|
| scosh.sa 3.1 12/10/90
|
| The entry point sCosh computes the hyperbolic cosine of
| an input argument; sCoshd does the same except for denormalized
| input.
|
| Input: Double-extended number X in location pointed to
| by address register a0.
|
| Output: The value cosh(X) returned in floating-point register Fp0.
|
| 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
| result is subsequently rounded to double precision. The
| result is provably monotonic in double precision.
|
| Speed: The program sCOSH takes approximately 250 cycles.
|
| Algorithm:
|
| COSH
| 1. If |X| > 16380 log2, go to 3.
|
| 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
| y = |X|, z = exp(Y), and
| cosh(X) = (1/2)*( z + 1/z ).
| Exit.
|
| 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
|
| 4. (16380 log2 < |X| <= 16480 log2)
| cosh(X) = sign(X) * exp(|X|)/2.
| However, invoking exp(|X|) may cause premature overflow.
| Thus, we calculate sinh(X) as follows:
| Y := |X|
| Fact := 2**(16380)
| Y' := Y - 16381 log2
| cosh(X) := Fact * exp(Y').
| Exit.
|
| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
| Huge*Huge to generate overflow and an infinity with
| the appropriate sign. Huge is the largest finite number in
| extended format. Exit.
|
|
| 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.
|SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
|xref t_ovfl
|xref t_frcinx
|xref setox
T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
.global scoshd
scoshd:
|--COSH(X) = 1 FOR DENORMALIZED X
fmoves #0x3F800000,%fp0
fmovel %d1,%FPCR
fadds #0x00800000,%fp0
bra t_frcinx
.global scosh
scosh:
fmovex (%a0),%fp0 | ...LOAD INPUT
movel (%a0),%d0
movew 4(%a0),%d0
andil #0x7FFFFFFF,%d0
cmpil #0x400CB167,%d0
bgts COSHBIG
|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
fabsx %fp0 | ...|X|
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
bsr setox | ...FP0 IS EXP(|X|)
fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|)
movel (%sp)+,%d1
fmoves #0x3E800000,%fp1 | ...(1/4)
fdivx %fp0,%fp1 | ...1/(2 EXP(|X|))
fmovel %d1,%FPCR
faddx %fp1,%fp0
bra t_frcinx
COSHBIG:
cmpil #0x400CB2B3,%d0
bgts COSHHUGE
fabsx %fp0
fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0)
bsr setox
fmovel (%sp)+,%fpcr
fmulx TWO16380(%pc),%fp0
bra t_frcinx
COSHHUGE:
fmovel #0,%fpsr |clr N bit if set by source
bclrb #7,(%a0) |always return positive value
fmovemx (%a0),%fp0-%fp0
bra t_ovfl
|end
