dc(1): fix modulo operations with fractional inputs

Our dc(1) has never correctly calculated remainders with fractional inputs.
Both bmod and bdivmod seem to have copy/pasted code from bdiv, which results
in the remainder having the wrong output scale.

PR:		162495
Reported by:	anonymous
Reviewed by:	pfg
Differential Revision:	https://reviews.freebsd.org/D13390

usr.bin/dc/bcode.c

@@ -1096,13 +1096,13 @@ bmod(void)
 
 	r = new_number();
 	scale = max(a->scale, b->scale);
-	r->scale = max(b->scale, a->scale + bmachine.scale);
+	r->scale = scale;
 
 	if (BN_is_zero(a->number))
 		warnx("remainder by zero");
 	else {
 		normalize(a, scale);
-		normalize(b, scale + bmachine.scale);
+		normalize(b, scale);
 
 		ctx = BN_CTX_new();
 		bn_checkp(ctx);
@@ -1117,7 +1117,7 @@ bmod(void)
 static void
 bdivmod(void)
 {
-	struct number *a, *b, *rdiv, *rmod;
+	struct number *a, *b, *frac, *quotient, *rdiv, *remainder;
 	BN_CTX *ctx;
 	u_int scale;
 
@@ -1131,25 +1131,44 @@ bdivmod(void)
 	}
 
 	rdiv = new_number();
-	rmod = new_number();
-	rdiv->scale = bmachine.scale;
-	rmod->scale = max(b->scale, a->scale + bmachine.scale);
+	quotient = new_number();
+	remainder = new_number();
+	scale = max(a->scale, b->scale);
+	rdiv->scale = 0;
+	remainder->scale = scale;
+	quotient->scale = bmachine.scale;
 	scale = max(a->scale, b->scale);
 
 	if (BN_is_zero(a->number))
 		warnx("divide by zero");
 	else {
 		normalize(a, scale);
-		normalize(b, scale + bmachine.scale);
+		normalize(b, scale);
 
 		ctx = BN_CTX_new();
 		bn_checkp(ctx);
-		bn_check(BN_div(rdiv->number, rmod->number,
+		/*
+		 * Unlike other languages' divmod operations, dc is specified
+		 * to return the remainder and the full quotient, rather than
+		 * the remainder and the floored quotient.  bn(3) has no
+		 * function to calculate both.  So we'll use BN_div to get the
+		 * remainder and floored quotient, then calculate the full
+		 * quotient from those.
+		 *
+		 * quotient = rdiv + remainder / divisor
+		 */
+		bn_check(BN_div(rdiv->number, remainder->number,
 		    b->number, a->number, ctx));
+		frac = div_number(remainder, a, bmachine.scale);
+		normalize(rdiv, bmachine.scale);
+		normalize(remainder, scale);
+		bn_check(BN_add(quotient->number, rdiv->number, frac->number));
+		free_number(frac);
 		BN_CTX_free(ctx);
 	}
-	push_number(rdiv);
-	push_number(rmod);
+	push_number(quotient);
+	push_number(remainder);
+	free_number(rdiv);
 	free_number(a);
 	free_number(b);
 }

usr.bin/dc/dc.1

@@ -35,7 +35,7 @@
 .\"
 .\"	@(#)dc.1	8.1 (Berkeley) 6/6/93
 .\"
-.Dd February 27, 2017
+.Dd December 5, 2017
 .Dt DC 1
 .Os
 .Sh NAME
@@ -139,8 +139,8 @@ The two entries are popped off the stack;
 the result is pushed on the stack in their place.
 Any fractional part of an exponent is ignored.
 .Pp
-For addition and subtraction, the scale of the result is the maximum
-of scales of the operands.
+For addition, subtraction, and remainder, the scale of the result is the
+maximum of scales of the operands.
 For division the scale of the result is defined
 by the scale set by the
 .Ic k

usr.bin/dc/tests/Makefile

@@ -3,5 +3,6 @@
 PACKAGE=	tests
 
 ATF_TESTS_SH=	inout
+ATF_TESTS_SH+=	bcode
 
 .include <bsd.test.mk>

usr.bin/dc/tests/bcode.sh

@@ -0,0 +1,144 @@
+# SPDX-License-Identifier: BSD-2-Clause-FreeBSD
+#
+# Copyright (c) 2017 Alan Somers
+# 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 AUTHOR 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 AUTHOR 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.
+#
+# $FreeBSD$
+
+atf_test_case bmod
+bmod_head()
+{
+	atf_set "descr" "Tests the remainder % operator"
+}
+bmod_body()
+{
+	cat > input.dc << EOF
+0 3 % p		# basic usage
+1 3 % p
+2 3 % p
+3 3 % p
+4 3 % p
+_1 3 % p	# negative dividends work like a remainder, not a modulo
+1 _3 % p	# negative divisors use the divisor's absolute value
+1k		# fractional remainders
+5 3 % p
+6 5 % p
+5.4 3 % p
+_.1 3 % p
+1.1 _3 % p
+1 .3 % p
+EOF
+	dc input.dc > output.txt
+	cat > expect.txt << EOF
+0
+1
+2
+0
+1
+-1
+1
+2
+1
+2.4
+-.1
+1.1
+.1
+EOF
+	atf_check cmp expect.txt output.txt
+}
+
+atf_test_case bmod_by_zero
+bmod_by_zero_head()
+{
+	atf_set "descr" "remaindering by zero should print a warning"
+}
+bmod_by_zero_body()
+{
+	atf_check -e match:"remainder by zero" dc -e '1 0 %'
+}
+
+atf_test_case bdivmod
+bdivmod_head()
+{
+	atf_set "descr" "Tests the divide and modulo ~ operator"
+}
+bdivmod_body()
+{
+	cat > input.dc << EOF
+0 3 ~ n32Pp	# basic usage
+1 3 ~ n32Pp
+2 3 ~ n32Pp
+3 3 ~ n32Pp
+4 3 ~ n32Pp
+_1 3 ~ n32Pp	# negative dividends work like a remainder, not a modulo
+_4 3 ~ n32Pp	# sign of quotient and divisor must agree
+1 _3 ~ n32Pp	# negative divisors use the divisor's absolute value
+1k		# fractional remainders
+5 3 ~ n32Pp
+6 5 ~ n32Pp
+5.4 3 ~ n32Pp
+_.1 3 ~ n32Pp
+1.1 _3 ~ n32Pp
+1 .3 ~ n32Pp
+4k
+.01 .003 ~ n32Pp	# divmod quotient always has scale=0
+EOF
+	dc input.dc > output.txt
+	cat > expect.txt << EOF
+0 0
+1 0
+2 0
+0 1
+1 1
+-1 0
+-1 -1
+1 0
+2 1.6
+1 1.2
+2.4 1.8
+-.1 0.0
+1.1 -.3
+.1 3.3
+.001 3.3333
+EOF
+	atf_check cmp expect.txt output.txt
+}
+
+atf_test_case bdivmod_by_zero
+bdivmod_by_zero_head()
+{
+	atf_set "descr" "divmodding by zero should print a warning"
+}
+bdivmod_by_zero_body()
+{
+	atf_check -e match:"divide by zero" dc -e '1 0 ~'
+}
+
+atf_init_test_cases()
+{
+	atf_add_test_case bmod
+	atf_add_test_case bmod_by_zero
+	atf_add_test_case bdivmod
+	atf_add_test_case bdivmod_by_zero
+}

usr.bin/dc/tests/inout.sh

@@ -52,8 +52,8 @@ base16_input_body()
 0.1 p	# Leading zeros are ignored
 00.1 p	# Leading zeros are ignored
 EOF
-dc input.dc > output.txt
-cat > expect.txt << EOF
+	dc input.dc > output.txt
+	cat > expect.txt << EOF
 0
 16
 1