patch-1.3.94 linux/arch/m68k/fpsp040/slogn.S

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Lines: 593
Date: Sat Feb 24 22:58:44 1996
Orig file: v1.3.93/linux/arch/m68k/fpsp040/slogn.S
Orig date: Thu Jan 1 02:00:00 1970

diff -u --recursive --new-file v1.3.93/linux/arch/m68k/fpsp040/slogn.S linux/arch/m68k/fpsp040/slogn.S
@@ -0,0 +1,592 @@
+|
+|	slogn.sa 3.1 12/10/90
+|
+|	slogn computes the natural logarithm of an
+|	input value. slognd does the same except the input value is a
+|	denormalized number. slognp1 computes log(1+X), and slognp1d
+|	computes log(1+X) for denormalized X.
+|
+|	Input: Double-extended value in memory location pointed to by address
+|		register a0.
+|
+|	Output:	log(X) or log(1+X) returned in floating-point register Fp0.
+|
+|	Accuracy and Monotonicity: The returned result is within 2 ulps in
+|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
+|		result is subsequently rounded to double precision. The 
+|		result is provably monotonic in double precision.
+|
+|	Speed: The program slogn takes approximately 190 cycles for input 
+|		argument X such that |X-1| >= 1/16, which is the the usual 
+|		situation. For those arguments, slognp1 takes approximately
+|		 210 cycles. For the less common arguments, the program will
+|		 run no worse than 10% slower.
+|
+|	Algorithm:
+|	LOGN:
+|	Step 1. If |X-1| < 1/16, approximate log(X) by an odd polynomial in
+|		u, where u = 2(X-1)/(X+1). Otherwise, move on to Step 2.
+|
+|	Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
+|		significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
+|		2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
+|
+|	Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
+|		log(1+u) = poly.
+|
+|	Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
+|		by k*log(2) + (log(F) + poly). The values of log(F) are calculated
+|		beforehand and stored in the program.
+|
+|	lognp1:
+|	Step 1: If |X| < 1/16, approximate log(1+X) by an odd polynomial in
+|		u where u = 2X/(2+X). Otherwise, move on to Step 2.
+|
+|	Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
+|		of the algorithm for LOGN and compute log(1+X) as
+|		k*log(2) + log(F) + poly where poly approximates log(1+u),
+|		u = (Y-F)/F. 
+|
+|	Implementation Notes:
+|	Note 1. There are 64 different possible values for F, thus 64 log(F)'s
+|		need to be tabulated. Moreover, the values of 1/F are also 
+|		tabulated so that the division in (Y-F)/F can be performed by a
+|		multiplication.
+|
+|	Note 2. In Step 2 of lognp1, in order to preserved accuracy, the value
+|		Y-F has to be calculated carefully when 1/2 <= X < 3/2. 
+|
+|	Note 3. To fully exploit the pipeline, polynomials are usually separated
+|		into two parts evaluated independently before being added up.
+|	
+
+|		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.
+
+|slogn	idnt	2,1 | Motorola 040 Floating Point Software Package
+
+	|section	8
+
+	.include "fpsp.h"
+
+BOUNDS1:  .long 0x3FFEF07D,0x3FFF8841
+BOUNDS2:  .long 0x3FFE8000,0x3FFFC000
+
+LOGOF2:	.long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
+
+one:	.long 0x3F800000
+zero:	.long 0x00000000
+infty:	.long 0x7F800000
+negone:	.long 0xBF800000
+
+LOGA6:	.long 0x3FC2499A,0xB5E4040B
+LOGA5:	.long 0xBFC555B5,0x848CB7DB
+
+LOGA4:	.long 0x3FC99999,0x987D8730
+LOGA3:	.long 0xBFCFFFFF,0xFF6F7E97
+
+LOGA2:	.long 0x3FD55555,0x555555a4
+LOGA1:	.long 0xBFE00000,0x00000008
+
+LOGB5:	.long 0x3F175496,0xADD7DAD6
+LOGB4:	.long 0x3F3C71C2,0xFE80C7E0
+
+LOGB3:	.long 0x3F624924,0x928BCCFF
+LOGB2:	.long 0x3F899999,0x999995EC
+
+LOGB1:	.long 0x3FB55555,0x55555555
+TWO:	.long 0x40000000,0x00000000
+
+LTHOLD:	.long 0x3f990000,0x80000000,0x00000000,0x00000000
+
+LOGTBL:
+	.long  0x3FFE0000,0xFE03F80F,0xE03F80FE,0x00000000
+	.long  0x3FF70000,0xFF015358,0x833C47E2,0x00000000
+	.long  0x3FFE0000,0xFA232CF2,0x52138AC0,0x00000000
+	.long  0x3FF90000,0xBDC8D83E,0xAD88D549,0x00000000
+	.long  0x3FFE0000,0xF6603D98,0x0F6603DA,0x00000000
+	.long  0x3FFA0000,0x9CF43DCF,0xF5EAFD48,0x00000000
+	.long  0x3FFE0000,0xF2B9D648,0x0F2B9D65,0x00000000
+	.long  0x3FFA0000,0xDA16EB88,0xCB8DF614,0x00000000
+	.long  0x3FFE0000,0xEF2EB71F,0xC4345238,0x00000000
+	.long  0x3FFB0000,0x8B29B775,0x1BD70743,0x00000000
+	.long  0x3FFE0000,0xEBBDB2A5,0xC1619C8C,0x00000000
+	.long  0x3FFB0000,0xA8D839F8,0x30C1FB49,0x00000000
+	.long  0x3FFE0000,0xE865AC7B,0x7603A197,0x00000000
+	.long  0x3FFB0000,0xC61A2EB1,0x8CD907AD,0x00000000
+	.long  0x3FFE0000,0xE525982A,0xF70C880E,0x00000000
+	.long  0x3FFB0000,0xE2F2A47A,0xDE3A18AF,0x00000000
+	.long  0x3FFE0000,0xE1FC780E,0x1FC780E2,0x00000000
+	.long  0x3FFB0000,0xFF64898E,0xDF55D551,0x00000000
+	.long  0x3FFE0000,0xDEE95C4C,0xA037BA57,0x00000000
+	.long  0x3FFC0000,0x8DB956A9,0x7B3D0148,0x00000000
+	.long  0x3FFE0000,0xDBEB61EE,0xD19C5958,0x00000000
+	.long  0x3FFC0000,0x9B8FE100,0xF47BA1DE,0x00000000
+	.long  0x3FFE0000,0xD901B203,0x6406C80E,0x00000000
+	.long  0x3FFC0000,0xA9372F1D,0x0DA1BD17,0x00000000
+	.long  0x3FFE0000,0xD62B80D6,0x2B80D62C,0x00000000
+	.long  0x3FFC0000,0xB6B07F38,0xCE90E46B,0x00000000
+	.long  0x3FFE0000,0xD3680D36,0x80D3680D,0x00000000
+	.long  0x3FFC0000,0xC3FD0329,0x06488481,0x00000000
+	.long  0x3FFE0000,0xD0B69FCB,0xD2580D0B,0x00000000
+	.long  0x3FFC0000,0xD11DE0FF,0x15AB18CA,0x00000000
+	.long  0x3FFE0000,0xCE168A77,0x25080CE1,0x00000000
+	.long  0x3FFC0000,0xDE1433A1,0x6C66B150,0x00000000
+	.long  0x3FFE0000,0xCB8727C0,0x65C393E0,0x00000000
+	.long  0x3FFC0000,0xEAE10B5A,0x7DDC8ADD,0x00000000
+	.long  0x3FFE0000,0xC907DA4E,0x871146AD,0x00000000
+	.long  0x3FFC0000,0xF7856E5E,0xE2C9B291,0x00000000
+	.long  0x3FFE0000,0xC6980C69,0x80C6980C,0x00000000
+	.long  0x3FFD0000,0x82012CA5,0xA68206D7,0x00000000
+	.long  0x3FFE0000,0xC4372F85,0x5D824CA6,0x00000000
+	.long  0x3FFD0000,0x882C5FCD,0x7256A8C5,0x00000000
+	.long  0x3FFE0000,0xC1E4BBD5,0x95F6E947,0x00000000
+	.long  0x3FFD0000,0x8E44C60B,0x4CCFD7DE,0x00000000
+	.long  0x3FFE0000,0xBFA02FE8,0x0BFA02FF,0x00000000
+	.long  0x3FFD0000,0x944AD09E,0xF4351AF6,0x00000000
+	.long  0x3FFE0000,0xBD691047,0x07661AA3,0x00000000
+	.long  0x3FFD0000,0x9A3EECD4,0xC3EAA6B2,0x00000000
+	.long  0x3FFE0000,0xBB3EE721,0xA54D880C,0x00000000
+	.long  0x3FFD0000,0xA0218434,0x353F1DE8,0x00000000
+	.long  0x3FFE0000,0xB92143FA,0x36F5E02E,0x00000000
+	.long  0x3FFD0000,0xA5F2FCAB,0xBBC506DA,0x00000000
+	.long  0x3FFE0000,0xB70FBB5A,0x19BE3659,0x00000000
+	.long  0x3FFD0000,0xABB3B8BA,0x2AD362A5,0x00000000
+	.long  0x3FFE0000,0xB509E68A,0x9B94821F,0x00000000
+	.long  0x3FFD0000,0xB1641795,0xCE3CA97B,0x00000000
+	.long  0x3FFE0000,0xB30F6352,0x8917C80B,0x00000000
+	.long  0x3FFD0000,0xB7047551,0x5D0F1C61,0x00000000
+	.long  0x3FFE0000,0xB11FD3B8,0x0B11FD3C,0x00000000
+	.long  0x3FFD0000,0xBC952AFE,0xEA3D13E1,0x00000000
+	.long  0x3FFE0000,0xAF3ADDC6,0x80AF3ADE,0x00000000
+	.long  0x3FFD0000,0xC2168ED0,0xF458BA4A,0x00000000
+	.long  0x3FFE0000,0xAD602B58,0x0AD602B6,0x00000000
+	.long  0x3FFD0000,0xC788F439,0xB3163BF1,0x00000000
+	.long  0x3FFE0000,0xAB8F69E2,0x8359CD11,0x00000000
+	.long  0x3FFD0000,0xCCECAC08,0xBF04565D,0x00000000
+	.long  0x3FFE0000,0xA9C84A47,0xA07F5638,0x00000000
+	.long  0x3FFD0000,0xD2420487,0x2DD85160,0x00000000
+	.long  0x3FFE0000,0xA80A80A8,0x0A80A80B,0x00000000
+	.long  0x3FFD0000,0xD7894992,0x3BC3588A,0x00000000
+	.long  0x3FFE0000,0xA655C439,0x2D7B73A8,0x00000000
+	.long  0x3FFD0000,0xDCC2C4B4,0x9887DACC,0x00000000
+	.long  0x3FFE0000,0xA4A9CF1D,0x96833751,0x00000000
+	.long  0x3FFD0000,0xE1EEBD3E,0x6D6A6B9E,0x00000000
+	.long  0x3FFE0000,0xA3065E3F,0xAE7CD0E0,0x00000000
+	.long  0x3FFD0000,0xE70D785C,0x2F9F5BDC,0x00000000
+	.long  0x3FFE0000,0xA16B312E,0xA8FC377D,0x00000000
+	.long  0x3FFD0000,0xEC1F392C,0x5179F283,0x00000000
+	.long  0x3FFE0000,0x9FD809FD,0x809FD80A,0x00000000
+	.long  0x3FFD0000,0xF12440D3,0xE36130E6,0x00000000
+	.long  0x3FFE0000,0x9E4CAD23,0xDD5F3A20,0x00000000
+	.long  0x3FFD0000,0xF61CCE92,0x346600BB,0x00000000
+	.long  0x3FFE0000,0x9CC8E160,0xC3FB19B9,0x00000000
+	.long  0x3FFD0000,0xFB091FD3,0x8145630A,0x00000000
+	.long  0x3FFE0000,0x9B4C6F9E,0xF03A3CAA,0x00000000
+	.long  0x3FFD0000,0xFFE97042,0xBFA4C2AD,0x00000000
+	.long  0x3FFE0000,0x99D722DA,0xBDE58F06,0x00000000
+	.long  0x3FFE0000,0x825EFCED,0x49369330,0x00000000
+	.long  0x3FFE0000,0x9868C809,0x868C8098,0x00000000
+	.long  0x3FFE0000,0x84C37A7A,0xB9A905C9,0x00000000
+	.long  0x3FFE0000,0x97012E02,0x5C04B809,0x00000000
+	.long  0x3FFE0000,0x87224C2E,0x8E645FB7,0x00000000
+	.long  0x3FFE0000,0x95A02568,0x095A0257,0x00000000
+	.long  0x3FFE0000,0x897B8CAC,0x9F7DE298,0x00000000
+	.long  0x3FFE0000,0x94458094,0x45809446,0x00000000
+	.long  0x3FFE0000,0x8BCF55DE,0xC4CD05FE,0x00000000
+	.long  0x3FFE0000,0x92F11384,0x0497889C,0x00000000
+	.long  0x3FFE0000,0x8E1DC0FB,0x89E125E5,0x00000000
+	.long  0x3FFE0000,0x91A2B3C4,0xD5E6F809,0x00000000
+	.long  0x3FFE0000,0x9066E68C,0x955B6C9B,0x00000000
+	.long  0x3FFE0000,0x905A3863,0x3E06C43B,0x00000000
+	.long  0x3FFE0000,0x92AADE74,0xC7BE59E0,0x00000000
+	.long  0x3FFE0000,0x8F1779D9,0xFDC3A219,0x00000000
+	.long  0x3FFE0000,0x94E9BFF6,0x15845643,0x00000000
+	.long  0x3FFE0000,0x8DDA5202,0x37694809,0x00000000
+	.long  0x3FFE0000,0x9723A1B7,0x20134203,0x00000000
+	.long  0x3FFE0000,0x8CA29C04,0x6514E023,0x00000000
+	.long  0x3FFE0000,0x995899C8,0x90EB8990,0x00000000
+	.long  0x3FFE0000,0x8B70344A,0x139BC75A,0x00000000
+	.long  0x3FFE0000,0x9B88BDAA,0x3A3DAE2F,0x00000000
+	.long  0x3FFE0000,0x8A42F870,0x5669DB46,0x00000000
+	.long  0x3FFE0000,0x9DB4224F,0xFFE1157C,0x00000000
+	.long  0x3FFE0000,0x891AC73A,0xE9819B50,0x00000000
+	.long  0x3FFE0000,0x9FDADC26,0x8B7A12DA,0x00000000
+	.long  0x3FFE0000,0x87F78087,0xF78087F8,0x00000000
+	.long  0x3FFE0000,0xA1FCFF17,0xCE733BD4,0x00000000
+	.long  0x3FFE0000,0x86D90544,0x7A34ACC6,0x00000000
+	.long  0x3FFE0000,0xA41A9E8F,0x5446FB9F,0x00000000
+	.long  0x3FFE0000,0x85BF3761,0x2CEE3C9B,0x00000000
+	.long  0x3FFE0000,0xA633CD7E,0x6771CD8B,0x00000000
+	.long  0x3FFE0000,0x84A9F9C8,0x084A9F9D,0x00000000
+	.long  0x3FFE0000,0xA8489E60,0x0B435A5E,0x00000000
+	.long  0x3FFE0000,0x83993052,0x3FBE3368,0x00000000
+	.long  0x3FFE0000,0xAA59233C,0xCCA4BD49,0x00000000
+	.long  0x3FFE0000,0x828CBFBE,0xB9A020A3,0x00000000
+	.long  0x3FFE0000,0xAC656DAE,0x6BCC4985,0x00000000
+	.long  0x3FFE0000,0x81848DA8,0xFAF0D277,0x00000000
+	.long  0x3FFE0000,0xAE6D8EE3,0x60BB2468,0x00000000
+	.long  0x3FFE0000,0x80808080,0x80808081,0x00000000
+	.long  0x3FFE0000,0xB07197A2,0x3C46C654,0x00000000
+
+	.set	ADJK,L_SCR1
+
+	.set	X,FP_SCR1
+	.set	XDCARE,X+2
+	.set	XFRAC,X+4
+
+	.set	F,FP_SCR2
+	.set	FFRAC,F+4
+
+	.set	KLOG2,FP_SCR3
+
+	.set	SAVEU,FP_SCR4
+
+	| xref	t_frcinx
+	|xref	t_extdnrm
+	|xref	t_operr
+	|xref	t_dz
+
+	.global	slognd
+slognd:
+|--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
+
+	movel		#-100,ADJK(%a6)	| ...INPUT = 2^(ADJK) * FP0
+
+|----normalize the input value by left shifting k bits (k to be determined
+|----below), adjusting exponent and storing -k to  ADJK
+|----the value TWOTO100 is no longer needed.
+|----Note that this code assumes the denormalized input is NON-ZERO.
+
+     moveml	%d2-%d7,-(%a7)		| ...save some registers 
+     movel	#0x00000000,%d3		| ...D3 is exponent of smallest norm. #
+     movel	4(%a0),%d4
+     movel	8(%a0),%d5		| ...(D4,D5) is (Hi_X,Lo_X)
+     clrl	%d2			| ...D2 used for holding K
+
+     tstl	%d4
+     bnes	HiX_not0
+
+HiX_0:
+     movel	%d5,%d4
+     clrl	%d5
+     movel	#32,%d2
+     clrl	%d6
+     bfffo      %d4{#0:#32},%d6
+     lsll      %d6,%d4
+     addl	%d6,%d2			| ...(D3,D4,D5) is normalized
+
+     movel	%d3,X(%a6)
+     movel	%d4,XFRAC(%a6)
+     movel	%d5,XFRAC+4(%a6)
+     negl	%d2
+     movel	%d2,ADJK(%a6)
+     fmovex	X(%a6),%fp0
+     moveml	(%a7)+,%d2-%d7		| ...restore registers
+     lea	X(%a6),%a0
+     bras	LOGBGN			| ...begin regular log(X)
+
+
+HiX_not0:
+     clrl	%d6
+     bfffo	%d4{#0:#32},%d6		| ...find first 1
+     movel	%d6,%d2			| ...get k
+     lsll	%d6,%d4
+     movel	%d5,%d7			| ...a copy of D5
+     lsll	%d6,%d5
+     negl	%d6
+     addil	#32,%d6
+     lsrl	%d6,%d7
+     orl	%d7,%d4			| ...(D3,D4,D5) normalized
+
+     movel	%d3,X(%a6)
+     movel	%d4,XFRAC(%a6)
+     movel	%d5,XFRAC+4(%a6)
+     negl	%d2
+     movel	%d2,ADJK(%a6)
+     fmovex	X(%a6),%fp0
+     moveml	(%a7)+,%d2-%d7		| ...restore registers
+     lea	X(%a6),%a0
+     bras	LOGBGN			| ...begin regular log(X)
+
+
+	.global	slogn
+slogn:
+|--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
+
+	fmovex		(%a0),%fp0	| ...LOAD INPUT
+	movel		#0x00000000,ADJK(%a6)
+
+LOGBGN:
+|--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
+|--A FINITE, NON-ZERO, NORMALIZED NUMBER.
+
+	movel	(%a0),%d0
+	movew	4(%a0),%d0
+
+	movel	(%a0),X(%a6)
+	movel	4(%a0),X+4(%a6)
+	movel	8(%a0),X+8(%a6)
+
+	cmpil	#0,%d0		| ...CHECK IF X IS NEGATIVE
+	blt	LOGNEG		| ...LOG OF NEGATIVE ARGUMENT IS INVALID
+	cmp2l	BOUNDS1,%d0	| ...X IS POSITIVE, CHECK IF X IS NEAR 1
+	bcc	LOGNEAR1	| ...BOUNDS IS ROUGHLY [15/16, 17/16]
+
+LOGMAIN:
+|--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
+
+|--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
+|--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
+|--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
+|--			 = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
+|--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
+|--LOG(1+U) CAN BE VERY EFFICIENT.
+|--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
+|--DIVISION IS NEEDED TO CALCULATE (Y-F)/F. 
+
+|--GET K, Y, F, AND ADDRESS OF 1/F.
+	asrl	#8,%d0
+	asrl	#8,%d0		| ...SHIFTED 16 BITS, BIASED EXPO. OF X
+	subil	#0x3FFF,%d0 	| ...THIS IS K
+	addl	ADJK(%a6),%d0	| ...ADJUST K, ORIGINAL INPUT MAY BE  DENORM.
+	lea	LOGTBL,%a0 	| ...BASE ADDRESS OF 1/F AND LOG(F)
+	fmovel	%d0,%fp1		| ...CONVERT K TO FLOATING-POINT FORMAT
+
+|--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
+	movel	#0x3FFF0000,X(%a6)	| ...X IS NOW Y, I.E. 2^(-K)*X
+	movel	XFRAC(%a6),FFRAC(%a6)
+	andil	#0xFE000000,FFRAC(%a6) | ...FIRST 7 BITS OF Y
+	oril	#0x01000000,FFRAC(%a6) | ...GET F: ATTACH A 1 AT THE EIGHTH BIT
+	movel	FFRAC(%a6),%d0	| ...READY TO GET ADDRESS OF 1/F
+	andil	#0x7E000000,%d0	
+	asrl	#8,%d0
+	asrl	#8,%d0
+	asrl	#4,%d0		| ...SHIFTED 20, D0 IS THE DISPLACEMENT
+	addal	%d0,%a0		| ...A0 IS THE ADDRESS FOR 1/F
+
+	fmovex	X(%a6),%fp0
+	movel	#0x3fff0000,F(%a6)
+	clrl	F+8(%a6)
+	fsubx	F(%a6),%fp0		| ...Y-F
+	fmovemx %fp2-%fp2/%fp3,-(%sp)	| ...SAVE FP2 WHILE FP0 IS NOT READY
+|--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
+|--REGISTERS SAVED: FPCR, FP1, FP2
+
+LP1CONT1:
+|--AN RE-ENTRY POINT FOR LOGNP1
+	fmulx	(%a0),%fp0	| ...FP0 IS U = (Y-F)/F
+	fmulx	LOGOF2,%fp1	| ...GET K*LOG2 WHILE FP0 IS NOT READY
+	fmovex	%fp0,%fp2
+	fmulx	%fp2,%fp2		| ...FP2 IS V=U*U
+	fmovex	%fp1,KLOG2(%a6)	| ...PUT K*LOG2 IN MEMEORY, FREE FP1
+
+|--LOG(1+U) IS APPROXIMATED BY
+|--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
+|--[U + V*(A1+V*(A3+V*A5))]  +  [U*V*(A2+V*(A4+V*A6))]
+
+	fmovex	%fp2,%fp3
+	fmovex	%fp2,%fp1	
+
+	fmuld	LOGA6,%fp1	| ...V*A6
+	fmuld	LOGA5,%fp2	| ...V*A5
+
+	faddd	LOGA4,%fp1	| ...A4+V*A6
+	faddd	LOGA3,%fp2	| ...A3+V*A5
+
+	fmulx	%fp3,%fp1		| ...V*(A4+V*A6)
+	fmulx	%fp3,%fp2		| ...V*(A3+V*A5)
+
+	faddd	LOGA2,%fp1	| ...A2+V*(A4+V*A6)
+	faddd	LOGA1,%fp2	| ...A1+V*(A3+V*A5)
+
+	fmulx	%fp3,%fp1		| ...V*(A2+V*(A4+V*A6))
+	addal	#16,%a0		| ...ADDRESS OF LOG(F)
+	fmulx	%fp3,%fp2		| ...V*(A1+V*(A3+V*A5)), FP3 RELEASED
+
+	fmulx	%fp0,%fp1		| ...U*V*(A2+V*(A4+V*A6))
+	faddx	%fp2,%fp0		| ...U+V*(A1+V*(A3+V*A5)), FP2 RELEASED
+
+	faddx	(%a0),%fp1	| ...LOG(F)+U*V*(A2+V*(A4+V*A6))
+	fmovemx  (%sp)+,%fp2-%fp2/%fp3	| ...RESTORE FP2
+	faddx	%fp1,%fp0		| ...FP0 IS LOG(F) + LOG(1+U)
+
+	fmovel	%d1,%fpcr
+	faddx	KLOG2(%a6),%fp0	| ...FINAL ADD
+	bra	t_frcinx
+
+
+LOGNEAR1:
+|--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
+	fmovex	%fp0,%fp1
+	fsubs	one,%fp1		| ...FP1 IS X-1
+	fadds	one,%fp0		| ...FP0 IS X+1
+	faddx	%fp1,%fp1		| ...FP1 IS 2(X-1)
+|--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
+|--IN U, U = 2(X-1)/(X+1) = FP1/FP0
+
+LP1CONT2:
+|--THIS IS AN RE-ENTRY POINT FOR LOGNP1
+	fdivx	%fp0,%fp1		| ...FP1 IS U
+	fmovemx %fp2-%fp2/%fp3,-(%sp)	 | ...SAVE FP2
+|--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
+|--LET V=U*U, W=V*V, CALCULATE
+|--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
+|--U + U*V*(  [B1 + W*(B3 + W*B5)]  +  [V*(B2 + W*B4)]  )
+	fmovex	%fp1,%fp0
+	fmulx	%fp0,%fp0	| ...FP0 IS V
+	fmovex	%fp1,SAVEU(%a6) | ...STORE U IN MEMORY, FREE FP1
+	fmovex	%fp0,%fp1	
+	fmulx	%fp1,%fp1	| ...FP1 IS W
+
+	fmoved	LOGB5,%fp3
+	fmoved	LOGB4,%fp2
+
+	fmulx	%fp1,%fp3	| ...W*B5
+	fmulx	%fp1,%fp2	| ...W*B4
+
+	faddd	LOGB3,%fp3 | ...B3+W*B5
+	faddd	LOGB2,%fp2 | ...B2+W*B4
+
+	fmulx	%fp3,%fp1	| ...W*(B3+W*B5), FP3 RELEASED
+
+	fmulx	%fp0,%fp2	| ...V*(B2+W*B4)
+
+	faddd	LOGB1,%fp1 | ...B1+W*(B3+W*B5)
+	fmulx	SAVEU(%a6),%fp0 | ...FP0 IS U*V
+
+	faddx	%fp2,%fp1	| ...B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
+	fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...FP2 RESTORED
+
+	fmulx	%fp1,%fp0	| ...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
+
+	fmovel	%d1,%fpcr
+	faddx	SAVEU(%a6),%fp0		
+	bra	t_frcinx
+	rts
+
+LOGNEG:
+|--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
+	bra	t_operr
+
+	.global	slognp1d
+slognp1d:
+|--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
+| Simply return the denorm
+
+	bra	t_extdnrm
+
+	.global	slognp1
+slognp1:
+|--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
+
+	fmovex	(%a0),%fp0	| ...LOAD INPUT
+	fabsx	%fp0		|test magnitude
+	fcmpx	LTHOLD,%fp0	|compare with min threshold
+	fbgt	LP1REAL		|if greater, continue
+	fmovel	#0,%fpsr		|clr N flag from compare
+	fmovel	%d1,%fpcr
+	fmovex	(%a0),%fp0	|return signed argument
+	bra	t_frcinx
+
+LP1REAL:
+	fmovex	(%a0),%fp0	| ...LOAD INPUT
+	movel	#0x00000000,ADJK(%a6)
+	fmovex	%fp0,%fp1	| ...FP1 IS INPUT Z
+	fadds	one,%fp0	| ...X := ROUND(1+Z)
+	fmovex	%fp0,X(%a6)
+	movew	XFRAC(%a6),XDCARE(%a6)
+	movel	X(%a6),%d0
+	cmpil	#0,%d0
+	ble	LP1NEG0	| ...LOG OF ZERO OR -VE
+	cmp2l	BOUNDS2,%d0
+	bcs	LOGMAIN	| ...BOUNDS2 IS [1/2,3/2]
+|--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
+|--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
+|--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
+
+LP1NEAR1:
+|--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
+	cmp2l	BOUNDS1,%d0
+	bcss	LP1CARE
+
+LP1ONE16:
+|--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
+|--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
+	faddx	%fp1,%fp1	| ...FP1 IS 2Z
+	fadds	one,%fp0	| ...FP0 IS 1+X
+|--U = FP1/FP0
+	bra	LP1CONT2
+
+LP1CARE:
+|--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
+|--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
+|--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
+|--THERE ARE ONLY TWO CASES.
+|--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
+|--CASE 2: 1+Z > 1, THEN K = 0  AND Y-F = (1-F) + Z
+|--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
+|--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
+
+	movel	XFRAC(%a6),FFRAC(%a6)
+	andil	#0xFE000000,FFRAC(%a6)
+	oril	#0x01000000,FFRAC(%a6)	| ...F OBTAINED
+	cmpil	#0x3FFF8000,%d0	| ...SEE IF 1+Z > 1
+	bges	KISZERO
+
+KISNEG1:
+	fmoves	TWO,%fp0
+	movel	#0x3fff0000,F(%a6)
+	clrl	F+8(%a6)
+	fsubx	F(%a6),%fp0	| ...2-F
+	movel	FFRAC(%a6),%d0
+	andil	#0x7E000000,%d0
+	asrl	#8,%d0
+	asrl	#8,%d0
+	asrl	#4,%d0		| ...D0 CONTAINS DISPLACEMENT FOR 1/F
+	faddx	%fp1,%fp1		| ...GET 2Z
+	fmovemx %fp2-%fp2/%fp3,-(%sp)	| ...SAVE FP2 
+	faddx	%fp1,%fp0		| ...FP0 IS Y-F = (2-F)+2Z
+	lea	LOGTBL,%a0	| ...A0 IS ADDRESS OF 1/F
+	addal	%d0,%a0
+	fmoves	negone,%fp1	| ...FP1 IS K = -1
+	bra	LP1CONT1
+
+KISZERO:
+	fmoves	one,%fp0
+	movel	#0x3fff0000,F(%a6)
+	clrl	F+8(%a6)
+	fsubx	F(%a6),%fp0		| ...1-F
+	movel	FFRAC(%a6),%d0
+	andil	#0x7E000000,%d0
+	asrl	#8,%d0
+	asrl	#8,%d0
+	asrl	#4,%d0
+	faddx	%fp1,%fp0		| ...FP0 IS Y-F
+	fmovemx %fp2-%fp2/%fp3,-(%sp)	| ...FP2 SAVED
+	lea	LOGTBL,%a0
+	addal	%d0,%a0	 	| ...A0 IS ADDRESS OF 1/F
+	fmoves	zero,%fp1	| ...FP1 IS K = 0
+	bra	LP1CONT1
+
+LP1NEG0:
+|--FPCR SAVED. D0 IS X IN COMPACT FORM.
+	cmpil	#0,%d0
+	blts	LP1NEG
+LP1ZERO:
+	fmoves	negone,%fp0
+
+	fmovel	%d1,%fpcr
+	bra t_dz
+
+LP1NEG:
+	fmoves	zero,%fp0
+
+	fmovel	%d1,%fpcr
+	bra	t_operr
+
+	|end
FUNET's LINUX-ADM group, linux-adm@nic.funet.fi
TCL-scripts by Sam Shen, slshen@lbl.gov with Sam's (original) version
of this