1 | 1 |
2 | slogn.sa 3.1 12/10/90 2 | slogn.sa 3.1 12/10/90
3 | 3 |
4 | slogn computes the natural logarithm o 4 | slogn computes the natural logarithm of an
5 | input value. slognd does the same exce 5 | input value. slognd does the same except the input value is a
6 | denormalized number. slognp1 computes 6 | denormalized number. slognp1 computes log(1+X), and slognp1d
7 | computes log(1+X) for denormalized X. 7 | computes log(1+X) for denormalized X.
8 | 8 |
9 | Input: Double-extended value in memory 9 | Input: Double-extended value in memory location pointed to by address
10 | register a0. 10 | register a0.
11 | 11 |
12 | Output: log(X) or log(1+X) returned in 12 | Output: log(X) or log(1+X) returned in floating-point register Fp0.
13 | 13 |
14 | Accuracy and Monotonicity: The returne 14 | Accuracy and Monotonicity: The returned result is within 2 ulps in
15 | 64 significant bit, i.e. withi 15 | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
16 | result is subsequently rounded 16 | result is subsequently rounded to double precision. The
17 | result is provably monotonic i 17 | result is provably monotonic in double precision.
18 | 18 |
19 | Speed: The program slogn takes approxi 19 | Speed: The program slogn takes approximately 190 cycles for input
20 | argument X such that |X-1| >= 20 | argument X such that |X-1| >= 1/16, which is the usual
21 | situation. For those arguments 21 | situation. For those arguments, slognp1 takes approximately
22 | 210 cycles. For the less comm 22 | 210 cycles. For the less common arguments, the program will
23 | run no worse than 10% slower. 23 | run no worse than 10% slower.
24 | 24 |
25 | Algorithm: 25 | Algorithm:
26 | LOGN: 26 | LOGN:
27 | Step 1. If |X-1| < 1/16, approximate l 27 | Step 1. If |X-1| < 1/16, approximate log(X) by an odd polynomial in
28 | u, where u = 2(X-1)/(X+1). Oth 28 | u, where u = 2(X-1)/(X+1). Otherwise, move on to Step 2.
29 | 29 |
30 | Step 2. X = 2**k * Y where 1 <= Y < 2. 30 | Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
31 | significant bits of Y plus 2** 31 | significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
32 | 2 where the six "x" match thos 32 | 2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
33 | 33 |
34 | Step 3. Define u = (Y-F)/F. Approximat 34 | Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
35 | log(1+u) = poly. 35 | log(1+u) = poly.
36 | 36 |
37 | Step 4. Reconstruct log(X) = log( 2**k 37 | Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
38 | by k*log(2) + (log(F) + poly). 38 | by k*log(2) + (log(F) + poly). The values of log(F) are calculated
39 | beforehand and stored in the p 39 | beforehand and stored in the program.
40 | 40 |
41 | lognp1: 41 | lognp1:
42 | Step 1: If |X| < 1/16, approximate log 42 | Step 1: If |X| < 1/16, approximate log(1+X) by an odd polynomial in
43 | u where u = 2X/(2+X). Otherwis 43 | u where u = 2X/(2+X). Otherwise, move on to Step 2.
44 | 44 |
45 | Step 2: Let 1+X = 2**k * Y, where 1 <= 45 | Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
46 | of the algorithm for LOGN and 46 | of the algorithm for LOGN and compute log(1+X) as
47 | k*log(2) + log(F) + poly where 47 | k*log(2) + log(F) + poly where poly approximates log(1+u),
48 | u = (Y-F)/F. 48 | u = (Y-F)/F.
49 | 49 |
50 | Implementation Notes: 50 | Implementation Notes:
51 | Note 1. There are 64 different possibl 51 | Note 1. There are 64 different possible values for F, thus 64 log(F)'s
52 | need to be tabulated. Moreover 52 | need to be tabulated. Moreover, the values of 1/F are also
53 | tabulated so that the division 53 | tabulated so that the division in (Y-F)/F can be performed by a
54 | multiplication. 54 | multiplication.
55 | 55 |
56 | Note 2. In Step 2 of lognp1, in order 56 | Note 2. In Step 2 of lognp1, in order to preserved accuracy, the value
57 | Y-F has to be calculated caref 57 | Y-F has to be calculated carefully when 1/2 <= X < 3/2.
58 | 58 |
59 | Note 3. To fully exploit the pipeline, 59 | Note 3. To fully exploit the pipeline, polynomials are usually separated
60 | into two parts evaluated indep 60 | into two parts evaluated independently before being added up.
61 | 61 |
62 62
63 | Copyright (C) Motorola, Inc. 1 63 | Copyright (C) Motorola, Inc. 1990
64 | All Rights Reserved 64 | All Rights Reserved
65 | 65 |
66 | For details on the license for this fi 66 | For details on the license for this file, please see the
67 | file, README, in this same directory. 67 | file, README, in this same directory.
68 68
69 |slogn idnt 2,1 | Motorola 040 Floating Po 69 |slogn idnt 2,1 | Motorola 040 Floating Point Software Package
70 70
71 |section 8 71 |section 8
72 72
73 #include "fpsp.h" 73 #include "fpsp.h"
74 74
75 BOUNDS1: .long 0x3FFEF07D,0x3FFF8841 75 BOUNDS1: .long 0x3FFEF07D,0x3FFF8841
76 BOUNDS2: .long 0x3FFE8000,0x3FFFC000 76 BOUNDS2: .long 0x3FFE8000,0x3FFFC000
77 77
78 LOGOF2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC 78 LOGOF2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
79 79
80 one: .long 0x3F800000 80 one: .long 0x3F800000
81 zero: .long 0x00000000 81 zero: .long 0x00000000
82 infty: .long 0x7F800000 82 infty: .long 0x7F800000
83 negone: .long 0xBF800000 83 negone: .long 0xBF800000
84 84
85 LOGA6: .long 0x3FC2499A,0xB5E4040B 85 LOGA6: .long 0x3FC2499A,0xB5E4040B
86 LOGA5: .long 0xBFC555B5,0x848CB7DB 86 LOGA5: .long 0xBFC555B5,0x848CB7DB
87 87
88 LOGA4: .long 0x3FC99999,0x987D8730 88 LOGA4: .long 0x3FC99999,0x987D8730
89 LOGA3: .long 0xBFCFFFFF,0xFF6F7E97 89 LOGA3: .long 0xBFCFFFFF,0xFF6F7E97
90 90
91 LOGA2: .long 0x3FD55555,0x555555a4 91 LOGA2: .long 0x3FD55555,0x555555a4
92 LOGA1: .long 0xBFE00000,0x00000008 92 LOGA1: .long 0xBFE00000,0x00000008
93 93
94 LOGB5: .long 0x3F175496,0xADD7DAD6 94 LOGB5: .long 0x3F175496,0xADD7DAD6
95 LOGB4: .long 0x3F3C71C2,0xFE80C7E0 95 LOGB4: .long 0x3F3C71C2,0xFE80C7E0
96 96
97 LOGB3: .long 0x3F624924,0x928BCCFF 97 LOGB3: .long 0x3F624924,0x928BCCFF
98 LOGB2: .long 0x3F899999,0x999995EC 98 LOGB2: .long 0x3F899999,0x999995EC
99 99
100 LOGB1: .long 0x3FB55555,0x55555555 100 LOGB1: .long 0x3FB55555,0x55555555
101 TWO: .long 0x40000000,0x00000000 101 TWO: .long 0x40000000,0x00000000
102 102
103 LTHOLD: .long 0x3f990000,0x80000000,0x00000000 103 LTHOLD: .long 0x3f990000,0x80000000,0x00000000,0x00000000
104 104
105 LOGTBL: 105 LOGTBL:
106 .long 0x3FFE0000,0xFE03F80F,0xE03F80F 106 .long 0x3FFE0000,0xFE03F80F,0xE03F80FE,0x00000000
107 .long 0x3FF70000,0xFF015358,0x833C47E 107 .long 0x3FF70000,0xFF015358,0x833C47E2,0x00000000
108 .long 0x3FFE0000,0xFA232CF2,0x52138AC 108 .long 0x3FFE0000,0xFA232CF2,0x52138AC0,0x00000000
109 .long 0x3FF90000,0xBDC8D83E,0xAD88D54 109 .long 0x3FF90000,0xBDC8D83E,0xAD88D549,0x00000000
110 .long 0x3FFE0000,0xF6603D98,0x0F6603D 110 .long 0x3FFE0000,0xF6603D98,0x0F6603DA,0x00000000
111 .long 0x3FFA0000,0x9CF43DCF,0xF5EAFD4 111 .long 0x3FFA0000,0x9CF43DCF,0xF5EAFD48,0x00000000
112 .long 0x3FFE0000,0xF2B9D648,0x0F2B9D6 112 .long 0x3FFE0000,0xF2B9D648,0x0F2B9D65,0x00000000
113 .long 0x3FFA0000,0xDA16EB88,0xCB8DF61 113 .long 0x3FFA0000,0xDA16EB88,0xCB8DF614,0x00000000
114 .long 0x3FFE0000,0xEF2EB71F,0xC434523 114 .long 0x3FFE0000,0xEF2EB71F,0xC4345238,0x00000000
115 .long 0x3FFB0000,0x8B29B775,0x1BD7074 115 .long 0x3FFB0000,0x8B29B775,0x1BD70743,0x00000000
116 .long 0x3FFE0000,0xEBBDB2A5,0xC1619C8 116 .long 0x3FFE0000,0xEBBDB2A5,0xC1619C8C,0x00000000
117 .long 0x3FFB0000,0xA8D839F8,0x30C1FB4 117 .long 0x3FFB0000,0xA8D839F8,0x30C1FB49,0x00000000
118 .long 0x3FFE0000,0xE865AC7B,0x7603A19 118 .long 0x3FFE0000,0xE865AC7B,0x7603A197,0x00000000
119 .long 0x3FFB0000,0xC61A2EB1,0x8CD907A 119 .long 0x3FFB0000,0xC61A2EB1,0x8CD907AD,0x00000000
120 .long 0x3FFE0000,0xE525982A,0xF70C880 120 .long 0x3FFE0000,0xE525982A,0xF70C880E,0x00000000
121 .long 0x3FFB0000,0xE2F2A47A,0xDE3A18A 121 .long 0x3FFB0000,0xE2F2A47A,0xDE3A18AF,0x00000000
122 .long 0x3FFE0000,0xE1FC780E,0x1FC780E 122 .long 0x3FFE0000,0xE1FC780E,0x1FC780E2,0x00000000
123 .long 0x3FFB0000,0xFF64898E,0xDF55D55 123 .long 0x3FFB0000,0xFF64898E,0xDF55D551,0x00000000
124 .long 0x3FFE0000,0xDEE95C4C,0xA037BA5 124 .long 0x3FFE0000,0xDEE95C4C,0xA037BA57,0x00000000
125 .long 0x3FFC0000,0x8DB956A9,0x7B3D014 125 .long 0x3FFC0000,0x8DB956A9,0x7B3D0148,0x00000000
126 .long 0x3FFE0000,0xDBEB61EE,0xD19C595 126 .long 0x3FFE0000,0xDBEB61EE,0xD19C5958,0x00000000
127 .long 0x3FFC0000,0x9B8FE100,0xF47BA1D 127 .long 0x3FFC0000,0x9B8FE100,0xF47BA1DE,0x00000000
128 .long 0x3FFE0000,0xD901B203,0x6406C80 128 .long 0x3FFE0000,0xD901B203,0x6406C80E,0x00000000
129 .long 0x3FFC0000,0xA9372F1D,0x0DA1BD1 129 .long 0x3FFC0000,0xA9372F1D,0x0DA1BD17,0x00000000
130 .long 0x3FFE0000,0xD62B80D6,0x2B80D62 130 .long 0x3FFE0000,0xD62B80D6,0x2B80D62C,0x00000000
131 .long 0x3FFC0000,0xB6B07F38,0xCE90E46 131 .long 0x3FFC0000,0xB6B07F38,0xCE90E46B,0x00000000
132 .long 0x3FFE0000,0xD3680D36,0x80D3680 132 .long 0x3FFE0000,0xD3680D36,0x80D3680D,0x00000000
133 .long 0x3FFC0000,0xC3FD0329,0x0648848 133 .long 0x3FFC0000,0xC3FD0329,0x06488481,0x00000000
134 .long 0x3FFE0000,0xD0B69FCB,0xD2580D0 134 .long 0x3FFE0000,0xD0B69FCB,0xD2580D0B,0x00000000
135 .long 0x3FFC0000,0xD11DE0FF,0x15AB18C 135 .long 0x3FFC0000,0xD11DE0FF,0x15AB18CA,0x00000000
136 .long 0x3FFE0000,0xCE168A77,0x25080CE 136 .long 0x3FFE0000,0xCE168A77,0x25080CE1,0x00000000
137 .long 0x3FFC0000,0xDE1433A1,0x6C66B15 137 .long 0x3FFC0000,0xDE1433A1,0x6C66B150,0x00000000
138 .long 0x3FFE0000,0xCB8727C0,0x65C393E 138 .long 0x3FFE0000,0xCB8727C0,0x65C393E0,0x00000000
139 .long 0x3FFC0000,0xEAE10B5A,0x7DDC8AD 139 .long 0x3FFC0000,0xEAE10B5A,0x7DDC8ADD,0x00000000
140 .long 0x3FFE0000,0xC907DA4E,0x871146A 140 .long 0x3FFE0000,0xC907DA4E,0x871146AD,0x00000000
141 .long 0x3FFC0000,0xF7856E5E,0xE2C9B29 141 .long 0x3FFC0000,0xF7856E5E,0xE2C9B291,0x00000000
142 .long 0x3FFE0000,0xC6980C69,0x80C6980 142 .long 0x3FFE0000,0xC6980C69,0x80C6980C,0x00000000
143 .long 0x3FFD0000,0x82012CA5,0xA68206D 143 .long 0x3FFD0000,0x82012CA5,0xA68206D7,0x00000000
144 .long 0x3FFE0000,0xC4372F85,0x5D824CA 144 .long 0x3FFE0000,0xC4372F85,0x5D824CA6,0x00000000
145 .long 0x3FFD0000,0x882C5FCD,0x7256A8C 145 .long 0x3FFD0000,0x882C5FCD,0x7256A8C5,0x00000000
146 .long 0x3FFE0000,0xC1E4BBD5,0x95F6E94 146 .long 0x3FFE0000,0xC1E4BBD5,0x95F6E947,0x00000000
147 .long 0x3FFD0000,0x8E44C60B,0x4CCFD7D 147 .long 0x3FFD0000,0x8E44C60B,0x4CCFD7DE,0x00000000
148 .long 0x3FFE0000,0xBFA02FE8,0x0BFA02F 148 .long 0x3FFE0000,0xBFA02FE8,0x0BFA02FF,0x00000000
149 .long 0x3FFD0000,0x944AD09E,0xF4351AF 149 .long 0x3FFD0000,0x944AD09E,0xF4351AF6,0x00000000
150 .long 0x3FFE0000,0xBD691047,0x07661AA 150 .long 0x3FFE0000,0xBD691047,0x07661AA3,0x00000000
151 .long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B 151 .long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B2,0x00000000
152 .long 0x3FFE0000,0xBB3EE721,0xA54D880 152 .long 0x3FFE0000,0xBB3EE721,0xA54D880C,0x00000000
153 .long 0x3FFD0000,0xA0218434,0x353F1DE 153 .long 0x3FFD0000,0xA0218434,0x353F1DE8,0x00000000
154 .long 0x3FFE0000,0xB92143FA,0x36F5E02 154 .long 0x3FFE0000,0xB92143FA,0x36F5E02E,0x00000000
155 .long 0x3FFD0000,0xA5F2FCAB,0xBBC506D 155 .long 0x3FFD0000,0xA5F2FCAB,0xBBC506DA,0x00000000
156 .long 0x3FFE0000,0xB70FBB5A,0x19BE365 156 .long 0x3FFE0000,0xB70FBB5A,0x19BE3659,0x00000000
157 .long 0x3FFD0000,0xABB3B8BA,0x2AD362A 157 .long 0x3FFD0000,0xABB3B8BA,0x2AD362A5,0x00000000
158 .long 0x3FFE0000,0xB509E68A,0x9B94821 158 .long 0x3FFE0000,0xB509E68A,0x9B94821F,0x00000000
159 .long 0x3FFD0000,0xB1641795,0xCE3CA97 159 .long 0x3FFD0000,0xB1641795,0xCE3CA97B,0x00000000
160 .long 0x3FFE0000,0xB30F6352,0x8917C80 160 .long 0x3FFE0000,0xB30F6352,0x8917C80B,0x00000000
161 .long 0x3FFD0000,0xB7047551,0x5D0F1C6 161 .long 0x3FFD0000,0xB7047551,0x5D0F1C61,0x00000000
162 .long 0x3FFE0000,0xB11FD3B8,0x0B11FD3 162 .long 0x3FFE0000,0xB11FD3B8,0x0B11FD3C,0x00000000
163 .long 0x3FFD0000,0xBC952AFE,0xEA3D13E 163 .long 0x3FFD0000,0xBC952AFE,0xEA3D13E1,0x00000000
164 .long 0x3FFE0000,0xAF3ADDC6,0x80AF3AD 164 .long 0x3FFE0000,0xAF3ADDC6,0x80AF3ADE,0x00000000
165 .long 0x3FFD0000,0xC2168ED0,0xF458BA4 165 .long 0x3FFD0000,0xC2168ED0,0xF458BA4A,0x00000000
166 .long 0x3FFE0000,0xAD602B58,0x0AD602B 166 .long 0x3FFE0000,0xAD602B58,0x0AD602B6,0x00000000
167 .long 0x3FFD0000,0xC788F439,0xB3163BF 167 .long 0x3FFD0000,0xC788F439,0xB3163BF1,0x00000000
168 .long 0x3FFE0000,0xAB8F69E2,0x8359CD1 168 .long 0x3FFE0000,0xAB8F69E2,0x8359CD11,0x00000000
169 .long 0x3FFD0000,0xCCECAC08,0xBF04565 169 .long 0x3FFD0000,0xCCECAC08,0xBF04565D,0x00000000
170 .long 0x3FFE0000,0xA9C84A47,0xA07F563 170 .long 0x3FFE0000,0xA9C84A47,0xA07F5638,0x00000000
171 .long 0x3FFD0000,0xD2420487,0x2DD8516 171 .long 0x3FFD0000,0xD2420487,0x2DD85160,0x00000000
172 .long 0x3FFE0000,0xA80A80A8,0x0A80A80 172 .long 0x3FFE0000,0xA80A80A8,0x0A80A80B,0x00000000
173 .long 0x3FFD0000,0xD7894992,0x3BC3588 173 .long 0x3FFD0000,0xD7894992,0x3BC3588A,0x00000000
174 .long 0x3FFE0000,0xA655C439,0x2D7B73A 174 .long 0x3FFE0000,0xA655C439,0x2D7B73A8,0x00000000
175 .long 0x3FFD0000,0xDCC2C4B4,0x9887DAC 175 .long 0x3FFD0000,0xDCC2C4B4,0x9887DACC,0x00000000
176 .long 0x3FFE0000,0xA4A9CF1D,0x9683375 176 .long 0x3FFE0000,0xA4A9CF1D,0x96833751,0x00000000
177 .long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9 177 .long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9E,0x00000000
178 .long 0x3FFE0000,0xA3065E3F,0xAE7CD0E 178 .long 0x3FFE0000,0xA3065E3F,0xAE7CD0E0,0x00000000
179 .long 0x3FFD0000,0xE70D785C,0x2F9F5BD 179 .long 0x3FFD0000,0xE70D785C,0x2F9F5BDC,0x00000000
180 .long 0x3FFE0000,0xA16B312E,0xA8FC377 180 .long 0x3FFE0000,0xA16B312E,0xA8FC377D,0x00000000
181 .long 0x3FFD0000,0xEC1F392C,0x5179F28 181 .long 0x3FFD0000,0xEC1F392C,0x5179F283,0x00000000
182 .long 0x3FFE0000,0x9FD809FD,0x809FD80 182 .long 0x3FFE0000,0x9FD809FD,0x809FD80A,0x00000000
183 .long 0x3FFD0000,0xF12440D3,0xE36130E 183 .long 0x3FFD0000,0xF12440D3,0xE36130E6,0x00000000
184 .long 0x3FFE0000,0x9E4CAD23,0xDD5F3A2 184 .long 0x3FFE0000,0x9E4CAD23,0xDD5F3A20,0x00000000
185 .long 0x3FFD0000,0xF61CCE92,0x346600B 185 .long 0x3FFD0000,0xF61CCE92,0x346600BB,0x00000000
186 .long 0x3FFE0000,0x9CC8E160,0xC3FB19B 186 .long 0x3FFE0000,0x9CC8E160,0xC3FB19B9,0x00000000
187 .long 0x3FFD0000,0xFB091FD3,0x8145630 187 .long 0x3FFD0000,0xFB091FD3,0x8145630A,0x00000000
188 .long 0x3FFE0000,0x9B4C6F9E,0xF03A3CA 188 .long 0x3FFE0000,0x9B4C6F9E,0xF03A3CAA,0x00000000
189 .long 0x3FFD0000,0xFFE97042,0xBFA4C2A 189 .long 0x3FFD0000,0xFFE97042,0xBFA4C2AD,0x00000000
190 .long 0x3FFE0000,0x99D722DA,0xBDE58F0 190 .long 0x3FFE0000,0x99D722DA,0xBDE58F06,0x00000000
191 .long 0x3FFE0000,0x825EFCED,0x4936933 191 .long 0x3FFE0000,0x825EFCED,0x49369330,0x00000000
192 .long 0x3FFE0000,0x9868C809,0x868C809 192 .long 0x3FFE0000,0x9868C809,0x868C8098,0x00000000
193 .long 0x3FFE0000,0x84C37A7A,0xB9A905C 193 .long 0x3FFE0000,0x84C37A7A,0xB9A905C9,0x00000000
194 .long 0x3FFE0000,0x97012E02,0x5C04B80 194 .long 0x3FFE0000,0x97012E02,0x5C04B809,0x00000000
195 .long 0x3FFE0000,0x87224C2E,0x8E645FB 195 .long 0x3FFE0000,0x87224C2E,0x8E645FB7,0x00000000
196 .long 0x3FFE0000,0x95A02568,0x095A025 196 .long 0x3FFE0000,0x95A02568,0x095A0257,0x00000000
197 .long 0x3FFE0000,0x897B8CAC,0x9F7DE29 197 .long 0x3FFE0000,0x897B8CAC,0x9F7DE298,0x00000000
198 .long 0x3FFE0000,0x94458094,0x4580944 198 .long 0x3FFE0000,0x94458094,0x45809446,0x00000000
199 .long 0x3FFE0000,0x8BCF55DE,0xC4CD05F 199 .long 0x3FFE0000,0x8BCF55DE,0xC4CD05FE,0x00000000
200 .long 0x3FFE0000,0x92F11384,0x0497889 200 .long 0x3FFE0000,0x92F11384,0x0497889C,0x00000000
201 .long 0x3FFE0000,0x8E1DC0FB,0x89E125E 201 .long 0x3FFE0000,0x8E1DC0FB,0x89E125E5,0x00000000
202 .long 0x3FFE0000,0x91A2B3C4,0xD5E6F80 202 .long 0x3FFE0000,0x91A2B3C4,0xD5E6F809,0x00000000
203 .long 0x3FFE0000,0x9066E68C,0x955B6C9 203 .long 0x3FFE0000,0x9066E68C,0x955B6C9B,0x00000000
204 .long 0x3FFE0000,0x905A3863,0x3E06C43 204 .long 0x3FFE0000,0x905A3863,0x3E06C43B,0x00000000
205 .long 0x3FFE0000,0x92AADE74,0xC7BE59E 205 .long 0x3FFE0000,0x92AADE74,0xC7BE59E0,0x00000000
206 .long 0x3FFE0000,0x8F1779D9,0xFDC3A21 206 .long 0x3FFE0000,0x8F1779D9,0xFDC3A219,0x00000000
207 .long 0x3FFE0000,0x94E9BFF6,0x1584564 207 .long 0x3FFE0000,0x94E9BFF6,0x15845643,0x00000000
208 .long 0x3FFE0000,0x8DDA5202,0x3769480 208 .long 0x3FFE0000,0x8DDA5202,0x37694809,0x00000000
209 .long 0x3FFE0000,0x9723A1B7,0x2013420 209 .long 0x3FFE0000,0x9723A1B7,0x20134203,0x00000000
210 .long 0x3FFE0000,0x8CA29C04,0x6514E02 210 .long 0x3FFE0000,0x8CA29C04,0x6514E023,0x00000000
211 .long 0x3FFE0000,0x995899C8,0x90EB899 211 .long 0x3FFE0000,0x995899C8,0x90EB8990,0x00000000
212 .long 0x3FFE0000,0x8B70344A,0x139BC75 212 .long 0x3FFE0000,0x8B70344A,0x139BC75A,0x00000000
213 .long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2 213 .long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2F,0x00000000
214 .long 0x3FFE0000,0x8A42F870,0x5669DB4 214 .long 0x3FFE0000,0x8A42F870,0x5669DB46,0x00000000
215 .long 0x3FFE0000,0x9DB4224F,0xFFE1157 215 .long 0x3FFE0000,0x9DB4224F,0xFFE1157C,0x00000000
216 .long 0x3FFE0000,0x891AC73A,0xE9819B5 216 .long 0x3FFE0000,0x891AC73A,0xE9819B50,0x00000000
217 .long 0x3FFE0000,0x9FDADC26,0x8B7A12D 217 .long 0x3FFE0000,0x9FDADC26,0x8B7A12DA,0x00000000
218 .long 0x3FFE0000,0x87F78087,0xF78087F 218 .long 0x3FFE0000,0x87F78087,0xF78087F8,0x00000000
219 .long 0x3FFE0000,0xA1FCFF17,0xCE733BD 219 .long 0x3FFE0000,0xA1FCFF17,0xCE733BD4,0x00000000
220 .long 0x3FFE0000,0x86D90544,0x7A34ACC 220 .long 0x3FFE0000,0x86D90544,0x7A34ACC6,0x00000000
221 .long 0x3FFE0000,0xA41A9E8F,0x5446FB9 221 .long 0x3FFE0000,0xA41A9E8F,0x5446FB9F,0x00000000
222 .long 0x3FFE0000,0x85BF3761,0x2CEE3C9 222 .long 0x3FFE0000,0x85BF3761,0x2CEE3C9B,0x00000000
223 .long 0x3FFE0000,0xA633CD7E,0x6771CD8 223 .long 0x3FFE0000,0xA633CD7E,0x6771CD8B,0x00000000
224 .long 0x3FFE0000,0x84A9F9C8,0x084A9F9 224 .long 0x3FFE0000,0x84A9F9C8,0x084A9F9D,0x00000000
225 .long 0x3FFE0000,0xA8489E60,0x0B435A5 225 .long 0x3FFE0000,0xA8489E60,0x0B435A5E,0x00000000
226 .long 0x3FFE0000,0x83993052,0x3FBE336 226 .long 0x3FFE0000,0x83993052,0x3FBE3368,0x00000000
227 .long 0x3FFE0000,0xAA59233C,0xCCA4BD4 227 .long 0x3FFE0000,0xAA59233C,0xCCA4BD49,0x00000000
228 .long 0x3FFE0000,0x828CBFBE,0xB9A020A 228 .long 0x3FFE0000,0x828CBFBE,0xB9A020A3,0x00000000
229 .long 0x3FFE0000,0xAC656DAE,0x6BCC498 229 .long 0x3FFE0000,0xAC656DAE,0x6BCC4985,0x00000000
230 .long 0x3FFE0000,0x81848DA8,0xFAF0D27 230 .long 0x3FFE0000,0x81848DA8,0xFAF0D277,0x00000000
231 .long 0x3FFE0000,0xAE6D8EE3,0x60BB246 231 .long 0x3FFE0000,0xAE6D8EE3,0x60BB2468,0x00000000
232 .long 0x3FFE0000,0x80808080,0x8080808 232 .long 0x3FFE0000,0x80808080,0x80808081,0x00000000
233 .long 0x3FFE0000,0xB07197A2,0x3C46C65 233 .long 0x3FFE0000,0xB07197A2,0x3C46C654,0x00000000
234 234
235 .set ADJK,L_SCR1 235 .set ADJK,L_SCR1
236 236
237 .set X,FP_SCR1 237 .set X,FP_SCR1
238 .set XDCARE,X+2 238 .set XDCARE,X+2
239 .set XFRAC,X+4 239 .set XFRAC,X+4
240 240
241 .set F,FP_SCR2 241 .set F,FP_SCR2
242 .set FFRAC,F+4 242 .set FFRAC,F+4
243 243
244 .set KLOG2,FP_SCR3 244 .set KLOG2,FP_SCR3
245 245
246 .set SAVEU,FP_SCR4 246 .set SAVEU,FP_SCR4
247 247
248 | xref t_frcinx 248 | xref t_frcinx
249 |xref t_extdnrm 249 |xref t_extdnrm
250 |xref t_operr 250 |xref t_operr
251 |xref t_dz 251 |xref t_dz
252 252
253 .global slognd 253 .global slognd
254 slognd: 254 slognd:
255 |--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INP 255 |--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
256 256
257 movel #-100,ADJK(%a6) | ...I 257 movel #-100,ADJK(%a6) | ...INPUT = 2^(ADJK) * FP0
258 258
259 |----normalize the input value by left shiftin 259 |----normalize the input value by left shifting k bits (k to be determined
260 |----below), adjusting exponent and storing -k 260 |----below), adjusting exponent and storing -k to ADJK
261 |----the value TWOTO100 is no longer needed. 261 |----the value TWOTO100 is no longer needed.
262 |----Note that this code assumes the denormali 262 |----Note that this code assumes the denormalized input is NON-ZERO.
263 263
264 moveml %d2-%d7,-(%a7) | ...s 264 moveml %d2-%d7,-(%a7) | ...save some registers
265 movel #0x00000000,%d3 | ...D 265 movel #0x00000000,%d3 | ...D3 is exponent of smallest norm. #
266 movel 4(%a0),%d4 266 movel 4(%a0),%d4
267 movel 8(%a0),%d5 | ...( 267 movel 8(%a0),%d5 | ...(D4,D5) is (Hi_X,Lo_X)
268 clrl %d2 | ...D 268 clrl %d2 | ...D2 used for holding K
269 269
270 tstl %d4 270 tstl %d4
271 bnes HiX_not0 271 bnes HiX_not0
272 272
273 HiX_0: 273 HiX_0:
274 movel %d5,%d4 274 movel %d5,%d4
275 clrl %d5 275 clrl %d5
276 movel #32,%d2 276 movel #32,%d2
277 clrl %d6 277 clrl %d6
278 bfffo %d4{#0:#32},%d6 278 bfffo %d4{#0:#32},%d6
279 lsll %d6,%d4 279 lsll %d6,%d4
280 addl %d6,%d2 | ...( 280 addl %d6,%d2 | ...(D3,D4,D5) is normalized
281 281
282 movel %d3,X(%a6) 282 movel %d3,X(%a6)
283 movel %d4,XFRAC(%a6) 283 movel %d4,XFRAC(%a6)
284 movel %d5,XFRAC+4(%a6) 284 movel %d5,XFRAC+4(%a6)
285 negl %d2 285 negl %d2
286 movel %d2,ADJK(%a6) 286 movel %d2,ADJK(%a6)
287 fmovex X(%a6),%fp0 287 fmovex X(%a6),%fp0
288 moveml (%a7)+,%d2-%d7 | ...r 288 moveml (%a7)+,%d2-%d7 | ...restore registers
289 lea X(%a6),%a0 289 lea X(%a6),%a0
290 bras LOGBGN | ...b 290 bras LOGBGN | ...begin regular log(X)
291 291
292 292
293 HiX_not0: 293 HiX_not0:
294 clrl %d6 294 clrl %d6
295 bfffo %d4{#0:#32},%d6 | ...f 295 bfffo %d4{#0:#32},%d6 | ...find first 1
296 movel %d6,%d2 | ...g 296 movel %d6,%d2 | ...get k
297 lsll %d6,%d4 297 lsll %d6,%d4
298 movel %d5,%d7 | ...a 298 movel %d5,%d7 | ...a copy of D5
299 lsll %d6,%d5 299 lsll %d6,%d5
300 negl %d6 300 negl %d6
301 addil #32,%d6 301 addil #32,%d6
302 lsrl %d6,%d7 302 lsrl %d6,%d7
303 orl %d7,%d4 | ...( 303 orl %d7,%d4 | ...(D3,D4,D5) normalized
304 304
305 movel %d3,X(%a6) 305 movel %d3,X(%a6)
306 movel %d4,XFRAC(%a6) 306 movel %d4,XFRAC(%a6)
307 movel %d5,XFRAC+4(%a6) 307 movel %d5,XFRAC+4(%a6)
308 negl %d2 308 negl %d2
309 movel %d2,ADJK(%a6) 309 movel %d2,ADJK(%a6)
310 fmovex X(%a6),%fp0 310 fmovex X(%a6),%fp0
311 moveml (%a7)+,%d2-%d7 | ...r 311 moveml (%a7)+,%d2-%d7 | ...restore registers
312 lea X(%a6),%a0 312 lea X(%a6),%a0
313 bras LOGBGN | ...b 313 bras LOGBGN | ...begin regular log(X)
314 314
315 315
316 .global slogn 316 .global slogn
317 slogn: 317 slogn:
318 |--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZE 318 |--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
319 319
320 fmovex (%a0),%fp0 | ...L 320 fmovex (%a0),%fp0 | ...LOAD INPUT
321 movel #0x00000000,ADJK(%a6) 321 movel #0x00000000,ADJK(%a6)
322 322
323 LOGBGN: 323 LOGBGN:
324 |--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*F 324 |--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
325 |--A FINITE, NON-ZERO, NORMALIZED NUMBER. 325 |--A FINITE, NON-ZERO, NORMALIZED NUMBER.
326 326
327 movel (%a0),%d0 327 movel (%a0),%d0
328 movew 4(%a0),%d0 328 movew 4(%a0),%d0
329 329
330 movel (%a0),X(%a6) 330 movel (%a0),X(%a6)
331 movel 4(%a0),X+4(%a6) 331 movel 4(%a0),X+4(%a6)
332 movel 8(%a0),X+8(%a6) 332 movel 8(%a0),X+8(%a6)
333 333
334 cmpil #0,%d0 | ...CHECK IF 334 cmpil #0,%d0 | ...CHECK IF X IS NEGATIVE
335 blt LOGNEG | ...LOG OF NE 335 blt LOGNEG | ...LOG OF NEGATIVE ARGUMENT IS INVALID
336 cmp2l BOUNDS1,%d0 | ...X IS POSI 336 cmp2l BOUNDS1,%d0 | ...X IS POSITIVE, CHECK IF X IS NEAR 1
337 bcc LOGNEAR1 | ...BOUNDS IS 337 bcc LOGNEAR1 | ...BOUNDS IS ROUGHLY [15/16, 17/16]
338 338
339 LOGMAIN: 339 LOGMAIN:
340 |--THIS SHOULD BE THE USUAL CASE, X NOT VERY C 340 |--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
341 341
342 |--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXX 342 |--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
343 |--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS 343 |--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
344 |--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y) 344 |--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
345 |-- = K*LOG2 + LOG(F) + L 345 |-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
346 |--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THU 346 |--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
347 |--LOG(1+U) CAN BE VERY EFFICIENT. 347 |--LOG(1+U) CAN BE VERY EFFICIENT.
348 |--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A 348 |--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
349 |--DIVISION IS NEEDED TO CALCULATE (Y-F)/F. 349 |--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
350 350
351 |--GET K, Y, F, AND ADDRESS OF 1/F. 351 |--GET K, Y, F, AND ADDRESS OF 1/F.
352 asrl #8,%d0 352 asrl #8,%d0
353 asrl #8,%d0 | ...SHIFTED 1 353 asrl #8,%d0 | ...SHIFTED 16 BITS, BIASED EXPO. OF X
354 subil #0x3FFF,%d0 | ...THIS IS K 354 subil #0x3FFF,%d0 | ...THIS IS K
355 addl ADJK(%a6),%d0 | ...ADJUST K, 355 addl ADJK(%a6),%d0 | ...ADJUST K, ORIGINAL INPUT MAY BE DENORM.
356 lea LOGTBL,%a0 | ...BASE ADDR 356 lea LOGTBL,%a0 | ...BASE ADDRESS OF 1/F AND LOG(F)
357 fmovel %d0,%fp1 | ...C 357 fmovel %d0,%fp1 | ...CONVERT K TO FLOATING-POINT FORMAT
358 358
359 |--WHILE THE CONVERSION IS GOING ON, WE GET F 359 |--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
360 movel #0x3FFF0000,X(%a6) | ...X 360 movel #0x3FFF0000,X(%a6) | ...X IS NOW Y, I.E. 2^(-K)*X
361 movel XFRAC(%a6),FFRAC(%a6) 361 movel XFRAC(%a6),FFRAC(%a6)
362 andil #0xFE000000,FFRAC(%a6) | ...FI 362 andil #0xFE000000,FFRAC(%a6) | ...FIRST 7 BITS OF Y
363 oril #0x01000000,FFRAC(%a6) | ...GE 363 oril #0x01000000,FFRAC(%a6) | ...GET F: ATTACH A 1 AT THE EIGHTH BIT
364 movel FFRAC(%a6),%d0 | ...READY TO 364 movel FFRAC(%a6),%d0 | ...READY TO GET ADDRESS OF 1/F
365 andil #0x7E000000,%d0 365 andil #0x7E000000,%d0
366 asrl #8,%d0 366 asrl #8,%d0
367 asrl #8,%d0 367 asrl #8,%d0
368 asrl #4,%d0 | ...SHIFTED 2 368 asrl #4,%d0 | ...SHIFTED 20, D0 IS THE DISPLACEMENT
369 addal %d0,%a0 | ...A0 IS THE 369 addal %d0,%a0 | ...A0 IS THE ADDRESS FOR 1/F
370 370
371 fmovex X(%a6),%fp0 371 fmovex X(%a6),%fp0
372 movel #0x3fff0000,F(%a6) 372 movel #0x3fff0000,F(%a6)
373 clrl F+8(%a6) 373 clrl F+8(%a6)
374 fsubx F(%a6),%fp0 | ...Y 374 fsubx F(%a6),%fp0 | ...Y-F
375 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...S 375 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...SAVE FP2 WHILE FP0 IS NOT READY
376 |--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, 376 |--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
377 |--REGISTERS SAVED: FPCR, FP1, FP2 377 |--REGISTERS SAVED: FPCR, FP1, FP2
378 378
379 LP1CONT1: 379 LP1CONT1:
380 |--AN RE-ENTRY POINT FOR LOGNP1 380 |--AN RE-ENTRY POINT FOR LOGNP1
381 fmulx (%a0),%fp0 | ...FP0 IS U 381 fmulx (%a0),%fp0 | ...FP0 IS U = (Y-F)/F
382 fmulx LOGOF2,%fp1 | ...GET K*LOG 382 fmulx LOGOF2,%fp1 | ...GET K*LOG2 WHILE FP0 IS NOT READY
383 fmovex %fp0,%fp2 383 fmovex %fp0,%fp2
384 fmulx %fp2,%fp2 | ...F 384 fmulx %fp2,%fp2 | ...FP2 IS V=U*U
385 fmovex %fp1,KLOG2(%a6) | ...PUT K*LOG 385 fmovex %fp1,KLOG2(%a6) | ...PUT K*LOG2 IN MEMORY, FREE FP1
386 386
387 |--LOG(1+U) IS APPROXIMATED BY 387 |--LOG(1+U) IS APPROXIMATED BY
388 |--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) 388 |--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
389 |--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4 389 |--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))]
390 390
391 fmovex %fp2,%fp3 391 fmovex %fp2,%fp3
392 fmovex %fp2,%fp1 392 fmovex %fp2,%fp1
393 393
394 fmuld LOGA6,%fp1 | ...V*A6 394 fmuld LOGA6,%fp1 | ...V*A6
395 fmuld LOGA5,%fp2 | ...V*A5 395 fmuld LOGA5,%fp2 | ...V*A5
396 396
397 faddd LOGA4,%fp1 | ...A4+V*A6 397 faddd LOGA4,%fp1 | ...A4+V*A6
398 faddd LOGA3,%fp2 | ...A3+V*A5 398 faddd LOGA3,%fp2 | ...A3+V*A5
399 399
400 fmulx %fp3,%fp1 | ...V 400 fmulx %fp3,%fp1 | ...V*(A4+V*A6)
401 fmulx %fp3,%fp2 | ...V 401 fmulx %fp3,%fp2 | ...V*(A3+V*A5)
402 402
403 faddd LOGA2,%fp1 | ...A2+V*(A4+ 403 faddd LOGA2,%fp1 | ...A2+V*(A4+V*A6)
404 faddd LOGA1,%fp2 | ...A1+V*(A3+ 404 faddd LOGA1,%fp2 | ...A1+V*(A3+V*A5)
405 405
406 fmulx %fp3,%fp1 | ...V 406 fmulx %fp3,%fp1 | ...V*(A2+V*(A4+V*A6))
407 addal #16,%a0 | ...ADDRESS O 407 addal #16,%a0 | ...ADDRESS OF LOG(F)
408 fmulx %fp3,%fp2 | ...V 408 fmulx %fp3,%fp2 | ...V*(A1+V*(A3+V*A5)), FP3 RELEASED
409 409
410 fmulx %fp0,%fp1 | ...U 410 fmulx %fp0,%fp1 | ...U*V*(A2+V*(A4+V*A6))
411 faddx %fp2,%fp0 | ...U 411 faddx %fp2,%fp0 | ...U+V*(A1+V*(A3+V*A5)), FP2 RELEASED
412 412
413 faddx (%a0),%fp1 | ...LOG(F)+U* 413 faddx (%a0),%fp1 | ...LOG(F)+U*V*(A2+V*(A4+V*A6))
414 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...R 414 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...RESTORE FP2
415 faddx %fp1,%fp0 | ...F 415 faddx %fp1,%fp0 | ...FP0 IS LOG(F) + LOG(1+U)
416 416
417 fmovel %d1,%fpcr 417 fmovel %d1,%fpcr
418 faddx KLOG2(%a6),%fp0 | ...FINAL ADD 418 faddx KLOG2(%a6),%fp0 | ...FINAL ADD
419 bra t_frcinx 419 bra t_frcinx
420 420
421 421
422 LOGNEAR1: 422 LOGNEAR1:
423 |--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS TH 423 |--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
424 fmovex %fp0,%fp1 424 fmovex %fp0,%fp1
425 fsubs one,%fp1 | ...F 425 fsubs one,%fp1 | ...FP1 IS X-1
426 fadds one,%fp0 | ...F 426 fadds one,%fp0 | ...FP0 IS X+1
427 faddx %fp1,%fp1 | ...F 427 faddx %fp1,%fp1 | ...FP1 IS 2(X-1)
428 |--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN 428 |--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
429 |--IN U, U = 2(X-1)/(X+1) = FP1/FP0 429 |--IN U, U = 2(X-1)/(X+1) = FP1/FP0
430 430
431 LP1CONT2: 431 LP1CONT2:
432 |--THIS IS AN RE-ENTRY POINT FOR LOGNP1 432 |--THIS IS AN RE-ENTRY POINT FOR LOGNP1
433 fdivx %fp0,%fp1 | ...F 433 fdivx %fp0,%fp1 | ...FP1 IS U
434 fmovemx %fp2-%fp2/%fp3,-(%sp) | ... 434 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...SAVE FP2
435 |--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3 435 |--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
436 |--LET V=U*U, W=V*V, CALCULATE 436 |--LET V=U*U, W=V*V, CALCULATE
437 |--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5) 437 |--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
438 |--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 438 |--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] )
439 fmovex %fp1,%fp0 439 fmovex %fp1,%fp0
440 fmulx %fp0,%fp0 | ...FP0 IS V 440 fmulx %fp0,%fp0 | ...FP0 IS V
441 fmovex %fp1,SAVEU(%a6) | ...STORE U I 441 fmovex %fp1,SAVEU(%a6) | ...STORE U IN MEMORY, FREE FP1
442 fmovex %fp0,%fp1 442 fmovex %fp0,%fp1
443 fmulx %fp1,%fp1 | ...FP1 IS W 443 fmulx %fp1,%fp1 | ...FP1 IS W
444 444
445 fmoved LOGB5,%fp3 445 fmoved LOGB5,%fp3
446 fmoved LOGB4,%fp2 446 fmoved LOGB4,%fp2
447 447
448 fmulx %fp1,%fp3 | ...W*B5 448 fmulx %fp1,%fp3 | ...W*B5
449 fmulx %fp1,%fp2 | ...W*B4 449 fmulx %fp1,%fp2 | ...W*B4
450 450
451 faddd LOGB3,%fp3 | ...B3+W*B5 451 faddd LOGB3,%fp3 | ...B3+W*B5
452 faddd LOGB2,%fp2 | ...B2+W*B4 452 faddd LOGB2,%fp2 | ...B2+W*B4
453 453
454 fmulx %fp3,%fp1 | ...W*(B3+W*B 454 fmulx %fp3,%fp1 | ...W*(B3+W*B5), FP3 RELEASED
455 455
456 fmulx %fp0,%fp2 | ...V*(B2+W*B 456 fmulx %fp0,%fp2 | ...V*(B2+W*B4)
457 457
458 faddd LOGB1,%fp1 | ...B1+W*(B3+W*B5) 458 faddd LOGB1,%fp1 | ...B1+W*(B3+W*B5)
459 fmulx SAVEU(%a6),%fp0 | ...FP0 IS U* 459 fmulx SAVEU(%a6),%fp0 | ...FP0 IS U*V
460 460
461 faddx %fp2,%fp1 | ...B1+W*(B3+ 461 faddx %fp2,%fp1 | ...B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
462 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...FP2 462 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...FP2 RESTORED
463 463
464 fmulx %fp1,%fp0 | ...U*V*( [B1 464 fmulx %fp1,%fp0 | ...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
465 465
466 fmovel %d1,%fpcr 466 fmovel %d1,%fpcr
467 faddx SAVEU(%a6),%fp0 467 faddx SAVEU(%a6),%fp0
468 bra t_frcinx 468 bra t_frcinx
469 rts 469 rts
470 470
471 LOGNEG: 471 LOGNEG:
472 |--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID 472 |--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
473 bra t_operr 473 bra t_operr
474 474
475 .global slognp1d 475 .global slognp1d
476 slognp1d: 476 slognp1d:
477 |--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED I 477 |--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
478 | Simply return the denorm 478 | Simply return the denorm
479 479
480 bra t_extdnrm 480 bra t_extdnrm
481 481
482 .global slognp1 482 .global slognp1
483 slognp1: 483 slognp1:
484 |--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON- 484 |--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
485 485
486 fmovex (%a0),%fp0 | ...LOAD INPU 486 fmovex (%a0),%fp0 | ...LOAD INPUT
487 fabsx %fp0 |test magnitud 487 fabsx %fp0 |test magnitude
488 fcmpx LTHOLD,%fp0 |compare with 488 fcmpx LTHOLD,%fp0 |compare with min threshold
489 fbgt LP1REAL |if greater, c 489 fbgt LP1REAL |if greater, continue
490 fmovel #0,%fpsr |clr N 490 fmovel #0,%fpsr |clr N flag from compare
491 fmovel %d1,%fpcr 491 fmovel %d1,%fpcr
492 fmovex (%a0),%fp0 |return signed 492 fmovex (%a0),%fp0 |return signed argument
493 bra t_frcinx 493 bra t_frcinx
494 494
495 LP1REAL: 495 LP1REAL:
496 fmovex (%a0),%fp0 | ...LOAD INPU 496 fmovex (%a0),%fp0 | ...LOAD INPUT
497 movel #0x00000000,ADJK(%a6) 497 movel #0x00000000,ADJK(%a6)
498 fmovex %fp0,%fp1 | ...FP1 IS IN 498 fmovex %fp0,%fp1 | ...FP1 IS INPUT Z
499 fadds one,%fp0 | ...X := ROUN 499 fadds one,%fp0 | ...X := ROUND(1+Z)
500 fmovex %fp0,X(%a6) 500 fmovex %fp0,X(%a6)
501 movew XFRAC(%a6),XDCARE(%a6) 501 movew XFRAC(%a6),XDCARE(%a6)
502 movel X(%a6),%d0 502 movel X(%a6),%d0
503 cmpil #0,%d0 503 cmpil #0,%d0
504 ble LP1NEG0 | ...LOG OF ZERO OR -V 504 ble LP1NEG0 | ...LOG OF ZERO OR -VE
505 cmp2l BOUNDS2,%d0 505 cmp2l BOUNDS2,%d0
506 bcs LOGMAIN | ...BOUNDS2 IS [1/2,3 506 bcs LOGMAIN | ...BOUNDS2 IS [1/2,3/2]
507 |--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS 507 |--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
508 |--CONTAINS AT LEAST 63 BITS OF INFORMATION OF 508 |--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
509 |--SIMPLY INVOKE LOG(X) FOR LOG(1+Z). 509 |--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
510 510
511 LP1NEAR1: 511 LP1NEAR1:
512 |--NEXT SEE IF EXP(-1/16) < X < EXP(1/16) 512 |--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
513 cmp2l BOUNDS1,%d0 513 cmp2l BOUNDS1,%d0
514 bcss LP1CARE 514 bcss LP1CARE
515 515
516 LP1ONE16: 516 LP1ONE16:
517 |--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG( 517 |--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
518 |--WHERE U = 2Z/(2+Z) = 2Z/(1+X). 518 |--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
519 faddx %fp1,%fp1 | ...FP1 IS 2Z 519 faddx %fp1,%fp1 | ...FP1 IS 2Z
520 fadds one,%fp0 | ...FP0 IS 1+ 520 fadds one,%fp0 | ...FP0 IS 1+X
521 |--U = FP1/FP0 521 |--U = FP1/FP0
522 bra LP1CONT2 522 bra LP1CONT2
523 523
524 LP1CARE: 524 LP1CARE:
525 |--HERE WE USE THE USUAL TABLE DRIVEN APPROACH 525 |--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
526 |--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFOR 526 |--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
527 |--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z I 527 |--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
528 |--THERE ARE ONLY TWO CASES. 528 |--THERE ARE ONLY TWO CASES.
529 |--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F 529 |--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
530 |--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F 530 |--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z
531 |--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN 531 |--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
532 |--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED. 532 |--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
533 533
534 movel XFRAC(%a6),FFRAC(%a6) 534 movel XFRAC(%a6),FFRAC(%a6)
535 andil #0xFE000000,FFRAC(%a6) 535 andil #0xFE000000,FFRAC(%a6)
536 oril #0x01000000,FFRAC(%a6) | ...F 536 oril #0x01000000,FFRAC(%a6) | ...F OBTAINED
537 cmpil #0x3FFF8000,%d0 | ...SEE IF 1+ 537 cmpil #0x3FFF8000,%d0 | ...SEE IF 1+Z > 1
538 bges KISZERO 538 bges KISZERO
539 539
540 KISNEG1: 540 KISNEG1:
541 fmoves TWO,%fp0 541 fmoves TWO,%fp0
542 movel #0x3fff0000,F(%a6) 542 movel #0x3fff0000,F(%a6)
543 clrl F+8(%a6) 543 clrl F+8(%a6)
544 fsubx F(%a6),%fp0 | ...2-F 544 fsubx F(%a6),%fp0 | ...2-F
545 movel FFRAC(%a6),%d0 545 movel FFRAC(%a6),%d0
546 andil #0x7E000000,%d0 546 andil #0x7E000000,%d0
547 asrl #8,%d0 547 asrl #8,%d0
548 asrl #8,%d0 548 asrl #8,%d0
549 asrl #4,%d0 | ...D0 CONTAI 549 asrl #4,%d0 | ...D0 CONTAINS DISPLACEMENT FOR 1/F
550 faddx %fp1,%fp1 | ...G 550 faddx %fp1,%fp1 | ...GET 2Z
551 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...S 551 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...SAVE FP2
552 faddx %fp1,%fp0 | ...F 552 faddx %fp1,%fp0 | ...FP0 IS Y-F = (2-F)+2Z
553 lea LOGTBL,%a0 | ...A0 IS ADD 553 lea LOGTBL,%a0 | ...A0 IS ADDRESS OF 1/F
554 addal %d0,%a0 554 addal %d0,%a0
555 fmoves negone,%fp1 | ...FP1 IS K 555 fmoves negone,%fp1 | ...FP1 IS K = -1
556 bra LP1CONT1 556 bra LP1CONT1
557 557
558 KISZERO: 558 KISZERO:
559 fmoves one,%fp0 559 fmoves one,%fp0
560 movel #0x3fff0000,F(%a6) 560 movel #0x3fff0000,F(%a6)
561 clrl F+8(%a6) 561 clrl F+8(%a6)
562 fsubx F(%a6),%fp0 | ...1 562 fsubx F(%a6),%fp0 | ...1-F
563 movel FFRAC(%a6),%d0 563 movel FFRAC(%a6),%d0
564 andil #0x7E000000,%d0 564 andil #0x7E000000,%d0
565 asrl #8,%d0 565 asrl #8,%d0
566 asrl #8,%d0 566 asrl #8,%d0
567 asrl #4,%d0 567 asrl #4,%d0
568 faddx %fp1,%fp0 | ...F 568 faddx %fp1,%fp0 | ...FP0 IS Y-F
569 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...F 569 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...FP2 SAVED
570 lea LOGTBL,%a0 570 lea LOGTBL,%a0
571 addal %d0,%a0 | ...A0 IS ADD 571 addal %d0,%a0 | ...A0 IS ADDRESS OF 1/F
572 fmoves zero,%fp1 | ...FP1 IS K 572 fmoves zero,%fp1 | ...FP1 IS K = 0
573 bra LP1CONT1 573 bra LP1CONT1
574 574
575 LP1NEG0: 575 LP1NEG0:
576 |--FPCR SAVED. D0 IS X IN COMPACT FORM. 576 |--FPCR SAVED. D0 IS X IN COMPACT FORM.
577 cmpil #0,%d0 577 cmpil #0,%d0
578 blts LP1NEG 578 blts LP1NEG
579 LP1ZERO: 579 LP1ZERO:
580 fmoves negone,%fp0 580 fmoves negone,%fp0
581 581
582 fmovel %d1,%fpcr 582 fmovel %d1,%fpcr
583 bra t_dz 583 bra t_dz
584 584
585 LP1NEG: 585 LP1NEG:
586 fmoves zero,%fp0 586 fmoves zero,%fp0
587 587
588 fmovel %d1,%fpcr 588 fmovel %d1,%fpcr
589 bra t_operr 589 bra t_operr
590 590
591 |end 591 |end
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