| 1 |
1623 |
jcastillo |
|
|
| 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 |
|
|
|
|
| 99 |
|
|
| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|
| 100 |
|
|
| The copyright notice above does not evidence any
|
| 101 |
|
|
| actual or intended publication of such source code.
|
| 102 |
|
|
|
| 103 |
|
|
|SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package
|
| 104 |
|
|
|
| 105 |
|
|
|section 8
|
| 106 |
|
|
|
| 107 |
|
|
|xref t_frcinx
|
| 108 |
|
|
|xref t_operr
|
| 109 |
|
|
|xref slogn
|
| 110 |
|
|
|xref slognd
|
| 111 |
|
|
|
| 112 |
|
|
INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
|
| 113 |
|
|
|
| 114 |
|
|
INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
|
| 115 |
|
|
|
| 116 |
|
|
.global slog10d
|
| 117 |
|
|
slog10d:
|
| 118 |
|
|
|--entry point for Log10(X), X is denormalized
|
| 119 |
|
|
movel (%a0),%d0
|
| 120 |
|
|
blt invalid
|
| 121 |
|
|
movel %d1,-(%sp)
|
| 122 |
|
|
clrl %d1
|
| 123 |
|
|
bsr slognd | ...log(X), X denorm.
|
| 124 |
|
|
fmovel (%sp)+,%fpcr
|
| 125 |
|
|
fmulx INV_L10,%fp0
|
| 126 |
|
|
bra t_frcinx
|
| 127 |
|
|
|
| 128 |
|
|
.global slog10
|
| 129 |
|
|
slog10:
|
| 130 |
|
|
|--entry point for Log10(X), X is normalized
|
| 131 |
|
|
|
| 132 |
|
|
movel (%a0),%d0
|
| 133 |
|
|
blt invalid
|
| 134 |
|
|
movel %d1,-(%sp)
|
| 135 |
|
|
clrl %d1
|
| 136 |
|
|
bsr slogn | ...log(X), X normal.
|
| 137 |
|
|
fmovel (%sp)+,%fpcr
|
| 138 |
|
|
fmulx INV_L10,%fp0
|
| 139 |
|
|
bra t_frcinx
|
| 140 |
|
|
|
| 141 |
|
|
|
| 142 |
|
|
.global slog2d
|
| 143 |
|
|
slog2d:
|
| 144 |
|
|
|--entry point for Log2(X), X is denormalized
|
| 145 |
|
|
|
| 146 |
|
|
movel (%a0),%d0
|
| 147 |
|
|
blt invalid
|
| 148 |
|
|
movel %d1,-(%sp)
|
| 149 |
|
|
clrl %d1
|
| 150 |
|
|
bsr slognd | ...log(X), X denorm.
|
| 151 |
|
|
fmovel (%sp)+,%fpcr
|
| 152 |
|
|
fmulx INV_L2,%fp0
|
| 153 |
|
|
bra t_frcinx
|
| 154 |
|
|
|
| 155 |
|
|
.global slog2
|
| 156 |
|
|
slog2:
|
| 157 |
|
|
|--entry point for Log2(X), X is normalized
|
| 158 |
|
|
movel (%a0),%d0
|
| 159 |
|
|
blt invalid
|
| 160 |
|
|
|
| 161 |
|
|
movel 8(%a0),%d0
|
| 162 |
|
|
bnes continue | ...X is not 2^k
|
| 163 |
|
|
|
| 164 |
|
|
movel 4(%a0),%d0
|
| 165 |
|
|
andl #0x7FFFFFFF,%d0
|
| 166 |
|
|
tstl %d0
|
| 167 |
|
|
bnes continue
|
| 168 |
|
|
|
| 169 |
|
|
|--X = 2^k.
|
| 170 |
|
|
movew (%a0),%d0
|
| 171 |
|
|
andl #0x00007FFF,%d0
|
| 172 |
|
|
subl #0x3FFF,%d0
|
| 173 |
|
|
fmovel %d1,%fpcr
|
| 174 |
|
|
fmovel %d0,%fp0
|
| 175 |
|
|
bra t_frcinx
|
| 176 |
|
|
|
| 177 |
|
|
continue:
|
| 178 |
|
|
movel %d1,-(%sp)
|
| 179 |
|
|
clrl %d1
|
| 180 |
|
|
bsr slogn | ...log(X), X normal.
|
| 181 |
|
|
fmovel (%sp)+,%fpcr
|
| 182 |
|
|
fmulx INV_L2,%fp0
|
| 183 |
|
|
bra t_frcinx
|
| 184 |
|
|
|
| 185 |
|
|
invalid:
|
| 186 |
|
|
bra t_operr
|
| 187 |
|
|
|
| 188 |
|
|
|end
|
