/* slog2.s - Motorola 68040 FP logarithmic routines (EXC) *//* Copyright 1991-1993 Wind River Systems, Inc. */	.data	.globl	_copyright_wind_river	.long	_copyright_wind_river/*modification history--------------------01e,21jul93,kdl  added .text (SPR #2372).01d,23aug92,jcf  changed bxxx to jxx.01c,26may92,rrr  the tree shuffle01b,10jan92,kdl  added modification history; general cleanup.01a,15aug91,kdl  original version, from Motorola FPSP v2.0.*//*DESCRIPTION	slog2sa 3.1 12/10/90       The entry point __x_slog10 computes the base-10	logarithm of an input argument X.	__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:       __x_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 __x_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.       __x_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 __x_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	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA	The copyright notice above does not evidence any	actual or intended publication of such source code.SLOG2    idnt    2,1 Motorola 040 Floating Point Software Package	section	8NOMANUAL*/|	xref	__x_t_frcinx|	xref	__x_t_operr|	xref	__x_slogn|	xref	__x_slogndINV_L10:  .long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000INV_L2:   .long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000	.text	.globl	__x_slog10d__x_slog10d:|--entry point for Log10(X), X is denormalized	movel		a0@,d0	jlt 		invalid	movel		d1,a7@-	clrl		d1	bsrl		__x_slognd			|...log(X), X denorm.	fmovel		a7@+,fpcr	fmulx		INV_L10,fp0	jra 		__x_t_frcinx	.globl	__x_slog10__x_slog10:|--entry point for Log10(X), X is normalized	movel		a0@,d0	jlt 		invalid	movel		d1,a7@-	clrl		d1	bsrl		__x_slogn			|...log(X), X normal.	fmovel		a7@+,fpcr	fmulx		INV_L10,fp0	jra 		__x_t_frcinx	.globl	__x_slog2d__x_slog2d:|--entry point for Log2(X), X is denormalized	movel		a0@,d0	jlt 		invalid	movel		d1,a7@-	clrl		d1	bsrl		__x_slognd			|...log(X), X denorm.	fmovel		a7@+,fpcr	fmulx		INV_L2,fp0	jra 		__x_t_frcinx	.globl	__x_slog2__x_slog2:|--entry point for Log2(X), X is normalized	movel		a0@,d0	jlt 		invalid	movel		a0@(8),d0	jne 		continue		|...X is not 2^k	movel		a0@(4),d0	andl		#0x7FFFFFFF,d0	tstl		d0	jne 		continue|--X = 2^k.	movew		a0@,d0	andl		#0x00007FFF,d0	subl		#0x3FFF,d0	fmovel		d1,fpcr	fmovel		d0,fp0	jra 		__x_t_frcinxcontinue:	movel		d1,a7@-	clrl		d1	bsrl		__x_slogn			|...log(X), X normal.	fmovel		a7@+,fpcr	fmulx		INV_L2,fp0	jra 		__x_t_frcinxinvalid:	jra 		__x_t_operr|	end