Annotation of sys/arch/m68k/fpsp/slog2.sa, Revision 1.1
1.1 ! nbrk 1: * $OpenBSD: slog2.sa,v 1.2 1996/05/29 21:05:39 niklas Exp $
! 2: * $NetBSD: slog2.sa,v 1.2 1994/10/26 07:49:52 cgd Exp $
! 3:
! 4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
! 5: * M68000 Hi-Performance Microprocessor Division
! 6: * M68040 Software Package
! 7: *
! 8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
! 9: * All rights reserved.
! 10: *
! 11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
! 12: * To the maximum extent permitted by applicable law,
! 13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
! 14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
! 15: * PARTICULAR PURPOSE and any warranty against infringement with
! 16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
! 17: * and any accompanying written materials.
! 18: *
! 19: * To the maximum extent permitted by applicable law,
! 20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
! 21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
! 22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
! 23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
! 24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
! 25: * and support of the SOFTWARE.
! 26: *
! 27: * You are hereby granted a copyright license to use, modify, and
! 28: * distribute the SOFTWARE so long as this entire notice is retained
! 29: * without alteration in any modified and/or redistributed versions,
! 30: * and that such modified versions are clearly identified as such.
! 31: * No licenses are granted by implication, estoppel or otherwise
! 32: * under any patents or trademarks of Motorola, Inc.
! 33:
! 34: *
! 35: * slog2.sa 3.1 12/10/90
! 36: *
! 37: * The entry point slog10 computes the base-10
! 38: * logarithm of an input argument X.
! 39: * slog10d does the same except the input value is a
! 40: * denormalized number.
! 41: * sLog2 and sLog2d are the base-2 analogues.
! 42: *
! 43: * INPUT: Double-extended value in memory location pointed to
! 44: * by address register a0.
! 45: *
! 46: * OUTPUT: log_10(X) or log_2(X) returned in floating-point
! 47: * register fp0.
! 48: *
! 49: * ACCURACY and MONOTONICITY: The returned result is within 1.7
! 50: * ulps in 64 significant bit, i.e. within 0.5003 ulp
! 51: * to 53 bits if the result is subsequently rounded
! 52: * to double precision. The result is provably monotonic
! 53: * in double precision.
! 54: *
! 55: * SPEED: Two timings are measured, both in the copy-back mode.
! 56: * The first one is measured when the function is invoked
! 57: * the first time (so the instructions and data are not
! 58: * in cache), and the second one is measured when the
! 59: * function is reinvoked at the same input argument.
! 60: *
! 61: * ALGORITHM and IMPLEMENTATION NOTES:
! 62: *
! 63: * slog10d:
! 64: *
! 65: * Step 0. If X < 0, create a NaN and raise the invalid operation
! 66: * flag. Otherwise, save FPCR in D1; set FpCR to default.
! 67: * Notes: Default means round-to-nearest mode, no floating-point
! 68: * traps, and precision control = double extended.
! 69: *
! 70: * Step 1. Call slognd to obtain Y = log(X), the natural log of X.
! 71: * Notes: Even if X is denormalized, log(X) is always normalized.
! 72: *
! 73: * Step 2. Compute log_10(X) = log(X) * (1/log(10)).
! 74: * 2.1 Restore the user FPCR
! 75: * 2.2 Return ans := Y * INV_L10.
! 76: *
! 77: *
! 78: * slog10:
! 79: *
! 80: * Step 0. If X < 0, create a NaN and raise the invalid operation
! 81: * flag. Otherwise, save FPCR in D1; set FpCR to default.
! 82: * Notes: Default means round-to-nearest mode, no floating-point
! 83: * traps, and precision control = double extended.
! 84: *
! 85: * Step 1. Call sLogN to obtain Y = log(X), the natural log of X.
! 86: *
! 87: * Step 2. Compute log_10(X) = log(X) * (1/log(10)).
! 88: * 2.1 Restore the user FPCR
! 89: * 2.2 Return ans := Y * INV_L10.
! 90: *
! 91: *
! 92: * sLog2d:
! 93: *
! 94: * Step 0. If X < 0, create a NaN and raise the invalid operation
! 95: * flag. Otherwise, save FPCR in D1; set FpCR to default.
! 96: * Notes: Default means round-to-nearest mode, no floating-point
! 97: * traps, and precision control = double extended.
! 98: *
! 99: * Step 1. Call slognd to obtain Y = log(X), the natural log of X.
! 100: * Notes: Even if X is denormalized, log(X) is always normalized.
! 101: *
! 102: * Step 2. Compute log_10(X) = log(X) * (1/log(2)).
! 103: * 2.1 Restore the user FPCR
! 104: * 2.2 Return ans := Y * INV_L2.
! 105: *
! 106: *
! 107: * sLog2:
! 108: *
! 109: * Step 0. If X < 0, create a NaN and raise the invalid operation
! 110: * flag. Otherwise, save FPCR in D1; set FpCR to default.
! 111: * Notes: Default means round-to-nearest mode, no floating-point
! 112: * traps, and precision control = double extended.
! 113: *
! 114: * Step 1. If X is not an integer power of two, i.e., X != 2^k,
! 115: * go to Step 3.
! 116: *
! 117: * Step 2. Return k.
! 118: * 2.1 Get integer k, X = 2^k.
! 119: * 2.2 Restore the user FPCR.
! 120: * 2.3 Return ans := convert-to-double-extended(k).
! 121: *
! 122: * Step 3. Call sLogN to obtain Y = log(X), the natural log of X.
! 123: *
! 124: * Step 4. Compute log_2(X) = log(X) * (1/log(2)).
! 125: * 4.1 Restore the user FPCR
! 126: * 4.2 Return ans := Y * INV_L2.
! 127: *
! 128:
! 129: SLOG2 IDNT 2,1 Motorola 040 Floating Point Software Package
! 130:
! 131: section 8
! 132:
! 133: xref t_frcinx
! 134: xref t_operr
! 135: xref slogn
! 136: xref slognd
! 137:
! 138: INV_L10 DC.L $3FFD0000,$DE5BD8A9,$37287195,$00000000
! 139:
! 140: INV_L2 DC.L $3FFF0000,$B8AA3B29,$5C17F0BC,$00000000
! 141:
! 142: xdef slog10d
! 143: slog10d:
! 144: *--entry point for Log10(X), X is denormalized
! 145: move.l (a0),d0
! 146: blt.w invalid
! 147: move.l d1,-(sp)
! 148: clr.l d1
! 149: bsr slognd ...log(X), X denorm.
! 150: fmove.l (sp)+,fpcr
! 151: fmul.x INV_L10,fp0
! 152: bra t_frcinx
! 153:
! 154: xdef slog10
! 155: slog10:
! 156: *--entry point for Log10(X), X is normalized
! 157:
! 158: move.l (a0),d0
! 159: blt.w invalid
! 160: move.l d1,-(sp)
! 161: clr.l d1
! 162: bsr slogn ...log(X), X normal.
! 163: fmove.l (sp)+,fpcr
! 164: fmul.x INV_L10,fp0
! 165: bra t_frcinx
! 166:
! 167:
! 168: xdef slog2d
! 169: slog2d:
! 170: *--entry point for Log2(X), X is denormalized
! 171:
! 172: move.l (a0),d0
! 173: blt.w invalid
! 174: move.l d1,-(sp)
! 175: clr.l d1
! 176: bsr slognd ...log(X), X denorm.
! 177: fmove.l (sp)+,fpcr
! 178: fmul.x INV_L2,fp0
! 179: bra t_frcinx
! 180:
! 181: xdef slog2
! 182: slog2:
! 183: *--entry point for Log2(X), X is normalized
! 184: move.l (a0),d0
! 185: blt.w invalid
! 186:
! 187: move.l 8(a0),d0
! 188: bne.b continue ...X is not 2^k
! 189:
! 190: move.l 4(a0),d0
! 191: and.l #$7FFFFFFF,d0
! 192: tst.l d0
! 193: bne.b continue
! 194:
! 195: *--X = 2^k.
! 196: move.w (a0),d0
! 197: and.l #$00007FFF,d0
! 198: sub.l #$3FFF,d0
! 199: fmove.l d1,fpcr
! 200: fmove.l d0,fp0
! 201: bra t_frcinx
! 202:
! 203: continue:
! 204: move.l d1,-(sp)
! 205: clr.l d1
! 206: bsr slogn ...log(X), X normal.
! 207: fmove.l (sp)+,fpcr
! 208: fmul.x INV_L2,fp0
! 209: bra t_frcinx
! 210:
! 211: invalid:
! 212: bra t_operr
! 213:
! 214: end
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