|
| setox.sa 3.1 12/10/90
|
| The entry point setox computes the exponential of a value.
| setoxd does the same except the input value is a denormalized
| number. setoxm1 computes exp(X)-1, and setoxm1d computes
| exp(X)-1 for denormalized X.
|
| INPUT
| -----
| Double-extended value in memory location pointed to by address
| register a0.
|
| OUTPUT
| ------
| exp(X) or exp(X)-1 returned in floating-point register fp0.
|
| ACCURACY and MONOTONICITY
| -------------------------
| The returned result is within 0.85 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
| -----
| 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.
|
| The program setox takes approximately 210/190 cycles for input
| argument X whose magnitude is less than 16380 log2, which
| is the usual situation. For the less common arguments,
| depending on their values, the program may run faster or slower --
| but no worse than 10% slower even in the extreme cases.
|
| The program setoxm1 takes approximately ??? / ??? cycles for input
| argument X, 0.25 <= |X| < 70log2. For |X| < 0.25, it takes
| approximately ??? / ??? cycles. For the less common arguments,
| depending on their values, the program may run faster or slower --
| but no worse than 10% slower even in the extreme cases.
|
| ALGORITHM and IMPLEMENTATION NOTES
| ----------------------------------
|
| setoxd
| ------
| Step 1. Set ans := 1.0
|
| Step 2. Return ans := ans + sign(X)*2^(-126). Exit.
| Notes: This will always generate one exception -- inexact.
|
|
| setox
| -----
|
| Step 1. Filter out extreme cases of input argument.
| 1.1 If |X| >= 2^(-65), go to Step 1.3.
| 1.2 Go to Step 7.
| 1.3 If |X| < 16380 log(2), go to Step 2.
| 1.4 Go to Step 8.
| Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.
| To avoid the use of floating-point comparisons, a
| compact representation of |X| is used. This format is a
| 32-bit integer, the upper (more significant) 16 bits are
| the sign and biased exponent field of |X|; the lower 16
| bits are the 16 most significant fraction (including the
| explicit bit) bits of |X|. Consequently, the comparisons
| in Steps 1.1 and 1.3 can be performed by integer comparison.
| Note also that the constant 16380 log(2) used in Step 1.3
| is also in the compact form. Thus taking the branch
| to Step 2 guarantees |X| < 16380 log(2). There is no harm
| to have a small number of cases where |X| is less than,
| but close to, 16380 log(2) and the branch to Step 9 is
| taken.
|
| Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ).
| 2.1 Set AdjFlag := 0 (indicates the branch 1.3 -> 2 was taken)
| 2.2 N := round-to-nearest-integer( X * 64/log2 ).
| 2.3 Calculate J = N mod 64; so J = 0,1,2,..., or 63.
| 2.4 Calculate M = (N - J)/64; so N = 64M + J.
| 2.5 Calculate the address of the stored value of 2^(J/64).
| 2.6 Create the value Scale = 2^M.
| Notes: The calculation in 2.2 is really performed by
|
| Z := X * constant
| N := round-to-nearest-integer(Z)
|
| where
|
| constant := single-precision( 64/log 2 ).
|
| Using a single-precision constant avoids memory access.
| Another effect of using a single-precision "constant" is
| that the calculated value Z is
|
| Z = X*(64/log2)*(1+eps), |eps| <= 2^(-24).
|
| This error has to be considered later in Steps 3 and 4.
|
| Step 3. Calculate X - N*log2/64.
| 3.1 R := X + N*L1, where L1 := single-precision(-log2/64).
| 3.2 R := R + N*L2, L2 := extended-precision(-log2/64 - L1).
| Notes: a) The way L1 and L2 are chosen ensures L1+L2 approximate
| the value -log2/64 to 88 bits of accuracy.
| b) N*L1 is exact because N is no longer than 22 bits and
| L1 is no longer than 24 bits.
| c) The calculation X+N*L1 is also exact due to cancellation.
| Thus, R is practically X+N(L1+L2) to full 64 bits.
| d) It is important to estimate how large can |R| be after
| Step 3.2.
|
| N = rnd-to-int( X*64/log2 (1+eps) ), |eps|<=2^(-24)
| X*64/log2 (1+eps) = N + f, |f| <= 0.5
| X*64/log2 - N = f - eps*X 64/log2
| X - N*log2/64 = f*log2/64 - eps*X
|
|
| Now |X| <= 16446 log2, thus
|
| |X - N*log2/64| <= (0.5 + 16446/2^(18))*log2/64
| <= 0.57 log2/64.
| This bound will be used in Step 4.
|
| Step 4. Approximate exp(R)-1 by a polynomial
| p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
| Notes: a) In order to reduce memory access, the coefficients are
| made as "short" as possible: A1 (which is 1/2), A4 and A5
| are single precision; A2 and A3 are double precision.
| b) Even with the restrictions above,
| |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062.
| Note that 0.0062 is slightly bigger than 0.57 log2/64.
| c) To fully utilize the pipeline, p is separated into
| two independent pieces of roughly equal complexities
| p = [ R + R*S*(A2 + S*A4) ] +
| [ S*(A1 + S*(A3 + S*A5)) ]
| where S = R*R.
|
| Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by
| ans := T + ( T*p + t)
| where T and t are the stored values for 2^(J/64).
| Notes: 2^(J/64) is stored as T and t where T+t approximates
| 2^(J/64) to roughly 85 bits; T is in extended precision
| and t is in single precision. Note also that T is rounded
| to 62 bits so that the last two bits of T are zero. The
| reason for such a special form is that T-1, T-2, and T-8
| will all be exact --- a property that will give much
| more accurate computation of the function EXPM1.
|
| Step 6. Reconstruction of exp(X)
| exp(X) = 2^M * 2^(J/64) * exp(R).
| 6.1 If AdjFlag = 0, go to 6.3
| 6.2 ans := ans * AdjScale
| 6.3 Restore the user FPCR
| 6.4 Return ans := ans * Scale. Exit.
| Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R,
| |M| <= 16380, and Scale = 2^M. Moreover, exp(X) will
| neither overflow nor underflow. If AdjFlag = 1, that
| means that
| X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380.
| Hence, exp(X) may overflow or underflow or neither.
| When that is the case, AdjScale = 2^(M1) where M1 is
| approximately M. Thus 6.2 will never cause over/underflow.
| Possible exception in 6.4 is overflow or underflow.
| The inexact exception is not generated in 6.4. Although
| one can argue that the inexact flag should always be
| raised, to simulate that exception cost to much than the
| flag is worth in practical uses.
|
| Step 7. Return 1 + X.
| 7.1 ans := X
| 7.2 Restore user FPCR.
| 7.3 Return ans := 1 + ans. Exit
| Notes: For non-zero X, the inexact exception will always be
| raised by 7.3. That is the only exception raised by 7.3.
| Note also that we use the FMOVEM instruction to move X
| in Step 7.1 to avoid unnecessary trapping. (Although
| the FMOVEM may not seem relevant since X is normalized,
| the precaution will be useful in the library version of
| this code where the separate entry for denormalized inputs
| will be done away with.)
|
| Step 8. Handle exp(X) where |X| >= 16380log2.
| 8.1 If |X| > 16480 log2, go to Step 9.
| (mimic 2.2 - 2.6)
| 8.2 N := round-to-integer( X * 64/log2 )
| 8.3 Calculate J = N mod 64, J = 0,1,...,63
| 8.4 K := (N-J)/64, M1 := truncate(K/2), M = K-M1, AdjFlag := 1.
| 8.5 Calculate the address of the stored value 2^(J/64).
| 8.6 Create the values Scale = 2^M, AdjScale = 2^M1.
| 8.7 Go to Step 3.
| Notes: Refer to notes for 2.2 - 2.6.
|
| Step 9. Handle exp(X), |X| > 16480 log2.
| 9.1 If X < 0, go to 9.3
| 9.2 ans := Huge, go to 9.4
| 9.3 ans := Tiny.
| 9.4 Restore user FPCR.
| 9.5 Return ans := ans * ans. Exit.
| Notes: Exp(X) will surely overflow or underflow, depending on
| X's sign. "Huge" and "Tiny" are respectively large/tiny
| extended-precision numbers whose square over/underflow
| with an inexact result. Thus, 9.5 always raises the
| inexact together with either overflow or underflow.
|
|
| setoxm1d
| --------
|
| Step 1. Set ans := 0
|
| Step 2. Return ans := X + ans. Exit.
| Notes: This will return X with the appropriate rounding
| precision prescribed by the user FPCR.
|
| setoxm1
| -------
|
| Step 1. Check |X|
| 1.1 If |X| >= 1/4, go to Step 1.3.
| 1.2 Go to Step 7.
| 1.3 If |X| < 70 log(2), go to Step 2.
| 1.4 Go to Step 10.
| Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.
| However, it is conceivable |X| can be small very often
| because EXPM1 is intended to evaluate exp(X)-1 accurately
| when |X| is small. For further details on the comparisons,
| see the notes on Step 1 of setox.
|
| Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ).
| 2.1 N := round-to-nearest-integer( X * 64/log2 ).
| 2.2 Calculate J = N mod 64; so J = 0,1,2,..., or 63.
| 2.3 Calculate M = (N - J)/64; so N = 64M + J.
| 2.4 Calculate the address of the stored value of 2^(J/64).
| 2.5 Create the values Sc = 2^M and OnebySc := -2^(-M).
| Notes: See the notes on Step 2 of setox.
|
| Step 3. Calculate X - N*log2/64.
| 3.1 R := X + N*L1, where L1 := single-precision(-log2/64).
| 3.2 R := R + N*L2, L2 := extended-precision(-log2/64 - L1).
| Notes: Applying the analysis of Step 3 of setox in this case
| shows that |R| <= 0.0055 (note that |X| <= 70 log2 in
| this case).
|
| Step 4. Approximate exp(R)-1 by a polynomial
| p = R+R*R*(A1+R*(A2+R*(A3+R*(A4+R*(A5+R*A6)))))
| Notes: a) In order to reduce memory access, the coefficients are
| made as "short" as possible: A1 (which is 1/2), A5 and A6
| are single precision; A2, A3 and A4 are double precision.
| b) Even with the restriction above,
| |p - (exp(R)-1)| < |R| * 2^(-72.7)
| for all |R| <= 0.0055.
| c) To fully utilize the pipeline, p is separated into
| two independent pieces of roughly equal complexity
| p = [ R*S*(A2 + S*(A4 + S*A6)) ] +
| [ R + S*(A1 + S*(A3 + S*A5)) ]
| where S = R*R.
|
| Step 5. Compute 2^(J/64)*p by
| p := T*p
| where T and t are the stored values for 2^(J/64).
| Notes: 2^(J/64) is stored as T and t where T+t approximates
| 2^(J/64) to roughly 85 bits; T is in extended precision
| and t is in single precision. Note also that T is rounded
| to 62 bits so that the last two bits of T are zero. The
| reason for such a special form is that T-1, T-2, and T-8
| will all be exact --- a property that will be exploited
| in Step 6 below. The total relative error in p is no
| bigger than 2^(-67.7) compared to the final result.
|
| Step 6. Reconstruction of exp(X)-1
| exp(X)-1 = 2^M * ( 2^(J/64) + p - 2^(-M) ).
| 6.1 If M <= 63, go to Step 6.3.
| 6.2 ans := T + (p + (t + OnebySc)). Go to 6.6
| 6.3 If M >= -3, go to 6.5.
| 6.4 ans := (T + (p + t)) + OnebySc. Go to 6.6
| 6.5 ans := (T + OnebySc) + (p + t).
| 6.6 Restore user FPCR.
| 6.7 Return ans := Sc * ans. Exit.
| Notes: The various arrangements of the expressions give accurate
| evaluations.
|
| Step 7. exp(X)-1 for |X| < 1/4.
| 7.1 If |X| >= 2^(-65), go to Step 9.
| 7.2 Go to Step 8.
|
| Step 8. Calculate exp(X)-1, |X| < 2^(-65).
| 8.1 If |X| < 2^(-16312), goto 8.3
| 8.2 Restore FPCR; return ans := X - 2^(-16382). Exit.
| 8.3 X := X * 2^(140).
| 8.4 Restore FPCR; ans := ans - 2^(-16382).
| Return ans := ans*2^(140). Exit
| Notes: The idea is to return "X - tiny" under the user
| precision and rounding modes. To avoid unnecessary
| inefficiency, we stay away from denormalized numbers the
| best we can. For |X| >= 2^(-16312), the straightforward
| 8.2 generates the inexact exception as the case warrants.
|
| Step 9. Calculate exp(X)-1, |X| < 1/4, by a polynomial
| p = X + X*X*(B1 + X*(B2 + ... + X*B12))
| Notes: a) In order to reduce memory access, the coefficients are
| made as "short" as possible: B1 (which is 1/2), B9 to B12
| are single precision; B3 to B8 are double precision; and
| B2 is double extended.
| b) Even with the restriction above,
| |p - (exp(X)-1)| < |X| 2^(-70.6)
| for all |X| <= 0.251.
| Note that 0.251 is slightly bigger than 1/4.
| c) To fully preserve accuracy, the polynomial is computed
| as X + ( S*B1 + Q ) where S = X*X and
| Q = X*S*(B2 + X*(B3 + ... + X*B12))
| d) To fully utilize the pipeline, Q is separated into
| two independent pieces of roughly equal complexity
| Q = [ X*S*(B2 + S*(B4 + ... + S*B12)) ] +
| [ S*S*(B3 + S*(B5 + ... + S*B11)) ]
|
| Step 10. Calculate exp(X)-1 for |X| >= 70 log 2.
| 10.1 If X >= 70log2 , exp(X) - 1 = exp(X) for all practical
| purposes. Therefore, go to Step 1 of setox.
| 10.2 If X <= -70log2, exp(X) - 1 = -1 for all practical purposes.
| ans := -1
| Restore user FPCR
| Return ans := ans + 2^(-126). Exit.
| Notes: 10.2 will always create an inexact and return -1 + tiny
| in the user rounding precision and mode.
|
|
| 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.
|setox idnt 2,1 | Motorola 040 Floating Point Software Package
.global setoxd
setoxd:
|--entry point for EXP(X), X is denormalized
movel (%a0),%d0
andil #0x80000000,%d0
oril #0x00800000,%d0 | ...sign(X)*2^(-126)
movel %d0,-(%sp)
fmoves #0x3F800000,%fp0
fmovel %d1,%fpcr
fadds (%sp)+,%fp0
bra t_frcinx
.global setox
setox:
|--entry point for EXP(X), here X is finite, non-zero, and not NaN's
|--Step 1.
movel (%a0),%d0 | ...load part of input X
andil #0x7FFF0000,%d0 | ...biased expo. of X
cmpil #0x3FBE0000,%d0 | ...2^(-65)
bges EXPC1 | ...normal case
bra EXPSM
EXPC1:
|--The case |X| >= 2^(-65)
movew 4(%a0),%d0 | ...expo. and partial sig. of |X|
cmpil #0x400CB167,%d0 | ...16380 log2 trunc. 16 bits
blts EXPMAIN | ...normal case
bra EXPBIG
EXPMAIN:
|--Step 2.
|--This is the normal branch: 2^(-65) <= |X| < 16380 log2.
fmovex (%a0),%fp0 | ...load input from (a0)
movel %d0,L_SCR1(%a6) | ...save N temporarily
andil #0x3F,%d0 | ...D0 is J = N mod 64
lsll #4,%d0
addal %d0,%a1 | ...address of 2^(J/64)
movel L_SCR1(%a6),%d0
asrl #6,%d0 | ...D0 is M
addiw #0x3FFF,%d0 | ...biased expo. of 2^(M)
movew L2,L_SCR1(%a6) | ...prefetch L2, no need in CB
EXPCONT1:
|--Step 3.
|--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
|--a0 points to 2^(J/64), D0 is biased expo. of 2^(M)
fmovex %fp0,%fp2
fmuls #0xBC317218,%fp0 | ...N * L1, L1 = lead(-log2/64)
fmulx L2,%fp2 | ...N * L2, L1+L2 = -log2/64
faddx %fp1,%fp0 | ...X + N*L1
faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
| MOVE.W #$3FA5,EXPA3 ...load EXPA3 in cache
|--Step 4.
|--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
|-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
|--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
|--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))]
fmovex %fp0,%fp1
fmulx %fp1,%fp1 | ...fp1 IS S = R*R
fmoves #0x3AB60B70,%fp2 | ...fp2 IS A5
| MOVE.W #0,2(%a1) ...load 2^(J/64) in cache
fmulx %fp1,%fp2 | ...fp2 IS S*A5
fmovex %fp1,%fp3
fmuls #0x3C088895,%fp3 | ...fp3 IS S*A4
faddd EXPA3,%fp2 | ...fp2 IS A3+S*A5
faddd EXPA2,%fp3 | ...fp3 IS A2+S*A4
fmulx %fp1,%fp2 | ...fp2 IS S*(A3+S*A5)
movew %d0,SCALE(%a6) | ...SCALE is 2^(M) in extended
clrw SCALE+2(%a6)
movel #0x80000000,SCALE+4(%a6)
clrl SCALE+8(%a6)
fmulx %fp1,%fp3 | ...fp3 IS S*(A2+S*A4)
fadds #0x3F000000,%fp2 | ...fp2 IS A1+S*(A3+S*A5)
fmulx %fp0,%fp3 | ...fp3 IS R*S*(A2+S*A4)
fmulx %fp1,%fp2 | ...fp2 IS S*(A1+S*(A3+S*A5))
faddx %fp3,%fp0 | ...fp0 IS R+R*S*(A2+S*A4),
| ...fp3 released
fmovex (%a1)+,%fp1 | ...fp1 is lead. pt. of 2^(J/64)
faddx %fp2,%fp0 | ...fp0 is EXP(R) - 1
| ...fp2 released
.global setoxm1d
setoxm1d:
|--entry point for EXPM1(X), here X is denormalized
|--Step 0.
bra t_extdnrm
.global setoxm1
setoxm1:
|--entry point for EXPM1(X), here X is finite, non-zero, non-NaN
|--Step 1.
|--Step 1.1
movel (%a0),%d0 | ...load part of input X
andil #0x7FFF0000,%d0 | ...biased expo. of X
cmpil #0x3FFD0000,%d0 | ...1/4
bges EM1CON1 | ...|X| >= 1/4
bra EM1SM
EM1CON1:
|--Step 1.3
|--The case |X| >= 1/4
movew 4(%a0),%d0 | ...expo. and partial sig. of |X|
cmpil #0x4004C215,%d0 | ...70log2 rounded up to 16 bits
bles EM1MAIN | ...1/4 <= |X| <= 70log2
bra EM1BIG
EM1MAIN:
|--Step 2.
|--This is the case: 1/4 <= |X| <= 70 log2.
fmovex (%a0),%fp0 | ...load input from (a0)
fmovex %fp0,%fp1
fmuls #0x42B8AA3B,%fp0 | ...64/log2 * X
fmovemx %fp2-%fp2/%fp3,-(%a7) | ...save fp2
| MOVE.W #$3F81,EM1A4 ...prefetch in CB mode
fmovel %fp0,%d0 | ...N = int( X * 64/log2 )
lea EXPTBL,%a1
fmovel %d0,%fp0 | ...convert to floating-format
movel %d0,L_SCR1(%a6) | ...save N temporarily
andil #0x3F,%d0 | ...D0 is J = N mod 64
lsll #4,%d0
addal %d0,%a1 | ...address of 2^(J/64)
movel L_SCR1(%a6),%d0
asrl #6,%d0 | ...D0 is M
movel %d0,L_SCR1(%a6) | ...save a copy of M
| MOVE.W #$3FDC,L2 ...prefetch L2 in CB mode
|--Step 3.
|--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
|--a0 points to 2^(J/64), D0 and a1 both contain M
fmovex %fp0,%fp2
fmuls #0xBC317218,%fp0 | ...N * L1, L1 = lead(-log2/64)
fmulx L2,%fp2 | ...N * L2, L1+L2 = -log2/64
faddx %fp1,%fp0 | ...X + N*L1
faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
| MOVE.W #$3FC5,EM1A2 ...load EM1A2 in cache
addiw #0x3FFF,%d0 | ...D0 is biased expo. of 2^M
|--Step 4.
|--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
|-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6)))))
|--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
|--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))]
fmovex %fp0,%fp1
fmulx %fp1,%fp1 | ...fp1 IS S = R*R
fmoves #0x3950097B,%fp2 | ...fp2 IS a6
| MOVE.W #0,2(%a1) ...load 2^(J/64) in cache
fmulx %fp1,%fp2 | ...fp2 IS S*A6
fmovex %fp1,%fp3
fmuls #0x3AB60B6A,%fp3 | ...fp3 IS S*A5
faddd EM1A4,%fp2 | ...fp2 IS A4+S*A6
faddd EM1A3,%fp3 | ...fp3 IS A3+S*A5
movew %d0,SC(%a6) | ...SC is 2^(M) in extended
clrw SC+2(%a6)
movel #0x80000000,SC+4(%a6)
clrl SC+8(%a6)
fmulx %fp1,%fp2 | ...fp2 IS S*(A4+S*A6)
movel L_SCR1(%a6),%d0 | ...D0 is M
negw %d0 | ...D0 is -M
fmulx %fp1,%fp3 | ...fp3 IS S*(A3+S*A5)
addiw #0x3FFF,%d0 | ...biased expo. of 2^(-M)
faddd EM1A2,%fp2 | ...fp2 IS A2+S*(A4+S*A6)
fadds #0x3F000000,%fp3 | ...fp3 IS A1+S*(A3+S*A5)
fmulx %fp1,%fp2 | ...fp2 IS S*(A2+S*(A4+S*A6))
oriw #0x8000,%d0 | ...signed/expo. of -2^(-M)
movew %d0,ONEBYSC(%a6) | ...OnebySc is -2^(-M)
clrw ONEBYSC+2(%a6)
movel #0x80000000,ONEBYSC+4(%a6)
clrl ONEBYSC+8(%a6)
fmulx %fp3,%fp1 | ...fp1 IS S*(A1+S*(A3+S*A5))
| ...fp3 released
fmulx %fp0,%fp2 | ...fp2 IS R*S*(A2+S*(A4+S*A6))
faddx %fp1,%fp0 | ...fp0 IS R+S*(A1+S*(A3+S*A5))
| ...fp1 released
faddx %fp2,%fp0 | ...fp0 IS EXP(R)-1
| ...fp2 released
fmovemx (%a7)+,%fp2-%fp2/%fp3 | ...fp2 restored
|--Step 5
|--Compute 2^(J/64)*p
fmulx (%a1),%fp0 | ...2^(J/64)*(Exp(R)-1)
|--Step 6
|--Step 6.1
movel L_SCR1(%a6),%d0 | ...retrieve M
cmpil #63,%d0
bles MLE63
|--Step 6.2 M >= 64
fmoves 12(%a1),%fp1 | ...fp1 is t
faddx ONEBYSC(%a6),%fp1 | ...fp1 is t+OnebySc
faddx %fp1,%fp0 | ...p+(t+OnebySc), fp1 released
faddx (%a1),%fp0 | ...T+(p+(t+OnebySc))
bras EM1SCALE
MLE63:
|--Step 6.3 M <= 63
cmpil #-3,%d0
bges MGEN3
MLTN3:
|--Step 6.4 M <= -4
fadds 12(%a1),%fp0 | ...p+t
faddx (%a1),%fp0 | ...T+(p+t)
faddx ONEBYSC(%a6),%fp0 | ...OnebySc + (T+(p+t))
bras EM1SCALE
MGEN3:
|--Step 6.5 -3 <= M <= 63
fmovex (%a1)+,%fp1 | ...fp1 is T
fadds (%a1),%fp0 | ...fp0 is p+t
faddx ONEBYSC(%a6),%fp1 | ...fp1 is T+OnebySc
faddx %fp1,%fp0 | ...(T+OnebySc)+(p+t)
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