| | 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 | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code.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