|
| ssinh.sa 3.1 12/10/90
|
| The entry point sSinh computes the hyperbolic sine of
| an input argument; sSinhd does the same except for denormalized
| input.
|
| Input: Double-extended number X in location pointed to
| by address register a0.
|
| Output: The value sinh(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 sSINH takes approximately 280 cycles.
|
| Algorithm:
|
| SINH
| 1. If |X| > 16380 log2, go to 3.
|
| 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
| y = |X|, sgn = sign(X), and z = expm1(Y),
| sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
| Exit.
|
| 3. If |X| > 16480 log2, go to 5.
|
| 4. (16380 log2 < |X| <= 16480 log2)
| sinh(X) = sign(X) * exp(|X|)/2.
| However, invoking exp(|X|) may cause premature overflow.
| Thus, we calculate sinh(X) as follows:
| Y := |X|
| sgn := sign(X)
| sgnFact := sgn * 2**(16380)
| Y' := Y - 16381 log2
| sinh(X) := sgnFact * exp(Y').
| Exit.
|
| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
| sign(X)*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.
|SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
|xref t_frcinx
|xref t_ovfl
|xref t_extdnrm
|xref setox
|xref setoxm1
.global ssinhd
ssinhd:
|--SINH(X) = X FOR DENORMALIZED X
bra t_extdnrm
.global ssinh
ssinh:
fmovex (%a0),%fp0 | ...LOAD INPUT
movel (%a0),%d0
movew 4(%a0),%d0
movel %d0,%a1 | save a copy of original (compacted) operand
andl #0x7FFFFFFF,%d0
cmpl #0x400CB167,%d0
bgts SINHBIG
|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
fabsx %fp0 | ...Y = |X|
moveml %a1/%d1,-(%sp)
fmovemx %fp0-%fp0,(%a0)
clrl %d1
bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
fmovel #0,%fpcr
moveml (%sp)+,%a1/%d1
fmovex %fp0,%fp1
fadds #0x3F800000,%fp1 | ...1+Z
fmovex %fp0,-(%sp)
fdivx %fp1,%fp0 | ...Z/(1+Z)
movel %a1,%d0
andl #0x80000000,%d0
orl #0x3F000000,%d0
faddx (%sp)+,%fp0
movel %d0,-(%sp)
fmovel %d1,%fpcr
fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
bra t_frcinx
SINHBIG:
cmpl #0x400CB2B3,%d0
bgt t_ovfl
fabsx %fp0
fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
movel #0,-(%sp)
movel #0x80000000,-(%sp)
movel %a1,%d0
andl #0x80000000,%d0
orl #0x7FFB0000,%d0
movel %d0,-(%sp) | ...EXTENDED FMT
fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0)
bsr setox
fmovel (%sp)+,%fpcr
fmulx (%sp)+,%fp0 |possible exception
bra t_frcinx
|end
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