|  | | | 
|  | |	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 |