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|
|
| slog2.sa 3.1 12/10/90
|
| The entry point slog10 computes the base-10
| logarithm of an input argument X.
| slog10d does the same except the input value is a
| denormalized number.
| sLog2 and sLog2d are the base-2 analogues.
|
| INPUT: Double-extended value in memory location pointed to
| by address register a0.
|
| OUTPUT: log_10(X) or log_2(X) returned in floating-point
| register fp0.
|
| ACCURACY and MONOTONICITY: The returned result is within 1.7
| ulps in 64 significant bit, i.e. within 0.5003 ulp
| to 53 bits if the result is subsequently rounded
| to double precision. The result is provably monotonic
| in double precision.
|
| SPEED: Two timings are measured, both in the copy-back mode.
| The first one is measured when the function is invoked
| the first time (so the instructions and data are not
| in cache), and the second one is measured when the
| function is reinvoked at the same input argument.
|
| ALGORITHM and IMPLEMENTATION NOTES:
|
| slog10d:
|
| Step 0. If X < 0, create a NaN and raise the invalid operation
| flag. Otherwise, save FPCR in D1; set FpCR to default.
| Notes: Default means round-to-nearest mode, no floating-point
| traps, and precision control = double extended.
|
| Step 1. Call slognd to obtain Y = log(X), the natural log of X.
| Notes: Even if X is denormalized, log(X) is always normalized.
|
| Step 2. Compute log_10(X) = log(X) * (1/log(10)).
| 2.1 Restore the user FPCR
| 2.2 Return ans := Y * INV_L10.
|
|
| slog10:
|
| Step 0. If X < 0, create a NaN and raise the invalid operation
| flag. Otherwise, save FPCR in D1; set FpCR to default.
| Notes: Default means round-to-nearest mode, no floating-point
| traps, and precision control = double extended.
|
| Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
|
| Step 2. Compute log_10(X) = log(X) * (1/log(10)).
| 2.1 Restore the user FPCR
| 2.2 Return ans := Y * INV_L10.
|
|
| sLog2d:
|
| Step 0. If X < 0, create a NaN and raise the invalid operation
| flag. Otherwise, save FPCR in D1; set FpCR to default.
| Notes: Default means round-to-nearest mode, no floating-point
| traps, and precision control = double extended.
|
| Step 1. Call slognd to obtain Y = log(X), the natural log of X.
| Notes: Even if X is denormalized, log(X) is always normalized.
|
| Step 2. Compute log_10(X) = log(X) * (1/log(2)).
| 2.1 Restore the user FPCR
| 2.2 Return ans := Y * INV_L2.
|
|
| sLog2:
|
| Step 0. If X < 0, create a NaN and raise the invalid operation
| flag. Otherwise, save FPCR in D1; set FpCR to default.
| Notes: Default means round-to-nearest mode, no floating-point
| traps, and precision control = double extended.
|
| Step 1. If X is not an integer power of two, i.e., X != 2^k,
| go to Step 3.
|
| Step 2. Return k.
| 2.1 Get integer k, X = 2^k.
| 2.2 Restore the user FPCR.
| 2.3 Return ans := convert-to-double-extended(k).
|
| Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
|
| Step 4. Compute log_2(X) = log(X) * (1/log(2)).
| 4.1 Restore the user FPCR
| 4.2 Return ans := Y * INV_L2.
|
| Copyright (C) Motorola, Inc. 1990
| All Rights Reserved
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|SLOG2 idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
|xref t_frcinx
|xref t_operr
|xref slogn
|xref slognd
INV_L10: .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
INV_L2: .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
.global slog10d
slog10d:
|--entry point for Log10(X), X is denormalized
movel (%a0),%d0
blt invalid
movel %d1,-(%sp)
clrl %d1
bsr slognd | ...log(X), X denorm.
fmovel (%sp)+,%fpcr
fmulx INV_L10,%fp0
bra t_frcinx
.global slog10
slog10:
|--entry point for Log10(X), X is normalized
movel (%a0),%d0
blt invalid
movel %d1,-(%sp)
clrl %d1
bsr slogn | ...log(X), X normal.
fmovel (%sp)+,%fpcr
fmulx INV_L10,%fp0
bra t_frcinx
.global slog2d
slog2d:
|--entry point for Log2(X), X is denormalized
movel (%a0),%d0
blt invalid
movel %d1,-(%sp)
clrl %d1
bsr slognd | ...log(X), X denorm.
fmovel (%sp)+,%fpcr
fmulx INV_L2,%fp0
bra t_frcinx
.global slog2
slog2:
|--entry point for Log2(X), X is normalized
movel (%a0),%d0
blt invalid
movel 8(%a0),%d0
bnes continue | ...X is not 2^k
movel 4(%a0),%d0
andl #0x7FFFFFFF,%d0
tstl %d0
bnes continue
|--X = 2^k.
movew (%a0),%d0
andl #0x00007FFF,%d0
subl #0x3FFF,%d0
fmovel %d1,%fpcr
fmovel %d0,%fp0
bra t_frcinx
continue:
movel %d1,-(%sp)
clrl %d1
bsr slogn | ...log(X), X normal.
fmovel (%sp)+,%fpcr
fmulx INV_L2,%fp0
bra t_frcinx
invalid:
bra t_operr
|end
|
