src/libm/e_rem_pio2.c
author Ryan C. Gordon <icculus@icculus.org>
Thu, 09 Apr 2015 22:28:37 -0400
changeset 9541 cf8fab52e33b
parent 6044 35448a5ea044
child 10650 b6ec7005ca15
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 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
     2 /*
     3  * ====================================================
     4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5  *
     6  * Developed at SunPro, a Sun Microsystems, Inc. business.
     7  * Permission to use, copy, modify, and distribute this
     8  * software is freely granted, provided that this notice
     9  * is preserved.
    10  * ====================================================
    11  */
    12 
    13 #if defined(LIBM_SCCS) && !defined(lint)
    14 static const char rcsid[] =
    15     "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
    16 #endif
    17 
    18 /* __ieee754_rem_pio2(x,y)
    19  *
    20  * return the remainder of x rem pi/2 in y[0]+y[1]
    21  * use __kernel_rem_pio2()
    22  */
    23 
    24 #include "math_libm.h"
    25 #include "math_private.h"
    26 
    27 libm_hidden_proto(fabs)
    28 
    29 /*
    30  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
    31  */
    32 #ifdef __STDC__
    33      static const int32_t two_over_pi[] = {
    34 #else
    35      static int32_t two_over_pi[] = {
    36 #endif
    37          0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
    38          0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
    39          0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
    40          0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
    41          0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
    42          0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
    43          0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
    44          0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
    45          0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
    46          0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
    47          0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
    48      };
    49 
    50 #ifdef __STDC__
    51 static const int32_t npio2_hw[] = {
    52 #else
    53 static int32_t npio2_hw[] = {
    54 #endif
    55     0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
    56     0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
    57     0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
    58     0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
    59     0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
    60     0x404858EB, 0x404921FB,
    61 };
    62 
    63 /*
    64  * invpio2:  53 bits of 2/pi
    65  * pio2_1:   first  33 bit of pi/2
    66  * pio2_1t:  pi/2 - pio2_1
    67  * pio2_2:   second 33 bit of pi/2
    68  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
    69  * pio2_3:   third  33 bit of pi/2
    70  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
    71  */
    72 
    73 #ifdef __STDC__
    74 static const double
    75 #else
    76 static double
    77 #endif
    78   zero = 0.00000000000000000000e+00,    /* 0x00000000, 0x00000000 */
    79     half = 5.00000000000000000000e-01,  /* 0x3FE00000, 0x00000000 */
    80     two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
    81     invpio2 = 6.36619772367581382433e-01,       /* 0x3FE45F30, 0x6DC9C883 */
    82     pio2_1 = 1.57079632673412561417e+00,        /* 0x3FF921FB, 0x54400000 */
    83     pio2_1t = 6.07710050650619224932e-11,       /* 0x3DD0B461, 0x1A626331 */
    84     pio2_2 = 6.07710050630396597660e-11,        /* 0x3DD0B461, 0x1A600000 */
    85     pio2_2t = 2.02226624879595063154e-21,       /* 0x3BA3198A, 0x2E037073 */
    86     pio2_3 = 2.02226624871116645580e-21,        /* 0x3BA3198A, 0x2E000000 */
    87     pio2_3t = 8.47842766036889956997e-32;       /* 0x397B839A, 0x252049C1 */
    88 
    89 #ifdef __STDC__
    90 int32_t attribute_hidden
    91 __ieee754_rem_pio2(double x, double *y)
    92 #else
    93 int32_t attribute_hidden
    94 __ieee754_rem_pio2(x, y)
    95      double x, y[];
    96 #endif
    97 {
    98     double z = 0.0, w, t, r, fn;
    99     double tx[3];
   100     int32_t e0, i, j, nx, n, ix, hx;
   101     u_int32_t low;
   102 
   103     GET_HIGH_WORD(hx, x);       /* high word of x */
   104     ix = hx & 0x7fffffff;
   105     if (ix <= 0x3fe921fb) {     /* |x| ~<= pi/4 , no need for reduction */
   106         y[0] = x;
   107         y[1] = 0;
   108         return 0;
   109     }
   110     if (ix < 0x4002d97c) {      /* |x| < 3pi/4, special case with n=+-1 */
   111         if (hx > 0) {
   112             z = x - pio2_1;
   113             if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
   114                 y[0] = z - pio2_1t;
   115                 y[1] = (z - y[0]) - pio2_1t;
   116             } else {            /* near pi/2, use 33+33+53 bit pi */
   117                 z -= pio2_2;
   118                 y[0] = z - pio2_2t;
   119                 y[1] = (z - y[0]) - pio2_2t;
   120             }
   121             return 1;
   122         } else {                /* negative x */
   123             z = x + pio2_1;
   124             if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
   125                 y[0] = z + pio2_1t;
   126                 y[1] = (z - y[0]) + pio2_1t;
   127             } else {            /* near pi/2, use 33+33+53 bit pi */
   128                 z += pio2_2;
   129                 y[0] = z + pio2_2t;
   130                 y[1] = (z - y[0]) + pio2_2t;
   131             }
   132             return -1;
   133         }
   134     }
   135     if (ix <= 0x413921fb) {     /* |x| ~<= 2^19*(pi/2), medium size */
   136         t = fabs(x);
   137         n = (int32_t) (t * invpio2 + half);
   138         fn = (double) n;
   139         r = t - fn * pio2_1;
   140         w = fn * pio2_1t;       /* 1st round good to 85 bit */
   141         if (n < 32 && ix != npio2_hw[n - 1]) {
   142             y[0] = r - w;       /* quick check no cancellation */
   143         } else {
   144             u_int32_t high;
   145             j = ix >> 20;
   146             y[0] = r - w;
   147             GET_HIGH_WORD(high, y[0]);
   148             i = j - ((high >> 20) & 0x7ff);
   149             if (i > 16) {       /* 2nd iteration needed, good to 118 */
   150                 t = r;
   151                 w = fn * pio2_2;
   152                 r = t - w;
   153                 w = fn * pio2_2t - ((t - r) - w);
   154                 y[0] = r - w;
   155                 GET_HIGH_WORD(high, y[0]);
   156                 i = j - ((high >> 20) & 0x7ff);
   157                 if (i > 49) {   /* 3rd iteration need, 151 bits acc */
   158                     t = r;      /* will cover all possible cases */
   159                     w = fn * pio2_3;
   160                     r = t - w;
   161                     w = fn * pio2_3t - ((t - r) - w);
   162                     y[0] = r - w;
   163                 }
   164             }
   165         }
   166         y[1] = (r - y[0]) - w;
   167         if (hx < 0) {
   168             y[0] = -y[0];
   169             y[1] = -y[1];
   170             return -n;
   171         } else
   172             return n;
   173     }
   174     /*
   175      * all other (large) arguments
   176      */
   177     if (ix >= 0x7ff00000) {     /* x is inf or NaN */
   178         y[0] = y[1] = x - x;
   179         return 0;
   180     }
   181     /* set z = scalbn(|x|,ilogb(x)-23) */
   182     GET_LOW_WORD(low, x);
   183     SET_LOW_WORD(z, low);
   184     e0 = (ix >> 20) - 1046;     /* e0 = ilogb(z)-23; */
   185     SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
   186     for (i = 0; i < 2; i++) {
   187         tx[i] = (double) ((int32_t) (z));
   188         z = (z - tx[i]) * two24;
   189     }
   190     tx[2] = z;
   191     nx = 3;
   192     while (tx[nx - 1] == zero)
   193         nx--;                   /* skip zero term */
   194     n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
   195     if (hx < 0) {
   196         y[0] = -y[0];
   197         y[1] = -y[1];
   198         return -n;
   199     }
   200     return n;
   201 }