Annotation of sys/arch/hppa/spmath/sfadd.c, Revision 1.1
1.1 ! nbrk 1: /* $OpenBSD: sfadd.c,v 1.6 2002/11/29 09:27:34 deraadt Exp $ */
! 2: /*
! 3: (c) Copyright 1986 HEWLETT-PACKARD COMPANY
! 4: To anyone who acknowledges that this file is provided "AS IS"
! 5: without any express or implied warranty:
! 6: permission to use, copy, modify, and distribute this file
! 7: for any purpose is hereby granted without fee, provided that
! 8: the above copyright notice and this notice appears in all
! 9: copies, and that the name of Hewlett-Packard Company not be
! 10: used in advertising or publicity pertaining to distribution
! 11: of the software without specific, written prior permission.
! 12: Hewlett-Packard Company makes no representations about the
! 13: suitability of this software for any purpose.
! 14: */
! 15: /* @(#)sfadd.c: Revision: 2.7.88.1 Date: 93/12/07 15:07:00 */
! 16:
! 17: #include "float.h"
! 18: #include "sgl_float.h"
! 19:
! 20: /*
! 21: * Single_add: add two single precision values.
! 22: */
! 23: int
! 24: sgl_fadd(leftptr, rightptr, dstptr, status)
! 25: sgl_floating_point *leftptr, *rightptr, *dstptr;
! 26: unsigned int *status;
! 27: {
! 28: register unsigned int left, right, result, extent;
! 29: register unsigned int signless_upper_left, signless_upper_right, save;
! 30:
! 31:
! 32: register int result_exponent, right_exponent, diff_exponent;
! 33: register int sign_save, jumpsize;
! 34: register int inexact = FALSE;
! 35: register int underflowtrap;
! 36:
! 37: /* Create local copies of the numbers */
! 38: left = *leftptr;
! 39: right = *rightptr;
! 40:
! 41: /* A zero "save" helps discover equal operands (for later), *
! 42: * and is used in swapping operands (if needed). */
! 43: Sgl_xortointp1(left,right,/*to*/save);
! 44:
! 45: /*
! 46: * check first operand for NaN's or infinity
! 47: */
! 48: if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
! 49: {
! 50: if (Sgl_iszero_mantissa(left))
! 51: {
! 52: if (Sgl_isnotnan(right))
! 53: {
! 54: if (Sgl_isinfinity(right) && save!=0)
! 55: {
! 56: /*
! 57: * invalid since operands are opposite signed infinity's
! 58: */
! 59: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
! 60: Set_invalidflag();
! 61: Sgl_makequietnan(result);
! 62: *dstptr = result;
! 63: return(NOEXCEPTION);
! 64: }
! 65: /*
! 66: * return infinity
! 67: */
! 68: *dstptr = left;
! 69: return(NOEXCEPTION);
! 70: }
! 71: }
! 72: else
! 73: {
! 74: /*
! 75: * is NaN; signaling or quiet?
! 76: */
! 77: if (Sgl_isone_signaling(left))
! 78: {
! 79: /* trap if INVALIDTRAP enabled */
! 80: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
! 81: /* make NaN quiet */
! 82: Set_invalidflag();
! 83: Sgl_set_quiet(left);
! 84: }
! 85: /*
! 86: * is second operand a signaling NaN?
! 87: */
! 88: else if (Sgl_is_signalingnan(right))
! 89: {
! 90: /* trap if INVALIDTRAP enabled */
! 91: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
! 92: /* make NaN quiet */
! 93: Set_invalidflag();
! 94: Sgl_set_quiet(right);
! 95: *dstptr = right;
! 96: return(NOEXCEPTION);
! 97: }
! 98: /*
! 99: * return quiet NaN
! 100: */
! 101: *dstptr = left;
! 102: return(NOEXCEPTION);
! 103: }
! 104: } /* End left NaN or Infinity processing */
! 105: /*
! 106: * check second operand for NaN's or infinity
! 107: */
! 108: if (Sgl_isinfinity_exponent(right))
! 109: {
! 110: if (Sgl_iszero_mantissa(right))
! 111: {
! 112: /* return infinity */
! 113: *dstptr = right;
! 114: return(NOEXCEPTION);
! 115: }
! 116: /*
! 117: * is NaN; signaling or quiet?
! 118: */
! 119: if (Sgl_isone_signaling(right))
! 120: {
! 121: /* trap if INVALIDTRAP enabled */
! 122: if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
! 123: /* make NaN quiet */
! 124: Set_invalidflag();
! 125: Sgl_set_quiet(right);
! 126: }
! 127: /*
! 128: * return quiet NaN
! 129: */
! 130: *dstptr = right;
! 131: return(NOEXCEPTION);
! 132: } /* End right NaN or Infinity processing */
! 133:
! 134: /* Invariant: Must be dealing with finite numbers */
! 135:
! 136: /* Compare operands by removing the sign */
! 137: Sgl_copytoint_exponentmantissa(left,signless_upper_left);
! 138: Sgl_copytoint_exponentmantissa(right,signless_upper_right);
! 139:
! 140: /* sign difference selects add or sub operation. */
! 141: if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
! 142: {
! 143: /* Set the left operand to the larger one by XOR swap *
! 144: * First finish the first word using "save" */
! 145: Sgl_xorfromintp1(save,right,/*to*/right);
! 146: Sgl_xorfromintp1(save,left,/*to*/left);
! 147: result_exponent = Sgl_exponent(left);
! 148: }
! 149: /* Invariant: left is not smaller than right. */
! 150:
! 151: if((right_exponent = Sgl_exponent(right)) == 0)
! 152: {
! 153: /* Denormalized operands. First look for zeroes */
! 154: if(Sgl_iszero_mantissa(right))
! 155: {
! 156: /* right is zero */
! 157: if(Sgl_iszero_exponentmantissa(left))
! 158: {
! 159: /* Both operands are zeros */
! 160: if(Is_rounding_mode(ROUNDMINUS))
! 161: {
! 162: Sgl_or_signs(left,/*with*/right);
! 163: }
! 164: else
! 165: {
! 166: Sgl_and_signs(left,/*with*/right);
! 167: }
! 168: }
! 169: else
! 170: {
! 171: /* Left is not a zero and must be the result. Trapped
! 172: * underflows are signaled if left is denormalized. Result
! 173: * is always exact. */
! 174: if( (result_exponent == 0) && Is_underflowtrap_enabled() )
! 175: {
! 176: /* need to normalize results mantissa */
! 177: sign_save = Sgl_signextendedsign(left);
! 178: Sgl_leftshiftby1(left);
! 179: Sgl_normalize(left,result_exponent);
! 180: Sgl_set_sign(left,/*using*/sign_save);
! 181: Sgl_setwrapped_exponent(left,result_exponent,unfl);
! 182: *dstptr = left;
! 183: return(UNDERFLOWEXCEPTION);
! 184: }
! 185: }
! 186: *dstptr = left;
! 187: return(NOEXCEPTION);
! 188: }
! 189:
! 190: /* Neither are zeroes */
! 191: Sgl_clear_sign(right); /* Exponent is already cleared */
! 192: if(result_exponent == 0 )
! 193: {
! 194: /* Both operands are denormalized. The result must be exact
! 195: * and is simply calculated. A sum could become normalized and a
! 196: * difference could cancel to a true zero. */
! 197: if( (/*signed*/int) save < 0 )
! 198: {
! 199: Sgl_subtract(left,/*minus*/right,/*into*/result);
! 200: if(Sgl_iszero_mantissa(result))
! 201: {
! 202: if(Is_rounding_mode(ROUNDMINUS))
! 203: {
! 204: Sgl_setone_sign(result);
! 205: }
! 206: else
! 207: {
! 208: Sgl_setzero_sign(result);
! 209: }
! 210: *dstptr = result;
! 211: return(NOEXCEPTION);
! 212: }
! 213: }
! 214: else
! 215: {
! 216: Sgl_addition(left,right,/*into*/result);
! 217: if(Sgl_isone_hidden(result))
! 218: {
! 219: *dstptr = result;
! 220: return(NOEXCEPTION);
! 221: }
! 222: }
! 223: if(Is_underflowtrap_enabled())
! 224: {
! 225: /* need to normalize result */
! 226: sign_save = Sgl_signextendedsign(result);
! 227: Sgl_leftshiftby1(result);
! 228: Sgl_normalize(result,result_exponent);
! 229: Sgl_set_sign(result,/*using*/sign_save);
! 230: Sgl_setwrapped_exponent(result,result_exponent,unfl);
! 231: *dstptr = result;
! 232: return(UNDERFLOWEXCEPTION);
! 233: }
! 234: *dstptr = result;
! 235: return(NOEXCEPTION);
! 236: }
! 237: right_exponent = 1; /* Set exponent to reflect different bias
! 238: * with denomalized numbers. */
! 239: }
! 240: else
! 241: {
! 242: Sgl_clear_signexponent_set_hidden(right);
! 243: }
! 244: Sgl_clear_exponent_set_hidden(left);
! 245: diff_exponent = result_exponent - right_exponent;
! 246:
! 247: /*
! 248: * Special case alignment of operands that would force alignment
! 249: * beyond the extent of the extension. A further optimization
! 250: * could special case this but only reduces the path length for this
! 251: * infrequent case.
! 252: */
! 253: if(diff_exponent > SGL_THRESHOLD)
! 254: {
! 255: diff_exponent = SGL_THRESHOLD;
! 256: }
! 257:
! 258: /* Align right operand by shifting to right */
! 259: Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
! 260: /*and lower to*/extent);
! 261:
! 262: /* Treat sum and difference of the operands separately. */
! 263: if( (/*signed*/int) save < 0 )
! 264: {
! 265: /*
! 266: * Difference of the two operands. Their can be no overflow. A
! 267: * borrow can occur out of the hidden bit and force a post
! 268: * normalization phase.
! 269: */
! 270: Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
! 271: if(Sgl_iszero_hidden(result))
! 272: {
! 273: /* Handle normalization */
! 274: /* A straight forward algorithm would now shift the result
! 275: * and extension left until the hidden bit becomes one. Not
! 276: * all of the extension bits need participate in the shift.
! 277: * Only the two most significant bits (round and guard) are
! 278: * needed. If only a single shift is needed then the guard
! 279: * bit becomes a significant low order bit and the extension
! 280: * must participate in the rounding. If more than a single
! 281: * shift is needed, then all bits to the right of the guard
! 282: * bit are zeros, and the guard bit may or may not be zero. */
! 283: sign_save = Sgl_signextendedsign(result);
! 284: Sgl_leftshiftby1_withextent(result,extent,result);
! 285:
! 286: /* Need to check for a zero result. The sign and exponent
! 287: * fields have already been zeroed. The more efficient test
! 288: * of the full object can be used.
! 289: */
! 290: if(Sgl_iszero(result))
! 291: /* Must have been "x-x" or "x+(-x)". */
! 292: {
! 293: if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
! 294: *dstptr = result;
! 295: return(NOEXCEPTION);
! 296: }
! 297: result_exponent--;
! 298: /* Look to see if normalization is finished. */
! 299: if(Sgl_isone_hidden(result))
! 300: {
! 301: if(result_exponent==0)
! 302: {
! 303: /* Denormalized, exponent should be zero. Left operand *
! 304: * was normalized, so extent (guard, round) was zero */
! 305: goto underflow;
! 306: }
! 307: else
! 308: {
! 309: /* No further normalization is needed. */
! 310: Sgl_set_sign(result,/*using*/sign_save);
! 311: Ext_leftshiftby1(extent);
! 312: goto round;
! 313: }
! 314: }
! 315:
! 316: /* Check for denormalized, exponent should be zero. Left *
! 317: * operand was normalized, so extent (guard, round) was zero */
! 318: if(!(underflowtrap = Is_underflowtrap_enabled()) &&
! 319: result_exponent==0) goto underflow;
! 320:
! 321: /* Shift extension to complete one bit of normalization and
! 322: * update exponent. */
! 323: Ext_leftshiftby1(extent);
! 324:
! 325: /* Discover first one bit to determine shift amount. Use a
! 326: * modified binary search. We have already shifted the result
! 327: * one position right and still not found a one so the remainder
! 328: * of the extension must be zero and simplifies rounding. */
! 329: /* Scan bytes */
! 330: while(Sgl_iszero_hiddenhigh7mantissa(result))
! 331: {
! 332: Sgl_leftshiftby8(result);
! 333: if((result_exponent -= 8) <= 0 && !underflowtrap)
! 334: goto underflow;
! 335: }
! 336: /* Now narrow it down to the nibble */
! 337: if(Sgl_iszero_hiddenhigh3mantissa(result))
! 338: {
! 339: /* The lower nibble contains the normalizing one */
! 340: Sgl_leftshiftby4(result);
! 341: if((result_exponent -= 4) <= 0 && !underflowtrap)
! 342: goto underflow;
! 343: }
! 344: /* Select case were first bit is set (already normalized)
! 345: * otherwise select the proper shift. */
! 346: if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
! 347: {
! 348: /* Already normalized */
! 349: if(result_exponent <= 0) goto underflow;
! 350: Sgl_set_sign(result,/*using*/sign_save);
! 351: Sgl_set_exponent(result,/*using*/result_exponent);
! 352: *dstptr = result;
! 353: return(NOEXCEPTION);
! 354: }
! 355: Sgl_sethigh4bits(result,/*using*/sign_save);
! 356: switch(jumpsize)
! 357: {
! 358: case 1:
! 359: {
! 360: Sgl_leftshiftby3(result);
! 361: result_exponent -= 3;
! 362: break;
! 363: }
! 364: case 2:
! 365: case 3:
! 366: {
! 367: Sgl_leftshiftby2(result);
! 368: result_exponent -= 2;
! 369: break;
! 370: }
! 371: case 4:
! 372: case 5:
! 373: case 6:
! 374: case 7:
! 375: {
! 376: Sgl_leftshiftby1(result);
! 377: result_exponent -= 1;
! 378: break;
! 379: }
! 380: }
! 381: if(result_exponent > 0)
! 382: {
! 383: Sgl_set_exponent(result,/*using*/result_exponent);
! 384: *dstptr = result;
! 385: return(NOEXCEPTION); /* Sign bit is already set */
! 386: }
! 387: /* Fixup potential underflows */
! 388: underflow:
! 389: if(Is_underflowtrap_enabled())
! 390: {
! 391: Sgl_set_sign(result,sign_save);
! 392: Sgl_setwrapped_exponent(result,result_exponent,unfl);
! 393: *dstptr = result;
! 394: /* inexact = FALSE; */
! 395: return(UNDERFLOWEXCEPTION);
! 396: }
! 397: /*
! 398: * Since we cannot get an inexact denormalized result,
! 399: * we can now return.
! 400: */
! 401: Sgl_right_align(result,/*by*/(1-result_exponent),extent);
! 402: Sgl_clear_signexponent(result);
! 403: Sgl_set_sign(result,sign_save);
! 404: *dstptr = result;
! 405: return(NOEXCEPTION);
! 406: } /* end if(hidden...)... */
! 407: /* Fall through and round */
! 408: } /* end if(save < 0)... */
! 409: else
! 410: {
! 411: /* Add magnitudes */
! 412: Sgl_addition(left,right,/*to*/result);
! 413: if(Sgl_isone_hiddenoverflow(result))
! 414: {
! 415: /* Prenormalization required. */
! 416: Sgl_rightshiftby1_withextent(result,extent,extent);
! 417: Sgl_arithrightshiftby1(result);
! 418: result_exponent++;
! 419: } /* end if hiddenoverflow... */
! 420: } /* end else ...add magnitudes... */
! 421:
! 422: /* Round the result. If the extension is all zeros,then the result is
! 423: * exact. Otherwise round in the correct direction. No underflow is
! 424: * possible. If a postnormalization is necessary, then the mantissa is
! 425: * all zeros so no shift is needed. */
! 426: round:
! 427: if(Ext_isnotzero(extent))
! 428: {
! 429: inexact = TRUE;
! 430: switch(Rounding_mode())
! 431: {
! 432: case ROUNDNEAREST: /* The default. */
! 433: if(Ext_isone_sign(extent))
! 434: {
! 435: /* at least 1/2 ulp */
! 436: if(Ext_isnotzero_lower(extent) ||
! 437: Sgl_isone_lowmantissa(result))
! 438: {
! 439: /* either exactly half way and odd or more than 1/2ulp */
! 440: Sgl_increment(result);
! 441: }
! 442: }
! 443: break;
! 444:
! 445: case ROUNDPLUS:
! 446: if(Sgl_iszero_sign(result))
! 447: {
! 448: /* Round up positive results */
! 449: Sgl_increment(result);
! 450: }
! 451: break;
! 452:
! 453: case ROUNDMINUS:
! 454: if(Sgl_isone_sign(result))
! 455: {
! 456: /* Round down negative results */
! 457: Sgl_increment(result);
! 458: }
! 459:
! 460: case ROUNDZERO:;
! 461: /* truncate is simple */
! 462: } /* end switch... */
! 463: if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
! 464: }
! 465: if(result_exponent == SGL_INFINITY_EXPONENT)
! 466: {
! 467: /* Overflow */
! 468: if(Is_overflowtrap_enabled())
! 469: {
! 470: Sgl_setwrapped_exponent(result,result_exponent,ovfl);
! 471: *dstptr = result;
! 472: if (inexact) {
! 473: if (Is_inexacttrap_enabled())
! 474: return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
! 475: else Set_inexactflag();
! 476: }
! 477: return(OVERFLOWEXCEPTION);
! 478: }
! 479: else
! 480: {
! 481: Set_overflowflag();
! 482: inexact = TRUE;
! 483: Sgl_setoverflow(result);
! 484: }
! 485: }
! 486: else Sgl_set_exponent(result,result_exponent);
! 487: *dstptr = result;
! 488: if(inexact) {
! 489: if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
! 490: else Set_inexactflag();
! 491: }
! 492: return(NOEXCEPTION);
! 493: }
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