ssinh.S
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- |
- | 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
- |
- | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
- | The copyright notice above does not evidence any
- | actual or intended publication of such source code.
- |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