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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
+|
+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
+| The copyright notice above does not evidence any
+| actual or intended publication of such source code.
+
+|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