sdl-ios-xcode: src/libm/e

annotate src/libm/e_pow.c @ 2922:dc4523c7c22d

Significant performance boost with blend mode none

author	Sam Lantinga <slouken@libsdl.org>
date	Mon, 29 Dec 2008 19:48:01 +0000
parents	a98604b691c8
children	9ac6f0782dd6

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 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	79 huge = 1.0e300, tiny = 1.0e-300,
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)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	202 return (hy < 0) ? huge * huge : tiny * tiny;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	203 if (ix >= 0x3ff00000)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	204 return (hy > 0) ? huge * huge : tiny * tiny;
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)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	208 return (hy < 0) ? huge * huge : tiny * tiny;
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	209 if (ix > 0x3ff00000)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	210 return (hy > 0) ? huge * huge : tiny * tiny;
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 */
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	296 return s * huge * huge; /* overflow */
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)
a98604b691c8 Expanded the libm support and put it into a separate directory. Sam Lantinga <slouken@libsdl.org> parents: diff changeset	299 return s * huge * huge; /* overflow */
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 @ 2922:dc4523c7c22d