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