| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | | | 
|  | 2 | |	slog2.sa 3.1 12/10/90 | 
|  | 3 | | | 
|  | 4 | |       The entry point slog10 computes the base-10 | 
|  | 5 | |	logarithm of an input argument X. | 
|  | 6 | |	slog10d does the same except the input value is a | 
|  | 7 | |	denormalized number. | 
|  | 8 | |	sLog2 and sLog2d are the base-2 analogues. | 
|  | 9 | | | 
|  | 10 | |       INPUT:	Double-extended value in memory location pointed to | 
|  | 11 | |		by address register a0. | 
|  | 12 | | | 
|  | 13 | |       OUTPUT: log_10(X) or log_2(X) returned in floating-point | 
|  | 14 | |		register fp0. | 
|  | 15 | | | 
|  | 16 | |       ACCURACY and MONOTONICITY: The returned result is within 1.7 | 
|  | 17 | |		ulps in 64 significant bit, i.e. within 0.5003 ulp | 
|  | 18 | |		to 53 bits if the result is subsequently rounded | 
|  | 19 | |		to double precision. The result is provably monotonic | 
|  | 20 | |		in double precision. | 
|  | 21 | | | 
|  | 22 | |       SPEED:	Two timings are measured, both in the copy-back mode. | 
|  | 23 | |		The first one is measured when the function is invoked | 
|  | 24 | |		the first time (so the instructions and data are not | 
|  | 25 | |		in cache), and the second one is measured when the | 
|  | 26 | |		function is reinvoked at the same input argument. | 
|  | 27 | | | 
|  | 28 | |       ALGORITHM and IMPLEMENTATION NOTES: | 
|  | 29 | | | 
|  | 30 | |       slog10d: | 
|  | 31 | | | 
|  | 32 | |       Step 0.   If X < 0, create a NaN and raise the invalid operation | 
|  | 33 | |                 flag. Otherwise, save FPCR in D1; set FpCR to default. | 
|  | 34 | |       Notes:    Default means round-to-nearest mode, no floating-point | 
|  | 35 | |                 traps, and precision control = double extended. | 
|  | 36 | | | 
|  | 37 | |       Step 1.   Call slognd to obtain Y = log(X), the natural log of X. | 
|  | 38 | |       Notes:    Even if X is denormalized, log(X) is always normalized. | 
|  | 39 | | | 
|  | 40 | |       Step 2.   Compute log_10(X) = log(X) * (1/log(10)). | 
|  | 41 | |            2.1  Restore the user FPCR | 
|  | 42 | |            2.2  Return ans := Y * INV_L10. | 
|  | 43 | | | 
|  | 44 | | | 
|  | 45 | |       slog10: | 
|  | 46 | | | 
|  | 47 | |       Step 0.   If X < 0, create a NaN and raise the invalid operation | 
|  | 48 | |                 flag. Otherwise, save FPCR in D1; set FpCR to default. | 
|  | 49 | |       Notes:    Default means round-to-nearest mode, no floating-point | 
|  | 50 | |                 traps, and precision control = double extended. | 
|  | 51 | | | 
|  | 52 | |       Step 1.   Call sLogN to obtain Y = log(X), the natural log of X. | 
|  | 53 | | | 
|  | 54 | |       Step 2.   Compute log_10(X) = log(X) * (1/log(10)). | 
|  | 55 | |            2.1  Restore the user FPCR | 
|  | 56 | |            2.2  Return ans := Y * INV_L10. | 
|  | 57 | | | 
|  | 58 | | | 
|  | 59 | |       sLog2d: | 
|  | 60 | | | 
|  | 61 | |       Step 0.   If X < 0, create a NaN and raise the invalid operation | 
|  | 62 | |                 flag. Otherwise, save FPCR in D1; set FpCR to default. | 
|  | 63 | |       Notes:    Default means round-to-nearest mode, no floating-point | 
|  | 64 | |                 traps, and precision control = double extended. | 
|  | 65 | | | 
|  | 66 | |       Step 1.   Call slognd to obtain Y = log(X), the natural log of X. | 
|  | 67 | |       Notes:    Even if X is denormalized, log(X) is always normalized. | 
|  | 68 | | | 
|  | 69 | |       Step 2.   Compute log_10(X) = log(X) * (1/log(2)). | 
|  | 70 | |            2.1  Restore the user FPCR | 
|  | 71 | |            2.2  Return ans := Y * INV_L2. | 
|  | 72 | | | 
|  | 73 | | | 
|  | 74 | |       sLog2: | 
|  | 75 | | | 
|  | 76 | |       Step 0.   If X < 0, create a NaN and raise the invalid operation | 
|  | 77 | |                 flag. Otherwise, save FPCR in D1; set FpCR to default. | 
|  | 78 | |       Notes:    Default means round-to-nearest mode, no floating-point | 
|  | 79 | |                 traps, and precision control = double extended. | 
|  | 80 | | | 
|  | 81 | |       Step 1.   If X is not an integer power of two, i.e., X != 2^k, | 
|  | 82 | |                 go to Step 3. | 
|  | 83 | | | 
|  | 84 | |       Step 2.   Return k. | 
|  | 85 | |            2.1  Get integer k, X = 2^k. | 
|  | 86 | |            2.2  Restore the user FPCR. | 
|  | 87 | |            2.3  Return ans := convert-to-double-extended(k). | 
|  | 88 | | | 
|  | 89 | |       Step 3.   Call sLogN to obtain Y = log(X), the natural log of X. | 
|  | 90 | | | 
|  | 91 | |       Step 4.   Compute log_2(X) = log(X) * (1/log(2)). | 
|  | 92 | |            4.1  Restore the user FPCR | 
|  | 93 | |            4.2  Return ans := Y * INV_L2. | 
|  | 94 | | | 
|  | 95 |  | 
|  | 96 | |		Copyright (C) Motorola, Inc. 1990 | 
|  | 97 | |			All Rights Reserved | 
|  | 98 | | | 
| Matt Waddel | e00d82d | 2006-02-11 17:55:48 -0800 | [diff] [blame] | 99 | |       For details on the license for this file, please see the | 
|  | 100 | |       file, README, in this same directory. | 
| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 101 |  | 
|  | 102 | |SLOG2    idnt    2,1 | Motorola 040 Floating Point Software Package | 
|  | 103 |  | 
|  | 104 | |section	8 | 
|  | 105 |  | 
|  | 106 | |xref	t_frcinx | 
|  | 107 | |xref	t_operr | 
|  | 108 | |xref	slogn | 
|  | 109 | |xref	slognd | 
|  | 110 |  | 
|  | 111 | INV_L10:  .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000 | 
|  | 112 |  | 
|  | 113 | INV_L2:   .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000 | 
|  | 114 |  | 
|  | 115 | .global	slog10d | 
|  | 116 | slog10d: | 
|  | 117 | |--entry point for Log10(X), X is denormalized | 
|  | 118 | movel		(%a0),%d0 | 
|  | 119 | blt		invalid | 
|  | 120 | movel		%d1,-(%sp) | 
|  | 121 | clrl		%d1 | 
|  | 122 | bsr		slognd			| ...log(X), X denorm. | 
|  | 123 | fmovel		(%sp)+,%fpcr | 
|  | 124 | fmulx		INV_L10,%fp0 | 
|  | 125 | bra		t_frcinx | 
|  | 126 |  | 
|  | 127 | .global	slog10 | 
|  | 128 | slog10: | 
|  | 129 | |--entry point for Log10(X), X is normalized | 
|  | 130 |  | 
|  | 131 | movel		(%a0),%d0 | 
|  | 132 | blt		invalid | 
|  | 133 | movel		%d1,-(%sp) | 
|  | 134 | clrl		%d1 | 
|  | 135 | bsr		slogn			| ...log(X), X normal. | 
|  | 136 | fmovel		(%sp)+,%fpcr | 
|  | 137 | fmulx		INV_L10,%fp0 | 
|  | 138 | bra		t_frcinx | 
|  | 139 |  | 
|  | 140 |  | 
|  | 141 | .global	slog2d | 
|  | 142 | slog2d: | 
|  | 143 | |--entry point for Log2(X), X is denormalized | 
|  | 144 |  | 
|  | 145 | movel		(%a0),%d0 | 
|  | 146 | blt		invalid | 
|  | 147 | movel		%d1,-(%sp) | 
|  | 148 | clrl		%d1 | 
|  | 149 | bsr		slognd			| ...log(X), X denorm. | 
|  | 150 | fmovel		(%sp)+,%fpcr | 
|  | 151 | fmulx		INV_L2,%fp0 | 
|  | 152 | bra		t_frcinx | 
|  | 153 |  | 
|  | 154 | .global	slog2 | 
|  | 155 | slog2: | 
|  | 156 | |--entry point for Log2(X), X is normalized | 
|  | 157 | movel		(%a0),%d0 | 
|  | 158 | blt		invalid | 
|  | 159 |  | 
|  | 160 | movel		8(%a0),%d0 | 
|  | 161 | bnes		continue		| ...X is not 2^k | 
|  | 162 |  | 
|  | 163 | movel		4(%a0),%d0 | 
|  | 164 | andl		#0x7FFFFFFF,%d0 | 
|  | 165 | tstl		%d0 | 
|  | 166 | bnes		continue | 
|  | 167 |  | 
|  | 168 | |--X = 2^k. | 
|  | 169 | movew		(%a0),%d0 | 
|  | 170 | andl		#0x00007FFF,%d0 | 
|  | 171 | subl		#0x3FFF,%d0 | 
|  | 172 | fmovel		%d1,%fpcr | 
|  | 173 | fmovel		%d0,%fp0 | 
|  | 174 | bra		t_frcinx | 
|  | 175 |  | 
|  | 176 | continue: | 
|  | 177 | movel		%d1,-(%sp) | 
|  | 178 | clrl		%d1 | 
|  | 179 | bsr		slogn			| ...log(X), X normal. | 
|  | 180 | fmovel		(%sp)+,%fpcr | 
|  | 181 | fmulx		INV_L2,%fp0 | 
|  | 182 | bra		t_frcinx | 
|  | 183 |  | 
|  | 184 | invalid: | 
|  | 185 | bra		t_operr | 
|  | 186 |  | 
|  | 187 | |end |