xref: /src/sys/arch/m68k/fpsp/slog2.sa

*	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
*	M68000 Hi-Performance Microprocessor Division
*	M68040 Software Package 
*
*	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
*	All rights reserved.
*
*	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
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*
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*
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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.
*

SLOG2    IDNT    2,1 Motorola 040 Floating Point Software Package

	section	8

	xref	t_frcinx	
	xref	t_operr
	xref	slogn
	xref	slognd

INV_L10  DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000

INV_L2   DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000

	xdef	slog10d
slog10d:
*--entry point for Log10(X), X is denormalized
	move.l		(a0),d0
	blt.w		invalid
	move.l		d1,-(sp)
	clr.l		d1
	bsr		slognd			...log(X), X denorm.
	fmove.l		(sp)+,fpcr
	fmul.x		INV_L10,fp0
	bra		t_frcinx

	xdef	slog10
slog10:
*--entry point for Log10(X), X is normalized

	move.l		(a0),d0
	blt.w		invalid
	move.l		d1,-(sp)
	clr.l		d1
	bsr		slogn			...log(X), X normal.
	fmove.l		(sp)+,fpcr
	fmul.x		INV_L10,fp0
	bra		t_frcinx


	xdef	slog2d
slog2d:
*--entry point for Log2(X), X is denormalized

	move.l		(a0),d0
	blt.w		invalid
	move.l		d1,-(sp)
	clr.l		d1
	bsr		slognd			...log(X), X denorm.
	fmove.l		(sp)+,fpcr
	fmul.x		INV_L2,fp0
	bra		t_frcinx

	xdef	slog2
slog2:
*--entry point for Log2(X), X is normalized
	move.l		(a0),d0
	blt.w		invalid

	move.l		8(a0),d0
	bne.b		continue		...X is not 2^k

	move.l		4(a0),d0
	and.l		#$7FFFFFFF,d0
	tst.l		d0
	bne.b		continue

*--X = 2^k.
	move.w		(a0),d0
	and.l		#$00007FFF,d0
	sub.l		#$3FFF,d0
	fmove.l		d1,fpcr
	fmove.l		d0,fp0
	bra		t_frcinx

continue:
	move.l		d1,-(sp)
	clr.l		d1
	bsr		slogn			...log(X), X normal.
	fmove.l		(sp)+,fpcr
	fmul.x		INV_L2,fp0
	bra		t_frcinx

invalid:
	bra		t_operr

	end