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215 lines
7.2 KiB
215 lines
7.2 KiB
/* file: round.c */
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/*
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**
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** COPYRIGHT (c) 1989 BY
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** DIGITAL EQUIPMENT CORPORATION, MAYNARD, MASSACHUSETTS.
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** ALL RIGHTS RESERVED.
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**
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** THIS SOFTWARE IS FURNISHED UNDER A LICENSE AND MAY BE USED AND COPIED
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** ONLY IN ACCORDANCE WITH THE TERMS OF SUCH LICENSE AND WITH THE
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** INCLUSION OF THE ABOVE COPYRIGHT NOTICE. THIS SOFTWARE OR ANY OTHER
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** COPIES THEREOF MAY NOT BE PROVIDED OR OTHERWISE MADE AVAILABLE TO ANY
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** OTHER PERSON. NO TITLE TO AND OWNERSHIP OF THE SOFTWARE IS HEREBY
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** TRANSFERRED.
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**
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** THE INFORMATION IN THIS SOFTWARE IS SUBJECT TO CHANGE WITHOUT NOTICE
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** AND SHOULD NOT BE CONSTRUED AS A COMMITMENT BY DIGITAL EQUIPMENT
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** CORPORATION.
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**
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** DIGITAL ASSUMES NO RESPONSIBILITY FOR THE USE OR RELIABILITY OF ITS
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** SOFTWARE ON EQUIPMENT WHICH IS NOT SUPPLIED BY DIGITAL.
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**
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*/
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/*
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**++
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** Facility:
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**
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** CVT Run-Time Library
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**
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** Abstract:
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**
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** This module is an include file.
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**
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** This module rounds CVT floating point data to any specified position.
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** Any of the following rounding modes can be applied:
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**
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** Note: None of the following implementations ever perform true truncation
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** on their values. Whenever truncation becomes necessary - either
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** by being specified directly or by being required indirectly
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** through rounding - values are actually left untouched. Users
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** of this routine must zero out fractional fields themselves if
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** true truncation is needed.
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**
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** VAX ROUNDING
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**
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** Input data are rounded such that the representable value nearest
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** the infinitely precise result is delivered; if two representable
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** values are equally near, the one greatest in magnitude is
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** delivered.
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**
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** ROUND TO NEAREST
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**
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** Input data are rounded such that the representable value nearest
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** the infinitely precise result is delivered; if two representable
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** values are equally near, the one with its least significant bit
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** zero is delivered.
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**
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** ROUND TO POSITIVE INFINITY
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**
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** Input data are rounded such that the representable value closest
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** to and no less than the infinitely precise result is delivered.
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**
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** ROUND TO NEGATIVE INFINITY
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**
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** Input data are rounded such that the representable value closest
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** to and no greater than the infinitely precise result is
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** delivered.
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**
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** TRUNCATION (ROUND TOWARDS ZERO)
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**
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** True truncation is not implemented here. Input values are
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** delivered in their original, untouched form.
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**
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** A definition of "true" truncation follows: Truncation, or
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** rounding towards zero, implies input data are rounded such
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** that the representable value closest to and no greater in
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** magnitude than the infinitely precise result is delivered.
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**
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** Authors:
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**
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** Math RTL
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**
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** Creation Date: December 5, 1989.
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**
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** Modification History:
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**
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** 1-001 Original created.
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** MRTL 5-Dec-1989.
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**
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**--
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*/
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/*
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**
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** Implicit input/output:
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**
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** r On input, a valid CVT floating point number.
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** On output, a rounded representation of the
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** input.
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**
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**
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** Implicit input:
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**
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** round_bit_position An integer specifying the position to round to.
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** 0 <= round_bit_position <= 127.
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**
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** Note: Valid CVT mantissa bits are addressed as 1
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** through 128. Accordingly, specifying 0 as a
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** position to round to implies an exponent
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** increase whenever rounding occurs. As for
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** truncation: truncation allways leaves a CVT
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** number untouched.
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**
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** options A valid CVT options bit mask in which at least
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** one, and only one, CVT rounding mode is
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** specified. If no rounding mode is specified,
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** results are unpredictable. Rounding is
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** performed in accordance with this mask.
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**
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** i An uninitialized integer used for indexing.
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**
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**
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** Note: for efficiency this routine performs no explicit error checking.
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**
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*/
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{
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int roundup, more_bits;
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unsigned long bit_mask;
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/* Check TRUNCATE option */
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if ( ! (options & CVT_C_TRUNCATE) ) {
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/* Determine which word the round bit resides in */
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i = (round_bit_position >> 5) + 1;
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/* Create a mask isolating the round bit */
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bit_mask = 0x1L << (31 - (round_bit_position & 0x1FL));
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/* Check VAX ROUNDING option */
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if (options & CVT_C_VAX_ROUNDING)
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roundup = r[i] & bit_mask;
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else {
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roundup = 0;
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switch ( r[i] & bit_mask ) {
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/* If round bit is clear, and ROUND TO NEAREST option */
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/* is selected we truncate */
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case 0 : if (options & CVT_C_ROUND_TO_NEAREST)
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break;
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/* Otherwise, make note of wheather there are any bits set */
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/* after the round bit, and then check the remaining cases */
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default : if ( ! (more_bits = r[i] & (bit_mask - 1)) )
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switch ( i ) {
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case 1 : more_bits = r[2];
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case 2 : more_bits |= r[3];
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case 3 : more_bits |= r[4];
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default : break;
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}
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/* Re-check ROUND TO NEAREST option. NOTE: if we've reached */
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/* this point and ROUND TO NEAREST has been selected, the */
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/* round bit is set. */
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if (options & CVT_C_ROUND_TO_NEAREST) {
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if ( ! ( roundup = more_bits ) )
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if ( bit_mask << 1 )
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roundup = r[i] & (bit_mask << 1);
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else if (i != 1)
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roundup = r[i-1] & 1;
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/* Check ROUND TO POSITIVE INFINITY option */
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} else if (options & CVT_C_ROUND_TO_POS) {
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if ( !(r[U_R_FLAGS] & U_R_NEGATIVE) )
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roundup = (r[i] & bit_mask) | more_bits;
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/* Check ROUND TO NEGITIVE INFINITY option */
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} else if (r[U_R_FLAGS] & U_R_NEGATIVE)
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roundup = (r[i] & bit_mask) | more_bits;
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}
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}
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if ( roundup ) { /* Perform rounding if necessary */
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/* Add 1 at round position */
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bit_mask <<= 1;
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r[i] = (r[i] & ~(bit_mask - 1)) + bit_mask;
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/* Propagate any carry */
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while ( ! r[i] )
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r[--i] += 1;
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/* If carry reaches exponent MSB gets zeroed and must be reset */
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if ( ! i )
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r[1] = 0x80000000L;
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}
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}
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}
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