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arith.c
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arith.c
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/* Copyright 2010-2024
* Kaz Kylheku <kaz@kylheku.com>
* Vancouver, Canada
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>
#include <string.h>
#include <wctype.h>
#include <wchar.h>
#include <math.h>
#include <signal.h>
#include <ctype.h>
#include <float.h>
#include "config.h"
#if HAVE_ROUNDING_CTL_H
#include <fenv.h>
#endif
#include "alloca.h"
#include "lib.h"
#include "signal.h"
#include "unwind.h"
#include "gc.h"
#include "args.h"
#include "eval.h"
#include "itypes.h"
#include "struct.h"
#include "txr.h"
#include "psquare.h"
#include "autoload.h"
#include "arith.h"
#define max(a, b) ((a) > (b) ? (a) : (b))
#define ABS(A) ((A) < 0 ? -(A) : (A))
val plus_s, minus_s, inv_minus_s, neg_s, abs_s, signum_s;
val mul_s, div_s, recip_s, inv_div_s;
val trunc1_s, trunc_s, r_trunc_s, mod_s, r_mod_s;
val zerop_s, plusp_s, minusp_s, evenp_s, oddp_s;
val gt_s, lt_s, ge_s, le_s, numeq_s;
val expt_s, r_expt_s, exptmod_s, isqrt_s, square_s;
val floor_s, floor1_s, r_floor_s;
val ceil_s, ceil1_s, r_ceil_s;
val round_s, round1_s, r_round_s;
val sin_s, cos_s, tan_s, asin_s, acos_s, atan_s, atan2_s, r_atan2_s;
val sinh_s, cosh_s, tanh_s, asinh_s, acosh_s, atanh_s;
val log_s, log2_s, log10_s, exp_s, sqrt_s;
val logand_s, logior_s, logxor_s;
val lognot1_s, lognot_s, r_lognot_s, logtrunc_s, r_logtrunc_s;
val sign_extend_s, ash_s, bit_s, width_s, bitset_s, logcount_s;
val cbrt_s, erf_s, erfc_s, exp10_s, exp2_s, expm1_s;
val gamma_s, j0_s, j1_s, lgamma_s, log1p_s, logb_s;
val nearbyint_s, rint_s, significand_s, tgamma_s, y0_s, y1_s;
val copysign_s, drem_s, fdim_s, fmax_s, fmin_s, hypot_s;
val jn_s, ldexp_s, nextafter_s, remainder_s, scalb_s;
val scalbln_s, yn_s;
val r_copysign_s, r_drem_s, r_fdim_s, r_fmax_s, r_fmin_s, r_hypot_s;
val r_jn_s, r_ldexp_s, r_nextafter_s, r_remainder_s, r_scalb_s;
val r_scalbln_s, r_yn_s;
val tofloat_s, toint_s;
val quant_state_s;
static struct cobj_class *quant_cls;
val make_bignum(void)
{
val n = make_obj();
n->bn.type = BGNUM;
mp_init(&n->bn.mp);
return n;
}
static val make_ubignum(void)
{
val n = make_obj();
n->bn.type = BGNUM;
mp_init_minimal(&n->bn.mp);
return n;
}
val bignum(cnum cn)
{
val n = make_bignum();
mp_set_intptr(mp(n), cn);
return n;
}
val bignum_from_long(long l)
{
#if SIZEOF_LONG <= SIZEOF_PTR
return bignum(l);
#else
val n = make_bignum();
mp_set_int(mp(n), l);
return n;
#endif
}
val bignum_from_uintptr(uint_ptr_t u)
{
val n = make_bignum();
mp_set_uintptr(mp(n), u);
return n;
}
val num_from_buffer(mem_t *buf, int bytes)
{
val n = make_bignum();
mp_err mpe = mp_read_unsigned_bin(mp(n), buf, bytes);
if (mpe != MP_OKAY)
do_mp_error(lit("buffer to number conversion"), mpe);
return normalize(n);
}
static NORETURN void not_number(val self, val obj)
{
uw_throwf(type_error_s, lit("~a: ~s is not a number"), self, obj, nao);
}
static NORETURN void not_integer(val self, val obj)
{
uw_throwf(type_error_s, lit("~a: ~s is not an integer"), self, obj, nao);
}
int num_to_buffer(val num, mem_t *buf, int bytes)
{
switch (type(num)) {
case CHR: case NUM:
{
cnum n = c_n(num);
mem_t *ptr = buf + bytes;
for (; n != 0; n >>= 8) {
if (ptr == buf)
return 0;
*--ptr = n & 0xff;
}
while (ptr > buf)
*--ptr = 0;
}
return 1;
case BGNUM:
return mp_to_unsigned_buf(mp(num), buf, bytes) == MP_OKAY ? 1 : 0;
default:
not_integer(lit("num-to-buffer"), num);
}
}
#if HAVE_DOUBLE_INTPTR_T
val bignum_dbl_ipt(double_intptr_t di)
{
val n = make_bignum();
mp_set_double_intptr(mp(n), di);
return n;
}
val bignum_dbl_uipt(double_uintptr_t dui)
{
val n = make_bignum();
mp_set_double_uintptr(mp(n), dui);
return n;
}
#endif
val normalize(val bignum)
{
if (!mp_in_range(mp(bignum), NUM_MAX, 0)) {
return bignum;
} else {
cnum fixnum;
mp_get_intptr(mp(bignum), &fixnum);
return num(fixnum);
}
}
ucnum c_unum(val num, val self)
{
switch (type(num)) {
case CHR:
{
cnum n = c_ch(num);
if (n >= 0)
return n;
}
goto range;
case NUM:
{
cnum n = c_n(num);
if (n >= 0)
return n;
}
goto range;
case BGNUM:
if (mp_in_uintptr_range(mp(num))) {
uint_ptr_t out;
mp_get_uintptr(mp(num), &out);
return out;
}
/* fallthrough */
range:
uw_throwf(error_s, lit("~a: ~s is out of allowed range [0, ~a]"),
self, num, unum(UINT_PTR_MAX), nao);
default:
uw_throwf(type_error_s, lit("~a: ~s is not an integer"), self, num, nao);
}
}
val unum(ucnum u)
{
if (u <= INT_PTR_MAX) {
return num(u);
} else {
val n = make_bignum();
mp_set_uintptr(mp(n), u);
return n;
}
}
#if HAVE_DOUBLE_INTPTR_T
dbl_cnum c_dbl_num(val n)
{
switch (type(n)) {
case CHR:
return c_ch(n);
case NUM:
return c_n(n);
case BGNUM:
if (mp_in_double_intptr_range(mp(n))) {
double_intptr_t out;
mp_get_double_intptr(mp(n), &out);
return out;
}
uw_throwf(error_s, lit("~s is out of signed ~a bit range"),
n, num_fast(SIZEOF_DOUBLE_INTPTR * CHAR_BIT), nao);
default:
type_mismatch(lit("~s is not an integer"), n, nao);
}
}
dbl_ucnum c_dbl_unum(val n)
{
switch (type(n)) {
case CHR:
{
dbl_cnum cn = c_ch(n);
if (cn >= 0)
return cn;
break;
}
case NUM:
{
dbl_cnum cn = c_n(n);
if (cn >= 0)
return cn;
break;
}
case BGNUM:
if (mp_in_double_uintptr_range(mp(n))) {
double_uintptr_t out;
mp_get_double_uintptr(mp(n), &out);
return out;
}
break;
default:
type_mismatch(lit("~s is not an integer"), n, nao);
}
uw_throwf(error_s, lit("~s is out of unsigned ~a bit range"),
n, num_fast(SIZEOF_DOUBLE_INTPTR * CHAR_BIT), nao);
}
#endif
val bignum_len(val num)
{
switch (type(num)) {
case CHR: case NUM:
return zero;
case BGNUM:
return unum(mp(num)->used);
default:
not_integer(lit("bignum-len"), num);
}
}
int highest_bit(int_ptr_t n)
{
#if defined __GNUC__ && SIZEOF_PTR == SIZEOF_INT
return (n == 0) ? 0 : (CHAR_BIT * SIZEOF_PTR - __builtin_clz(n));
#elif defined __GNUC__ && SIZEOF_PTR == SIZEOF_LONG
return (n == 0) ? 0 : (CHAR_BIT * SIZEOF_PTR - __builtin_clzl(n));
#elif defined __GNUC__ && SIZEOF_PTR == SIZEOF_LONGLONG_T
return (n == 0) ? 0 : (CHAR_BIT * SIZEOF_PTR - __builtin_clzll(n));
#elif CHAR_BIT * SIZEOF_PTR == 64
if (n & 0x7FFFFFFF00000000) {
if (n & 0x7FFF000000000000) {
if (n & 0x7F00000000000000) {
if (n & 0x7000000000000000) {
if (n & 0x4000000000000000)
return 63;
else
return (n & 0x2000000000000000) ? 62 : 61;
} else {
if (n & 0x0C00000000000000)
return (n & 0x0800000000000000) ? 60 : 59;
else
return (n & 0x0200000000000000) ? 58 : 57;
}
} else {
if (n & 0x00F0000000000000) {
if (n & 0x00C0000000000000)
return (n & 0x0080000000000000) ? 56 : 55;
else
return (n & 0x0020000000000000) ? 54 : 53;
} else {
if (n & 0x000C000000000000)
return (n & 0x0008000000000000) ? 52 : 51;
else
return (n & 0x0002000000000000) ? 50 : 49;
}
}
} else {
if (n & 0x0000FF0000000000) {
if (n & 0x0000F00000000000) {
if (n & 0x0000C00000000000)
return (n & 0x0000800000000000) ? 48 : 47;
else
return (n & 0x0000200000000000) ? 46 : 45;
} else {
if (n & 0x00000C0000000000)
return (n & 0x0000080000000000) ? 44 : 43;
else
return (n & 0x0000020000000000) ? 42 : 41;
}
} else {
if (n & 0x000000F000000000) {
if (n & 0x000000C000000000)
return (n & 0x0000008000000000) ? 40 : 39;
else
return (n & 0x0000002000000000) ? 38 : 37;
} else {
if (n & 0x0000000C00000000)
return (n & 0x0000000800000000) ? 36 : 35;
else
return (n & 0x0000000200000000) ? 34 : 33;
}
}
}
} else {
if (n & 0x00000000FFFF0000) {
if (n & 0x00000000FF000000) {
if (n & 0x00000000F0000000) {
if (n & 0x00000000C0000000)
return (n & 0x0000000080000000) ? 32 : 31;
else
return (n & 0x0000000020000000) ? 30 : 29;
} else {
if (n & 0x000000000C000000)
return (n & 0x0000000008000000) ? 28 : 27;
else
return (n & 0x0000000002000000) ? 26 : 25;
}
} else {
if (n & 0x0000000000F00000) {
if (n & 0x0000000000C00000)
return (n & 0x0000000000800000) ? 24 : 23;
else
return (n & 0x0000000000200000) ? 22 : 21;
} else {
if (n & 0x00000000000C0000)
return (n & 0x0000000000080000) ? 20 : 19;
else
return (n & 0x0000000000020000) ? 18 : 17;
}
}
} else {
if (n & 0x000000000000FF00) {
if (n & 0x000000000000F000) {
if (n & 0x000000000000C000)
return (n & 0x0000000000008000) ? 16 : 15;
else
return (n & 0x0000000000002000) ? 14 : 13;
} else {
if (n & 0x0000000000000C00)
return (n & 0x0000000000000800) ? 12 : 11;
else
return (n & 0x0000000000000200) ? 10 : 9;
}
} else {
if (n & 0x00000000000000F0) {
if (n & 0x00000000000000C0)
return (n & 0x0000000000000080) ? 8 : 7;
else
return (n & 0x0000000000000020) ? 6 : 5;
} else {
if (n & 0x000000000000000C)
return (n & 0x0000000000000008) ? 4 : 3;
else
return (n & 0x0000000000000002) ? 2 : (n ? 1 : 0);
}
}
}
}
#elif CHAR_BIT * SIZEOF_PTR == 32
if (n & 0x7FFF0000) {
if (n & 0x7F000000) {
if (n & 0x70000000) {
if (n & 0x40000000)
return 31;
else
return (n & 0x20000000) ? 30 : 29;
} else {
if (n & 0x0C000000)
return (n & 0x08000000) ? 28 : 27;
else
return (n & 0x02000000) ? 26 : 25;
}
} else {
if (n & 0x00F00000) {
if (n & 0x00C00000)
return (n & 0x00800000) ? 24 : 23;
else
return (n & 0x00200000) ? 22 : 21;
} else {
if (n & 0x000C0000)
return (n & 0x00080000) ? 20 : 19;
else
return (n & 0x00020000) ? 18 : 17;
}
}
} else {
if (n & 0x0000FF00) {
if (n & 0x0000F000) {
if (n & 0x0000C000)
return (n & 0x00008000) ? 16 : 15;
else
return (n & 0x00002000) ? 14 : 13;
} else {
if (n & 0x00000C00)
return (n & 0x00000800) ? 12 : 11;
else
return (n & 0x00000200) ? 10 : 9;
}
} else {
if (n & 0x000000F0) {
if (n & 0x000000C0)
return (n & 0x00000080) ? 8 : 7;
else
return (n & 0x00000020) ? 6 : 5;
} else {
if (n & 0x0000000C)
return (n & 0x00000008) ? 4 : 3;
else
return (n & 0x00000002) ? 2 : (n ? 1 : 0);
}
}
}
#else
#error fixme: only 4 or 8 byte pointers supported
#endif
/* notreached */
abort();
}
static int highest_significant_bit(int_ptr_t n)
{
if (n >= 0)
return highest_bit(n);
return highest_bit(-n - 1);
}
static UNUSED NORETURN void not_available(val name)
{
uw_throwf(file_error_s, lit("~a is not available on this platform"),
name, nao);
}
void do_mp_error(val self, mp_err code)
{
val errstr = string_utf8(mp_strerror(code));
uw_throwf(numeric_error_s, lit("~a: ~a"), self, errstr, nao);
}
static NORETURN void not_struct_error(val self, val obj)
{
uw_throwf(error_s, lit("~a: ~s isn't a structure"),
self, obj, nao);
}
static NORETURN void method_error(val self, val obj, val fun)
{
uw_throwf(error_s, lit("~a: object ~s lacks ~a method"),
self, obj, fun, nao);
}
static val do_unary_method(val self, val sym, val obj)
{
val meth = maybe_slot(obj, sym);
if (!obj_struct_p(obj))
not_struct_error(self, obj);
if (!meth)
method_error(self, obj, sym);
return funcall1(meth, obj);
}
static val do_binary_method(val self, val sym, val obj, val arg)
{
val meth = maybe_slot(obj, sym);
if (!obj_struct_p(obj))
not_struct_error(self, obj);
if (!meth)
method_error(self, obj, sym);
return funcall2(meth, obj, arg);
}
static val do_ternary_method(val self, val sym, val obj, val arg1, val arg2)
{
val meth = maybe_slot(obj, sym);
if (!obj_struct_p(obj))
not_struct_error(self, obj);
if (!meth)
method_error(self, obj, sym);
return funcall3(meth, obj, arg1, arg2);
}
val plus(val anum, val bnum)
{
val self = plus_s;
tail:
switch (TAG_PAIR(tag(anum), tag(bnum))) {
case TAG_PAIR(TAG_NUM, TAG_NUM):
{
cnum a = c_n(anum);
cnum b = c_n(bnum);
cnum sum = a + b;
if (sum < NUM_MIN || sum > NUM_MAX)
return bignum(sum);
return num_fast(sum);
}
case TAG_PAIR(TAG_NUM, TAG_PTR):
switch (type(bnum)) {
case BGNUM:
{
val n;
mp_err mpe;
if (anum == zero)
return bnum;
n = make_bignum();
if (sizeof (int_ptr_t) <= sizeof (mp_digit)) {
cnum a = c_n(anum);
cnum ap = ABS(a);
if (a > 0)
mpe = mp_add_d(mp(bnum), ap, mp(n));
else
mpe = mp_sub_d(mp(bnum), ap, mp(n));
} else {
mp_int tmp;
mp_init(&tmp);
mp_set_intptr(&tmp, c_n(anum));
mpe = mp_add(mp(bnum), &tmp, mp(n));
mp_clear(&tmp);
}
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case FLNUM:
return flo(c_n(anum) + c_flo(bnum, self));
case RNG:
return rcons(plus(anum, from(bnum)), plus(anum, to(bnum)));
case COBJ:
return do_binary_method(self, self, bnum, anum);
default:
break;
}
break;
case TAG_PAIR(TAG_PTR, TAG_NUM):
switch (type(anum)) {
case BGNUM:
{
val n;
mp_err mpe;
n = make_bignum();
if (bnum == zero)
return anum;
if (sizeof (int_ptr_t) <= sizeof (mp_digit)) {
cnum b = c_n(bnum);
cnum bp = ABS(b);
if (b > 0)
mpe = mp_add_d(mp(anum), bp, mp(n));
else
mpe = mp_sub_d(mp(anum), bp, mp(n));
} else {
mp_int tmp;
mp_init(&tmp);
mp_set_intptr(&tmp, c_n(bnum));
mpe = mp_add(mp(anum), &tmp, mp(n));
mp_clear(&tmp);
}
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case FLNUM:
return flo(c_n(bnum) + c_flo(anum, self));
case RNG:
return rcons(plus(from(anum), bnum), plus(to(anum), bnum));
case COBJ:
return do_binary_method(self, self, anum, bnum);
default:
break;
}
break;
case TAG_PAIR(TAG_PTR, TAG_PTR):
switch (TYPE_PAIR(type(anum), type(bnum))) {
case TYPE_PAIR(BGNUM, BGNUM):
{
val n;
mp_err mpe;
n = make_bignum();
mpe = mp_add(mp(anum), mp(bnum), mp(n));
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case TYPE_PAIR(FLNUM, FLNUM):
return flo(c_flo(anum, self) + c_flo(bnum, self));
case TYPE_PAIR(BGNUM, FLNUM):
anum = flo_int(anum);
goto tail;
case TYPE_PAIR(FLNUM, BGNUM):
bnum = flo_int(bnum);
goto tail;
case TYPE_PAIR(RNG, RNG):
return rcons(plus(from(anum), from(bnum)), plus(to(anum), to(bnum)));
case TYPE_PAIR(BGNUM, RNG):
case TYPE_PAIR(FLNUM, RNG):
return rcons(plus(anum, from(bnum)), plus(anum, to(bnum)));
case TYPE_PAIR(RNG, BGNUM):
case TYPE_PAIR(RNG, FLNUM):
return rcons(plus(from(anum), bnum), plus(to(anum), bnum));
case TYPE_PAIR(COBJ, BGNUM):
case TYPE_PAIR(COBJ, FLNUM):
case TYPE_PAIR(COBJ, RNG):
case TYPE_PAIR(COBJ, COBJ):
return do_binary_method(self, self, anum, bnum);
case TYPE_PAIR(BGNUM, COBJ):
case TYPE_PAIR(FLNUM, COBJ):
case TYPE_PAIR(RNG, COBJ):
return do_binary_method(self, self, bnum, anum);
default:
break;
}
break;
case TAG_PAIR(TAG_CHR, TAG_NUM):
{
wchar_t a = c_ch(anum);
cnum b = c_n(bnum);
cnum sum = a + b;
if (sum < 0 || sum > 0x10FFFF)
goto char_range;
return chr(sum);
}
case TAG_PAIR(TAG_NUM, TAG_CHR):
{
cnum a = c_n(anum);
wchar_t b = c_ch(bnum);
cnum sum = a + b;
if (sum < 0 || sum > 0x10FFFF)
goto char_range;
return chr(sum);
}
case TAG_PAIR(TAG_CHR, TAG_PTR):
if (type(bnum) == RNG)
return rcons(plus(anum, from(bnum)), plus(anum, to(bnum)));
break;
case TAG_PAIR(TAG_PTR, TAG_CHR):
if (type(anum) == RNG)
return rcons(plus(from(anum), bnum), plus(to(anum), bnum));
break;
}
invalid_ops(self, anum, bnum);
char_range:
uw_throwf(numeric_error_s,
lit("~a: sum of ~s and ~s is out of character range"),
self, anum, bnum, nao);
}
val minus(val anum, val bnum)
{
val self = minus_s;
tail:
switch (TAG_PAIR(tag(anum), tag(bnum))) {
case TAG_PAIR(TAG_CHR, TAG_CHR):
{
cnum a = c_ch(anum);
cnum b = c_ch(bnum);
cnum sum = a - b;
if (sum < NUM_MIN || sum > NUM_MAX)
return bignum(sum);
return num_fast(sum);
}
case TAG_PAIR(TAG_NUM, TAG_NUM):
{
cnum a = c_n(anum);
cnum b = c_n(bnum);
cnum sum = a - b;
if (sum < NUM_MIN || sum > NUM_MAX)
return bignum(sum);
return num_fast(sum);
}
case TAG_PAIR(TAG_NUM, TAG_PTR):
switch (type(bnum)) {
case BGNUM:
{
val n;
mp_err mpe;
n = make_bignum();
if (anum == zero) {
mp_neg(mp(bnum), mp(n));
return n;
}
if (sizeof (int_ptr_t) <= sizeof (mp_digit)) {
cnum a = c_n(anum);
cnum ap = ABS(a);
if (ap > 0)
mpe = mp_sub_d(mp(bnum), ap, mp(n));
else
mpe = mp_add_d(mp(bnum), ap, mp(n));
if (mpe == MP_OKAY)
mp_neg(mp(n), mp(n));
} else {
mp_int tmp;
mp_init(&tmp);
mp_set_intptr(&tmp, c_n(anum));
mpe = mp_sub(mp(bnum), &tmp, mp(n));
mp_clear(&tmp);
}
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case FLNUM:
return flo(c_n(anum) - c_flo(bnum, self));
case RNG:
return rcons(minus(anum, from(bnum)), minus(anum, to(bnum)));
case COBJ:
return do_binary_method(self, inv_minus_s, bnum, anum);
default:
break;
}
break;
case TAG_PAIR(TAG_PTR, TAG_NUM):
switch (type(anum)) {
case BGNUM:
{
val n;
mp_err mpe;
if (bnum == zero)
return anum;
n = make_bignum();
if (sizeof (int_ptr_t) <= sizeof (mp_digit)) {
cnum b = c_n(bnum);
cnum bp = ABS(b);
if (b > 0)
mpe = mp_sub_d(mp(anum), bp, mp(n));
else
mpe = mp_add_d(mp(anum), bp, mp(n));
} else {
mp_int tmp;
mp_init(&tmp);
mp_set_intptr(&tmp, c_n(bnum));
mpe = mp_sub(mp(anum), &tmp, mp(n));
mp_clear(&tmp);
}
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case FLNUM:
return flo(c_flo(anum, self) - c_n(bnum));
case RNG:
return rcons(minus(from(anum), bnum), minus(to(anum), bnum));
case COBJ:
return do_binary_method(self, self, anum, bnum);
default:
break;
}
break;
case TAG_PAIR(TAG_PTR, TAG_PTR):
switch (TYPE_PAIR(type(anum), type(bnum))) {
case TYPE_PAIR(BGNUM, BGNUM):
{
val n;
mp_err mpe;
n = make_bignum();
mpe = mp_sub(mp(anum), mp(bnum), mp(n));
if (mpe != MP_OKAY)
do_mp_error(self, mpe);
return normalize(n);
}
case TYPE_PAIR(FLNUM, FLNUM):
return flo(c_flo(anum, self) - c_flo(bnum, self));
case TYPE_PAIR(BGNUM, FLNUM):
anum = flo_int(anum);
goto tail;
case TYPE_PAIR(FLNUM, BGNUM):
bnum = flo_int(bnum);
goto tail;
case TYPE_PAIR(RNG, RNG):
return rcons(minus(from(anum), from(bnum)), minus(to(anum), to(bnum)));
case TYPE_PAIR(BGNUM, RNG):
case TYPE_PAIR(FLNUM, RNG):
return rcons(minus(anum, from(bnum)), minus(anum, to(bnum)));
case TYPE_PAIR(RNG, BGNUM):
case TYPE_PAIR(RNG, FLNUM):
return rcons(minus(from(anum), bnum), minus(to(anum), bnum));
case TYPE_PAIR(COBJ, BGNUM):
case TYPE_PAIR(COBJ, FLNUM):
case TYPE_PAIR(COBJ, RNG):
case TYPE_PAIR(COBJ, COBJ):
return do_binary_method(self, self, anum, bnum);
case TYPE_PAIR(BGNUM, COBJ):
case TYPE_PAIR(FLNUM, COBJ):
case TYPE_PAIR(RNG, COBJ):
return do_binary_method(self, inv_minus_s, bnum, anum);
default:
break;
}
break;
case TAG_PAIR(TAG_CHR, TAG_NUM):
{
wchar_t a = c_ch(anum);
cnum b = c_n(bnum);
cnum sum = a - b;
if (sum < 0 || sum > 0x10FFFF)
uw_throwf(numeric_error_s,
lit("~a: difference of ~s and ~s is out of character range"),
self, anum, bnum, nao);
return chr(sum);
}
case TAG_PAIR(TAG_CHR, TAG_PTR):
if (type(bnum) == RNG)
return rcons(minus(anum, from(bnum)), minus(anum, to(bnum)));
break;
case TAG_PAIR(TAG_PTR, TAG_CHR):
if (type(anum) == RNG)
return rcons(minus(from(anum), bnum), minus(to(anum), bnum));
break;
}
invalid_ops(self, anum, bnum);
}
val neg(val anum)
{
val self = minus_s;
switch (type(anum)) {
case BGNUM:
{
val n = make_bignum();
mp_neg(mp(anum), mp(n));
return n;
}
case FLNUM:
return flo(-c_flo(anum, self));
case NUM:
return num(-c_n(anum));
case RNG:
return rcons(neg(from(anum)), neg(to(anum)));
case COBJ:
return do_unary_method(self, neg_s, anum);
default:
not_number(self, anum);
}
}
val abso(val anum)
{
val self = abs_s;
switch (type(anum)) {
case BGNUM:
{
val n = make_bignum();
mp_abs(mp(anum), mp(n));
return n;
}
case FLNUM:
return flo(fabs(c_flo(anum, self)));
case NUM:
{
cnum n = c_n(anum);
return num(n < 0 ? -n : n);
}
case RNG:
return rcons(abso(from(anum)), abso(to(anum)));
case COBJ:
return do_unary_method(self, self, anum);
default:
not_number(self, anum);
}
}
static val signum(val anum)
{
val self = signum_s;
switch (type(anum)) {
case BGNUM:
return if3(mp_isneg(mp(anum)), negone, one);
case FLNUM:
{
double a = c_f(anum);
return flo(if3(a > 0, 1.0, if3(a < 0, -1.0, 0.0)));
}
case NUM:
{
cnum a = c_n(anum);
return if3(a > 0, one, if3(a < 0, negone, zero));
}
case COBJ:
return do_unary_method(self, self, anum);
default:
not_number(self, anum);
}
}
val mul(val anum, val bnum)
{
val self = mul_s;
tail:
switch (TAG_PAIR(tag(anum), tag(bnum))) {
case TAG_PAIR(TAG_NUM, TAG_NUM):
{
cnum a = c_n(anum);
cnum b = c_n(bnum);
#if HAVE_DOUBLE_INTPTR_T
double_intptr_t product = a * convert(double_intptr_t, b);
if (product < NUM_MIN || product > NUM_MAX)
return bignum_dbl_ipt(product);
return num_fast(product);
#else
cnum ap = ABS(a);
cnum bp = ABS(b);
if (highest_bit(ap) + highest_bit(bp) < PTR_BIT - 1) {
cnum product = a * b;
if (product >= NUM_MIN && product <= NUM_MAX)
return num_fast(product);
return bignum(product);
} else {