src/libm/s_atan.c
author Ryan C. Gordon <icculus@icculus.org>
Thu, 09 Apr 2015 22:28:37 -0400
changeset 9541 cf8fab52e33b
parent 8056 abd9434c5d3e
child 11683 48bcba563d9c
permissions -rw-r--r--
Merged Alex Szpakowski's iOS-improvement branch to default.

Fixes Bugzilla #2798.
Fixes Bugzilla #2212.
Fixes Bugzilla #2826.
Fixes Bugzilla #2661.
Fixes Bugzilla #1885.
Fixes Bugzilla #1578.
Fixes Bugzilla #2751.

(whew!)

Notable changes, from Alex's notes:

- The SDL_WINDOW_ALLOW_HIGHDPI flag is now needed (along with SDL_GL_GetDrawableSize or SDL_GetRendererOutputSize) to use Retina / high DPI resolutions, bringing SDL’s Retina-related behavior on iOS in line with Mac OS X. Window dimensions and display modes are now in the “points” (non-high DPI) coordinate system rather than pixels, whereas SDL_GL_GetDrawableSize is in pixels.

- Reworked the custom extended launch screen code:
- It now hides after the first SDL_PumpEvents call rather than SDL_CreateWindow, and it fades out in a similar manner to the system launch screen behavior.
- It now mirrors the system launch screen behavior when deciding which image to display: it falls back to using the Launch Images dictionary in Info.plist if the iOS 8+ launch screen nib isn’t available, and if the Launch Images dictionary doesn’t exist it uses the old standard launch image names.
- The extended launch screen can now be disabled via the SDL_IPHONE_LAUNCHSCREEN define in SDL_config_iphoneos.h.

- Added support for SDL_HINT_ACCELEROMETER_AS_JOYSTICK.

- Added access to a window view's renderbuffer and framebuffer to syswm.

- Added OpenGL ES debug labels for the Renderbuffer and Framebuffer Objects created with SDL_GL_CreateContext.

- Added support for sRGB OpenGL ES contexts on iOS 7+.

- Updated OpenGL ES contexts to support native-resolution rendering (when SDL_WINDOW_ALLOW_HIGHDPI is enabled) on the iPhone 6 Plus, i.e. 1080x1920 rather than 1242x2208.

- Updated SDL_GL_CreateContext, SDL_GL_SwapWindow, SDL_GL_MakeCurrent, and SDL_GL_DeleteContext to be more robust.

- Updated SDL windows to display a UIView at all times, even when an OpenGL context is not active. This allows rotation, touch events, and other windowing-related events to work properly without an active OpenGL context. It also makes it easier to use SDL_GetWindowWMInfo after creating a SDL window.

- Updated the iOS-specific Objective-C code to use cleaner and more modern language features and APIs, including ARC instead of manual reference counting.

- Updated SDL_HINT_ORIENTATIONS to allow disabling custom orientations if the hint is set with no valid orientation names.

- Fixed several rotation and orientation bugs with windows and display modes, especially in iOS 8+.

- Fixed SDL_SetWindowFullscreen failing to update the status bar visibility on iOS 7+.

- Fixed the orientation of the offset applied to the window’s view when the onscreen keyboard is shown in iOS 8+.

- Fixed SDL_IsScreenKeyboardShown (patch by Phil Hassey.)

- Fixed several major memory leaks caused by missing autorelease pool blocks in the iOS-specific Objective-C code.

- Removed several dead code paths.

- The iOS 7 SDK (Xcode 5) or newer is now required to build SDL for iOS.
     1 /*
     2  * ====================================================
     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     4  *
     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
     6  * Permission to use, copy, modify, and distribute this
     7  * software is freely granted, provided that this notice
     8  * is preserved.
     9  * ====================================================
    10  */
    11 
    12 /* atan(x)
    13  * Method
    14  *   1. Reduce x to positive by atan(x) = -atan(-x).
    15  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
    16  *      is further reduced to one of the following intervals and the
    17  *      arctangent of t is evaluated by the corresponding formula:
    18  *
    19  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
    20  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
    21  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
    22  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
    23  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
    24  *
    25  * Constants:
    26  * The hexadecimal values are the intended ones for the following
    27  * constants. The decimal values may be used, provided that the
    28  * compiler will convert from decimal to binary accurately enough
    29  * to produce the hexadecimal values shown.
    30  */
    31 
    32 #include "math_libm.h"
    33 #include "math_private.h"
    34 
    35 static const double atanhi[] = {
    36   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    37   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    38   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    39   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
    40 };
    41 
    42 static const double atanlo[] = {
    43   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    44   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    45   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    46   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
    47 };
    48 
    49 static const double aT[] = {
    50   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
    51  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
    52   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
    53  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
    54   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
    55  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
    56   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
    57  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
    58   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
    59  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
    60   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
    61 };
    62 
    63 static const double
    64 one   = 1.0,
    65 huge   = 1.0e300;
    66 
    67 double atan(double x)
    68 {
    69 	double w,s1,s2,z;
    70 	int32_t ix,hx,id;
    71 
    72 	GET_HIGH_WORD(hx,x);
    73 	ix = hx&0x7fffffff;
    74 	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
    75 	    u_int32_t low;
    76 	    GET_LOW_WORD(low,x);
    77 	    if(ix>0x7ff00000||
    78 		(ix==0x7ff00000&&(low!=0)))
    79 		return x+x;		/* NaN */
    80 	    if(hx>0) return  atanhi[3]+atanlo[3];
    81 	    else     return -atanhi[3]-atanlo[3];
    82 	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
    83 	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
    84 		if(huge+x>one) return x;	/* raise inexact */
    85 	    }
    86 	    id = -1;
    87 	} else {
    88 	x = fabs(x);
    89 	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
    90 	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
    91 		id = 0; x = (2.0*x-one)/(2.0+x);
    92 	    } else {			/* 11/16<=|x|< 19/16 */
    93 		id = 1; x  = (x-one)/(x+one);
    94 	    }
    95 	} else {
    96 	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
    97 		id = 2; x  = (x-1.5)/(one+1.5*x);
    98 	    } else {			/* 2.4375 <= |x| < 2^66 */
    99 		id = 3; x  = -1.0/x;
   100 	    }
   101 	}}
   102     /* end of argument reduction */
   103 	z = x*x;
   104 	w = z*z;
   105     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
   106 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
   107 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
   108 	if (id<0) return x - x*(s1+s2);
   109 	else {
   110 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
   111 	    return (hx<0)? -z:z;
   112 	}
   113 }
   114 libm_hidden_def(atan)
   115