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+|
+| stanh.sa 3.1 12/10/90
+|
+| The entry point sTanh computes the hyperbolic tangent of
+| an input argument; sTanhd does the same except for denormalized
+| input.
+|
+| Input: Double-extended number X in location pointed to
+| by address register a0.
+|
+| Output: The value tanh(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 stanh takes approximately 270 cycles.
+|
+| Algorithm:
+|
+| TANH
+| 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
+|
+| 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
+| sgn := sign(X), y := 2|X|, z := expm1(Y), and
+| tanh(X) = sgn*( z/(2+z) ).
+| Exit.
+|
+| 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
+| go to 7.
+|
+| 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
+|
+| 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
+| sgn := sign(X), y := 2|X|, z := exp(Y),
+| tanh(X) = sgn - [ sgn*2/(1+z) ].
+| Exit.
+|
+| 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
+| calculate Tanh(X) by
+| sgn := sign(X), Tiny := 2**(-126),
+| tanh(X) := sgn - sgn*Tiny.
+| Exit.
+|
+| 7. (|X| < 2**(-40)). Tanh(X) = X. 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+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
+
+|STANH idnt 2,1 | Motorola 040 Floating Point Software Package
+
+ |section 8
+
+#include "fpsp.h"
+
+ .set X,FP_SCR5
+ .set XDCARE,X+2
+ .set XFRAC,X+4
+
+ .set SGN,L_SCR3
+
+ .set V,FP_SCR6
+
+BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
+
+ |xref t_frcinx
+ |xref t_extdnrm
+ |xref setox
+ |xref setoxm1
+
+ .global stanhd
+stanhd:
+|--TANH(X) = X FOR DENORMALIZED X
+
+ bra t_extdnrm
+
+ .global stanh
+stanh:
+ fmovex (%a0),%fp0 | ...LOAD INPUT
+
+ fmovex %fp0,X(%a6)
+ movel (%a0),%d0
+ movew 4(%a0),%d0
+ movel %d0,X(%a6)
+ andl #0x7FFFFFFF,%d0
+ cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ?
+ bcss TANHBORS
+
+|--THIS IS THE USUAL CASE
+|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
+
+ movel X(%a6),%d0
+ movel %d0,SGN(%a6)
+ andl #0x7FFF0000,%d0
+ addl #0x00010000,%d0 | ...EXPONENT OF 2|X|
+ movel %d0,X(%a6)
+ andl #0x80000000,SGN(%a6)
+ fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X|
+
+ movel %d1,-(%a7)
+ clrl %d1
+ fmovemx %fp0-%fp0,(%a0)
+ bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
+ movel (%a7)+,%d1
+
+ fmovex %fp0,%fp1
+ fadds #0x40000000,%fp1 | ...Z+2
+ movel SGN(%a6),%d0
+ fmovex %fp1,V(%a6)
+ eorl %d0,V(%a6)
+
+ fmovel %d1,%FPCR |restore users exceptions
+ fdivx V(%a6),%fp0
+ bra t_frcinx
+
+TANHBORS:
+ cmpl #0x3FFF8000,%d0
+ blt TANHSM
+
+ cmpl #0x40048AA1,%d0
+ bgt TANHHUGE
+
+|-- (5/2) LOG2 < |X| < 50 LOG2,
+|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
+|--TANH(X) = SGN - SGN*2/[EXP(Y)+1].
+
+ movel X(%a6),%d0
+ movel %d0,SGN(%a6)
+ andl #0x7FFF0000,%d0
+ addl #0x00010000,%d0 | ...EXPO OF 2|X|
+ movel %d0,X(%a6) | ...Y = 2|X|
+ andl #0x80000000,SGN(%a6)
+ movel SGN(%a6),%d0
+ fmovex X(%a6),%fp0 | ...Y = 2|X|
+
+ movel %d1,-(%a7)
+ clrl %d1
+ fmovemx %fp0-%fp0,(%a0)
+ bsr setox | ...FP0 IS EXP(Y)
+ movel (%a7)+,%d1
+ movel SGN(%a6),%d0
+ fadds #0x3F800000,%fp0 | ...EXP(Y)+1
+
+ eorl #0xC0000000,%d0 | ...-SIGN(X)*2
+ fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT
+ fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ]
+
+ movel SGN(%a6),%d0
+ orl #0x3F800000,%d0 | ...SGN
+ fmoves %d0,%fp0 | ...SGN IN SGL FMT
+
+ fmovel %d1,%FPCR |restore users exceptions
+ faddx %fp1,%fp0
+
+ bra t_frcinx
+
+TANHSM:
+ movew #0x0000,XDCARE(%a6)
+
+ fmovel %d1,%FPCR |restore users exceptions
+ fmovex X(%a6),%fp0 |last inst - possible exception set
+
+ bra t_frcinx
+
+TANHHUGE:
+|---RETURN SGN(X) - SGN(X)EPS
+ movel X(%a6),%d0
+ andl #0x80000000,%d0
+ orl #0x3F800000,%d0
+ fmoves %d0,%fp0
+ andl #0x80000000,%d0
+ eorl #0x80800000,%d0 | ...-SIGN(X)*EPS
+
+ fmovel %d1,%FPCR |restore users exceptions
+ fadds %d0,%fp0
+
+ bra t_frcinx
+
+ |end