1/*---------------------------------------------------------------------------+
2 |  poly_2xm1.c                                                              |
3 |                                                                           |
4 | Function to compute 2^x-1 by a polynomial approximation.                  |
5 |                                                                           |
6 | Copyright (C) 1992,1993,1994,1997                                         |
7 |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
8 |                  E-mail   billm@suburbia.net                              |
9 |                                                                           |
10 |                                                                           |
11 +---------------------------------------------------------------------------*/
12
13#include "exception.h"
14#include "reg_constant.h"
15#include "fpu_emu.h"
16#include "fpu_system.h"
17#include "control_w.h"
18#include "poly.h"
19
20#define	HIPOWER	11
21static const unsigned long long lterms[HIPOWER] = {
22	0x0000000000000000LL,	/* This term done separately as 12 bytes */
23	0xf5fdeffc162c7543LL,
24	0x1c6b08d704a0bfa6LL,
25	0x0276556df749cc21LL,
26	0x002bb0ffcf14f6b8LL,
27	0x0002861225ef751cLL,
28	0x00001ffcbfcd5422LL,
29	0x00000162c005d5f1LL,
30	0x0000000da96ccb1bLL,
31	0x0000000078d1b897LL,
32	0x000000000422b029LL
33};
34
35static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
36
37/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
38   These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
39 */
40static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
41static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
42static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
43static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
44
45static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
46	&shiftterm2, &shiftterm3
47};
48
49/*--- poly_2xm1() -----------------------------------------------------------+
50 | Requires st(0) which is TAG_Valid and < 1.                                |
51 +---------------------------------------------------------------------------*/
52int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
53{
54	long int exponent, shift;
55	unsigned long long Xll;
56	Xsig accumulator, Denom, argSignif;
57	u_char tag;
58
59	exponent = exponent16(arg);
60
61#ifdef PARANOID
62	if (exponent >= 0) {	/* Don't want a |number| >= 1.0 */
63		/* Number negative, too large, or not Valid. */
64		EXCEPTION(EX_INTERNAL | 0x127);
65		return 1;
66	}
67#endif /* PARANOID */
68
69	argSignif.lsw = 0;
70	XSIG_LL(argSignif) = Xll = significand(arg);
71
72	if (exponent == -1) {
73		shift = (argSignif.msw & 0x40000000) ? 3 : 2;
74		/* subtract 0.5 or 0.75 */
75		exponent -= 2;
76		XSIG_LL(argSignif) <<= 2;
77		Xll <<= 2;
78	} else if (exponent == -2) {
79		shift = 1;
80		/* subtract 0.25 */
81		exponent--;
82		XSIG_LL(argSignif) <<= 1;
83		Xll <<= 1;
84	} else
85		shift = 0;
86
87	if (exponent < -2) {
88		/* Shift the argument right by the required places. */
89		if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
90			Xll++;	/* round up */
91	}
92
93	accumulator.lsw = accumulator.midw = accumulator.msw = 0;
94	polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
95	mul_Xsig_Xsig(&accumulator, &argSignif);
96	shr_Xsig(&accumulator, 3);
97
98	mul_Xsig_Xsig(&argSignif, &hiterm);	/* The leading term */
99	add_two_Xsig(&accumulator, &argSignif, &exponent);
100
101	if (shift) {
102		/* The argument is large, use the identity:
103		   f(x+a) = f(a) * (f(x) + 1) - 1;
104		 */
105		shr_Xsig(&accumulator, -exponent);
106		accumulator.msw |= 0x80000000;	/* add 1.0 */
107		mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
108		accumulator.msw &= 0x3fffffff;	/* subtract 1.0 */
109		exponent = 1;
110	}
111
112	if (sign != SIGN_POS) {
113		/* The argument is negative, use the identity:
114		   f(-x) = -f(x) / (1 + f(x))
115		 */
116		Denom.lsw = accumulator.lsw;
117		XSIG_LL(Denom) = XSIG_LL(accumulator);
118		if (exponent < 0)
119			shr_Xsig(&Denom, -exponent);
120		else if (exponent > 0) {
121			/* exponent must be 1 here */
122			XSIG_LL(Denom) <<= 1;
123			if (Denom.lsw & 0x80000000)
124				XSIG_LL(Denom) |= 1;
125			(Denom.lsw) <<= 1;
126		}
127		Denom.msw |= 0x80000000;	/* add 1.0 */
128		div_Xsig(&accumulator, &Denom, &accumulator);
129	}
130
131	/* Convert to 64 bit signed-compatible */
132	exponent += round_Xsig(&accumulator);
133
134	result = &st(0);
135	significand(result) = XSIG_LL(accumulator);
136	setexponent16(result, exponent);
137
138	tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
139
140	setsign(result, sign);
141	FPU_settag0(tag);
142
143	return 0;
144
145}
146