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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