing: libmd.a mtst time-it
time-it "mtst > /dev/null"
touch stamp-timing
time-it: time-it.o
$(CC) -o time-it time-it.o
time-it.o: time-it.c
$(CC) -O2 -c time-it.c
dcalc: dcalc.o libmd.a
$(CC) -o dcalc dcalc.o libmd.a
# aout2exe mtst
mtst: mtst.o libmd.a
$(CC) -v -o mtst mtst.o libmd.a
# gcc -Wl,-verbose -b i486-linuxaout -v -o mtst mtst.o libmd.a
# coff2exe mtst
mtst.o: mtst.c
$(CC) -O2 -Wall -c mtst.c
dtestvec: dtestvec.o libmd.a
$(CC) -o dtestvec dtestvec.o libmd.a
dtestvec.o: dtestvec.c
$(CC) -g -c dtestvec.c
paranoia: paranoia.o setprec.o libmd.a
$(CC) -o paranoia paranoia.o setprec.o libmd.a
paranoia.o: paranoia.c
$(CC) $(CFLAGS) -c paranoia.c
libmd.a: $(OBJS) $(INCS)
# for real Unix:
$(AR) rv libmd.a $(OBJS)
# for djgcc MSDOS:
# >libmd.rf -rv libmd.a $(OBJS)
# $(AR) @libmd.rf
$(RANLIB) libmd.a
# If the following are all commented out, the C versions
# will be used by default.
# IBM PC:
#sqrt.o: sqrt.387
# $(AS) -o sqrt.o sqrt.387
#
#floor.o: floor.387
# $(AS) -o floor.o floor.387
#
#setprec.o: setprec.387
# $(AS) -o setprec.o setprec.387
# ELF versions for linux (no underscores)
sqrt.o: sqrtelf.387
$(AS) -o sqrt.o sqrtelf.387
#floor.o: floorelf.387
# $(AS) -o floor.o floorelf.387
setprec.o: setprelf.387
$(AS) -o setprec.o setprelf.387
# Motorola 68881. Caution, subroutine return conventions vary.
#sqrt.o: sqrt.688
# $(AS) -o sqrt.o sqrt.688
#
#setprec.o: setprec.688
# $(AS) -o setprec.o setprec.688
# SPARC:
#sqrt.o: sqrt.spa
# $(AS) -o sqrt.o sqrt.spa
clean:
rm -f *.o
rm -f mtst
rm -f paranoia
rm -f dcalc
rm -f libmd.a
rm -f time-it
rm -f dtestvec