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1836 lines
83 KiB
C
1836 lines
83 KiB
C
/* ------------------------------------------------------------------ */
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/* decCommon.c -- common code for all three fixed-size types */
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/* ------------------------------------------------------------------ */
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/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */
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/* */
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/* This software is made available under the terms of the */
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/* ICU License -- ICU 1.8.1 and later. */
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/* */
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/* The description and User's Guide ("The decNumber C Library") for */
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/* this software is included in the package as decNumber.pdf. This */
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/* document is also available in HTML, together with specifications, */
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/* testcases, and Web links, on the General Decimal Arithmetic page. */
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/* */
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/* Please send comments, suggestions, and corrections to the author: */
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/* mfc@uk.ibm.com */
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/* Mike Cowlishaw, IBM Fellow */
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/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
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/* ------------------------------------------------------------------ */
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/* This module comprises code that is shared between all the formats */
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/* (decSingle, decDouble, and decQuad); it includes set and extract */
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/* of format components, widening, narrowing, and string conversions. */
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/* */
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/* Unlike decNumber, parameterization takes place at compile time */
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/* rather than at runtime. The parameters are set in the decDouble.c */
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/* (etc.) files, which then include this one to produce the compiled */
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/* code. The functions here, therefore, are code shared between */
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/* multiple formats. */
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/* ------------------------------------------------------------------ */
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// Names here refer to decFloat rather than to decDouble, etc., and
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// the functions are in strict alphabetical order.
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// Constants, tables, and debug function(s) are included only for QUAD
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// (which will always be compiled if DOUBLE or SINGLE are used).
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//
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// Whenever a decContext is used, only the status may be set (using
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// OR) or the rounding mode read; all other fields are ignored and
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// untouched.
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// names for simpler testing and default context
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#if DECPMAX==7
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#define SINGLE 1
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#define DOUBLE 0
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#define QUAD 0
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#define DEFCONTEXT DEC_INIT_DECIMAL32
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#elif DECPMAX==16
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#define SINGLE 0
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#define DOUBLE 1
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#define QUAD 0
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#define DEFCONTEXT DEC_INIT_DECIMAL64
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#elif DECPMAX==34
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#define SINGLE 0
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#define DOUBLE 0
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#define QUAD 1
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#define DEFCONTEXT DEC_INIT_DECIMAL128
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#else
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#error Unexpected DECPMAX value
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#endif
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/* Assertions */
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#if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34
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#error Unexpected Pmax (DECPMAX) value for this module
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#endif
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// Assert facts about digit characters, etc.
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#if ('9'&0x0f)!=9
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#error This module assumes characters are of the form 0b....nnnn
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// where .... are don't care 4 bits and nnnn is 0000 through 1001
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#endif
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#if ('9'&0xf0)==('.'&0xf0)
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#error This module assumes '.' has a different mask than a digit
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#endif
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// Assert ToString lay-out conditions
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#if DECSTRING<DECPMAX+9
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#error ToString needs at least 8 characters for lead-in and dot
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#endif
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#if DECPMAX+DECEMAXD+5 > DECSTRING
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#error Exponent form can be too long for ToString to lay out safely
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#endif
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#if DECEMAXD > 4
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#error Exponent form is too long for ToString to lay out
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// Note: code for up to 9 digits exists in archives [decOct]
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#endif
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/* Private functions used here and possibly in decBasic.c, etc. */
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static decFloat * decFinalize(decFloat *, bcdnum *, decContext *);
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static Flag decBiStr(const char *, const char *, const char *);
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/* Macros and private tables; those which are not format-dependent */
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/* are only included if decQuad is being built. */
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/* ------------------------------------------------------------------ */
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/* Combination field lookup tables (uInts to save measurable work) */
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/* */
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/* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */
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/* 10), shifted left for format, or DECFLOAT_Inf/NaN */
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/* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */
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/* DECCOMBMSD - 4-bit most-significant-digit */
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/* [0 if the index is a special (Infinity or NaN)] */
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/* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */
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/* (placed in uInt so no shift is needed) */
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/* */
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/* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */
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/* and 5-bit combination field (0-63, the second half of the table */
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/* identical to the first half) */
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/* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */
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/* */
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/* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */
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/* only included once, when QUAD is being built */
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/* ------------------------------------------------------------------ */
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static const uInt DECCOMBEXP[64]={
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0, 0, 0, 0, 0, 0, 0, 0,
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1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
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1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
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2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
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2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
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0, 0, 1<<DECECONL, 1<<DECECONL,
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2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN,
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0, 0, 0, 0, 0, 0, 0, 0,
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1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
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1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
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2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
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2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
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0, 0, 1<<DECECONL, 1<<DECECONL,
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2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN};
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#if !QUAD
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static const uInt DECCOMBWEXP[64]={
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0, 0, 0, 0, 0, 0, 0, 0,
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1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
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1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
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0, 0, 1<<DECWECONL, 1<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN,
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0, 0, 0, 0, 0, 0, 0, 0,
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1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
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1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
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0, 0, 1<<DECWECONL, 1<<DECWECONL,
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2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN};
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#endif
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#if QUAD
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const uInt DECCOMBMSD[64]={
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0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0,
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0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0};
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const uInt DECCOMBFROM[48]={
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0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000,
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0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000,
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0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000,
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0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000,
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0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
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0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000,
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0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000,
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0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
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/* ------------------------------------------------------------------ */
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/* Request and include the tables to use for conversions */
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/* ------------------------------------------------------------------ */
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#define DEC_BCD2DPD 1 // 0-0x999 -> DPD
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#define DEC_BIN2DPD 1 // 0-999 -> DPD
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#define DEC_BIN2BCD8 1 // 0-999 -> ddd, len
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#define DEC_DPD2BCD8 1 // DPD -> ddd, len
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#define DEC_DPD2BIN 1 // DPD -> 0-999
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#define DEC_DPD2BINK 1 // DPD -> 0-999000
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#define DEC_DPD2BINM 1 // DPD -> 0-999000000
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#include "decDPD.h" // source of the lookup tables
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#endif
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/* ----------------------------------------------------------------- */
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/* decBiStr -- compare string with pairwise options */
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/* */
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/* targ is the string to compare */
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/* str1 is one of the strings to compare against (length may be 0) */
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/* str2 is the other; it must be the same length as str1 */
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/* */
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/* returns 1 if strings compare equal, (that is, targ is the same */
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/* length as str1 and str2, and each character of targ is in one */
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/* of str1 or str2 in the corresponding position), or 0 otherwise */
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/* */
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/* This is used for generic caseless compare, including the awkward */
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/* case of the Turkish dotted and dotless Is. Use as (for example): */
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/* if (decBiStr(test, "mike", "MIKE")) ... */
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/* ----------------------------------------------------------------- */
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static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
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for (;;targ++, str1++, str2++) {
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if (*targ!=*str1 && *targ!=*str2) return 0;
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// *targ has a match in one (or both, if terminator)
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if (*targ=='\0') break;
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} // forever
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return 1;
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} // decBiStr
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/* ------------------------------------------------------------------ */
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/* decFinalize -- adjust and store a final result */
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/* */
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/* df is the decFloat format number which gets the final result */
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/* num is the descriptor of the number to be checked and encoded */
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/* [its values, including the coefficient, may be modified] */
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/* set is the context to use */
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/* returns df */
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/* */
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/* The num descriptor may point to a bcd8 string of any length; this */
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/* string may have leading insignificant zeros. If it has more than */
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/* DECPMAX digits then the final digit can be a round-for-reround */
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/* digit (i.e., it may include a sticky bit residue). */
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/* */
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/* The exponent (q) may be one of the codes for a special value and */
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/* can be up to 999999999 for conversion from string. */
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/* */
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/* No error is possible, but Inexact, Underflow, and/or Overflow may */
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/* be set. */
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/* ------------------------------------------------------------------ */
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// Constant whose size varies with format; also the check for surprises
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static uByte allnines[DECPMAX]=
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#if SINGLE
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{9, 9, 9, 9, 9, 9, 9};
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#elif DOUBLE
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{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
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#elif QUAD
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{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
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9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
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#endif
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static decFloat * decFinalize(decFloat *df, bcdnum *num,
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decContext *set) {
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uByte *ub; // work
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uInt dpd; // ..
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uInt uiwork; // for macros
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uByte *umsd=num->msd; // local copy
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uByte *ulsd=num->lsd; // ..
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uInt encode; // encoding accumulator
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Int length; // coefficient length
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#if DECCHECK
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Int clen=ulsd-umsd+1;
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#if QUAD
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#define COEXTRA 2 // extra-long coefficent
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#else
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#define COEXTRA 0
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#endif
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if (clen<1 || clen>DECPMAX*3+2+COEXTRA)
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printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen);
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if (num->sign!=0 && num->sign!=DECFLOAT_Sign)
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printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign);
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if (!EXPISSPECIAL(num->exponent)
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&& (num->exponent>1999999999 || num->exponent<-1999999999))
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printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent);
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// decShowNum(num, "final");
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#endif
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// A special will have an 'exponent' which is very positive and a
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// coefficient < DECPMAX
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length=(uInt)(ulsd-umsd+1); // coefficient length
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if (!NUMISSPECIAL(num)) {
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Int drop; // digits to be dropped
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// skip leading insignificant zeros to calculate an exact length
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// [this is quite expensive]
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if (*umsd==0) {
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for (; umsd+3<ulsd && UBTOUI(umsd)==0;) umsd+=4;
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for (; *umsd==0 && umsd<ulsd;) umsd++;
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length=ulsd-umsd+1; // recalculate
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}
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drop=MAXI(length-DECPMAX, DECQTINY-num->exponent);
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// drop can now be > digits for bottom-clamp (subnormal) cases
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if (drop>0) { // rounding needed
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// (decFloatQuantize has very similar code to this, so any
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// changes may need to be made there, too)
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uByte *roundat; // -> re-round digit
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uByte reround; // reround value
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// printf("Rounding; drop=%ld\n", (LI)drop);
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num->exponent+=drop; // always update exponent
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// Three cases here:
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// 1. new LSD is in coefficient (almost always)
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// 2. new LSD is digit to left of coefficient (so MSD is
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// round-for-reround digit)
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// 3. new LSD is to left of case 2 (whole coefficient is sticky)
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// [duplicate check-stickies code to save a test]
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// [by-digit check for stickies as runs of zeros are rare]
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if (drop<length) { // NB lengths not addresses
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roundat=umsd+length-drop;
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reround=*roundat;
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for (ub=roundat+1; ub<=ulsd; ub++) {
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if (*ub!=0) { // non-zero to be discarded
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reround=DECSTICKYTAB[reround]; // apply sticky bit
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break; // [remainder don't-care]
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}
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} // check stickies
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ulsd=roundat-1; // new LSD
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}
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else { // edge case
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if (drop==length) {
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roundat=umsd;
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reround=*roundat;
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}
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else {
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roundat=umsd-1;
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reround=0;
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}
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for (ub=roundat+1; ub<=ulsd; ub++) {
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if (*ub!=0) { // non-zero to be discarded
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reround=DECSTICKYTAB[reround]; // apply sticky bit
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break; // [remainder don't-care]
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}
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} // check stickies
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*umsd=0; // coefficient is a 0
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ulsd=umsd; // ..
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}
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if (reround!=0) { // discarding non-zero
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uInt bump=0;
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set->status|=DEC_Inexact;
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// if adjusted exponent [exp+digits-1] is < EMIN then num is
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// subnormal -- so raise Underflow
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if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN)
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set->status|=DEC_Underflow;
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// next decide whether increment of the coefficient is needed
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if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case
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if (reround>5) bump=1; // >0.5 goes up
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else if (reround==5) // exactly 0.5000 ..
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bump=*ulsd & 0x01; // .. up iff [new] lsd is odd
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} // r-h-e
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else switch (set->round) {
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case DEC_ROUND_DOWN: {
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// no change
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break;} // r-d
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case DEC_ROUND_HALF_DOWN: {
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if (reround>5) bump=1;
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break;} // r-h-d
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case DEC_ROUND_HALF_UP: {
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if (reround>=5) bump=1;
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break;} // r-h-u
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case DEC_ROUND_UP: {
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if (reround>0) bump=1;
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break;} // r-u
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case DEC_ROUND_CEILING: {
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// same as _UP for positive numbers, and as _DOWN for negatives
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if (!num->sign && reround>0) bump=1;
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break;} // r-c
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case DEC_ROUND_FLOOR: {
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// same as _UP for negative numbers, and as _DOWN for positive
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// [negative reround cannot occur on 0]
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if (num->sign && reround>0) bump=1;
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break;} // r-f
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case DEC_ROUND_05UP: {
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if (reround>0) { // anything out there is 'sticky'
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// bump iff lsd=0 or 5; this cannot carry so it could be
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// effected immediately with no bump -- but the code
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// is clearer if this is done the same way as the others
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if (*ulsd==0 || *ulsd==5) bump=1;
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}
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break;} // r-r
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default: { // e.g., DEC_ROUND_MAX
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set->status|=DEC_Invalid_context;
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#if DECCHECK
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printf("Unknown rounding mode: %ld\n", (LI)set->round);
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#endif
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break;}
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} // switch (not r-h-e)
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// printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump);
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if (bump!=0) { // need increment
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// increment the coefficient; this might end up with 1000...
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// (after the all nines case)
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ub=ulsd;
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for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) {
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UBFROMUI(ub-3, 0); // to 00000000
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}
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// [note ub could now be to left of msd, and it is not safe
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// to write to the the left of the msd]
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// now at most 3 digits left to non-9 (usually just the one)
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for (; ub>=umsd; *ub=0, ub--) {
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if (*ub==9) continue; // carry
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*ub+=1;
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break;
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}
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if (ub<umsd) { // had all-nines
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*umsd=1; // coefficient to 1000...
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// usually the 1000... coefficient can be used as-is
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if ((ulsd-umsd+1)==DECPMAX) {
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num->exponent++;
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}
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else {
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// if coefficient is shorter than Pmax then num is
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// subnormal, so extend it; this is safe as drop>0
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// (or, if the coefficient was supplied above, it could
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// not be 9); this may make the result normal.
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ulsd++;
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*ulsd=0;
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// [exponent unchanged]
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#if DECCHECK
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if (num->exponent!=DECQTINY) // sanity check
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printf("decFinalize: bad all-nines extend [^%ld, %ld]\n",
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(LI)num->exponent, (LI)(ulsd-umsd+1));
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#endif
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} // subnormal extend
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} // had all-nines
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} // bump needed
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} // inexact rounding
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length=ulsd-umsd+1; // recalculate (may be <DECPMAX)
|
|
} // need round (drop>0)
|
|
|
|
// The coefficient will now fit and has final length unless overflow
|
|
// decShowNum(num, "rounded");
|
|
|
|
// if exponent is >=emax may have to clamp, overflow, or fold-down
|
|
if (num->exponent>DECEMAX-(DECPMAX-1)) { // is edge case
|
|
// printf("overflow checks...\n");
|
|
if (*ulsd==0 && ulsd==umsd) { // have zero
|
|
num->exponent=DECEMAX-(DECPMAX-1); // clamp to max
|
|
}
|
|
else if ((num->exponent+length-1)>DECEMAX) { // > Nmax
|
|
// Overflow -- these could go straight to encoding, here, but
|
|
// instead num is adjusted to keep the code cleaner
|
|
Flag needmax=0; // 1 for finite result
|
|
set->status|=(DEC_Overflow | DEC_Inexact);
|
|
switch (set->round) {
|
|
case DEC_ROUND_DOWN: {
|
|
needmax=1; // never Infinity
|
|
break;} // r-d
|
|
case DEC_ROUND_05UP: {
|
|
needmax=1; // never Infinity
|
|
break;} // r-05
|
|
case DEC_ROUND_CEILING: {
|
|
if (num->sign) needmax=1; // Infinity iff non-negative
|
|
break;} // r-c
|
|
case DEC_ROUND_FLOOR: {
|
|
if (!num->sign) needmax=1; // Infinity iff negative
|
|
break;} // r-f
|
|
default: break; // Infinity in all other cases
|
|
}
|
|
if (!needmax) { // easy .. set Infinity
|
|
num->exponent=DECFLOAT_Inf;
|
|
*umsd=0; // be clean: coefficient to 0
|
|
ulsd=umsd; // ..
|
|
}
|
|
else { // return Nmax
|
|
umsd=allnines; // use constant array
|
|
ulsd=allnines+DECPMAX-1;
|
|
num->exponent=DECEMAX-(DECPMAX-1);
|
|
}
|
|
}
|
|
else { // no overflow but non-zero and may have to fold-down
|
|
Int shift=num->exponent-(DECEMAX-(DECPMAX-1));
|
|
if (shift>0) { // fold-down needed
|
|
// fold down needed; must copy to buffer in order to pad
|
|
// with zeros safely; fortunately this is not the worst case
|
|
// path because cannot have had a round
|
|
uByte buffer[ROUNDUP(DECPMAX+3, 4)]; // [+3 allows uInt padding]
|
|
uByte *s=umsd; // source
|
|
uByte *t=buffer; // safe target
|
|
uByte *tlsd=buffer+(ulsd-umsd)+shift; // target LSD
|
|
// printf("folddown shift=%ld\n", (LI)shift);
|
|
for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s));
|
|
for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); // pad 0s
|
|
num->exponent-=shift;
|
|
umsd=buffer;
|
|
ulsd=tlsd;
|
|
}
|
|
} // fold-down?
|
|
length=ulsd-umsd+1; // recalculate length
|
|
} // high-end edge case
|
|
} // finite number
|
|
|
|
/*------------------------------------------------------------------*/
|
|
/* At this point the result will properly fit the decFloat */
|
|
/* encoding, and it can be encoded with no possibility of error */
|
|
/*------------------------------------------------------------------*/
|
|
// Following code does not alter coefficient (could be allnines array)
|
|
|
|
// fast path possible when DECPMAX digits
|
|
if (length==DECPMAX) {
|
|
return decFloatFromBCD(df, num->exponent, umsd, num->sign);
|
|
} // full-length
|
|
|
|
// slower path when not a full-length number; must care about length
|
|
// [coefficient length here will be < DECPMAX]
|
|
if (!NUMISSPECIAL(num)) { // is still finite
|
|
// encode the combination field and exponent continuation
|
|
uInt uexp=(uInt)(num->exponent+DECBIAS); // biased exponent
|
|
uInt code=(uexp>>DECECONL)<<4; // top two bits of exp
|
|
// [msd==0]
|
|
// look up the combination field and make high word
|
|
encode=DECCOMBFROM[code]; // indexed by (0-2)*16+msd
|
|
encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation
|
|
}
|
|
else encode=num->exponent; // special [already in word]
|
|
encode|=num->sign; // add sign
|
|
|
|
// private macro to extract a declet, n (where 0<=n<DECLETS and 0
|
|
// refers to the declet from the least significant three digits)
|
|
// and put the corresponding DPD code into dpd. Access to umsd and
|
|
// ulsd (pointers to the most and least significant digit of the
|
|
// variable-length coefficient) is assumed, along with use of a
|
|
// working pointer, uInt *ub.
|
|
// As not full-length then chances are there are many leading zeros
|
|
// [and there may be a partial triad]
|
|
#define getDPDt(dpd, n) ub=ulsd-(3*(n))-2; \
|
|
if (ub<umsd-2) dpd=0; \
|
|
else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \
|
|
else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];}
|
|
|
|
// place the declets in the encoding words and copy to result (df),
|
|
// according to endianness; in all cases complete the sign word
|
|
// first
|
|
#if DECPMAX==7
|
|
getDPDt(dpd, 1);
|
|
encode|=dpd<<10;
|
|
getDPDt(dpd, 0);
|
|
encode|=dpd;
|
|
DFWORD(df, 0)=encode; // just the one word
|
|
|
|
#elif DECPMAX==16
|
|
getDPDt(dpd, 4); encode|=dpd<<8;
|
|
getDPDt(dpd, 3); encode|=dpd>>2;
|
|
DFWORD(df, 0)=encode;
|
|
encode=dpd<<30;
|
|
getDPDt(dpd, 2); encode|=dpd<<20;
|
|
getDPDt(dpd, 1); encode|=dpd<<10;
|
|
getDPDt(dpd, 0); encode|=dpd;
|
|
DFWORD(df, 1)=encode;
|
|
|
|
#elif DECPMAX==34
|
|
getDPDt(dpd,10); encode|=dpd<<4;
|
|
getDPDt(dpd, 9); encode|=dpd>>6;
|
|
DFWORD(df, 0)=encode;
|
|
|
|
encode=dpd<<26;
|
|
getDPDt(dpd, 8); encode|=dpd<<16;
|
|
getDPDt(dpd, 7); encode|=dpd<<6;
|
|
getDPDt(dpd, 6); encode|=dpd>>4;
|
|
DFWORD(df, 1)=encode;
|
|
|
|
encode=dpd<<28;
|
|
getDPDt(dpd, 5); encode|=dpd<<18;
|
|
getDPDt(dpd, 4); encode|=dpd<<8;
|
|
getDPDt(dpd, 3); encode|=dpd>>2;
|
|
DFWORD(df, 2)=encode;
|
|
|
|
encode=dpd<<30;
|
|
getDPDt(dpd, 2); encode|=dpd<<20;
|
|
getDPDt(dpd, 1); encode|=dpd<<10;
|
|
getDPDt(dpd, 0); encode|=dpd;
|
|
DFWORD(df, 3)=encode;
|
|
#endif
|
|
|
|
// printf("Status: %08lx\n", (LI)set->status);
|
|
// decFloatShow(df, "final2");
|
|
return df;
|
|
} // decFinalize
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */
|
|
/* */
|
|
/* df is the target decFloat */
|
|
/* exp is the in-range unbiased exponent, q, or a special value in */
|
|
/* the form returned by decFloatGetExponent */
|
|
/* bcdar holds DECPMAX digits to set the coefficient from, one */
|
|
/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
|
|
/* if df is a NaN; all are ignored if df is infinite. */
|
|
/* All bytes must be in 0-9; results are undefined otherwise. */
|
|
/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
|
|
/* returns df, which will be canonical */
|
|
/* */
|
|
/* No error is possible, and no status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar,
|
|
Int sig) {
|
|
uInt encode, dpd; // work
|
|
const uByte *ub; // ..
|
|
|
|
if (EXPISSPECIAL(exp)) encode=exp|sig;// specials already encoded
|
|
else { // is finite
|
|
// encode the combination field and exponent continuation
|
|
uInt uexp=(uInt)(exp+DECBIAS); // biased exponent
|
|
uInt code=(uexp>>DECECONL)<<4; // top two bits of exp
|
|
code+=bcdar[0]; // add msd
|
|
// look up the combination field and make high word
|
|
encode=DECCOMBFROM[code]|sig; // indexed by (0-2)*16+msd
|
|
encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation
|
|
}
|
|
|
|
// private macro to extract a declet, n (where 0<=n<DECLETS and 0
|
|
// refers to the declet from the least significant three digits)
|
|
// and put the corresponding DPD code into dpd.
|
|
// Use of a working pointer, uInt *ub, is assumed.
|
|
|
|
#define getDPDb(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2; \
|
|
dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
|
|
|
|
// place the declets in the encoding words and copy to result (df),
|
|
// according to endianness; in all cases complete the sign word
|
|
// first
|
|
#if DECPMAX==7
|
|
getDPDb(dpd, 1);
|
|
encode|=dpd<<10;
|
|
getDPDb(dpd, 0);
|
|
encode|=dpd;
|
|
DFWORD(df, 0)=encode; // just the one word
|
|
|
|
#elif DECPMAX==16
|
|
getDPDb(dpd, 4); encode|=dpd<<8;
|
|
getDPDb(dpd, 3); encode|=dpd>>2;
|
|
DFWORD(df, 0)=encode;
|
|
encode=dpd<<30;
|
|
getDPDb(dpd, 2); encode|=dpd<<20;
|
|
getDPDb(dpd, 1); encode|=dpd<<10;
|
|
getDPDb(dpd, 0); encode|=dpd;
|
|
DFWORD(df, 1)=encode;
|
|
|
|
#elif DECPMAX==34
|
|
getDPDb(dpd,10); encode|=dpd<<4;
|
|
getDPDb(dpd, 9); encode|=dpd>>6;
|
|
DFWORD(df, 0)=encode;
|
|
|
|
encode=dpd<<26;
|
|
getDPDb(dpd, 8); encode|=dpd<<16;
|
|
getDPDb(dpd, 7); encode|=dpd<<6;
|
|
getDPDb(dpd, 6); encode|=dpd>>4;
|
|
DFWORD(df, 1)=encode;
|
|
|
|
encode=dpd<<28;
|
|
getDPDb(dpd, 5); encode|=dpd<<18;
|
|
getDPDb(dpd, 4); encode|=dpd<<8;
|
|
getDPDb(dpd, 3); encode|=dpd>>2;
|
|
DFWORD(df, 2)=encode;
|
|
|
|
encode=dpd<<30;
|
|
getDPDb(dpd, 2); encode|=dpd<<20;
|
|
getDPDb(dpd, 1); encode|=dpd<<10;
|
|
getDPDb(dpd, 0); encode|=dpd;
|
|
DFWORD(df, 3)=encode;
|
|
#endif
|
|
// decFloatShow(df, "fromB");
|
|
return df;
|
|
} // decFloatFromBCD
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatFromPacked -- set decFloat from exponent and packed BCD */
|
|
/* */
|
|
/* df is the target decFloat */
|
|
/* exp is the in-range unbiased exponent, q, or a special value in */
|
|
/* the form returned by decFloatGetExponent */
|
|
/* packed holds DECPMAX packed decimal digits plus a sign nibble */
|
|
/* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */
|
|
/* and all except sign are ignored if df is infinite. For DOUBLE */
|
|
/* and QUAD the first (pad) nibble is also ignored in all cases. */
|
|
/* All coefficient nibbles must be in 0-9 and sign in A-F; results */
|
|
/* are undefined otherwise. */
|
|
/* returns df, which will be canonical */
|
|
/* */
|
|
/* No error is possible, and no status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) {
|
|
uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]
|
|
const uByte *ip; // ..
|
|
uByte *op; // ..
|
|
Int sig=0; // sign
|
|
|
|
// expand coefficient and sign to BCDAR
|
|
#if SINGLE
|
|
op=bcdar+1; // no pad digit
|
|
#else
|
|
op=bcdar; // first (pad) digit ignored
|
|
#endif
|
|
for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
|
|
*op++=*ip>>4;
|
|
*op++=(uByte)(*ip&0x0f); // [final nibble is sign]
|
|
}
|
|
op--; // -> sign byte
|
|
if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
|
|
|
|
if (EXPISSPECIAL(exp)) { // Infinity or NaN
|
|
if (!EXPISINF(exp)) bcdar[1]=0; // a NaN: ignore MSD
|
|
else memset(bcdar+1, 0, DECPMAX); // Infinite: coefficient to 0
|
|
}
|
|
return decFloatFromBCD(df, exp, bcdar+1, sig);
|
|
} // decFloatFromPacked
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatFromPackedChecked -- set from exponent and packed; checked */
|
|
/* */
|
|
/* df is the target decFloat */
|
|
/* exp is the in-range unbiased exponent, q, or a special value in */
|
|
/* the form returned by decFloatGetExponent */
|
|
/* packed holds DECPMAX packed decimal digits plus a sign nibble */
|
|
/* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */
|
|
/* and all digits must be 0 if df is infinite. For DOUBLE and */
|
|
/* QUAD the first (pad) nibble must be 0. */
|
|
/* All coefficient nibbles must be in 0-9 and sign in A-F. */
|
|
/* returns df, which will be canonical or NULL if any of the */
|
|
/* requirements are not met (if this case df is unchanged); that */
|
|
/* is, the input data must be as returned by decFloatToPacked, */
|
|
/* except that all six sign codes are acccepted. */
|
|
/* */
|
|
/* No status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatFromPackedChecked(decFloat *df, Int exp,
|
|
const uByte *packed) {
|
|
uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]
|
|
const uByte *ip; // ..
|
|
uByte *op; // ..
|
|
Int sig=0; // sign
|
|
|
|
// expand coefficient and sign to BCDAR
|
|
#if SINGLE
|
|
op=bcdar+1; // no pad digit
|
|
#else
|
|
op=bcdar; // first (pad) digit here
|
|
#endif
|
|
for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
|
|
*op=*ip>>4;
|
|
if (*op>9) return NULL;
|
|
op++;
|
|
*op=(uByte)(*ip&0x0f); // [final nibble is sign]
|
|
if (*op>9 && ip<packed+((DECPMAX+2)/2)-1) return NULL;
|
|
op++;
|
|
}
|
|
op--; // -> sign byte
|
|
if (*op<=9) return NULL; // bad sign
|
|
if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
|
|
|
|
#if !SINGLE
|
|
if (bcdar[0]!=0) return NULL; // bad pad nibble
|
|
#endif
|
|
|
|
if (EXPISNAN(exp)) { // a NaN
|
|
if (bcdar[1]!=0) return NULL; // bad msd
|
|
} // NaN
|
|
else if (EXPISINF(exp)) { // is infinite
|
|
Int i;
|
|
for (i=0; i<DECPMAX; i++) {
|
|
if (bcdar[i+1]!=0) return NULL; // should be all zeros
|
|
}
|
|
} // infinity
|
|
else { // finite
|
|
// check the exponent is in range
|
|
if (exp>DECEMAX-DECPMAX+1) return NULL;
|
|
if (exp<DECEMIN-DECPMAX+1) return NULL;
|
|
}
|
|
return decFloatFromBCD(df, exp, bcdar+1, sig);
|
|
} // decFloatFromPacked
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatFromString -- conversion from numeric string */
|
|
/* */
|
|
/* result is the decFloat format number which gets the result of */
|
|
/* the conversion */
|
|
/* *string is the character string which should contain a valid */
|
|
/* number (which may be a special value), \0-terminated */
|
|
/* If there are too many significant digits in the */
|
|
/* coefficient it will be rounded. */
|
|
/* set is the context */
|
|
/* returns result */
|
|
/* */
|
|
/* The length of the coefficient and the size of the exponent are */
|
|
/* checked by this routine, so the correct error (Underflow or */
|
|
/* Overflow) can be reported or rounding applied, as necessary. */
|
|
/* */
|
|
/* There is no limit to the coefficient length for finite inputs; */
|
|
/* NaN payloads must be integers with no more than DECPMAX-1 digits. */
|
|
/* Exponents may have up to nine significant digits. */
|
|
/* */
|
|
/* If bad syntax is detected, the result will be a quiet NaN. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatFromString(decFloat *result, const char *string,
|
|
decContext *set) {
|
|
Int digits; // count of digits in coefficient
|
|
const char *dotchar=NULL; // where dot was found [NULL if none]
|
|
const char *cfirst=string; // -> first character of decimal part
|
|
const char *c; // work
|
|
uByte *ub; // ..
|
|
uInt uiwork; // for macros
|
|
bcdnum num; // collects data for finishing
|
|
uInt error=DEC_Conversion_syntax; // assume the worst
|
|
uByte buffer[ROUNDUP(DECSTRING+11, 8)]; // room for most coefficents,
|
|
// some common rounding, +3, & pad
|
|
#if DECTRACE
|
|
// printf("FromString %s ...\n", string);
|
|
#endif
|
|
|
|
for(;;) { // once-only 'loop'
|
|
num.sign=0; // assume non-negative
|
|
num.msd=buffer; // MSD is here always
|
|
|
|
// detect and validate the coefficient, including any leading,
|
|
// trailing, or embedded '.'
|
|
// [could test four-at-a-time here (saving 10% for decQuads),
|
|
// but that risks storage violation because the position of the
|
|
// terminator is unknown]
|
|
for (c=string;; c++) { // -> input character
|
|
if (((unsigned)(*c-'0'))<=9) continue; // '0' through '9' is good
|
|
if (*c=='\0') break; // most common non-digit
|
|
if (*c=='.') {
|
|
if (dotchar!=NULL) break; // not first '.'
|
|
dotchar=c; // record offset into decimal part
|
|
continue;}
|
|
if (c==string) { // first in string...
|
|
if (*c=='-') { // valid - sign
|
|
cfirst++;
|
|
num.sign=DECFLOAT_Sign;
|
|
continue;}
|
|
if (*c=='+') { // valid + sign
|
|
cfirst++;
|
|
continue;}
|
|
}
|
|
// *c is not a digit, terminator, or a valid +, -, or '.'
|
|
break;
|
|
} // c loop
|
|
|
|
digits=(uInt)(c-cfirst); // digits (+1 if a dot)
|
|
|
|
if (digits>0) { // had digits and/or dot
|
|
const char *clast=c-1; // note last coefficient char position
|
|
Int exp=0; // exponent accumulator
|
|
if (*c!='\0') { // something follows the coefficient
|
|
uInt edig; // unsigned work
|
|
// had some digits and more to come; expect E[+|-]nnn now
|
|
const char *firstexp; // exponent first non-zero
|
|
if (*c!='E' && *c!='e') break;
|
|
c++; // to (optional) sign
|
|
if (*c=='-' || *c=='+') c++; // step over sign (c=clast+2)
|
|
if (*c=='\0') break; // no digits! (e.g., '1.2E')
|
|
for (; *c=='0';) c++; // skip leading zeros [even last]
|
|
firstexp=c; // remember start [maybe '\0']
|
|
// gather exponent digits
|
|
edig=(uInt)*c-(uInt)'0';
|
|
if (edig<=9) { // [check not bad or terminator]
|
|
exp+=edig; // avoid initial X10
|
|
c++;
|
|
for (;; c++) {
|
|
edig=(uInt)*c-(uInt)'0';
|
|
if (edig>9) break;
|
|
exp=exp*10+edig;
|
|
}
|
|
}
|
|
// if not now on the '\0', *c must not be a digit
|
|
if (*c!='\0') break;
|
|
|
|
// (this next test must be after the syntax checks)
|
|
// if definitely more than the possible digits for format then
|
|
// the exponent may have wrapped, so simply set it to a certain
|
|
// over/underflow value
|
|
if (c>firstexp+DECEMAXD) exp=DECEMAX*2;
|
|
if (*(clast+2)=='-') exp=-exp; // was negative
|
|
} // exponent part
|
|
|
|
if (dotchar!=NULL) { // had a '.'
|
|
digits--; // remove from digits count
|
|
if (digits==0) break; // was dot alone: bad syntax
|
|
exp-=(Int)(clast-dotchar); // adjust exponent
|
|
// [the '.' can now be ignored]
|
|
}
|
|
num.exponent=exp; // exponent is good; store it
|
|
|
|
// Here when whole string has been inspected and syntax is good
|
|
// cfirst->first digit or dot, clast->last digit or dot
|
|
error=0; // no error possible now
|
|
|
|
// if the number of digits in the coefficient will fit in buffer
|
|
// then it can simply be converted to bcd8 and copied -- decFinalize
|
|
// will take care of leading zeros and rounding; the buffer is big
|
|
// enough for all canonical coefficients, including 0.00000nn...
|
|
ub=buffer;
|
|
if (digits<=(Int)(sizeof(buffer)-3)) { // [-3 allows by-4s copy]
|
|
c=cfirst;
|
|
if (dotchar!=NULL) { // a dot to worry about
|
|
if (*(c+1)=='.') { // common canonical case
|
|
*ub++=(uByte)(*c-'0'); // copy leading digit
|
|
c+=2; // prepare to handle rest
|
|
}
|
|
else for (; c<=clast;) { // '.' could be anywhere
|
|
// as usual, go by fours when safe; NB it has been asserted
|
|
// that a '.' does not have the same mask as a digit
|
|
if (c<=clast-3 // safe for four
|
|
&& (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // test four
|
|
UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8
|
|
ub+=4;
|
|
c+=4;
|
|
continue;
|
|
}
|
|
if (*c=='.') { // found the dot
|
|
c++; // step over it ..
|
|
break; // .. and handle the rest
|
|
}
|
|
*ub++=(uByte)(*c++-'0');
|
|
}
|
|
} // had dot
|
|
// Now no dot; do this by fours (where safe)
|
|
for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f);
|
|
for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0');
|
|
num.lsd=buffer+digits-1; // record new LSD
|
|
} // fits
|
|
|
|
else { // too long for buffer
|
|
// [This is a rare and unusual case; arbitrary-length input]
|
|
// strip leading zeros [but leave final 0 if all 0's]
|
|
if (*cfirst=='.') cfirst++; // step past dot at start
|
|
if (*cfirst=='0') { // [cfirst always -> digit]
|
|
for (; cfirst<clast; cfirst++) {
|
|
if (*cfirst!='0') { // non-zero found
|
|
if (*cfirst=='.') continue; // [ignore]
|
|
break; // done
|
|
}
|
|
digits--; // 0 stripped
|
|
} // cfirst
|
|
} // at least one leading 0
|
|
|
|
// the coefficient is now as short as possible, but may still
|
|
// be too long; copy up to Pmax+1 digits to the buffer, then
|
|
// just record any non-zeros (set round-for-reround digit)
|
|
for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) {
|
|
// (see commentary just above)
|
|
if (c<=clast-3 // safe for four
|
|
&& (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // four digits
|
|
UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8
|
|
ub+=4;
|
|
c+=3; // [will become 4]
|
|
continue;
|
|
}
|
|
if (*c=='.') continue; // [ignore]
|
|
*ub++=(uByte)(*c-'0');
|
|
}
|
|
ub--; // -> LSD
|
|
for (; c<=clast; c++) { // inspect remaining chars
|
|
if (*c!='0') { // sticky bit needed
|
|
if (*c=='.') continue; // [ignore]
|
|
*ub=DECSTICKYTAB[*ub]; // update round-for-reround
|
|
break; // no need to look at more
|
|
}
|
|
}
|
|
num.lsd=ub; // record LSD
|
|
// adjust exponent for dropped digits
|
|
num.exponent+=digits-(Int)(ub-buffer+1);
|
|
} // too long for buffer
|
|
} // digits and/or dot
|
|
|
|
else { // no digits or dot were found
|
|
// only Infinities and NaNs are allowed, here
|
|
if (*c=='\0') break; // nothing there is bad
|
|
buffer[0]=0; // default a coefficient of 0
|
|
num.lsd=buffer; // ..
|
|
if (decBiStr(c, "infinity", "INFINITY")
|
|
|| decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf;
|
|
else { // should be a NaN
|
|
num.exponent=DECFLOAT_qNaN; // assume quiet NaN
|
|
if (*c=='s' || *c=='S') { // probably an sNaN
|
|
num.exponent=DECFLOAT_sNaN; // effect the 's'
|
|
c++; // and step over it
|
|
}
|
|
if (*c!='N' && *c!='n') break; // check caseless "NaN"
|
|
c++;
|
|
if (*c!='a' && *c!='A') break; // ..
|
|
c++;
|
|
if (*c!='N' && *c!='n') break; // ..
|
|
c++;
|
|
// now either nothing, or nnnn payload (no dots), expected
|
|
// -> start of integer, and skip leading 0s [including plain 0]
|
|
for (cfirst=c; *cfirst=='0';) cfirst++;
|
|
if (*cfirst!='\0') { // not empty or all-0, payload
|
|
// payload found; check all valid digits and copy to buffer as bcd8
|
|
ub=buffer;
|
|
for (c=cfirst;; c++, ub++) {
|
|
if ((unsigned)(*c-'0')>9) break; // quit if not 0-9
|
|
if (c-cfirst==DECPMAX-1) break; // too many digits
|
|
*ub=(uByte)(*c-'0'); // good bcd8
|
|
}
|
|
if (*c!='\0') break; // not all digits, or too many
|
|
num.lsd=ub-1; // record new LSD
|
|
}
|
|
} // NaN or sNaN
|
|
error=0; // syntax is OK
|
|
} // digits=0 (special expected)
|
|
break; // drop out
|
|
} // [for(;;) once-loop]
|
|
|
|
// decShowNum(&num, "fromStr");
|
|
|
|
if (error!=0) {
|
|
set->status|=error;
|
|
num.exponent=DECFLOAT_qNaN; // set up quiet NaN
|
|
num.sign=0; // .. with 0 sign
|
|
buffer[0]=0; // .. and coefficient
|
|
num.lsd=buffer; // ..
|
|
// decShowNum(&num, "oops");
|
|
}
|
|
|
|
// decShowNum(&num, "dffs");
|
|
decFinalize(result, &num, set); // round, check, and lay out
|
|
// decFloatShow(result, "fromString");
|
|
return result;
|
|
} // decFloatFromString
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatFromWider -- conversion from next-wider format */
|
|
/* */
|
|
/* result is the decFloat format number which gets the result of */
|
|
/* the conversion */
|
|
/* wider is the decFloatWider format number which will be narrowed */
|
|
/* set is the context */
|
|
/* returns result */
|
|
/* */
|
|
/* Narrowing can cause rounding, overflow, etc., but not Invalid */
|
|
/* operation (sNaNs are copied and do not signal). */
|
|
/* ------------------------------------------------------------------ */
|
|
// narrow-to is not possible for decQuad format numbers; simply omit
|
|
#if !QUAD
|
|
decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider,
|
|
decContext *set) {
|
|
bcdnum num; // collects data for finishing
|
|
uByte bcdar[DECWPMAX]; // room for wider coefficient
|
|
uInt widerhi=DFWWORD(wider, 0); // top word
|
|
Int exp;
|
|
|
|
GETWCOEFF(wider, bcdar);
|
|
|
|
num.msd=bcdar; // MSD is here always
|
|
num.lsd=bcdar+DECWPMAX-1; // LSD is here always
|
|
num.sign=widerhi&0x80000000; // extract sign [DECFLOAT_Sign=Neg]
|
|
|
|
// decode the wider combination field to exponent
|
|
exp=DECCOMBWEXP[widerhi>>26]; // decode from wider combination field
|
|
// if it is a special there's nothing to do unless sNaN; if it's
|
|
// finite then add the (wider) exponent continuation and unbias
|
|
if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; // include sNaN selector
|
|
else exp+=GETWECON(wider)-DECWBIAS;
|
|
num.exponent=exp;
|
|
|
|
// decShowNum(&num, "dffw");
|
|
return decFinalize(result, &num, set);// round, check, and lay out
|
|
} // decFloatFromWider
|
|
#endif
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatGetCoefficient -- get coefficient as BCD8 */
|
|
/* */
|
|
/* df is the decFloat from which to extract the coefficient */
|
|
/* bcdar is where DECPMAX bytes will be written, one BCD digit in */
|
|
/* each byte (BCD8 encoding); if df is a NaN the first byte will */
|
|
/* be zero, and if it is infinite they will all be zero */
|
|
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
|
|
/* 0 otherwise) */
|
|
/* */
|
|
/* No error is possible, and no status will be set. If df is a */
|
|
/* special value the array is set to zeros (for Infinity) or to the */
|
|
/* payload of a qNaN or sNaN. */
|
|
/* ------------------------------------------------------------------ */
|
|
Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) {
|
|
if (DFISINF(df)) memset(bcdar, 0, DECPMAX);
|
|
else {
|
|
GETCOEFF(df, bcdar); // use macro
|
|
if (DFISNAN(df)) bcdar[0]=0; // MSD needs correcting
|
|
}
|
|
return GETSIGN(df);
|
|
} // decFloatGetCoefficient
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatGetExponent -- get unbiased exponent */
|
|
/* */
|
|
/* df is the decFloat from which to extract the exponent */
|
|
/* returns the exponent, q. */
|
|
/* */
|
|
/* No error is possible, and no status will be set. If df is a */
|
|
/* special value the first seven bits of the decFloat are returned, */
|
|
/* left adjusted and with the first (sign) bit set to 0 (followed by */
|
|
/* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */
|
|
/* ------------------------------------------------------------------ */
|
|
Int decFloatGetExponent(const decFloat *df) {
|
|
if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000;
|
|
return GETEXPUN(df);
|
|
} // decFloatGetExponent
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatSetCoefficient -- set coefficient from BCD8 */
|
|
/* */
|
|
/* df is the target decFloat (and source of exponent/special value) */
|
|
/* bcdar holds DECPMAX digits to set the coefficient from, one */
|
|
/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
|
|
/* if df is a NaN; all are ignored if df is infinite. */
|
|
/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
|
|
/* returns df, which will be canonical */
|
|
/* */
|
|
/* No error is possible, and no status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar,
|
|
Int sig) {
|
|
uInt exp; // for exponent
|
|
uByte bcdzero[DECPMAX]; // for infinities
|
|
|
|
// Exponent/special code is extracted from df
|
|
if (DFISSPECIAL(df)) {
|
|
exp=DFWORD(df, 0)&0x7e000000;
|
|
if (DFISINF(df)) {
|
|
memset(bcdzero, 0, DECPMAX);
|
|
return decFloatFromBCD(df, exp, bcdzero, sig);
|
|
}
|
|
}
|
|
else exp=GETEXPUN(df);
|
|
return decFloatFromBCD(df, exp, bcdar, sig);
|
|
} // decFloatSetCoefficient
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatSetExponent -- set exponent or special value */
|
|
/* */
|
|
/* df is the target decFloat (and source of coefficient/payload) */
|
|
/* set is the context for reporting status */
|
|
/* exp is the unbiased exponent, q, or a special value in the form */
|
|
/* returned by decFloatGetExponent */
|
|
/* returns df, which will be canonical */
|
|
/* */
|
|
/* No error is possible, but Overflow or Underflow might occur. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) {
|
|
uByte bcdcopy[DECPMAX]; // for coefficient
|
|
bcdnum num; // work
|
|
num.exponent=exp;
|
|
num.sign=decFloatGetCoefficient(df, bcdcopy); // extract coefficient
|
|
if (DFISSPECIAL(df)) { // MSD or more needs correcting
|
|
if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX);
|
|
bcdcopy[0]=0;
|
|
}
|
|
num.msd=bcdcopy;
|
|
num.lsd=bcdcopy+DECPMAX-1;
|
|
return decFinalize(df, &num, set);
|
|
} // decFloatSetExponent
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatRadix -- returns the base (10) */
|
|
/* */
|
|
/* df is any decFloat of this format */
|
|
/* ------------------------------------------------------------------ */
|
|
uInt decFloatRadix(const decFloat *df) {
|
|
if (df) return 10; // to placate compiler
|
|
return 10;
|
|
} // decFloatRadix
|
|
|
|
/* The following function is not available if DECPRINT=0 */
|
|
#if DECPRINT
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatShow -- printf a decFloat in hexadecimal and decimal */
|
|
/* df is the decFloat to show */
|
|
/* tag is a tag string displayed with the number */
|
|
/* */
|
|
/* This is a debug aid; the precise format of the string may change. */
|
|
/* ------------------------------------------------------------------ */
|
|
void decFloatShow(const decFloat *df, const char *tag) {
|
|
char hexbuf[DECBYTES*2+DECBYTES/4+1]; // NB blank after every fourth
|
|
char buff[DECSTRING]; // for value in decimal
|
|
Int i, j=0;
|
|
|
|
for (i=0; i<DECBYTES; i++) {
|
|
#if DECLITEND
|
|
sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]);
|
|
#else
|
|
sprintf(&hexbuf[j], "%02x", df->bytes[i]);
|
|
#endif
|
|
j+=2;
|
|
// the next line adds blank (and terminator) after final pair, too
|
|
if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;}
|
|
}
|
|
decFloatToString(df, buff);
|
|
printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff);
|
|
return;
|
|
} // decFloatShow
|
|
#endif
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */
|
|
/* */
|
|
/* df is the source decFloat */
|
|
/* exp will be set to the unbiased exponent, q, or to a special */
|
|
/* value in the form returned by decFloatGetExponent */
|
|
/* bcdar is where DECPMAX bytes will be written, one BCD digit in */
|
|
/* each byte (BCD8 encoding); if df is a NaN the first byte will */
|
|
/* be zero, and if it is infinite they will all be zero */
|
|
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
|
|
/* 0 otherwise) */
|
|
/* */
|
|
/* No error is possible, and no status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) {
|
|
if (DFISINF(df)) {
|
|
memset(bcdar, 0, DECPMAX);
|
|
*exp=DFWORD(df, 0)&0x7e000000;
|
|
}
|
|
else {
|
|
GETCOEFF(df, bcdar); // use macro
|
|
if (DFISNAN(df)) {
|
|
bcdar[0]=0; // MSD needs correcting
|
|
*exp=DFWORD(df, 0)&0x7e000000;
|
|
}
|
|
else { // finite
|
|
*exp=GETEXPUN(df);
|
|
}
|
|
}
|
|
return GETSIGN(df);
|
|
} // decFloatToBCD
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatToEngString -- conversion to numeric string, engineering */
|
|
/* */
|
|
/* df is the decFloat format number to convert */
|
|
/* string is the string where the result will be laid out */
|
|
/* */
|
|
/* string must be at least DECPMAX+9 characters (the worst case is */
|
|
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
|
|
/* DECEMAXD<=4); this condition is asserted above */
|
|
/* */
|
|
/* No error is possible, and no status will be set */
|
|
/* ------------------------------------------------------------------ */
|
|
char * decFloatToEngString(const decFloat *df, char *string){
|
|
uInt msd; // coefficient MSD
|
|
Int exp; // exponent top two bits or full
|
|
uInt comb; // combination field
|
|
char *cstart; // coefficient start
|
|
char *c; // output pointer in string
|
|
char *s, *t; // .. (source, target)
|
|
Int pre, e; // work
|
|
const uByte *u; // ..
|
|
uInt uiwork; // for macros [one compiler needs
|
|
// volatile here to avoid bug, but
|
|
// that doubles execution time]
|
|
|
|
// Source words; macro handles endianness
|
|
uInt sourhi=DFWORD(df, 0); // word with sign
|
|
#if DECPMAX==16
|
|
uInt sourlo=DFWORD(df, 1);
|
|
#elif DECPMAX==34
|
|
uInt sourmh=DFWORD(df, 1);
|
|
uInt sourml=DFWORD(df, 2);
|
|
uInt sourlo=DFWORD(df, 3);
|
|
#endif
|
|
|
|
c=string; // where result will go
|
|
if (((Int)sourhi)<0) *c++='-'; // handle sign
|
|
comb=sourhi>>26; // sign+combination field
|
|
msd=DECCOMBMSD[comb]; // decode the combination field
|
|
exp=DECCOMBEXP[comb]; // ..
|
|
|
|
if (EXPISSPECIAL(exp)) { // special
|
|
if (exp==DECFLOAT_Inf) { // infinity
|
|
strcpy(c, "Inf");
|
|
strcpy(c+3, "inity");
|
|
return string; // easy
|
|
}
|
|
if (sourhi&0x02000000) *c++='s'; // sNaN
|
|
strcpy(c, "NaN"); // complete word
|
|
c+=3; // step past
|
|
// quick exit if the payload is zero
|
|
#if DECPMAX==7
|
|
if ((sourhi&0x000fffff)==0) return string;
|
|
#elif DECPMAX==16
|
|
if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
|
|
#elif DECPMAX==34
|
|
if (sourlo==0 && sourml==0 && sourmh==0
|
|
&& (sourhi&0x00003fff)==0) return string;
|
|
#endif
|
|
// otherwise drop through to add integer; set correct exp etc.
|
|
exp=0; msd=0; // setup for following code
|
|
}
|
|
else { // complete exponent; top two bits are in place
|
|
exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias
|
|
}
|
|
|
|
/* convert the digits of the significand to characters */
|
|
cstart=c; // save start of coefficient
|
|
if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit
|
|
|
|
// Decode the declets. After extracting each declet, it is
|
|
// decoded to a 4-uByte sequence by table lookup; the four uBytes
|
|
// are the three encoded BCD8 digits followed by a 1-byte length
|
|
// (significant digits, except that 000 has length 0). This allows
|
|
// us to left-align the first declet with non-zero content, then
|
|
// the remaining ones are full 3-char length. Fixed-length copies
|
|
// are used because variable-length memcpy causes a subroutine call
|
|
// in at least two compilers. (The copies are length 4 for speed
|
|
// and are safe because the last item in the array is of length
|
|
// three and has the length byte following.)
|
|
#define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
|
|
if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
|
|
else if (*(u+3)) { \
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
|
|
|
|
#if DECPMAX==7
|
|
dpd2char(sourhi>>10); // declet 1
|
|
dpd2char(sourhi); // declet 2
|
|
|
|
#elif DECPMAX==16
|
|
dpd2char(sourhi>>8); // declet 1
|
|
dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2
|
|
dpd2char(sourlo>>20); // declet 3
|
|
dpd2char(sourlo>>10); // declet 4
|
|
dpd2char(sourlo); // declet 5
|
|
|
|
#elif DECPMAX==34
|
|
dpd2char(sourhi>>4); // declet 1
|
|
dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2
|
|
dpd2char(sourmh>>16); // declet 3
|
|
dpd2char(sourmh>>6); // declet 4
|
|
dpd2char((sourmh<<4) | (sourml>>28)); // declet 5
|
|
dpd2char(sourml>>18); // declet 6
|
|
dpd2char(sourml>>8); // declet 7
|
|
dpd2char((sourml<<2) | (sourlo>>30)); // declet 8
|
|
dpd2char(sourlo>>20); // declet 9
|
|
dpd2char(sourlo>>10); // declet 10
|
|
dpd2char(sourlo); // declet 11
|
|
#endif
|
|
|
|
if (c==cstart) *c++='0'; // all zeros, empty -- make "0"
|
|
|
|
if (exp==0) { // integer or NaN case -- easy
|
|
*c='\0'; // terminate
|
|
return string;
|
|
}
|
|
/* non-0 exponent */
|
|
|
|
e=0; // assume no E
|
|
pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]
|
|
// [here, pre-exp is the digits count (==1 for zero)]
|
|
|
|
if (exp>0 || pre<-5) { // need exponential form
|
|
e=pre-1; // calculate E value
|
|
pre=1; // assume one digit before '.'
|
|
if (e!=0) { // engineering: may need to adjust
|
|
Int adj; // adjustment
|
|
// The C remainder operator is undefined for negative numbers, so
|
|
// a positive remainder calculation must be used here
|
|
if (e<0) {
|
|
adj=(-e)%3;
|
|
if (adj!=0) adj=3-adj;
|
|
}
|
|
else { // e>0
|
|
adj=e%3;
|
|
}
|
|
e=e-adj;
|
|
// if dealing with zero still produce an exponent which is a
|
|
// multiple of three, as expected, but there will only be the
|
|
// one zero before the E, still. Otherwise note the padding.
|
|
if (!DFISZERO(df)) pre+=adj;
|
|
else { // is zero
|
|
if (adj!=0) { // 0.00Esnn needed
|
|
e=e+3;
|
|
pre=-(2-adj);
|
|
}
|
|
} // zero
|
|
} // engineering adjustment
|
|
} // exponential form
|
|
// printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp);
|
|
|
|
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
|
|
if (pre>0) { // ddd.ddd (plain), perhaps with E
|
|
// or dd00 padding for engineering
|
|
char *dotat=cstart+pre;
|
|
if (dotat<c) { // if embedded dot needed...
|
|
// move by fours; there must be space for junk at the end
|
|
// because there is still space for exponent
|
|
s=dotat+ROUNDDOWN4(c-dotat); // source
|
|
t=s+1; // target
|
|
// open the gap [cannot use memcpy]
|
|
for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
|
|
*dotat='.';
|
|
c++; // length increased by one
|
|
} // need dot?
|
|
else for (; c<dotat; c++) *c='0'; // pad for engineering
|
|
} // pre>0
|
|
else {
|
|
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have
|
|
E, but only for 0.00E+3 kind of case -- with plenty of spare
|
|
space in this case */
|
|
pre=-pre+2; // gap width, including "0."
|
|
t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point
|
|
// backoff if too far to the right
|
|
if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit
|
|
// now shift the entire coefficient to the right, being careful not
|
|
// to access to the left of string [cannot use memcpy]
|
|
for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
|
|
// for Quads and Singles there may be a character or two left...
|
|
s+=3; // where next would come from
|
|
for(; s>=cstart; s--, t--) *(t+3)=*(s);
|
|
// now have fill 0. through 0.00000; use overlaps to avoid tests
|
|
if (pre>=4) {
|
|
memcpy(cstart+pre-4, "0000", 4);
|
|
memcpy(cstart, "0.00", 4);
|
|
}
|
|
else { // 2 or 3
|
|
*(cstart+pre-1)='0';
|
|
memcpy(cstart, "0.", 2);
|
|
}
|
|
c+=pre; // to end
|
|
}
|
|
|
|
// finally add the E-part, if needed; it will never be 0, and has
|
|
// a maximum length of 3 or 4 digits (asserted above)
|
|
if (e!=0) {
|
|
memcpy(c, "E+", 2); // starts with E, assume +
|
|
c++;
|
|
if (e<0) {
|
|
*c='-'; // oops, need '-'
|
|
e=-e; // uInt, please
|
|
}
|
|
c++;
|
|
// Three-character exponents are easy; 4-character a little trickier
|
|
#if DECEMAXD<=3
|
|
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
|
|
// copy fixed 4 characters [is safe], starting at non-zero
|
|
// and with character mask to convert BCD to char
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
|
|
c+=*(u+3); // bump pointer appropriately
|
|
#elif DECEMAXD==4
|
|
if (e<1000) { // 3 (or fewer) digits case
|
|
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
|
|
c+=*(u+3); // bump pointer appropriately
|
|
}
|
|
else { // 4-digits
|
|
Int thou=((e>>3)*1049)>>17; // e/1000
|
|
Int rem=e-(1000*thou); // e%1000
|
|
*c++=(char)('0'+(char)thou); // the thousands digit
|
|
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u)|CHARMASK);// copy fixed 3+1 characters [is safe]
|
|
c+=3; // bump pointer, always 3 digits
|
|
}
|
|
#endif
|
|
}
|
|
*c='\0'; // terminate
|
|
//printf("res %s\n", string);
|
|
return string;
|
|
} // decFloatToEngString
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatToPacked -- convert decFloat to Packed decimal + exponent */
|
|
/* */
|
|
/* df is the source decFloat */
|
|
/* exp will be set to the unbiased exponent, q, or to a special */
|
|
/* value in the form returned by decFloatGetExponent */
|
|
/* packed is where DECPMAX nibbles will be written with the sign as */
|
|
/* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */
|
|
/* of zero, and an infinity is all zeros. decDouble and decQuad */
|
|
/* have a additional leading zero nibble, leading to result */
|
|
/* lengths of 4, 9, and 18 bytes. */
|
|
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
|
|
/* 0 otherwise) */
|
|
/* */
|
|
/* No error is possible, and no status will be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) {
|
|
uByte bcdar[DECPMAX+2]; // work buffer
|
|
uByte *ip=bcdar, *op=packed; // work pointers
|
|
if (DFISINF(df)) {
|
|
memset(bcdar, 0, DECPMAX+2);
|
|
*exp=DECFLOAT_Inf;
|
|
}
|
|
else {
|
|
GETCOEFF(df, bcdar+1); // use macro
|
|
if (DFISNAN(df)) {
|
|
bcdar[1]=0; // MSD needs clearing
|
|
*exp=DFWORD(df, 0)&0x7e000000;
|
|
}
|
|
else { // finite
|
|
*exp=GETEXPUN(df);
|
|
}
|
|
}
|
|
// now pack; coefficient currently at bcdar+1
|
|
#if SINGLE
|
|
ip++; // ignore first byte
|
|
#else
|
|
*ip=0; // need leading zero
|
|
#endif
|
|
// set final byte to Packed BCD sign value
|
|
bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS);
|
|
// pack an even number of bytes...
|
|
for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) {
|
|
*op=(uByte)((*ip<<4)+*(ip+1));
|
|
}
|
|
return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0);
|
|
} // decFloatToPacked
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatToString -- conversion to numeric string */
|
|
/* */
|
|
/* df is the decFloat format number to convert */
|
|
/* string is the string where the result will be laid out */
|
|
/* */
|
|
/* string must be at least DECPMAX+9 characters (the worst case is */
|
|
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
|
|
/* DECEMAXD<=4); this condition is asserted above */
|
|
/* */
|
|
/* No error is possible, and no status will be set */
|
|
/* ------------------------------------------------------------------ */
|
|
char * decFloatToString(const decFloat *df, char *string){
|
|
uInt msd; // coefficient MSD
|
|
Int exp; // exponent top two bits or full
|
|
uInt comb; // combination field
|
|
char *cstart; // coefficient start
|
|
char *c; // output pointer in string
|
|
char *s, *t; // .. (source, target)
|
|
Int pre, e; // work
|
|
const uByte *u; // ..
|
|
uInt uiwork; // for macros [one compiler needs
|
|
// volatile here to avoid bug, but
|
|
// that doubles execution time]
|
|
|
|
// Source words; macro handles endianness
|
|
uInt sourhi=DFWORD(df, 0); // word with sign
|
|
#if DECPMAX==16
|
|
uInt sourlo=DFWORD(df, 1);
|
|
#elif DECPMAX==34
|
|
uInt sourmh=DFWORD(df, 1);
|
|
uInt sourml=DFWORD(df, 2);
|
|
uInt sourlo=DFWORD(df, 3);
|
|
#endif
|
|
|
|
c=string; // where result will go
|
|
if (((Int)sourhi)<0) *c++='-'; // handle sign
|
|
comb=sourhi>>26; // sign+combination field
|
|
msd=DECCOMBMSD[comb]; // decode the combination field
|
|
exp=DECCOMBEXP[comb]; // ..
|
|
|
|
if (!EXPISSPECIAL(exp)) { // finite
|
|
// complete exponent; top two bits are in place
|
|
exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias
|
|
}
|
|
else { // IS special
|
|
if (exp==DECFLOAT_Inf) { // infinity
|
|
strcpy(c, "Infinity");
|
|
return string; // easy
|
|
}
|
|
if (sourhi&0x02000000) *c++='s'; // sNaN
|
|
strcpy(c, "NaN"); // complete word
|
|
c+=3; // step past
|
|
// quick exit if the payload is zero
|
|
#if DECPMAX==7
|
|
if ((sourhi&0x000fffff)==0) return string;
|
|
#elif DECPMAX==16
|
|
if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
|
|
#elif DECPMAX==34
|
|
if (sourlo==0 && sourml==0 && sourmh==0
|
|
&& (sourhi&0x00003fff)==0) return string;
|
|
#endif
|
|
// otherwise drop through to add integer; set correct exp etc.
|
|
exp=0; msd=0; // setup for following code
|
|
}
|
|
|
|
/* convert the digits of the significand to characters */
|
|
cstart=c; // save start of coefficient
|
|
if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit
|
|
|
|
// Decode the declets. After extracting each declet, it is
|
|
// decoded to a 4-uByte sequence by table lookup; the four uBytes
|
|
// are the three encoded BCD8 digits followed by a 1-byte length
|
|
// (significant digits, except that 000 has length 0). This allows
|
|
// us to left-align the first declet with non-zero content, then
|
|
// the remaining ones are full 3-char length. Fixed-length copies
|
|
// are used because variable-length memcpy causes a subroutine call
|
|
// in at least two compilers. (The copies are length 4 for speed
|
|
// and are safe because the last item in the array is of length
|
|
// three and has the length byte following.)
|
|
#define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
|
|
if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
|
|
else if (*(u+3)) { \
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
|
|
|
|
#if DECPMAX==7
|
|
dpd2char(sourhi>>10); // declet 1
|
|
dpd2char(sourhi); // declet 2
|
|
|
|
#elif DECPMAX==16
|
|
dpd2char(sourhi>>8); // declet 1
|
|
dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2
|
|
dpd2char(sourlo>>20); // declet 3
|
|
dpd2char(sourlo>>10); // declet 4
|
|
dpd2char(sourlo); // declet 5
|
|
|
|
#elif DECPMAX==34
|
|
dpd2char(sourhi>>4); // declet 1
|
|
dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2
|
|
dpd2char(sourmh>>16); // declet 3
|
|
dpd2char(sourmh>>6); // declet 4
|
|
dpd2char((sourmh<<4) | (sourml>>28)); // declet 5
|
|
dpd2char(sourml>>18); // declet 6
|
|
dpd2char(sourml>>8); // declet 7
|
|
dpd2char((sourml<<2) | (sourlo>>30)); // declet 8
|
|
dpd2char(sourlo>>20); // declet 9
|
|
dpd2char(sourlo>>10); // declet 10
|
|
dpd2char(sourlo); // declet 11
|
|
#endif
|
|
|
|
if (c==cstart) *c++='0'; // all zeros, empty -- make "0"
|
|
|
|
//[This fast path is valid but adds 3-5 cycles to worst case length]
|
|
//if (exp==0) { // integer or NaN case -- easy
|
|
// *c='\0'; // terminate
|
|
// return string;
|
|
// }
|
|
|
|
e=0; // assume no E
|
|
pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]
|
|
// [here, pre-exp is the digits count (==1 for zero)]
|
|
|
|
if (exp>0 || pre<-5) { // need exponential form
|
|
e=pre-1; // calculate E value
|
|
pre=1; // assume one digit before '.'
|
|
} // exponential form
|
|
|
|
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
|
|
if (pre>0) { // ddd.ddd (plain), perhaps with E
|
|
char *dotat=cstart+pre;
|
|
if (dotat<c) { // if embedded dot needed...
|
|
// [memmove is a disaster, here]
|
|
// move by fours; there must be space for junk at the end
|
|
// because exponent is still possible
|
|
s=dotat+ROUNDDOWN4(c-dotat); // source
|
|
t=s+1; // target
|
|
// open the gap [cannot use memcpy]
|
|
for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
|
|
*dotat='.';
|
|
c++; // length increased by one
|
|
} // need dot?
|
|
|
|
// finally add the E-part, if needed; it will never be 0, and has
|
|
// a maximum length of 3 or 4 digits (asserted above)
|
|
if (e!=0) {
|
|
memcpy(c, "E+", 2); // starts with E, assume +
|
|
c++;
|
|
if (e<0) {
|
|
*c='-'; // oops, need '-'
|
|
e=-e; // uInt, please
|
|
}
|
|
c++;
|
|
// Three-character exponents are easy; 4-character a little trickier
|
|
#if DECEMAXD<=3
|
|
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
|
|
// copy fixed 4 characters [is safe], starting at non-zero
|
|
// and with character mask to convert BCD to char
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
|
|
c+=*(u+3); // bump pointer appropriately
|
|
#elif DECEMAXD==4
|
|
if (e<1000) { // 3 (or fewer) digits case
|
|
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
|
|
c+=*(u+3); // bump pointer appropriately
|
|
}
|
|
else { // 4-digits
|
|
Int thou=((e>>3)*1049)>>17; // e/1000
|
|
Int rem=e-(1000*thou); // e%1000
|
|
*c++=(char)('0'+(char)thou); // the thousands digit
|
|
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]
|
|
c+=3; // bump pointer, always 3 digits
|
|
}
|
|
#endif
|
|
}
|
|
*c='\0'; // add terminator
|
|
//printf("res %s\n", string);
|
|
return string;
|
|
} // pre>0
|
|
|
|
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
|
|
// Surprisingly, this is close to being the worst-case path, so the
|
|
// shift is done by fours; this is a little tricky because the
|
|
// rightmost character to be written must not be beyond where the
|
|
// rightmost terminator could be -- so backoff to not touch
|
|
// terminator position if need be (this can make exact alignments
|
|
// for full Doubles, but in some cases needs care not to access too
|
|
// far to the left)
|
|
|
|
pre=-pre+2; // gap width, including "0."
|
|
t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point
|
|
// backoff if too far to the right
|
|
if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit
|
|
// now shift the entire coefficient to the right, being careful not
|
|
// to access to the left of string [cannot use memcpy]
|
|
for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
|
|
// for Quads and Singles there may be a character or two left...
|
|
s+=3; // where next would come from
|
|
for(; s>=cstart; s--, t--) *(t+3)=*(s);
|
|
// now have fill 0. through 0.00000; use overlaps to avoid tests
|
|
if (pre>=4) {
|
|
memcpy(cstart+pre-4, "0000", 4);
|
|
memcpy(cstart, "0.00", 4);
|
|
}
|
|
else { // 2 or 3
|
|
*(cstart+pre-1)='0';
|
|
memcpy(cstart, "0.", 2);
|
|
}
|
|
*(c+pre)='\0'; // terminate
|
|
return string;
|
|
} // decFloatToString
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatToWider -- conversion to next-wider format */
|
|
/* */
|
|
/* source is the decFloat format number which gets the result of */
|
|
/* the conversion */
|
|
/* wider is the decFloatWider format number which will be narrowed */
|
|
/* returns wider */
|
|
/* */
|
|
/* Widening is always exact; no status is set (sNaNs are copied and */
|
|
/* do not signal). The result will be canonical if the source is, */
|
|
/* and may or may not be if the source is not. */
|
|
/* ------------------------------------------------------------------ */
|
|
// widening is not possible for decQuad format numbers; simply omit
|
|
#if !QUAD
|
|
decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) {
|
|
uInt msd;
|
|
|
|
/* Construct and copy the sign word */
|
|
if (DFISSPECIAL(source)) {
|
|
// copy sign, combination, and first bit of exponent (sNaN selector)
|
|
DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000;
|
|
msd=0;
|
|
}
|
|
else { // is finite number
|
|
uInt exp=GETEXPUN(source)+DECWBIAS; // get unbiased exponent and rebias
|
|
uInt code=(exp>>DECWECONL)<<29; // set two bits of exp [msd=0]
|
|
code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; // add exponent continuation
|
|
code|=DFWORD(source, 0)&0x80000000; // add sign
|
|
DFWWORD(wider, 0)=code; // .. and place top word in wider
|
|
msd=GETMSD(source); // get source coefficient MSD [0-9]
|
|
}
|
|
/* Copy the coefficient and clear any 'unused' words to left */
|
|
#if SINGLE
|
|
DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20);
|
|
#elif DOUBLE
|
|
DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18);
|
|
DFWWORD(wider, 3)=DFWORD(source, 1);
|
|
DFWWORD(wider, 1)=0;
|
|
#endif
|
|
return wider;
|
|
} // decFloatToWider
|
|
#endif
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatVersion -- return package version string */
|
|
/* */
|
|
/* returns a constant string describing this package */
|
|
/* ------------------------------------------------------------------ */
|
|
const char *decFloatVersion(void) {
|
|
return DECVERSION;
|
|
} // decFloatVersion
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decFloatZero -- set to canonical (integer) zero */
|
|
/* */
|
|
/* df is the decFloat format number to integer +0 (q=0, c=+0) */
|
|
/* returns df */
|
|
/* */
|
|
/* No error is possible, and no status can be set. */
|
|
/* ------------------------------------------------------------------ */
|
|
decFloat * decFloatZero(decFloat *df){
|
|
DFWORD(df, 0)=ZEROWORD; // set appropriate top word
|
|
#if DOUBLE || QUAD
|
|
DFWORD(df, 1)=0;
|
|
#if QUAD
|
|
DFWORD(df, 2)=0;
|
|
DFWORD(df, 3)=0;
|
|
#endif
|
|
#endif
|
|
// decFloatShow(df, "zero");
|
|
return df;
|
|
} // decFloatZero
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* Private generic function (not format-specific) for development use */
|
|
/* ------------------------------------------------------------------ */
|
|
// This is included once only, for all to use
|
|
#if QUAD && (DECCHECK || DECTRACE)
|
|
/* ---------------------------------------------------------------- */
|
|
/* decShowNum -- display bcd8 number in debug form */
|
|
/* */
|
|
/* num is the bcdnum to display */
|
|
/* tag is a string to label the display */
|
|
/* ---------------------------------------------------------------- */
|
|
void decShowNum(const bcdnum *num, const char *tag) {
|
|
const char *csign="+"; // sign character
|
|
uByte *ub; // work
|
|
uInt uiwork; // for macros
|
|
if (num->sign==DECFLOAT_Sign) csign="-";
|
|
|
|
printf(">%s> ", tag);
|
|
if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign);
|
|
else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign);
|
|
else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign);
|
|
else { // finite
|
|
char qbuf[10]; // for right-aligned q
|
|
char *c; // work
|
|
const uByte *u; // ..
|
|
Int e=num->exponent; // .. exponent
|
|
strcpy(qbuf, "q=");
|
|
c=&qbuf[2]; // where exponent will go
|
|
// lay out the exponent
|
|
if (e<0) {
|
|
*c++='-'; // add '-'
|
|
e=-e; // uInt, please
|
|
}
|
|
#if DECEMAXD>4
|
|
#error Exponent form is too long for ShowNum to lay out
|
|
#endif
|
|
if (e==0) *c++='0'; // 0-length case
|
|
else if (e<1000) { // 3 (or fewer) digits case
|
|
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
|
|
c+=*(u+3); // bump pointer appropriately
|
|
}
|
|
else { // 4-digits
|
|
Int thou=((e>>3)*1049)>>17; // e/1000
|
|
Int rem=e-(1000*thou); // e%1000
|
|
*c++=(char)('0'+(char)thou); // the thousands digit
|
|
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
|
|
UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]
|
|
c+=3; // bump pointer, always 3 digits
|
|
}
|
|
*c='\0'; // add terminator
|
|
printf("%7s c=%s", qbuf, csign);
|
|
}
|
|
|
|
if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) {
|
|
for (ub=num->msd; ub<=num->lsd; ub++) { // coefficient...
|
|
printf("%1x", *ub);
|
|
if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); // 4-space
|
|
}
|
|
}
|
|
printf("\n");
|
|
} // decShowNum
|
|
#endif
|