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1da177e4 LT |
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 | ||
1da177e4 | 20 | #define HIPOWER 11 |
3d0d14f9 IM |
21 | static 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 | |
1da177e4 LT |
33 | }; |
34 | ||
35 | static 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 | */ | |
40 | static const Xsig shiftterm0 = MK_XSIG(0, 0, 0); | |
41 | static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318); | |
42 | static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3); | |
43 | static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9); | |
44 | ||
45 | static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1, | |
3d0d14f9 IM |
46 | &shiftterm2, &shiftterm3 |
47 | }; | |
1da177e4 LT |
48 | |
49 | /*--- poly_2xm1() -----------------------------------------------------------+ | |
50 | | Requires st(0) which is TAG_Valid and < 1. | | |
51 | +---------------------------------------------------------------------------*/ | |
e8d591dc | 52 | int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) |
1da177e4 | 53 | { |
3d0d14f9 IM |
54 | long int exponent, shift; |
55 | unsigned long long Xll; | |
56 | Xsig accumulator, Denom, argSignif; | |
57 | u_char tag; | |
1da177e4 | 58 | |
3d0d14f9 | 59 | exponent = exponent16(arg); |
1da177e4 LT |
60 | |
61 | #ifdef PARANOID | |
3d0d14f9 IM |
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 | } | |
1da177e4 LT |
67 | #endif /* PARANOID */ |
68 | ||
3d0d14f9 IM |
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); | |
1da177e4 | 129 | } |
1da177e4 | 130 | |
3d0d14f9 IM |
131 | /* Convert to 64 bit signed-compatible */ |
132 | exponent += round_Xsig(&accumulator); | |
1da177e4 | 133 | |
3d0d14f9 IM |
134 | result = &st(0); |
135 | significand(result) = XSIG_LL(accumulator); | |
136 | setexponent16(result, exponent); | |
1da177e4 | 137 | |
3d0d14f9 | 138 | tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); |
1da177e4 | 139 | |
3d0d14f9 IM |
140 | setsign(result, sign); |
141 | FPU_settag0(tag); | |
1da177e4 | 142 | |
3d0d14f9 | 143 | return 0; |
1da177e4 LT |
144 | |
145 | } |