sdl-ios-xcode: src/video/e

annotate src/video/e_pow.h @ 3796:b19680c84cdf SDL-ryan-multiple-audio-device

Bunch of 1.3 audio cleanups to remove FIXMEs, get driver specific crap out of the core and into the drivers where it belongs, and push generic responsibilities out of the drivers and into the core where they belong.

author	Ryan C. Gordon <icculus@icculus.org>
date	Wed, 04 Oct 2006 19:54:23 +0000
parents	c121d94672cb
children	edd2839b36f7

rev	line source
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	1 /* @(#)e_pow.c 5.1 93/09/24 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	2 /*
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	3 * ====================================================
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	5 *
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	6 * Developed at SunPro, a Sun Microsystems, Inc. business.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	7 * Permission to use, copy, modify, and distribute this
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	8 * software is freely granted, provided that this notice
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	9 * is preserved.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	10 * ====================================================
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	11 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	12
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	13 #if defined(LIBM_SCCS) && !defined(lint)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	14 static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	15 #endif
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	16
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	17 /* __ieee754_pow(x,y) return x**y
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	18 *
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	19 * n
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	20 * Method: Let x = 2 * (1+f)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	21 * 1. Compute and return log2(x) in two pieces:
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	22 * log2(x) = w1 + w2,
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	23 * where w1 has 53-24 = 29 bit trailing zeros.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	24 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	25 * arithmetic, where \|y'\|<=0.5.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	26 * 3. Return xy = 2nexp(y'log2)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	27 *
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	28 * Special cases:
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	29 * 1. (anything) ** 0 is 1
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	30 * 2. (anything) ** 1 is itself
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	31 * 3. (anything) ** NAN is NAN
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	32 * 4. NAN ** (anything except 0) is NAN
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	33 * 5. +-(\|x\| > 1) ** +INF is +INF
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	34 * 6. +-(\|x\| > 1) ** -INF is +0
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	35 * 7. +-(\|x\| < 1) ** +INF is +0
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	36 * 8. +-(\|x\| < 1) ** -INF is +INF
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	37 * 9. +-1 ** +-INF is NAN
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	38 * 10. +0 ** (+anything except 0, NAN) is +0
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	39 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	40 * 12. +0 ** (-anything except 0, NAN) is +INF
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	41 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	42 * 14. -0 (odd integer) = -( +0 (odd integer) )
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	43 * 15. +INF ** (+anything except 0,NAN) is +INF
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	44 * 16. +INF ** (-anything except 0,NAN) is +0
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	45 * 17. -INF (anything) = -0 (-anything)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	46 * 18. (-anything) (integer) is (-1)(integer)(+anything*integer)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	47 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	48 *
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	49 * Accuracy:
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	50 * pow(x,y) returns x**y nearly rounded. In particular
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	51 * pow(integer,integer)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	52 * always returns the correct integer provided it is
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	53 * representable.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	54 *
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	55 * Constants :
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	56 * The hexadecimal values are the intended ones for the following
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	57 * constants. The decimal values may be used, provided that the
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	58 * compiler will convert from decimal to binary accurately enough
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	59 * to produce the hexadecimal values shown.
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	60 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	61
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	62 /#include "math.h"/
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	63 #include "math_private.h"
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	64
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	65 #ifdef __STDC__
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	66 static const double
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	67 #else
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	68 static double
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	69 #endif
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	70 bp[] = { 1.0, 1.5, }, dp_h[] = {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	71 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	72
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	73 dp_l[] = {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	74 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	75
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	76 /* poly coefs for (3/2)(log(x)-2s-2/3s*3 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	77 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	78 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	79 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	80 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	81 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	82 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	83 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	84 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	85 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	86 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	87 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	88 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	89 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	90 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	91 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	92 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	93 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	94 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	95 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	96 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	97 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	98
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	99 #ifdef __STDC__
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	100 double
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	101 __ieee754_pow(double x, double y)
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	102 #else
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	103 double
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	104 __ieee754_pow(x, y)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	105 double x, y;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	106 #endif
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	107 {
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	108 double z, ax, z_h, z_l, p_h, p_l;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	109 double y1, t1, t2, r, s, t, u, v, w;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	110 int32_t i, j, k, yisint, n;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	111 int32_t hx, hy, ix, iy;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	112 u_int32_t lx, ly;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	113
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	114 EXTRACT_WORDS(hx, lx, x);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	115 EXTRACT_WORDS(hy, ly, y);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	116 ix = hx & 0x7fffffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	117 iy = hy & 0x7fffffff;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	118
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	119 /* y==zero: x*0 = 1 /
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	120 if ((iy \| ly) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	121 return one;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	122
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	123 /* +-NaN return x+y */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	124 if (ix > 0x7ff00000 \|\| ((ix == 0x7ff00000) && (lx != 0)) \|\|
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	125 iy > 0x7ff00000 \|\| ((iy == 0x7ff00000) && (ly != 0)))
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	126 return x + y;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	127
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	128 /* determine if y is an odd int when x < 0
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	129 * yisint = 0 ... y is not an integer
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	130 * yisint = 1 ... y is an odd int
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	131 * yisint = 2 ... y is an even int
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	132 */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	133 yisint = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	134 if (hx < 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	135 if (iy >= 0x43400000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	136 yisint = 2; /* even integer y */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	137 else if (iy >= 0x3ff00000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	138 k = (iy >> 20) - 0x3ff; /* exponent */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	139 if (k > 20) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	140 j = ly >> (52 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	141 if ((u_int32_t) (j << (52 - k)) == ly)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	142 yisint = 2 - (j & 1);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	143 } else if (ly == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	144 j = iy >> (20 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	145 if ((j << (20 - k)) == iy)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	146 yisint = 2 - (j & 1);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	147 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	148 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	149 }
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	150
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	151 /* special value of y */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	152 if (ly == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	153 if (iy == 0x7ff00000) { /* y is +-inf */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	154 if (((ix - 0x3ff00000) \| lx) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	155 return y - y; /* inf*+-1 is NaN /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	156 else if (ix >= 0x3ff00000) /* (\|x\|>1)*+-inf = inf,0 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	157 return (hy >= 0) ? y : zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	158 else /* (\|x\|<1)*-,+inf = inf,0 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	159 return (hy < 0) ? -y : zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	160 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	161 if (iy == 0x3ff00000) { /* y is +-1 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	162 if (hy < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	163 return one / x;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	164 else
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	165 return x;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	166 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	167 if (hy == 0x40000000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	168 return x * x; /* y is 2 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	169 if (hy == 0x3fe00000) { /* y is 0.5 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	170 if (hx >= 0) /* x >= +0 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	171 return __ieee754_sqrt(x);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	172 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	173 }
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	174
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	175 ax = x < 0 ? -x : x; /fabs(x); /
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	176 /* special value of x */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	177 if (lx == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	178 if (ix == 0x7ff00000 \|\| ix == 0 \|\| ix == 0x3ff00000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	179 z = ax; /x is +-0,+-inf,+-1 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	180 if (hy < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	181 z = one / z; /* z = (1/\|x\|) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	182 if (hx < 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	183 if (((ix - 0x3ff00000) \| yisint) == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	184 z = (z - z) / (z - z); /* (-1)*non-int is NaN /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	185 } else if (yisint == 1)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	186 z = -z; /* (x<0)odd = -(\|x\|odd) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	187 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	188 return z;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	189 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	190 }
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	191
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	192 /* (x<0)*(non-int) is NaN /
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	193 if (((((u_int32_t) hx >> 31) - 1) \| yisint) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	194 return (x - x) / (x - x);
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	195
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	196 /* \|y\| is huge */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	197 if (iy > 0x41e00000) { /* if \|y\| > 2*31 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	198 if (iy > 0x43f00000) { /* if \|y\| > 2*64, must o/uflow /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	199 if (ix <= 0x3fefffff)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	200 return (hy < 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	201 if (ix >= 0x3ff00000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	202 return (hy > 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	203 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	204 /* over/underflow if x is not close to one */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	205 if (ix < 0x3fefffff)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	206 return (hy < 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	207 if (ix > 0x3ff00000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	208 return (hy > 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	209 /* now \|1-x\| is tiny <= 2**-20, suffice to compute
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	210 log(x) by x-x^2/2+x^3/3-x^4/4 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	211 t = x - 1; /* t has 20 trailing zeros */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	212 w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	213 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	214 v = t * ivln2_l - w * ivln2;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	215 t1 = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	216 SET_LOW_WORD(t1, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	217 t2 = v - (t1 - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	218 } else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	219 double s2, s_h, s_l, t_h, t_l;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	220 n = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	221 /* take care subnormal number */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	222 if (ix < 0x00100000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	223 ax *= two53;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	224 n -= 53;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	225 GET_HIGH_WORD(ix, ax);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	226 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	227 n += ((ix) >> 20) - 0x3ff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	228 j = ix & 0x000fffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	229 /* determine interval */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	230 ix = j \| 0x3ff00000; /* normalize ix */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	231 if (j <= 0x3988E)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	232 k = 0; /* \|x\|<sqrt(3/2) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	233 else if (j < 0xBB67A)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	234 k = 1; /* \|x\|<sqrt(3) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	235 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	236 k = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	237 n += 1;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	238 ix -= 0x00100000;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	239 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	240 SET_HIGH_WORD(ax, ix);
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	241
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	242 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	243 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	244 v = one / (ax + bp[k]);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	245 s = u * v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	246 s_h = s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	247 SET_LOW_WORD(s_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	248 /* t_h=ax+bp[k] High */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	249 t_h = zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	250 SET_HIGH_WORD(t_h, ((ix >> 1) \| 0x20000000) + 0x00080000 + (k << 18));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	251 t_l = ax - (t_h - bp[k]);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	252 s_l = v * ((u - s_h * t_h) - s_h * t_l);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	253 /* compute log(ax) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	254 s2 = s * s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	255 r = s2 * s2 * (L1 +
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	256 s2 * (L2 +
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	257 s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	258 r += s_l * (s_h + s);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	259 s2 = s_h * s_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	260 t_h = 3.0 + s2 + r;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	261 SET_LOW_WORD(t_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	262 t_l = r - ((t_h - 3.0) - s2);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	263 /* u+v = s(1+...) /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	264 u = s_h * t_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	265 v = s_l * t_h + t_l * s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	266 /* 2/(3log2)(s+...) /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	267 p_h = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	268 SET_LOW_WORD(p_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	269 p_l = v - (p_h - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	270 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3log2) /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	271 z_l = cp_l * p_h + p_l * cp + dp_l[k];
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	272 /* log2(ax) = (s+..)2/(3log2) = n + dp_h + z_h + z_l */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	273 t = (double) n;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	274 t1 = (((z_h + z_l) + dp_h[k]) + t);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	275 SET_LOW_WORD(t1, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	276 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	277 }
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	278
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	279 s = one; /* s (sign of result -ve*odd) = -1 else = 1 /
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	280 if (((((u_int32_t) hx >> 31) - 1) \| (yisint - 1)) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	281 s = -one; /* (-ve)*(odd int) /
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	282
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	283 /* split up y into y1+y2 and compute (y1+y2)(t1+t2) /
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	284 y1 = y;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	285 SET_LOW_WORD(y1, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	286 p_l = (y - y1) * t1 + y * t2;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	287 p_h = y1 * t1;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	288 z = p_l + p_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	289 EXTRACT_WORDS(j, i, z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	290 if (j >= 0x40900000) { /* z >= 1024 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	291 if (((j - 0x40900000) \| i) != 0) /* if z > 1024 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	292 return s * huge * huge; /* overflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	293 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	294 if (p_l + ovt > z - p_h)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	295 return s * huge * huge; /* overflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	296 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	297 } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	298 if (((j - 0xc090cc00) \| i) != 0) /* z < -1075 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	299 return s * tiny * tiny; /* underflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	300 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	301 if (p_l <= z - p_h)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	302 return s * tiny * tiny; /* underflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	303 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	304 }
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	305 /*
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	306 * compute 2**(p_h+p_l)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	307 */
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	308 i = j & 0x7fffffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	309 k = (i >> 20) - 0x3ff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	310 n = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	311 if (i > 0x3fe00000) { /* if \|z\| > 0.5, set n = [z+0.5] */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	312 n = j + (0x00100000 >> (k + 1));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	313 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	314 t = zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	315 SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	316 n = ((n & 0x000fffff) \| 0x00100000) >> (20 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	317 if (j < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	318 n = -n;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	319 p_h -= t;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	320 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	321 t = p_l + p_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	322 SET_LOW_WORD(t, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	323 u = t * lg2_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	324 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	325 z = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	326 w = v - (z - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	327 t = z * z;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	328 t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	329 r = (z * t1) / (t1 - two) - (w + z * w);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	330 z = one - (r - z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	331 GET_HIGH_WORD(j, z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	332 j += (n << 20);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	333 if ((j >> 20) <= 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	334 z = SDL_NAME(scalbn) (z, n); /* subnormal output */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	335 else
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	336 SET_HIGH_WORD(z, j);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	337 return s * z;
1330 450721ad5436 It's now possible to build SDL without any C runtime at all on Windows, Sam Lantinga <slouken@libsdl.org> parents: diff changeset	338 }
1895 c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	339
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head. Sam Lantinga <slouken@libsdl.org> parents: 1424 diff changeset	340 /* vi: set ts=4 sw=4 expandtab: */

Mercurial > sdl-ios-xcode

annotate src/video/e_pow.h @ 3796:b19680c84cdf SDL-ryan-multiple-audio-device