| | |
| | 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 |