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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