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0b3496fb4f
Made possible by EIREXE, xsellier and the SDL team. This commit includes statically linked SDL3 for Windows, Linux and macOS. The vendored copy of SDL3 was setup to only build the required subsystems for gamepad/joystick support, with some patches to be able to make it as minimal as possible and reduce the impact on binary size and code size. Co-authored-by: Álex Román Núñez <eirexe123@gmail.com> Co-authored-by: Xavier Sellier <xsellier@gmail.com> Co-authored-by: Rémi Verschelde <rverschelde@gmail.com>
84 lines
2.9 KiB
C
84 lines
2.9 KiB
C
#include "SDL_internal.h"
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* __kernel_cos( x, y )
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* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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*
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* Algorithm
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* 1. Since cos(-x) = cos(x), we need only to consider positive x.
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* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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* 3. cos(x) is approximated by a polynomial of degree 14 on
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* [0,pi/4]
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* 4 14
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* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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* where the remez error is
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*
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* | 2 4 6 8 10 12 14 | -58
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* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
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* | |
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*
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* 4 6 8 10 12 14
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* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
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* cos(x) = 1 - x*x/2 + r
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* since cos(x+y) ~ cos(x) - sin(x)*y
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* ~ cos(x) - x*y,
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* a correction term is necessary in cos(x) and hence
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* cos(x+y) = 1 - (x*x/2 - (r - x*y))
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* For better accuracy when x > 0.3, let qx = |x|/4 with
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* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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* Then
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* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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* magnitude of the latter is at least a quarter of x*x/2,
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* thus, reducing the rounding error in the subtraction.
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*/
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#include "math_libm.h"
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#include "math_private.h"
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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double attribute_hidden __kernel_cos(double x, double y)
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{
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double a,hz,z,r,qx;
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int32_t ix;
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GET_HIGH_WORD(ix,x);
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ix &= 0x7fffffff; /* ix = |x|'s high word*/
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if(ix<0x3e400000) { /* if x < 2**27 */
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if(((int)x)==0) return one; /* generate inexact */
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}
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z = x*x;
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r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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if(ix < 0x3FD33333) /* if |x| < 0.3 */
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return one - (0.5*z - (z*r - x*y));
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else {
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if(ix > 0x3fe90000) { /* x > 0.78125 */
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qx = 0.28125;
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} else {
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INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
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}
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hz = 0.5*z-qx;
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a = one-qx;
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return a - (hz - (z*r-x*y));
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}
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}
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