annotate src/libm/e_log.c @ 4532:dc4a3de60d3a

Logitech G15 on Ubuntu 10.04: code = 1, sym = 0xFF1B (Escape) scancode = 41 (Escape) code = 2, sym = 0x31 (1) scancode = 30 (1) code = 3, sym = 0x32 (2) scancode = 31 (2) code = 4, sym = 0x33 (3) scancode = 32 (3) code = 5, sym = 0x34 (4) scancode = 33 (4) code = 6, sym = 0x35 (5) scancode = 34 (5) code = 7, sym = 0x36 (6) scancode = 35 (6) code = 8, sym = 0x37 (7) scancode = 36 (7) code = 9, sym = 0x38 (8) scancode = 37 (8) code = 10, sym = 0x39 (9) scancode = 38 (9) code = 11, sym = 0x30 (0) scancode = 39 (0) code = 12, sym = 0x2D (minus) scancode = 45 (-) code = 13, sym = 0x3D (equal) scancode = 46 (=) code = 14, sym = 0xFF08 (BackSpace) scancode = 42 (Backspace) code = 15, sym = 0xFF09 (Tab) scancode = 43 (Tab) code = 16, sym = 0x71 (q) scancode = 20 (Q) code = 17, sym = 0x77 (w) scancode = 26 (W) code = 18, sym = 0x65 (e) scancode = 8 (E) code = 19, sym = 0x72 (r) scancode = 21 (R) code = 20, sym = 0x74 (t) scancode = 23 (T) code = 21, sym = 0x79 (y) scancode = 28 (Y) code = 22, sym = 0x75 (u) scancode = 24 (U) code = 23, sym = 0x69 (i) scancode = 12 (I) code = 24, sym = 0x6F (o) scancode = 18 (O) code = 25, sym = 0x70 (p) scancode = 19 (P) code = 26, sym = 0x5B (bracketleft) scancode = 47 ([) code = 27, sym = 0x5D (bracketright) scancode = 48 (]) code = 28, sym = 0xFF0D (Return) scancode = 40 (Return) code = 29, sym = 0xFFE3 (Control_L) scancode = 224 (Left Ctrl) code = 30, sym = 0x61 (a) scancode = 4 (A) code = 31, sym = 0x73 (s) scancode = 22 (S) code = 32, sym = 0x64 (d) scancode = 7 (D) code = 33, sym = 0x66 (f) scancode = 9 (F) code = 34, sym = 0x67 (g) scancode = 10 (G) code = 35, sym = 0x68 (h) scancode = 11 (H) code = 36, sym = 0x6A (j) scancode = 13 (J) code = 37, sym = 0x6B (k) scancode = 14 (K) code = 38, sym = 0x6C (l) scancode = 15 (L) code = 39, sym = 0x3B (semicolon) scancode = 51 (;) code = 40, sym = 0x27 (apostrophe) scancode = 52 (') code = 41, sym = 0x60 (grave) scancode = 53 (`) code = 42, sym = 0xFFE1 (Shift_L) scancode = 225 (Left Shift) code = 43, sym = 0x5C (backslash) scancode = 49 (\) code = 44, sym = 0x7A (z) scancode = 29 (Z) code = 45, sym = 0x78 (x) scancode = 27 (X) code = 46, sym = 0x63 (c) scancode = 6 (C) code = 47, sym = 0x76 (v) scancode = 25 (V) code = 48, sym = 0x62 (b) scancode = 5 (B) code = 49, sym = 0x6E (n) scancode = 17 (N) code = 50, sym = 0x6D (m) scancode = 16 (M) code = 51, sym = 0x2C (comma) scancode = 54 (,) code = 52, sym = 0x2E (period) scancode = 55 (.) code = 53, sym = 0x2F (slash) scancode = 56 (/) code = 54, sym = 0xFFE2 (Shift_R) scancode = 229 (Right Shift) code = 55, sym = 0xFFAA (KP_Multiply) scancode = 85 (Keypad *) code = 56, sym = 0xFFE9 (Alt_L) scancode = 226 (Left Alt) code = 57, sym = 0x20 (space) scancode = 44 (Space) code = 58, sym = 0xFFE5 (Caps_Lock) scancode = 57 (CapsLock) code = 59, sym = 0xFFBE (F1) scancode = 58 (F1) code = 60, sym = 0xFFBF (F2) scancode = 59 (F2) code = 61, sym = 0xFFC0 (F3) scancode = 60 (F3) code = 62, sym = 0xFFC1 (F4) scancode = 61 (F4) code = 63, sym = 0xFFC2 (F5) scancode = 62 (F5) code = 64, sym = 0xFFC3 (F6) scancode = 63 (F6) code = 65, sym = 0xFFC4 (F7) scancode = 64 (F7) code = 66, sym = 0xFFC5 (F8) scancode = 65 (F8) code = 67, sym = 0xFFC6 (F9) scancode = 66 (F9) code = 68, sym = 0xFFC7 (F10) scancode = 67 (F10) code = 69, sym = 0xFF7F (Num_Lock) scancode = 83 (Numlock) code = 70, sym = 0xFF14 (Scroll_Lock) scancode = 71 (ScrollLock) code = 71, sym = 0xFF95 (KP_Home) scancode = 95 (Keypad 7) code = 72, sym = 0xFF97 (KP_Up) scancode = 96 (Keypad 8) code = 73, sym = 0xFF9A (KP_Prior) scancode = 97 (Keypad 9) code = 74, sym = 0xFFAD (KP_Subtract) scancode = 86 (Keypad -) code = 75, sym = 0xFF96 (KP_Left) scancode = 92 (Keypad 4) code = 76, sym = 0xFF9D (KP_Begin) scancode = 93 (Keypad 5) code = 77, sym = 0xFF98 (KP_Right) scancode = 94 (Keypad 6) code = 78, sym = 0xFFAB (KP_Add) scancode = 87 (Keypad +) code = 79, sym = 0xFF9C (KP_End) scancode = 89 (Keypad 1) code = 80, sym = 0xFF99 (KP_Down) scancode = 90 (Keypad 2) code = 81, sym = 0xFF9B (KP_Next) scancode = 91 (Keypad 3) code = 82, sym = 0xFF9E (KP_Insert) scancode = 98 (Keypad 0) code = 83, sym = 0xFF9F (KP_Delete) scancode = 99 (Keypad .) code = 84, sym = 0xFE03 (ISO_Level3_Shift) scancode = 0 () code = 86, sym = 0x3C (less) scancode not found code = 87, sym = 0xFFC8 (F11) scancode = 68 (F11) code = 88, sym = 0xFFC9 (F12) scancode = 69 (F12) code = 90, sym = 0xFF26 (Katakana) scancode = 0 () code = 91, sym = 0xFF25 (Hiragana) scancode = 0 () code = 92, sym = 0xFF23 (Henkan_Mode) scancode = 0 () code = 93, sym = 0xFF27 (Hiragana_Katakana) scancode = 0 () code = 94, sym = 0xFF22 (Muhenkan) scancode = 0 () code = 96, sym = 0xFF8D (KP_Enter) scancode = 88 (Keypad Enter) code = 97, sym = 0xFFE4 (Control_R) scancode = 228 (Right Ctrl) code = 98, sym = 0xFFAF (KP_Divide) scancode = 84 (Keypad /) code = 99, sym = 0xFF61 (Print) scancode = 70 (PrintScreen) code = 100, sym = 0xFFEA (Alt_R) scancode = 230 (Right Alt) code = 101, sym = 0xFF0A (Linefeed) scancode = 0 () code = 102, sym = 0xFF50 (Home) scancode = 74 (Home) code = 103, sym = 0xFF52 (Up) scancode = 82 (Up) code = 104, sym = 0xFF55 (Prior) scancode = 75 (PageUp) code = 105, sym = 0xFF51 (Left) scancode = 80 (Left) code = 106, sym = 0xFF53 (Right) scancode = 79 (Right) code = 107, sym = 0xFF57 (End) scancode = 77 (End) code = 108, sym = 0xFF54 (Down) scancode = 81 (Down) code = 109, sym = 0xFF56 (Next) scancode = 78 (PageDown) code = 110, sym = 0xFF63 (Insert) scancode = 73 (Insert) code = 111, sym = 0xFFFF (Delete) scancode = 76 (Delete) code = 113, sym = 0x1008FF12 (XF86AudioMute) scancode = 0 () code = 114, sym = 0x1008FF11 (XF86AudioLowerVolume) scancode = 0 () code = 115, sym = 0x1008FF13 (XF86AudioRaiseVolume) scancode = 0 () code = 116, sym = 0x1008FF2A (XF86PowerOff) scancode = 0 () code = 117, sym = 0xFFBD (KP_Equal) scancode = 103 (Keypad =) code = 118, sym = 0xB1 (plusminus) scancode not found code = 119, sym = 0xFF13 (Pause) scancode = 72 (Pause) code = 120, sym = 0x1008FF4A (XF86LaunchA) scancode = 0 () code = 121, sym = 0xFFAE (KP_Decimal) scancode = 99 (Keypad .) code = 122, sym = 0xFF31 (Hangul) scancode = 0 () code = 123, sym = 0xFF34 (Hangul_Hanja) scancode = 0 () code = 125, sym = 0xFFEB (Super_L) scancode = 227 (Left GUI) code = 126, sym = 0xFFEC (Super_R) scancode = 231 (Right GUI) code = 127, sym = 0xFF67 (Menu) scancode = 118 (Menu) code = 128, sym = 0xFF69 (Cancel) scancode = 120 (Stop) code = 129, sym = 0xFF66 (Redo) scancode = 121 (Again) code = 130, sym = 0x1005FF70 (SunProps) scancode = 0 () code = 131, sym = 0xFF65 (Undo) scancode = 122 (Undo) code = 132, sym = 0x1005FF71 (SunFront) scancode = 0 () code = 133, sym = 0x1008FF57 (XF86Copy) scancode = 0 () code = 134, sym = 0x1005FF73 (SunOpen) scancode = 0 () code = 135, sym = 0x1008FF6D (XF86Paste) scancode = 0 () code = 136, sym = 0xFF68 (Find) scancode = 126 (Find) code = 137, sym = 0x1008FF58 (XF86Cut) scancode = 0 () code = 138, sym = 0xFF6A (Help) scancode = 117 (Help) code = 139, sym = 0x1008FF65 (XF86MenuKB) scancode = 0 () code = 140, sym = 0x1008FF1D (XF86Calculator) scancode = 0 () code = 142, sym = 0x1008FF2F (XF86Sleep) scancode = 0 () code = 143, sym = 0x1008FF2B (XF86WakeUp) scancode = 0 () code = 144, sym = 0x1008FF5D (XF86Explorer) scancode = 0 () code = 145, sym = 0x1008FF7B (XF86Send) scancode = 0 () code = 147, sym = 0x1008FF8A (XF86Xfer) scancode = 0 () code = 148, sym = 0x1008FF41 (XF86Launch1) scancode = 0 () code = 149, sym = 0x1008FF42 (XF86Launch2) scancode = 0 () code = 150, sym = 0x1008FF2E (XF86WWW) scancode = 0 () code = 151, sym = 0x1008FF5A (XF86DOS) scancode = 0 () code = 152, sym = 0x1008FF2D (XF86ScreenSaver) scancode = 0 () code = 154, sym = 0x1008FF74 (XF86RotateWindows) scancode = 0 () code = 155, sym = 0x1008FF19 (XF86Mail) scancode = 0 () code = 156, sym = 0x1008FF30 (XF86Favorites) scancode = 0 () code = 157, sym = 0x1008FF33 (XF86MyComputer) scancode = 0 () code = 158, sym = 0x1008FF26 (XF86Back) scancode = 0 () code = 159, sym = 0x1008FF27 (XF86Forward) scancode = 0 () code = 161, sym = 0x1008FF2C (XF86Eject) scancode = 0 () code = 162, sym = 0x1008FF2C (XF86Eject) scancode = 0 () code = 163, sym = 0x1008FF17 (XF86AudioNext) scancode = 0 () code = 164, sym = 0x1008FF14 (XF86AudioPlay) scancode = 0 () code = 165, sym = 0x1008FF16 (XF86AudioPrev) scancode = 0 () code = 166, sym = 0x1008FF15 (XF86AudioStop) scancode = 0 () code = 167, sym = 0x1008FF1C (XF86AudioRecord) scancode = 0 () code = 168, sym = 0x1008FF3E (XF86AudioRewind) scancode = 0 () code = 169, sym = 0x1008FF6E (XF86Phone) scancode = 0 () code = 171, sym = 0x1008FF81 (XF86Tools) scancode = 0 () code = 172, sym = 0x1008FF18 (XF86HomePage) scancode = 0 () code = 173, sym = 0x1008FF73 (XF86Reload) scancode = 0 () code = 174, sym = 0x1008FF56 (XF86Close) scancode = 0 () code = 177, sym = 0x1008FF78 (XF86ScrollUp) scancode = 0 () code = 178, sym = 0x1008FF79 (XF86ScrollDown) scancode = 0 () code = 179, sym = 0x28 (parenleft) scancode not found code = 180, sym = 0x29 (parenright) scancode not found code = 181, sym = 0x1008FF68 (XF86New) scancode = 0 () code = 182, sym = 0xFF66 (Redo) scancode = 121 (Again) code = 183, sym = 0x1008FF81 (XF86Tools) scancode = 0 () code = 184, sym = 0x1008FF45 (XF86Launch5) scancode = 0 () code = 185, sym = 0x1008FF65 (XF86MenuKB) scancode = 0 () code = 192, sym = 0x1008FFA9 (XF86TouchpadToggle) scancode = 0 () code = 195, sym = 0xFF7E (Mode_switch) scancode = 257 (ModeSwitch) code = 200, sym = 0x1008FF14 (XF86AudioPlay) scancode = 0 () code = 201, sym = 0x1008FF31 (XF86AudioPause) scancode = 0 () code = 202, sym = 0x1008FF43 (XF86Launch3) scancode = 0 () code = 203, sym = 0x1008FF44 (XF86Launch4) scancode = 0 () code = 204, sym = 0x1008FF4B (XF86LaunchB) scancode = 0 () code = 205, sym = 0x1008FFA7 (XF86Suspend) scancode = 0 () code = 206, sym = 0x1008FF56 (XF86Close) scancode = 0 () code = 207, sym = 0x1008FF14 (XF86AudioPlay) scancode = 0 () code = 208, sym = 0x1008FF97 (XF86AudioForward) scancode = 0 () code = 210, sym = 0xFF61 (Print) scancode = 70 (PrintScreen) code = 212, sym = 0x1008FF8F (XF86WebCam) scancode = 0 () code = 215, sym = 0x1008FF19 (XF86Mail) scancode = 0 () code = 217, sym = 0x1008FF1B (XF86Search) scancode = 0 () code = 219, sym = 0x1008FF3C (XF86Finance) scancode = 0 () code = 221, sym = 0x1008FF36 (XF86Shop) scancode = 0 () code = 223, sym = 0xFF69 (Cancel) scancode = 120 (Stop) code = 224, sym = 0x1008FF03 (XF86MonBrightnessDown) scancode = 0 () code = 225, sym = 0x1008FF02 (XF86MonBrightnessUp) scancode = 0 () code = 226, sym = 0x1008FF32 (XF86AudioMedia) scancode = 0 () code = 227, sym = 0x1008FF59 (XF86Display) scancode = 0 () code = 228, sym = 0x1008FF04 (XF86KbdLightOnOff) scancode = 0 () code = 229, sym = 0x1008FF06 (XF86KbdBrightnessDown) scancode = 0 () code = 230, sym = 0x1008FF05 (XF86KbdBrightnessUp) scancode = 0 () code = 231, sym = 0x1008FF7B (XF86Send) scancode = 0 () code = 232, sym = 0x1008FF72 (XF86Reply) scancode = 0 () code = 233, sym = 0x1008FF90 (XF86MailForward) scancode = 0 () code = 234, sym = 0x1008FF77 (XF86Save) scancode = 0 () code = 235, sym = 0x1008FF5B (XF86Documents) scancode = 0 () code = 236, sym = 0x1008FF93 (XF86Battery) scancode = 0 () code = 237, sym = 0x1008FF94 (XF86Bluetooth) scancode = 0 () code = 238, sym = 0x1008FF95 (XF86WLAN) scancode = 0 ()
author Sam Lantinga <slouken@libsdl.org>
date Sun, 18 Jul 2010 00:40:17 -0700
parents dc1eb82ffdaa
children
rev   line source
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1 /* @(#)e_log.c 5.1 93/09/24 */
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2 /*
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3 * ====================================================
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4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 *
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6 * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 * Permission to use, copy, modify, and distribute this
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8 * software is freely granted, provided that this notice
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9 * is preserved.
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10 * ====================================================
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11 */
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12
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13 #if defined(LIBM_SCCS) && !defined(lint)
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14 static const char rcsid[] =
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15 "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
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16 #endif
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17
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18 /* __ieee754_log(x)
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19 * Return the logrithm of x
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20 *
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21 * Method :
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22 * 1. Argument Reduction: find k and f such that
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23 * x = 2^k * (1+f),
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24 * where sqrt(2)/2 < 1+f < sqrt(2) .
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25 *
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26 * 2. Approximation of log(1+f).
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27 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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28 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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29 * = 2s + s*R
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30 * We use a special Reme algorithm on [0,0.1716] to generate
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31 * a polynomial of degree 14 to approximate R The maximum error
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32 * of this polynomial approximation is bounded by 2**-58.45. In
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33 * other words,
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34 * 2 4 6 8 10 12 14
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35 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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36 * (the values of Lg1 to Lg7 are listed in the program)
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37 * and
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38 * | 2 14 | -58.45
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39 * | Lg1*s +...+Lg7*s - R(z) | <= 2
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40 * | |
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41 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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42 * In order to guarantee error in log below 1ulp, we compute log
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43 * by
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44 * log(1+f) = f - s*(f - R) (if f is not too large)
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45 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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46 *
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47 * 3. Finally, log(x) = k*ln2 + log(1+f).
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48 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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49 * Here ln2 is split into two floating point number:
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50 * ln2_hi + ln2_lo,
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51 * where n*ln2_hi is always exact for |n| < 2000.
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52 *
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53 * Special cases:
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54 * log(x) is NaN with signal if x < 0 (including -INF) ;
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55 * log(+INF) is +INF; log(0) is -INF with signal;
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56 * log(NaN) is that NaN with no signal.
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57 *
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58 * Accuracy:
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59 * according to an error analysis, the error is always less than
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60 * 1 ulp (unit in the last place).
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61 *
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62 * Constants:
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63 * The hexadecimal values are the intended ones for the following
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64 * constants. The decimal values may be used, provided that the
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65 * compiler will convert from decimal to binary accurately enough
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66 * to produce the hexadecimal values shown.
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67 */
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68
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69 #include "math.h"
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70 #include "math_private.h"
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71
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72 #ifdef __STDC__
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73 static const double
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74 #else
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75 static double
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76 #endif
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77 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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78 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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79 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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80 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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81 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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82 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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83 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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84 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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85 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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86 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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87
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88 #ifdef __STDC__
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89 static const double zero = 0.0;
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90 #else
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91 static double zero = 0.0;
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92 #endif
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93
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94 #ifdef __STDC__
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95 double attribute_hidden
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96 __ieee754_log(double x)
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97 #else
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98 double attribute_hidden
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99 __ieee754_log(x)
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100 double x;
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101 #endif
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102 {
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103 double hfsq, f, s, z, R, w, t1, t2, dk;
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104 int32_t k, hx, i, j;
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105 u_int32_t lx;
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106
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107 EXTRACT_WORDS(hx, lx, x);
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108
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109 k = 0;
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110 if (hx < 0x00100000) { /* x < 2**-1022 */
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111 if (((hx & 0x7fffffff) | lx) == 0)
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112 return -two54 / zero; /* log(+-0)=-inf */
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113 if (hx < 0)
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114 return (x - x) / zero; /* log(-#) = NaN */
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115 k -= 54;
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116 x *= two54; /* subnormal number, scale up x */
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117 GET_HIGH_WORD(hx, x);
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118 }
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119 if (hx >= 0x7ff00000)
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120 return x + x;
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121 k += (hx >> 20) - 1023;
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122 hx &= 0x000fffff;
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123 i = (hx + 0x95f64) & 0x100000;
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124 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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125 k += (i >> 20);
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126 f = x - 1.0;
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127 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
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128 if (f == zero) {
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129 if (k == 0)
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130 return zero;
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131 else {
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132 dk = (double) k;
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133 return dk * ln2_hi + dk * ln2_lo;
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134 }
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135 }
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136 R = f * f * (0.5 - 0.33333333333333333 * f);
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137 if (k == 0)
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138 return f - R;
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139 else {
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140 dk = (double) k;
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141 return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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142 }
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143 }
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144 s = f / (2.0 + f);
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145 dk = (double) k;
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146 z = s * s;
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147 i = hx - 0x6147a;
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148 w = z * z;
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149 j = 0x6b851 - hx;
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150 t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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151 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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152 i |= j;
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153 R = t2 + t1;
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154 if (i > 0) {
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155 hfsq = 0.5 * f * f;
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156 if (k == 0)
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157 return f - (hfsq - s * (hfsq + R));
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158 else
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159 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
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160 f);
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161 } else {
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162 if (k == 0)
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163 return f - s * (f - R);
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164 else
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165 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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166 }
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167 }