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187 lines
5.1 KiB
187 lines
5.1 KiB
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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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| |
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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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