| /* hp2100_fp.c: HP 2100 floating point instructions | |
| Copyright (c) 2002-2005, Robert M. Supnik | |
| Permission is hereby granted, free of charge, to any person obtaining a | |
| copy of this software and associated documentation files (the "Software"), | |
| to deal in the Software without restriction, including without limitation | |
| the rights to use, copy, modify, merge, publish, distribute, sublicense, | |
| and/or sell copies of the Software, and to permit persons to whom the | |
| Software is furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in | |
| all copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL | |
| ROBERT M SUPNIK BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER | |
| IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN | |
| CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. | |
| Except as contained in this notice, the name of Robert M Supnik shall not be | |
| used in advertising or otherwise to promote the sale, use or other dealings | |
| in this Software without prior written authorization from Robert M Supnik. | |
| 22-Jul-05 RMS Fixed compiler warning in Solaris (from Doug Glyn) | |
| 25-Feb-05 JDB Added FFP helpers f_pack, f_unpack, f_pwr2 | |
| 11-Feb-05 JDB Fixed missing negative overflow renorm in StoreFP | |
| 26-Dec-04 RMS Separated A/B from M[0/1] for DMA IO (from Dave Bryan) | |
| 15-Jul-03 RMS Fixed signed/unsigned warning | |
| 21-Oct-02 RMS Recoded for compatibility with 21MX microcode algorithms | |
| The HP2100 uses a unique binary floating point format: | |
| 15 14 0 | |
| +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | |
| |S | fraction high | : A | |
| +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | |
| | fraction low | exponent |XS| : A + 1 | |
| +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | |
| 15 8 7 1 0 | |
| where S = 0 for plus fraction, 1 for minus fraction | |
| fraction = s.bbbbb..., 24 binary digits | |
| exponent = 2**+/-n | |
| XS = 0 for plus exponent, 1 for minus exponent | |
| Numbers can be normalized or unnormalized but are always normalized | |
| when loaded. | |
| Unpacked floating point numbers are stored in structure ufp | |
| exp = exponent, 2's complement | |
| h'l = fraction, 2's comp, left justified | |
| This routine tries to reproduce the algorithms of the 2100/21MX | |
| microcode in order to achieve 'bug-for-bug' compatibility. In | |
| particular, | |
| - The FIX code produces various results in B. | |
| - The fraction multiply code uses 16b x 16b multiplies to produce | |
| a 31b result. It always loses the low order bit of the product. | |
| - The fraction divide code is an approximation that may produce | |
| an error of 1 LSB. | |
| - Signs are tracked implicitly as part of the fraction. Unnormalized | |
| inputs may cause the packup code to produce the wrong sign. | |
| - "Unclean" zeros (zero fraction, non-zero exponent) are processed | |
| like normal operands. | |
| */ | |
| #include "hp2100_defs.h" | |
| struct ufp { /* unpacked fp */ | |
| int32 exp; /* exp */ | |
| uint32 fr; /* frac */ | |
| }; | |
| #define FP_V_SIGN 31 /* sign */ | |
| #define FP_M_SIGN 01 | |
| #define FP_V_FR 8 /* fraction */ | |
| #define FP_M_FR 077777777 | |
| #define FP_V_EXP 1 /* exponent */ | |
| #define FP_M_EXP 0177 | |
| #define FP_V_EXPS 0 /* exp sign */ | |
| #define FP_M_EXPS 01 | |
| #define FP_SIGN (FP_M_SIGN << FP_V_SIGN) | |
| #define FP_FR (FP_M_FR << FP_V_FR) | |
| #define FP_EXP (FP_M_EXP << FP_V_EXP) | |
| #define FP_EXPS (FP_M_EXPS << FP_V_EXPS) | |
| #define FP_GETSIGN(x) (((x) >> FP_V_SIGN) & FP_M_SIGN) | |
| #define FP_GETEXP(x) (((x) >> FP_V_EXP) & FP_M_EXP) | |
| #define FP_GETEXPS(x) (((x) >> FP_V_EXPS) & FP_M_EXPS) | |
| #define FP_NORM (1 << (FP_V_SIGN - 1)) /* normalized */ | |
| #define FP_LOW (1 << FP_V_FR) | |
| #define FP_RNDP (1 << (FP_V_FR - 1)) /* round for plus */ | |
| #define FP_RNDM (FP_RNDP - 1) /* round for minus */ | |
| #define FPAB ((((uint32) AR) << 16) | ((uint32) BR)) | |
| #define DMASK32 0xFFFFFFFF | |
| /* Fraction shift; 0 < shift < 32 */ | |
| #define FR_ARS(v,s) (((v) >> (s)) | (((v) & FP_SIGN)? \ | |
| (((uint32) DMASK32) << (32 - (s))): 0)) & DMASK32 | |
| #define FR_NEG(v) ((~(v) + 1) & DMASK32) | |
| extern uint16 ABREG[2]; | |
| uint32 UnpackFP (struct ufp *fop, uint32 opnd); | |
| void NegFP (struct ufp *fop); | |
| void NormFP (struct ufp *fop); | |
| uint32 StoreFP (struct ufp *fop); | |
| /* Floating to integer conversion */ | |
| uint32 f_fix (void) | |
| { | |
| struct ufp fop; | |
| uint32 res = 0; | |
| UnpackFP (&fop, FPAB); /* unpack op */ | |
| if (fop.exp < 0) { /* exp < 0? */ | |
| AR = 0; /* result = 0 */ | |
| return 0; /* B unchanged */ | |
| } | |
| if (fop.exp > 15) { /* exp > 15? */ | |
| BR = AR; /* B has high bits */ | |
| AR = 077777; /* result = 77777 */ | |
| return 1; /* overflow */ | |
| } | |
| if (fop.exp < 15) { /* if not aligned */ | |
| res = FR_ARS (fop.fr, 15 - fop.exp); /* shift right */ | |
| AR = (res >> 16) & DMASK; /* AR gets result */ | |
| } | |
| BR = AR; | |
| if ((AR & SIGN) && ((fop.fr | res) & DMASK)) /* any low bits lost? */ | |
| AR = (AR + 1) & DMASK; /* round up */ | |
| return 0; | |
| } | |
| /* Integer to floating conversion */ | |
| uint32 f_flt (void) | |
| { | |
| struct ufp res = { 15, 0 }; /* +, 2**15 */ | |
| res.fr = ((uint32) AR) << 16; /* left justify */ | |
| StoreFP (&res); /* store result */ | |
| return 0; /* clr overflow */ | |
| } | |
| /* Floating point add/subtract */ | |
| uint32 f_as (uint32 opnd, t_bool sub) | |
| { | |
| struct ufp fop1, fop2, t; | |
| int32 ediff; | |
| UnpackFP (&fop1, FPAB); /* unpack A-B */ | |
| UnpackFP (&fop2, opnd); /* get op */ | |
| if (sub) { /* subtract? */ | |
| fop2.fr = FR_NEG (fop2.fr); /* negate frac */ | |
| if (fop2.fr == ((uint32) FP_SIGN)) { /* -1/2? */ | |
| fop2.fr = fop2.fr >> 1; /* special case */ | |
| fop2.exp = fop2.exp + 1; | |
| } | |
| } | |
| if (fop1.fr == 0) fop1 = fop2; /* op1 = 0? res = op2 */ | |
| else if (fop2.fr != 0) { /* op2 = 0? no add */ | |
| if (fop1.exp < fop2.exp) { /* |op1| < |op2|? */ | |
| t = fop2; /* swap operands */ | |
| fop2 = fop1; | |
| fop1 = t; | |
| } | |
| ediff = fop1.exp - fop2.exp; /* get exp diff */ | |
| if (ediff <= 24) { | |
| if (ediff) fop2.fr = FR_ARS (fop2.fr, ediff); /* denorm, signed */ | |
| if ((fop1.fr ^ fop2.fr) & FP_SIGN) /* unlike signs? */ | |
| fop1.fr = fop1.fr + fop2.fr; /* eff subtract */ | |
| else { /* like signs */ | |
| fop1.fr = fop1.fr + fop2.fr; /* eff add */ | |
| if (fop2.fr & FP_SIGN) { /* both -? */ | |
| if ((fop1.fr & FP_SIGN) == 0) { /* overflow? */ | |
| fop1.fr = FP_SIGN | (fop1.fr >> 1); /* renormalize */ | |
| fop1.exp = fop1.exp + 1; /* incr exp */ | |
| } | |
| } | |
| else if (fop1.fr & FP_SIGN) { /* both +, cry out? */ | |
| fop1.fr = fop1.fr >> 1; /* renormalize */ | |
| fop1.exp = fop1.exp + 1; /* incr exp */ | |
| } | |
| } /* end else like */ | |
| } /* end if ediff */ | |
| } /* end if fop2 */ | |
| return StoreFP (&fop1); /* store result */ | |
| } | |
| /* Floating point multiply - passes diagnostic */ | |
| uint32 f_mul (uint32 opnd) | |
| { | |
| struct ufp fop1, fop2; | |
| struct ufp res = { 0, 0 }; | |
| int32 shi1, shi2, t1, t2, t3, t4, t5; | |
| UnpackFP (&fop1, FPAB); /* unpack A-B */ | |
| UnpackFP (&fop2, opnd); /* unpack op */ | |
| if (fop1.fr && fop2.fr) { /* if both != 0 */ | |
| res.exp = fop1.exp + fop2.exp + 1; /* exp = sum */ | |
| shi1 = SEXT (fop1.fr >> 16); /* mpy hi */ | |
| shi2 = SEXT (fop2.fr >> 16); /* mpc hi */ | |
| t1 = shi2 * ((int32) ((fop1.fr >> 1) & 077600)); /* mpc hi * (mpy lo/2) */ | |
| t2 = shi1 * ((int32) ((fop2.fr >> 1) & 077600)); /* mpc lo * (mpy hi/2) */ | |
| t3 = t1 + t2; /* cross product */ | |
| t4 = (shi1 * shi2) & ~1; /* mpy hi * mpc hi */ | |
| t5 = (SEXT (t3 >> 16)) << 1; /* add in cross */ | |
| res.fr = (t4 + t5) & DMASK32; /* bit<0> is lost */ | |
| } | |
| return StoreFP (&res); /* store */ | |
| } | |
| /* Floating point divide - reverse engineered from diagnostic */ | |
| uint32 divx (uint32 ba, uint32 dvr, uint32 *rem) | |
| { | |
| int32 sdvd = 0, sdvr = 0; | |
| uint32 q, r; | |
| if (ba & FP_SIGN) sdvd = 1; /* 32b/16b signed dvd */ | |
| if (dvr & SIGN) sdvr = 1; /* use old-fashioned */ | |
| if (sdvd) ba = (~ba + 1) & DMASK32; /* unsigned divides, */ | |
| if (sdvr) dvr = (~dvr + 1) & DMASK; /* as results may ovflo */ | |
| q = ba / dvr; | |
| r = ba % dvr; | |
| if (sdvd ^ sdvr) q = (~q + 1) & DMASK; | |
| if (sdvd) r = (~r + 1) & DMASK; | |
| if (rem) *rem = r; | |
| return q; | |
| } | |
| uint32 f_div (uint32 opnd) | |
| { | |
| struct ufp fop1, fop2; | |
| struct ufp quo = { 0, 0 }; | |
| uint32 ba, q0, q1, q2, dvrh; | |
| UnpackFP (&fop1, FPAB); /* unpack A-B */ | |
| UnpackFP (&fop2, opnd); /* unpack op */ | |
| dvrh = (fop2.fr >> 16) & DMASK; /* high divisor */ | |
| if (dvrh == 0) { /* div by zero? */ | |
| AR = 0077777; /* return most pos */ | |
| BR = 0177776; | |
| return 1; | |
| } | |
| if (fop1.fr) { /* dvd != 0? */ | |
| quo.exp = fop1.exp - fop2.exp + 1; /* exp = diff */ | |
| ba = FR_ARS (fop1.fr, 2); /* prevent ovflo */ | |
| q0 = divx (ba, dvrh, &ba); /* Q0 = dvd / dvrh */ | |
| ba = (ba & ~1) << 16; /* remainder */ | |
| ba = FR_ARS (ba, 1); /* prevent ovflo */ | |
| q1 = divx (ba, dvrh, NULL); /* Q1 = rem / dvrh */ | |
| ba = (fop2.fr & 0xFF00) << 13; /* dvrl / 8 */ | |
| q2 = divx (ba, dvrh, NULL); /* dvrl / dvrh */ | |
| ba = -(SEXT (q2)) * (SEXT (q0)); /* -Q0 * Q2 */ | |
| ba = (ba >> 16) & 0xFFFF; /* save ms half */ | |
| if (q1 & SIGN) quo.fr = quo.fr - 0x00010000; /* Q1 < 0? -1 */ | |
| if (ba & SIGN) quo.fr = quo.fr - 0x00010000; /* -Q0*Q2 < 0? */ | |
| quo.fr = quo.fr + ((ba << 2) & 0xFFFF) + q1; /* rest prod, add Q1 */ | |
| quo.fr = quo.fr << 1; /* shift result */ | |
| quo.fr = quo.fr + (q0 << 16); /* add Q0 */ | |
| } /* end if fop1.h */ | |
| return StoreFP (&quo); /* store result */ | |
| } | |
| /* Fast FORTRAN Processor helpers. */ | |
| /* Pack mantissa in A/B and exponent and return fp in A/B */ | |
| uint32 f_pack (int32 expon) | |
| { | |
| struct ufp fop; | |
| fop.fr = FPAB; | |
| fop.exp = expon; | |
| return StoreFP (&fop); | |
| } | |
| /* Unpack fp number in A/B into A (exponent) and B (lower mantissa) */ | |
| void f_unpack (void) | |
| { | |
| AR = FP_GETEXP (BR); /* get exponent */ | |
| if (FP_GETEXPS (BR)) AR = (AR | ~FP_M_EXP) & DMASK; /* < 0? sext */ | |
| BR = BR & (uint16) ~(FP_EXP | FP_EXPS); /* clear exp */ | |
| return; | |
| } | |
| /* Multiply fp number in A/B by 2**n and return in A/B. | |
| Exponent overflow or underflow wraps around. */ | |
| void f_pwr2 (int32 n) | |
| { | |
| uint32 save_a; | |
| if (AR | BR) { /* microcode test */ | |
| save_a = AR; | |
| f_unpack (); /* unpack exponent */ | |
| AR = AR + n; /* multiply */ | |
| BR = BR | ((AR & FP_M_EXP) << FP_V_EXP) | /* merge exponent */ | |
| ((AR & SIGN)? (1 << FP_V_EXPS): 0); /* and exponent sign */ | |
| AR = save_a; | |
| } | |
| return; | |
| } | |
| /* Utility routines */ | |
| /* Unpack operand */ | |
| uint32 UnpackFP (struct ufp *fop, uint32 opnd) | |
| { | |
| fop->fr = opnd & FP_FR; /* get frac */ | |
| fop->exp = FP_GETEXP (opnd); /* get exp */ | |
| if (FP_GETEXPS (opnd)) fop->exp = fop->exp | ~FP_M_EXP; /* < 0? sext */ | |
| return FP_GETSIGN (opnd); /* return sign */ | |
| } | |
| /* Normalize unpacked floating point number */ | |
| void NormFP (struct ufp *fop) | |
| { | |
| if (fop->fr) { /* any fraction? */ | |
| uint32 test = (fop->fr >> 1) & FP_NORM; | |
| while ((fop->fr & FP_NORM) == test) { /* until norm */ | |
| fop->exp = fop->exp - 1; | |
| fop->fr = (fop->fr << 1); | |
| } | |
| } | |
| else fop->exp = 0; /* clean 0 */ | |
| return; | |
| } | |
| /* Round fp number, store, generate overflow */ | |
| uint32 StoreFP (struct ufp *fop) | |
| { | |
| uint32 sign, svfr, hi, ov = 0; | |
| NormFP (fop); /* normalize */ | |
| svfr = fop->fr; /* save fraction */ | |
| sign = FP_GETSIGN (fop->fr); /* save sign */ | |
| fop->fr = (fop->fr + (sign? FP_RNDM: FP_RNDP)) & FP_FR; /* round */ | |
| if ((fop->fr ^ svfr) & FP_SIGN) { /* sign change? */ | |
| fop->fr = fop->fr >> 1; /* renormalize */ | |
| fop->exp = fop->exp + 1; | |
| } | |
| else NormFP (fop); /* check for norm */ | |
| if (fop->fr == 0) hi = 0; /* result 0? */ | |
| else if (fop->exp < -(FP_M_EXP + 1)) { /* underflow? */ | |
| hi = 0; /* store clean 0 */ | |
| ov = 1; | |
| } | |
| else if (fop->exp > FP_M_EXP) { /* overflow? */ | |
| hi = 0x7FFFFFFE; /* all 1's */ | |
| ov = 1; | |
| } | |
| else hi = (fop->fr & FP_FR) | /* merge frac */ | |
| ((fop->exp & FP_M_EXP) << FP_V_EXP) | /* and exp */ | |
| ((fop->exp < 0)? (1 << FP_V_EXPS): 0); /* add exp sign */ | |
| AR = (hi >> 16) & DMASK; | |
| BR = hi & DMASK; | |
| return ov; | |
| } |