slog2.S
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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