sdl-ios-xcode: src/libm/e

annotate src/libm/e_pow.c @ 5282:8e421890cdb8

Fixed bug #1117 There's a new event that's always sent when the window changes size, and that event is what the renderers listen for to determine if they need to rebind their context.

author	Sam Lantinga <slouken@libsdl.org>
date	Sat, 12 Feb 2011 19:02:14 -0800
parents	9ac6f0782dd6
children

rev	line source
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	1 /* @(#)e_pow.c 5.1 93/09/24 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	2 /*
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	3 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	5 *
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	6 * Developed at SunPro, a Sun Microsystems, Inc. business.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	7 * Permission to use, copy, modify, and distribute this
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	8 * software is freely granted, provided that this notice
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	9 * is preserved.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	10 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	11 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	12
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	13 #if defined(LIBM_SCCS) && !defined(lint)
a98604b691c8 Expanded the libm support and put it into a separate directory. 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 $";
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	15 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	16
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	17 /* __ieee754_pow(x,y) return x**y
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	18 *
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	19 * n
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	20 * Method: Let x = 2 * (1+f)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	21 * 1. Compute and return log2(x) in two pieces:
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	22 * log2(x) = w1 + w2,
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	23 * where w1 has 53-24 = 29 bit trailing zeros.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	24 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	25 * arithmetic, where \|y'\|<=0.5.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	26 * 3. Return xy = 2nexp(y'log2)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	27 *
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	28 * Special cases:
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	29 * 1. (anything) ** 0 is 1
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	30 * 2. (anything) ** 1 is itself
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	31 * 3. (anything) ** NAN is NAN
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	32 * 4. NAN ** (anything except 0) is NAN
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	33 * 5. +-(\|x\| > 1) ** +INF is +INF
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	34 * 6. +-(\|x\| > 1) ** -INF is +0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	35 * 7. +-(\|x\| < 1) ** +INF is +0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	36 * 8. +-(\|x\| < 1) ** -INF is +INF
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	37 * 9. +-1 ** +-INF is NAN
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	38 * 10. +0 ** (+anything except 0, NAN) is +0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	39 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	40 * 12. +0 ** (-anything except 0, NAN) is +INF
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	41 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	42 * 14. -0 (odd integer) = -( +0 (odd integer) )
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	43 * 15. +INF ** (+anything except 0,NAN) is +INF
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	44 * 16. +INF ** (-anything except 0,NAN) is +0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	45 * 17. -INF (anything) = -0 (-anything)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	46 * 18. (-anything) (integer) is (-1)(integer)(+anything*integer)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	47 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	48 *
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	49 * Accuracy:
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	50 * pow(x,y) returns x**y nearly rounded. In particular
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	51 * pow(integer,integer)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	52 * always returns the correct integer provided it is
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	53 * representable.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	54 *
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	55 * Constants :
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	56 * The hexadecimal values are the intended ones for the following
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	57 * constants. The decimal values may be used, provided that the
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	58 * compiler will convert from decimal to binary accurately enough
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	59 * to produce the hexadecimal values shown.
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	60 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	61
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	62 #include "math.h"
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	63 #include "math_private.h"
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	64
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	65 libm_hidden_proto(scalbn)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	66 libm_hidden_proto(fabs)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	67 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	68 static const double
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	69 #else
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	70 static double
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	71 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	72 bp[] = { 1.0, 1.5, }, dp_h[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	73 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	74
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	75 dp_l[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	76 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	77
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	78 zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	79 huge_val = 1.0e300, tiny = 1.0e-300,
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	80 /* poly coefs for (3/2)(log(x)-2s-2/3s*3 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	81 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	82 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	83 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	84 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	85 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	86 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	87 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	88 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	89 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	90 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	91 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	92 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	93 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	94 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	95 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	96 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	97 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	98 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	99 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	100 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	101 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	102
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	103 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	104 double attribute_hidden __ieee754_pow(double x, double y)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	105 #else
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	106 double attribute_hidden __ieee754_pow(x, y)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	107 double x, y;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	108 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	109 {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	110 double z, ax, z_h, z_l, p_h, p_l;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	111 double y1, t1, t2, r, s, t, u, v, w;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	112 int32_t i, j, k, yisint, n;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	113 int32_t hx, hy, ix, iy;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	114 u_int32_t lx, ly;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	115
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	116 EXTRACT_WORDS(hx, lx, x);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	117 EXTRACT_WORDS(hy, ly, y);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	118 ix = hx & 0x7fffffff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	119 iy = hy & 0x7fffffff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	120
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	121 /* y==zero: x*0 = 1 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	122 if ((iy \| ly) == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	123 return one;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	124
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	125 /* +-NaN return x+y */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	126 if (ix > 0x7ff00000 \|\| ((ix == 0x7ff00000) && (lx != 0)) \|\|
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	127 iy > 0x7ff00000 \|\| ((iy == 0x7ff00000) && (ly != 0)))
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	128 return x + y;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	129
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	130 /* determine if y is an odd int when x < 0
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	131 * yisint = 0 ... y is not an integer
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	132 * yisint = 1 ... y is an odd int
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	133 * yisint = 2 ... y is an even int
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	134 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	135 yisint = 0;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	136 if (hx < 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	137 if (iy >= 0x43400000)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	138 yisint = 2; /* even integer y */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	139 else if (iy >= 0x3ff00000) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	140 k = (iy >> 20) - 0x3ff; /* exponent */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	141 if (k > 20) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	142 j = ly >> (52 - k);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	143 if ((j << (52 - k)) == ly)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	144 yisint = 2 - (j & 1);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	145 } else if (ly == 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	146 j = iy >> (20 - k);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	147 if ((j << (20 - k)) == iy)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	148 yisint = 2 - (j & 1);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	149 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	150 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	151 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	152
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	153 /* special value of y */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	154 if (ly == 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	155 if (iy == 0x7ff00000) { /* y is +-inf */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	156 if (((ix - 0x3ff00000) \| lx) == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	157 return y - y; /* inf*+-1 is NaN /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	158 else if (ix >= 0x3ff00000) /* (\|x\|>1)*+-inf = inf,0 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	159 return (hy >= 0) ? y : zero;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	160 else /* (\|x\|<1)*-,+inf = inf,0 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	161 return (hy < 0) ? -y : zero;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	162 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	163 if (iy == 0x3ff00000) { /* y is +-1 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	164 if (hy < 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	165 return one / x;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	166 else
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	167 return x;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	168 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	169 if (hy == 0x40000000)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	170 return x * x; /* y is 2 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	171 if (hy == 0x3fe00000) { /* y is 0.5 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	172 if (hx >= 0) /* x >= +0 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	173 return __ieee754_sqrt(x);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	174 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	175 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	176
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	177 ax = fabs(x);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	178 /* special value of x */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	179 if (lx == 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	180 if (ix == 0x7ff00000 \|\| ix == 0 \|\| ix == 0x3ff00000) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	181 z = ax; /x is +-0,+-inf,+-1 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	182 if (hy < 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	183 z = one / z; /* z = (1/\|x\|) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	184 if (hx < 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	185 if (((ix - 0x3ff00000) \| yisint) == 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	186 z = (z - z) / (z - z); /* (-1)*non-int is NaN /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	187 } else if (yisint == 1)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	188 z = -z; /* (x<0)odd = -(\|x\|odd) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	189 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	190 return z;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	191 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	192 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	193
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	194 /* (x<0)*(non-int) is NaN /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	195 if (((((u_int32_t) hx >> 31) - 1) \| yisint) == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	196 return (x - x) / (x - x);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	197
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	198 /* \|y\| is huge */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	199 if (iy > 0x41e00000) { /* if \|y\| > 2*31 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	200 if (iy > 0x43f00000) { /* if \|y\| > 2*64, must o/uflow /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	201 if (ix <= 0x3fefffff)
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	202 return (hy < 0) ? huge_val * huge_val : tiny * tiny;
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	203 if (ix >= 0x3ff00000)
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	204 return (hy > 0) ? huge_val * huge_val : tiny * tiny;
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	205 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	206 /* over/underflow if x is not close to one */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	207 if (ix < 0x3fefffff)
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	208 return (hy < 0) ? huge_val * huge_val : tiny * tiny;
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	209 if (ix > 0x3ff00000)
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	210 return (hy > 0) ? huge_val * huge_val : tiny * tiny;
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	211 /* now \|1-x\| is tiny <= 2**-20, suffice to compute
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	212 log(x) by x-x^2/2+x^3/3-x^4/4 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	213 t = x - 1; /* t has 20 trailing zeros */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	214 w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	215 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	216 v = t * ivln2_l - w * ivln2;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	217 t1 = u + v;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	218 SET_LOW_WORD(t1, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	219 t2 = v - (t1 - u);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	220 } else {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	221 double s2, s_h, s_l, t_h, t_l;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	222 n = 0;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	223 /* take care subnormal number */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	224 if (ix < 0x00100000) {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	225 ax *= two53;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	226 n -= 53;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	227 GET_HIGH_WORD(ix, ax);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	228 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	229 n += ((ix) >> 20) - 0x3ff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	230 j = ix & 0x000fffff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	231 /* determine interval */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	232 ix = j \| 0x3ff00000; /* normalize ix */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	233 if (j <= 0x3988E)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	234 k = 0; /* \|x\|<sqrt(3/2) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	235 else if (j < 0xBB67A)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	236 k = 1; /* \|x\|<sqrt(3) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	237 else {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	238 k = 0;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	239 n += 1;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	240 ix -= 0x00100000;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	241 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	242 SET_HIGH_WORD(ax, ix);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	243
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	244 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	245 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	246 v = one / (ax + bp[k]);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	247 s = u * v;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	248 s_h = s;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	249 SET_LOW_WORD(s_h, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	250 /* t_h=ax+bp[k] High */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	251 t_h = zero;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	252 SET_HIGH_WORD(t_h,
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	253 ((ix >> 1) \| 0x20000000) + 0x00080000 + (k << 18));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	254 t_l = ax - (t_h - bp[k]);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	255 s_l = v * ((u - s_h * t_h) - s_h * t_l);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	256 /* compute log(ax) */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	257 s2 = s * s;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	258 r = s2 * s2 * (L1 +
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	259 s2 * (L2 +
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	260 s2 * (L3 +
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	261 s2 * (L4 + s2 * (L5 + s2 * L6)))));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	262 r += s_l * (s_h + s);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	263 s2 = s_h * s_h;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	264 t_h = 3.0 + s2 + r;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	265 SET_LOW_WORD(t_h, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	266 t_l = r - ((t_h - 3.0) - s2);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	267 /* u+v = s(1+...) /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	268 u = s_h * t_h;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	269 v = s_l * t_h + t_l * s;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	270 /* 2/(3log2)(s+...) /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	271 p_h = u + v;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	272 SET_LOW_WORD(p_h, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	273 p_l = v - (p_h - u);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	274 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3log2) /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	275 z_l = cp_l * p_h + p_l * cp + dp_l[k];
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	276 /* log2(ax) = (s+..)2/(3log2) = n + dp_h + z_h + z_l */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	277 t = (double) n;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	278 t1 = (((z_h + z_l) + dp_h[k]) + t);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	279 SET_LOW_WORD(t1, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	280 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	281 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	282
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	283 s = one; /* s (sign of result -ve*odd) = -1 else = 1 /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	284 if (((((u_int32_t) hx >> 31) - 1) \| (yisint - 1)) == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	285 s = -one; /* (-ve)*(odd int) /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	286
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	287 /* split up y into y1+y2 and compute (y1+y2)(t1+t2) /
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	288 y1 = y;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	289 SET_LOW_WORD(y1, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	290 p_l = (y - y1) * t1 + y * t2;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	291 p_h = y1 * t1;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	292 z = p_l + p_h;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	293 EXTRACT_WORDS(j, i, z);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	294 if (j >= 0x40900000) { /* z >= 1024 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	295 if (((j - 0x40900000) \| i) != 0) /* if z > 1024 */
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	296 return s * huge_val * huge_val; /* overflow */
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	297 else {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	298 if (p_l + ovt > z - p_h)
3337 9ac6f0782dd6 Fixed bug #814 Sam Lantinga <slouken@libsdl.org> parents: 2756 diff changeset	299 return s * huge_val * huge_val; /* overflow */
2756 a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	300 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	301 } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	302 if (((j - 0xc090cc00) \| i) != 0) /* z < -1075 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	303 return s * tiny * tiny; /* underflow */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	304 else {
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	305 if (p_l <= z - p_h)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	306 return s * tiny * tiny; /* underflow */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	307 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	308 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	309 /*
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	310 * compute 2**(p_h+p_l)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	311 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	312 i = j & 0x7fffffff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	313 k = (i >> 20) - 0x3ff;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	314 n = 0;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	315 if (i > 0x3fe00000) { /* if \|z\| > 0.5, set n = [z+0.5] */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	316 n = j + (0x00100000 >> (k + 1));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	317 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	318 t = zero;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	319 SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	320 n = ((n & 0x000fffff) \| 0x00100000) >> (20 - k);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	321 if (j < 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	322 n = -n;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	323 p_h -= t;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	324 }
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	325 t = p_l + p_h;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	326 SET_LOW_WORD(t, 0);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	327 u = t * lg2_h;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	328 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	329 z = u + v;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	330 w = v - (z - u);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	331 t = z * z;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	332 t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	333 r = (z * t1) / (t1 - two) - (w + z * w);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	334 z = one - (r - z);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	335 GET_HIGH_WORD(j, z);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	336 j += (n << 20);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	337 if ((j >> 20) <= 0)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	338 z = scalbn(z, n); /* subnormal output */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	339 else
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	340 SET_HIGH_WORD(z, j);
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	341 return s * z;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	342 }

Mercurial > sdl-ios-xcode

annotate src/libm/e_pow.c @ 5282:8e421890cdb8