/* @(#)base_conversion.h 1.1 94/10/31 SMI */ /* * Copyright (c) 1988 by Sun Microsystems, Inc. */ #include #include #ifdef DEBUG #include #include #endif /* Sun floating-point PRIVATE include file. */ /* PRIVATE MACROS */ #ifdef DEBUG #define PRIVATE #else #define PRIVATE static #endif /* PRIVATE CONSTANTS */ #define SINGLE_BIAS 127 #define DOUBLE_BIAS 1023 #define EXTENDED_BIAS 16383 #define QUAD_BIAS 16383 #define SINGLE_MAXE 97 /* Maximum decimal exponent we need to * consider. */ #define DOUBLE_MAXE 771 /* Maximum decimal exponent we need to * consider. */ #define EXTENDED_MAXE 12330 /* Maximum decimal exponent we need to * consider. */ #define QUAD_MAXE 12330 /* Maximum decimal exponent we need to * consider. */ #define UNPACKED_SIZE 5 /* Size of unpacked significand. */ /* PRIVATE TYPES */ typedef struct { /* Unpack floating-point internal format. *//* V * alue is 0.s0s1..sn * 2**(1+exponent) */ int sign; enum fp_class_type fpclass; int exponent; /* Unbiased exponent. */ unsigned significand[UNPACKED_SIZE]; /* Last word is round * and sticky. */ } unpacked; #ifdef i386 typedef struct { /* Most significant word formats. */ unsigned significand:23; unsigned exponent:8; unsigned sign:1; } single_msw; typedef struct { unsigned significand:20; unsigned exponent:11; unsigned sign:1; } double_msw; typedef struct { unsigned exponent:15; unsigned sign:1; unsigned unused:16; } extended_msw; typedef struct { unsigned significand:16; unsigned exponent:15; unsigned sign:1; } quadruple_msw; typedef struct { /* Floating-point formats in detail. */ single_msw msw; } single_formatted; typedef struct { unsigned significand2; double_msw msw; } double_formatted; typedef struct { unsigned significand2; unsigned significand; extended_msw msw; } extended_formatted; typedef struct { unsigned significand4; unsigned significand3; unsigned significand2; quadruple_msw msw; } quadruple_formatted; #else typedef struct { /* Most significant word formats. */ unsigned sign:1; unsigned exponent:8; unsigned significand:23; } single_msw; typedef struct { unsigned sign:1; unsigned exponent:11; unsigned significand:20; } double_msw; typedef struct { unsigned sign:1; unsigned exponent:15; unsigned unused:16; } extended_msw; typedef struct { unsigned sign:1; unsigned exponent:15; unsigned significand:16; } quadruple_msw; typedef struct { /* Floating-point formats in detail. */ single_msw msw; } single_formatted; typedef struct { double_msw msw; unsigned significand2; } double_formatted; typedef struct { extended_msw msw; unsigned significand; unsigned significand2; } extended_formatted; typedef struct { quadruple_msw msw; unsigned significand2; unsigned significand3; unsigned significand4; } quadruple_formatted; #endif typedef union { /* Floating-point formats equivalenced. */ single_formatted f; single x; } single_equivalence; typedef union { double_formatted f; double x; } double_equivalence; typedef union { extended_formatted f; extended x; } extended_equivalence; typedef union { quadruple_formatted f; quadruple x; } quadruple_equivalence; /* PRIVATE GLOBAL VARIABLES */ fp_exception_field_type _fp_current_exceptions; /* Current floating-point * exceptions. */ enum fp_direction_type _fp_current_direction; /* Current rounding direction. */ enum fp_precision_type _fp_current_precision; /* Current rounding precision. */ /* PRIVATE FUNCTIONS */ extern void _fp_normalize( /* pu */ ); /* unpacked *pu ; /* unpacked operand and result */ extern void _fp_leftshift( /* pu, n */ ); /* * unpacked *pu; unsigned n; */ extern void _fp_set_exception( /* ex */ ); /* enum fp_exception_type ex ; /* exception to be set in curexcep */ /* * Default size for _big_float - suitable for single and double precision. */ #define _BIG_FLOAT_SIZE (DECIMAL_STRING_LENGTH/2) #define _BIG_FLOAT_DIGIT short unsigned /* big_float significand type */ #define _INTEGER_SIZE 4932 /* Maximum number of integer digits in a * representable extended or quad. */ typedef struct { /* Variable-precision floating-point type * used for intermediate results. */ unsigned short bsize; /* Maximum allowable logical length of * significand. */ unsigned short blength;/* Logical length of significand. */ short int bexponent; /* Exponent to be attached to least * significant word of significand. * exponent >= 0 implies all integer, * with decimal point to right of * least significant word of * significand, and is equivalent to * number of omitted trailing zeros * of significand. -length < exponent * < 0 implies decimal point within * significand. exponent = -length * implies decimal point to left of * most significand word. exponent < * -length implies decimal point to * left of most significant word with * -length-exponent leading zeros. */ /* * NOTE: bexponent represents a power of 2 or 10, even though big * digits are powers of 2**16 or 10**4. */ _BIG_FLOAT_DIGIT bsignificand[_BIG_FLOAT_SIZE]; /* * Significand of digits in base 10**4 or 2**16. significand[0] is * least significant, significand[length-1] is most significant. */ } _big_float; #define BIG_FLOAT_TIMES_NOMEM (_big_float *)0 #define BIG_FLOAT_TIMES_TOOBIG (_big_float *)1 /* Internal functions defined in base conversion support routines. */ extern void _multiply_base_ten(); extern void _multiply_base_two_carry(); extern void _multiply_base_ten_by_two(); extern void _multiply_base_two(); extern void _multiply_base_two_by_two(); extern void _carry_propagate_two(); extern void _carry_propagate_ten(); extern void _multiply_base_two_vector(); extern void _multiply_base_ten_vector(); extern void _fourdigitsquick(); extern void _unpacked_to_big_float(); extern void _big_binary_to_big_decimal(); extern void _left_shift_base_ten(); extern void _left_shift_base_two(); extern void _right_shift_base_two(); extern void _free_big_float(); extern void _base_conversion_abort(); extern void _display_big_float(); extern void _integerstring_to_big_decimal(); extern void _fractionstring_to_big_decimal(); extern void _big_decimal_to_big_binary(); extern void _fp_rightshift(); extern void _fp_leftshift(); extern void _fp_normalize(); extern void _pack_single(); extern void _pack_double(); extern void _pack_extended(); extern void _pack_quadruple(); extern void _unpack_single(); extern void _unpack_double(); extern void _unpack_extended(); extern void _unpack_quadruple(); extern void _unpacked_to_decimal(); extern enum fp_class_type _class_single(); extern enum fp_class_type _class_double(); extern enum fp_class_type _class_extended(); extern enum fp_class_type _class_quadruple(); /* Fundamental utilities that multiply or add two shorts into a unsigned long, sometimes add an unsigned long carry, compute quotient and remainder in underlying base, and return quo<<16 | rem as a unsigned long. */ extern unsigned long _umac(); /* p = x * y + c ; return p */ /* extern unsigned long _prodc_b65536(); /* p = x * y + c ; return p */ #define _prodc_b65536(x,y,c) (_umac((x),(y),(c))) extern unsigned long _prodc_b10000(); /* p = x * y + c ; return (p/10000 << extern unsigned long _prod_b65536(); /* p = x * y ; return p */ extern unsigned long _prod_b10000(); /* p = x * y ; return (p/10000 << 16 | p%10000) */ extern unsigned long _prod_10000_b65536(); /* p = x * 10000 + c ; return * p */ extern unsigned long _prod_65536_b10000(); /* p = x * 65536 + c ; return * (p/10000 << 16 | p%10000) */ /* extern unsigned long _rshift_b65536(); /* p = x << n + c<<16 ; return p */ #define _rshift_b65536(x,n,c) ((((unsigned long) (x)) << (16-(n))) + ((c)<<16)) /* extern unsigned long _lshift_b65536(); /* p = x << n + c ; return p */ #define _lshift_b65536(x,n,c) ((((unsigned long) (x)) << (n)) + (c)) extern unsigned long _lshift_b10000(); /* p = x << n + c ; return (p/10000 * << 16 | p%10000) */ /* extern unsigned long _carry_in_b65536(); /* p = x + c ; return p */ #define _carry_in_b65536(x,c) ((x) + (c)) extern unsigned long _carry_in_b10000(); /* p = x + c ; return * (p/10000 << 16 | p%10000) */ /* extern unsigned long _carry_out_b65536(); /* p = c ; return p */ #define _carry_out_b65536(c) (c) extern unsigned long _carry_out_b10000(); /* p = c ; return (p/10000 << * 16 | p%10000) */ /* * Header file for revised "fast" base conversion based upon table look-up * methods. */ extern void _big_float_times_power( #ifdef notdef /* function to multiply a big_float times a positive power of two or ten. */ _big_float * pbf; /* Operand x, to be replaced * by the product x * mult ** * n. */ int mult; /* if mult is two, x is base 10**4; if mult * is ten, x is base 2**16 */ int n; int precision; /* Number of bits of precision * ultimately required (mult=10) or * number of digits of precision * ultimately required (mult=2). * Extra bits are allowed internally * to permit correct rounding. */ _big_float **pnewbf; /* Return result *pnewbf is set to: pbf f * uneventful: *pbf holds the product ; * BIG_FLOAT_TIMES_TOOBIG if n is * bigger than the tables permit ; * BIG_FLOAT_TIMES_NOMEM if * pbf->blength was insufficient to hold the * product, and malloc failed to produce a * new block ; &newbf if * pbf->blength was insufficient to hold the * product, and a new _big_float was * allocated by malloc. newbf holds the * product. It's the caller's responsibility * to free this space when no longer needed. */ #endif ); /* Variables defined in _small_powers.c and _big_powers.c */ /* Used in base conversion. */ /* * The run-time structure consists of two large tables of powers - either * powers of 10**4 in base 2**16 or vice versa. * * Suppose it's powers of T in base B. Then * * _tiny_powers_T contains TTINY entries, T**0, T**1, ... T**TTINY-1 where * T is 2 or 10, TTINY is 16 or 4 _small_powers_T contains TSMALL * entries, T**0, T**1, ... T**TSMALL-1 where T is 2**TTINY or 10**TTINY * _big_powers_T contains TBIG entries, T**0, T**1, ... T**TBIG-1 * where T is (2**TTINY)**TSMALL or (10**TTINY)**TSMALL * * so that any power of T from 0 to T**(TTINY*TSMALL*TBIG-1) can be represented * as a product of just two table entries. Since the powers vary greatly in * size, the tables are condensed to exclude leading and trailing zeros. The * following tables * * _max_tiny_powers_T contains one entry, TTINY * _start_tiny_powers_T contains TTINY entries * _leading_zeros_tiny_powers_T contains TTINY entries * _max_small_powers_T contains one entry, TSMALL * _start_small_powers_T contains TSMALL entries * _leading_zeros_small_powers_T contains TSMALL entries * _max_big_powers_T contains one entry, TBIG * _start_big_powers_T contains TBIG entries * _leading_zeros_big_powers_T contains TBIG entries * * The powers are maintained with x[start] less significant than x[start+1], so * * The powers are maintained with x[start] less significant than x[start+1], so * that the interpretation of a _small_powers_T entry is that * T**i = (B**leading_zeros[i]) * (x[start[i]] + x[start[i]+1] * B + ... * x[start[i+1]-1] * B**(start[i+1]-start[i]) ) * * where B = (2 or 10)**TTINY * * The powers are listed consecutively in the tables, with start index and * leading zero information retained and printed out at the end. * */ extern unsigned short _max_tiny_powers_ten; extern unsigned short _tiny_powers_ten[]; extern unsigned short _start_tiny_powers_ten[]; extern unsigned short _leading_zeros_tiny_powers_ten[]; extern unsigned short _max_tiny_powers_two; extern unsigned short _tiny_powers_two[]; extern unsigned short _start_tiny_powers_two[]; extern unsigned short _max_small_powers_ten; extern unsigned short _small_powers_ten[]; extern unsigned short _start_small_powers_ten[]; extern unsigned short _leading_zeros_small_powers_ten[]; extern unsigned short _max_small_powers_two; extern unsigned short _small_powers_two[]; extern unsigned short _start_small_powers_two[]; extern unsigned short _max_big_powers_ten; extern unsigned short _big_powers_ten[]; extern unsigned short _start_big_powers_ten[]; extern unsigned short _leading_zeros_big_powers_ten[]; extern unsigned short _max_big_powers_two; extern unsigned short _big_powers_two[]; extern unsigned short _start_big_powers_two[];