|
|
|
|
| satanh.sa 3.3 12/19/90
|
| satanh.sa 3.3 12/19/90
|
|
|
|
|
| The entry point satanh computes the inverse
|
| The entry point satanh computes the inverse
|
| hyperbolic tangent of
|
| hyperbolic tangent of
|
| an input argument; satanhd does the same except for denormalized
|
| an input argument; satanhd does the same except for denormalized
|
| input.
|
| input.
|
|
|
|
|
| Input: Double-extended number X in location pointed to
|
| Input: Double-extended number X in location pointed to
|
| by address register a0.
|
| by address register a0.
|
|
|
|
|
| Output: The value arctanh(X) returned in floating-point register Fp0.
|
| Output: The value arctanh(X) returned in floating-point register Fp0.
|
|
|
|
|
| Accuracy and Monotonicity: The returned result is within 3 ulps in
|
| Accuracy and Monotonicity: The returned result is within 3 ulps in
|
| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|
| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|
| result is subsequently rounded to double precision. The
|
| result is subsequently rounded to double precision. The
|
| result is provably monotonic in double precision.
|
| result is provably monotonic in double precision.
|
|
|
|
|
| Speed: The program satanh takes approximately 270 cycles.
|
| Speed: The program satanh takes approximately 270 cycles.
|
|
|
|
|
| Algorithm:
|
| Algorithm:
|
|
|
|
|
| ATANH
|
| ATANH
|
| 1. If |X| >= 1, go to 3.
|
| 1. If |X| >= 1, go to 3.
|
|
|
|
|
| 2. (|X| < 1) Calculate atanh(X) by
|
| 2. (|X| < 1) Calculate atanh(X) by
|
| sgn := sign(X)
|
| sgn := sign(X)
|
| y := |X|
|
| y := |X|
|
| z := 2y/(1-y)
|
| z := 2y/(1-y)
|
| atanh(X) := sgn * (1/2) * logp1(z)
|
| atanh(X) := sgn * (1/2) * logp1(z)
|
| Exit.
|
| Exit.
|
|
|
|
|
| 3. If |X| > 1, go to 5.
|
| 3. If |X| > 1, go to 5.
|
|
|
|
|
| 4. (|X| = 1) Generate infinity with an appropriate sign and
|
| 4. (|X| = 1) Generate infinity with an appropriate sign and
|
| divide-by-zero by
|
| divide-by-zero by
|
| sgn := sign(X)
|
| sgn := sign(X)
|
| atan(X) := sgn / (+0).
|
| atan(X) := sgn / (+0).
|
| Exit.
|
| Exit.
|
|
|
|
|
| 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
|
| 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
|
| Exit.
|
| Exit.
|
|
|
|
|
|
|
| Copyright (C) Motorola, Inc. 1990
|
| Copyright (C) Motorola, Inc. 1990
|
| All Rights Reserved
|
| All Rights Reserved
|
|
|
|
|
| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|
| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|
| The copyright notice above does not evidence any
|
| The copyright notice above does not evidence any
|
| actual or intended publication of such source code.
|
| actual or intended publication of such source code.
|
|
|
|satanh idnt 2,1 | Motorola 040 Floating Point Software Package
|
|satanh idnt 2,1 | Motorola 040 Floating Point Software Package
|
|
|
|section 8
|
|section 8
|
|
|
|xref t_dz
|
|xref t_dz
|
|xref t_operr
|
|xref t_operr
|
|xref t_frcinx
|
|xref t_frcinx
|
|xref t_extdnrm
|
|xref t_extdnrm
|
|xref slognp1
|
|xref slognp1
|
|
|
.global satanhd
|
.global satanhd
|
satanhd:
|
satanhd:
|
|--ATANH(X) = X FOR DENORMALIZED X
|
|--ATANH(X) = X FOR DENORMALIZED X
|
|
|
bra t_extdnrm
|
bra t_extdnrm
|
|
|
.global satanh
|
.global satanh
|
satanh:
|
satanh:
|
movel (%a0),%d0
|
movel (%a0),%d0
|
movew 4(%a0),%d0
|
movew 4(%a0),%d0
|
andil #0x7FFFFFFF,%d0
|
andil #0x7FFFFFFF,%d0
|
cmpil #0x3FFF8000,%d0
|
cmpil #0x3FFF8000,%d0
|
bges ATANHBIG
|
bges ATANHBIG
|
|
|
|--THIS IS THE USUAL CASE, |X| < 1
|
|--THIS IS THE USUAL CASE, |X| < 1
|
|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
|
|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
|
|
|
fabsx (%a0),%fp0 | ...Y = |X|
|
fabsx (%a0),%fp0 | ...Y = |X|
|
fmovex %fp0,%fp1
|
fmovex %fp0,%fp1
|
fnegx %fp1 | ...-Y
|
fnegx %fp1 | ...-Y
|
faddx %fp0,%fp0 | ...2Y
|
faddx %fp0,%fp0 | ...2Y
|
fadds #0x3F800000,%fp1 | ...1-Y
|
fadds #0x3F800000,%fp1 | ...1-Y
|
fdivx %fp1,%fp0 | ...2Y/(1-Y)
|
fdivx %fp1,%fp0 | ...2Y/(1-Y)
|
movel (%a0),%d0
|
movel (%a0),%d0
|
andil #0x80000000,%d0
|
andil #0x80000000,%d0
|
oril #0x3F000000,%d0 | ...SIGN(X)*HALF
|
oril #0x3F000000,%d0 | ...SIGN(X)*HALF
|
movel %d0,-(%sp)
|
movel %d0,-(%sp)
|
|
|
fmovemx %fp0-%fp0,(%a0) | ...overwrite input
|
fmovemx %fp0-%fp0,(%a0) | ...overwrite input
|
movel %d1,-(%sp)
|
movel %d1,-(%sp)
|
clrl %d1
|
clrl %d1
|
bsr slognp1 | ...LOG1P(Z)
|
bsr slognp1 | ...LOG1P(Z)
|
fmovel (%sp)+,%fpcr
|
fmovel (%sp)+,%fpcr
|
fmuls (%sp)+,%fp0
|
fmuls (%sp)+,%fp0
|
bra t_frcinx
|
bra t_frcinx
|
|
|
ATANHBIG:
|
ATANHBIG:
|
fabsx (%a0),%fp0 | ...|X|
|
fabsx (%a0),%fp0 | ...|X|
|
fcmps #0x3F800000,%fp0
|
fcmps #0x3F800000,%fp0
|
fbgt t_operr
|
fbgt t_operr
|
bra t_dz
|
bra t_dz
|
|
|
|end
|
|end
|
|
|
