|
| 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 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
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|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 MEMORY, 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
