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184 lines
4.0 KiB
184 lines
4.0 KiB
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| stanh.sa 3.1 12/10/90 |
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| The entry point sTanh computes the hyperbolic tangent of |
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| an input argument; sTanhd does the same except for denormalized |
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| input. |
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| Input: Double-extended number X in location pointed to |
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| by address register a0. |
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| Output: The value tanh(X) returned in floating-point register Fp0. |
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| Accuracy and Monotonicity: The returned result is within 3 ulps in |
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the |
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| result is subsequently rounded to double precision. The |
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| result is provably monotonic in double precision. |
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| Speed: The program stanh takes approximately 270 cycles. |
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| Algorithm: |
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| TANH |
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| 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. |
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| 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by |
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| sgn := sign(X), y := 2|X|, z := expm1(Y), and |
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| tanh(X) = sgn*( z/(2+z) ). |
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| Exit. |
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| |
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| 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, |
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| go to 7. |
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| 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. |
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| 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by |
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| sgn := sign(X), y := 2|X|, z := exp(Y), |
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| tanh(X) = sgn - [ sgn*2/(1+z) ]. |
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| Exit. |
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| |
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| 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we |
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| calculate Tanh(X) by |
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| sgn := sign(X), Tiny := 2**(-126), |
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| tanh(X) := sgn - sgn*Tiny. |
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| Exit. |
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| |
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| 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. |
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| Copyright (C) Motorola, Inc. 1990 |
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| All Rights Reserved |
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| |
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| For details on the license for this file, please see the |
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| file, README, in this same directory. |
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|STANH idnt 2,1 | Motorola 040 Floating Point Software Package |
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|section 8 |
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#include "fpsp.h" |
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.set X,FP_SCR5 |
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.set XDCARE,X+2 |
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.set XFRAC,X+4 |
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.set SGN,L_SCR3 |
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.set V,FP_SCR6 |
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BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2 |
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|xref t_frcinx |
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|xref t_extdnrm |
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|xref setox |
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|xref setoxm1 |
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.global stanhd |
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stanhd: |
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|--TANH(X) = X FOR DENORMALIZED X |
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bra t_extdnrm |
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.global stanh |
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stanh: |
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fmovex (%a0),%fp0 | ...LOAD INPUT |
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fmovex %fp0,X(%a6) |
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movel (%a0),%d0 |
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movew 4(%a0),%d0 |
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movel %d0,X(%a6) |
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andl #0x7FFFFFFF,%d0 |
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cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ? |
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bcss TANHBORS |
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|--THIS IS THE USUAL CASE |
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|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). |
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movel X(%a6),%d0 |
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movel %d0,SGN(%a6) |
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andl #0x7FFF0000,%d0 |
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addl #0x00010000,%d0 | ...EXPONENT OF 2|X| |
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movel %d0,X(%a6) |
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andl #0x80000000,SGN(%a6) |
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fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X| |
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movel %d1,-(%a7) |
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clrl %d1 |
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fmovemx %fp0-%fp0,(%a0) |
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bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) |
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movel (%a7)+,%d1 |
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fmovex %fp0,%fp1 |
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fadds #0x40000000,%fp1 | ...Z+2 |
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movel SGN(%a6),%d0 |
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fmovex %fp1,V(%a6) |
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eorl %d0,V(%a6) |
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fmovel %d1,%FPCR |restore users exceptions |
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fdivx V(%a6),%fp0 |
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bra t_frcinx |
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TANHBORS: |
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cmpl #0x3FFF8000,%d0 |
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blt TANHSM |
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cmpl #0x40048AA1,%d0 |
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bgt TANHHUGE |
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|-- (5/2) LOG2 < |X| < 50 LOG2, |
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|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), |
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|--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. |
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movel X(%a6),%d0 |
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movel %d0,SGN(%a6) |
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andl #0x7FFF0000,%d0 |
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addl #0x00010000,%d0 | ...EXPO OF 2|X| |
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movel %d0,X(%a6) | ...Y = 2|X| |
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andl #0x80000000,SGN(%a6) |
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movel SGN(%a6),%d0 |
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fmovex X(%a6),%fp0 | ...Y = 2|X| |
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movel %d1,-(%a7) |
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clrl %d1 |
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fmovemx %fp0-%fp0,(%a0) |
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bsr setox | ...FP0 IS EXP(Y) |
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movel (%a7)+,%d1 |
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movel SGN(%a6),%d0 |
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fadds #0x3F800000,%fp0 | ...EXP(Y)+1 |
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eorl #0xC0000000,%d0 | ...-SIGN(X)*2 |
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fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT |
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fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ] |
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movel SGN(%a6),%d0 |
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orl #0x3F800000,%d0 | ...SGN |
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fmoves %d0,%fp0 | ...SGN IN SGL FMT |
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fmovel %d1,%FPCR |restore users exceptions |
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faddx %fp1,%fp0 |
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bra t_frcinx |
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TANHSM: |
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movew #0x0000,XDCARE(%a6) |
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fmovel %d1,%FPCR |restore users exceptions |
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fmovex X(%a6),%fp0 |last inst - possible exception set |
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bra t_frcinx |
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TANHHUGE: |
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|---RETURN SGN(X) - SGN(X)EPS |
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movel X(%a6),%d0 |
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andl #0x80000000,%d0 |
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orl #0x3F800000,%d0 |
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fmoves %d0,%fp0 |
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andl #0x80000000,%d0 |
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eorl #0x80800000,%d0 | ...-SIGN(X)*EPS |
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fmovel %d1,%FPCR |restore users exceptions |
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fadds %d0,%fp0 |
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bra t_frcinx |
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|end
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