Changeset 600478d

Timestamp:

Jun 17, 2023, 6:46:20 PM (17 months ago)

Author:

Peter A. Buhr <pabuhr@…>

Branches:

master

Children:

b38f6da

Parents:

6527150

Message:

change ceiling function to work with negative values

Files:

• libcfa/src/math.hfa (modified) (3 diffs)
• tests/.expect/mathX.x64.txt (modified) (5 diffs)

libcfa/src/math.hfa

@@ -10 +10 @@
 // Created On       : Mon Apr 18 23:37:04 2016
 // Last Modified By : Peter A. Buhr
-// Last Modified On : Sat Oct  8 08:40:42 2022
-// Update Count     : 136
+// Last Modified On : Sat Jun 17 18:42:45 2023
+// Update Count     : 198
 //
 
@@ -236 +236 @@
 
         return (i << 32) + (sum);
-}
+} // log2_u32_32
 
 //---------------------- Trigonometric ----------------------
@@ -396 +396 @@
         unsigned long long int ceiling_div( unsigned long long int n, unsigned long long int align ) { return (n + (align - 1)) / align; }
 
-        // forall( T | { T ?+?( T, T ); T ?-?( T, T ); T ?%?( T, T ); } )
-        // T ceiling_div( T n, T align ) { verify( is_pow2( align ) );return (n + (align - 1)) / align; }
-
-        // gcc notices the div/mod pair and saves both so only one div.
-        signed char ceiling( signed char n, signed char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned char ceiling( unsigned char n, unsigned char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        short int ceiling( short int n, short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned short int ceiling( unsigned short int n, unsigned short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        int ceiling( int n, int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned int ceiling( unsigned int n, unsigned int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        long int ceiling( long int n, long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned long int ceiling( unsigned long int n, unsigned long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0) , align); }
-        long long int ceiling( long long int n, long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned long long int ceiling( unsigned long long int n, unsigned long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-
-        // forall( T | { void ?{}( T &, one_t ); T ?+?( T, T ); T ?-?( T, T ); T ?/?( T, T ); } )
-        // T ceiling( T n, T align ) { return return floor( n + (n % align != 0 ? align - 1 : 0), align ); *}
+        signed char ceiling( signed char n, char align ) {
+                align = align < 0 ? -align : align;                             // align must be signed
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        unsigned char ceiling( unsigned char n, unsigned char align ) {
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        short int ceiling( short int n, short int align ) {
+                align = align < 0 ? -align : align;                             // align must be signed
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        unsigned short int ceiling( unsigned short int n, unsigned short int align ) {
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        int ceiling( int n, int align ) {
+                align = align < 0 ? -align : align;                             // align must be signed
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        unsigned int ceiling( unsigned int n, unsigned int align ) {
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        long int ceiling( long int n, long int align ) {
+                align = align < 0 ? -align : align;                             // align must be signed
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        unsigned long int ceiling( unsigned long int n, unsigned long int align ) {
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        long long int ceiling( long long int n, signed long long int align ) {
+                align = align < 0 ? -align : align;                             // align must be signed
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
+        unsigned long long int ceiling( unsigned long long int n, unsigned long long int align ) {
+                typeof(n) trunc = floor( n, align );
+                return n >= 0 ? trunc + (trunc != n ? align : 0) : trunc;
+        }
 
         float floor( float x ) { return floorf( x ); }

tests/.expect/mathX.x64.txt

@@ -787 +787 @@
 ceiling(1, 1) = 1, ceiling(3, 1) = 3, ceiling(-3, 1) = -3
 ceiling(2, 2) = 2, ceiling(4, 2) = 4, ceiling(-4, 2) = -4
-ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = 0
-ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = 0
-ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = 0
-ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = 0
-ceiling(64, 64) = 64, ceiling(66, 64) = -128, ceiling(-66, 64) = 0
-ceiling(-128, -128) = -128, ceiling(-126, -128) = -128, ceiling(126, -128) = 0
+ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = -4
+ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = -8
+ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = -16
+ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = -32
+ceiling(64, 64) = 64, ceiling(66, 64) = -128, ceiling(-66, 64) = -64
+ceiling(-128, -128) = -128, ceiling(-126, -128) = 0, ceiling(126, -128) = -128
 
 unsigned char
@@ -807 +807 @@
 ceiling(1, 1) = 1, ceiling(3, 1) = 3, ceiling(-3, 1) = -3
 ceiling(2, 2) = 2, ceiling(4, 2) = 4, ceiling(-4, 2) = -4
-ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = 0
-ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = 0
-ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = 0
-ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = 0
-ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = 0
-ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = 0
-ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = 0
-ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = 0
-ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = 0
-ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = 0
-ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = 0
-ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = 0
-ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = -32768, ceiling(-16386, 16384) = 0
-ceiling(-32768, -32768) = -32768, ceiling(-32766, -32768) = -32768, ceiling(32766, -32768) = 0
+ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = -4
+ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = -8
+ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = -16
+ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = -32
+ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = -64
+ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = -128
+ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = -256
+ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = -512
+ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = -1024
+ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = -2048
+ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = -4096
+ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = -8192
+ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = -32768, ceiling(-16386, 16384) = -16384
+ceiling(-32768, -32768) = -32768, ceiling(-32766, -32768) = 0, ceiling(32766, -32768) = -32768
 
 unsigned short int
@@ -843 +843 @@
 ceiling(1, 1) = 1, ceiling(3, 1) = 3, ceiling(-3, 1) = -3
 ceiling(2, 2) = 2, ceiling(4, 2) = 4, ceiling(-4, 2) = -4
-ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = 0
-ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = 0
-ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = 0
-ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = 0
-ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = 0
-ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = 0
-ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = 0
-ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = 0
-ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = 0
-ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = 0
-ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = 0
-ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = 0
-ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = 0
-ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = 0
-ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = 0
-ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = 0
-ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = 0
-ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = 0
-ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = 0
-ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = 0
-ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = 0
-ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = 0
-ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = 0
-ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = 0
-ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = 0
-ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = 0
-ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = 0
-ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = 0
-ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = -1073741824, ceiling(-1073741826, 1073741824) = 0
-ceiling(-2147483648, -2147483648) = -2147483648, ceiling(-2147483646, -2147483648) = 0, ceiling(2147483646, -2147483648) = 0
+ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = -4
+ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = -8
+ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = -16
+ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = -32
+ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = -64
+ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = -128
+ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = -256
+ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = -512
+ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = -1024
+ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = -2048
+ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = -4096
+ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = -8192
+ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = -16384
+ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = -32768
+ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = -65536
+ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = -131072
+ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = -262144
+ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = -524288
+ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = -1048576
+ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = -2097152
+ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = -4194304
+ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = -8388608
+ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = -16777216
+ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = -33554432
+ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = -67108864
+ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = -134217728
+ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = -268435456
+ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = -536870912
+ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = -2147483648, ceiling(-1073741826, 1073741824) = -1073741824
+ceiling(-2147483648, -2147483648) = -2147483648, ceiling(-2147483646, -2147483648) = 0, ceiling(2147483646, -2147483648) = -2147483648
 
 unsigned int
@@ -911 +911 @@
 ceiling(1, 1) = 1, ceiling(3, 1) = 3, ceiling(-3, 1) = -3
 ceiling(2, 2) = 2, ceiling(4, 2) = 4, ceiling(-4, 2) = -4
-ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = 0
-ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = 0
-ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = 0
-ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = 0
-ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = 0
-ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = 0
-ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = 0
-ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = 0
-ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = 0
-ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = 0
-ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = 0
-ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = 0
-ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = 0
-ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = 0
-ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = 0
-ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = 0
-ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = 0
-ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = 0
-ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = 0
-ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = 0
-ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = 0
-ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = 0
-ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = 0
-ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = 0
-ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = 0
-ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = 0
-ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = 0
-ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = 0
-ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = 2147483648, ceiling(-1073741826, 1073741824) = 0
-ceiling(2147483648, 2147483648) = 2147483648, ceiling(2147483650, 2147483648) = 4294967296, ceiling(-2147483650, 2147483648) = 0
-ceiling(4294967296, 4294967296) = 4294967296, ceiling(4294967298, 4294967296) = 8589934592, ceiling(-4294967298, 4294967296) = 0
-ceiling(8589934592, 8589934592) = 8589934592, ceiling(8589934594, 8589934592) = 17179869184, ceiling(-8589934594, 8589934592) = 0
-ceiling(17179869184, 17179869184) = 17179869184, ceiling(17179869186, 17179869184) = 34359738368, ceiling(-17179869186, 17179869184) = 0
-ceiling(34359738368, 34359738368) = 34359738368, ceiling(34359738370, 34359738368) = 68719476736, ceiling(-34359738370, 34359738368) = 0
-ceiling(68719476736, 68719476736) = 68719476736, ceiling(68719476738, 68719476736) = 137438953472, ceiling(-68719476738, 68719476736) = 0
-ceiling(137438953472, 137438953472) = 137438953472, ceiling(137438953474, 137438953472) = 274877906944, ceiling(-137438953474, 137438953472) = 0
-ceiling(274877906944, 274877906944) = 274877906944, ceiling(274877906946, 274877906944) = 549755813888, ceiling(-274877906946, 274877906944) = 0
-ceiling(549755813888, 549755813888) = 549755813888, ceiling(549755813890, 549755813888) = 1099511627776, ceiling(-549755813890, 549755813888) = 0
-ceiling(1099511627776, 1099511627776) = 1099511627776, ceiling(1099511627778, 1099511627776) = 2199023255552, ceiling(-1099511627778, 1099511627776) = 0
-ceiling(2199023255552, 2199023255552) = 2199023255552, ceiling(2199023255554, 2199023255552) = 4398046511104, ceiling(-2199023255554, 2199023255552) = 0
-ceiling(4398046511104, 4398046511104) = 4398046511104, ceiling(4398046511106, 4398046511104) = 8796093022208, ceiling(-4398046511106, 4398046511104) = 0
-ceiling(8796093022208, 8796093022208) = 8796093022208, ceiling(8796093022210, 8796093022208) = 17592186044416, ceiling(-8796093022210, 8796093022208) = 0
-ceiling(17592186044416, 17592186044416) = 17592186044416, ceiling(17592186044418, 17592186044416) = 35184372088832, ceiling(-17592186044418, 17592186044416) = 0
-ceiling(35184372088832, 35184372088832) = 35184372088832, ceiling(35184372088834, 35184372088832) = 70368744177664, ceiling(-35184372088834, 35184372088832) = 0
-ceiling(70368744177664, 70368744177664) = 70368744177664, ceiling(70368744177666, 70368744177664) = 140737488355328, ceiling(-70368744177666, 70368744177664) = 0
-ceiling(140737488355328, 140737488355328) = 140737488355328, ceiling(140737488355330, 140737488355328) = 281474976710656, ceiling(-140737488355330, 140737488355328) = 0
-ceiling(281474976710656, 281474976710656) = 281474976710656, ceiling(281474976710658, 281474976710656) = 562949953421312, ceiling(-281474976710658, 281474976710656) = 0
-ceiling(562949953421312, 562949953421312) = 562949953421312, ceiling(562949953421314, 562949953421312) = 1125899906842624, ceiling(-562949953421314, 562949953421312) = 0
-ceiling(1125899906842624, 1125899906842624) = 1125899906842624, ceiling(1125899906842626, 1125899906842624) = 2251799813685248, ceiling(-1125899906842626, 1125899906842624) = 0
-ceiling(2251799813685248, 2251799813685248) = 2251799813685248, ceiling(2251799813685250, 2251799813685248) = 4503599627370496, ceiling(-2251799813685250, 2251799813685248) = 0
-ceiling(4503599627370496, 4503599627370496) = 4503599627370496, ceiling(4503599627370498, 4503599627370496) = 9007199254740992, ceiling(-4503599627370498, 4503599627370496) = 0
-ceiling(9007199254740992, 9007199254740992) = 9007199254740992, ceiling(9007199254740994, 9007199254740992) = 18014398509481984, ceiling(-9007199254740994, 9007199254740992) = 0
-ceiling(18014398509481984, 18014398509481984) = 18014398509481984, ceiling(18014398509481986, 18014398509481984) = 36028797018963968, ceiling(-18014398509481986, 18014398509481984) = 0
-ceiling(36028797018963968, 36028797018963968) = 36028797018963968, ceiling(36028797018963970, 36028797018963968) = 72057594037927936, ceiling(-36028797018963970, 36028797018963968) = 0
-ceiling(72057594037927936, 72057594037927936) = 72057594037927936, ceiling(72057594037927938, 72057594037927936) = 144115188075855872, ceiling(-72057594037927938, 72057594037927936) = 0
-ceiling(144115188075855872, 144115188075855872) = 144115188075855872, ceiling(144115188075855874, 144115188075855872) = 288230376151711744, ceiling(-144115188075855874, 144115188075855872) = 0
-ceiling(288230376151711744, 288230376151711744) = 288230376151711744, ceiling(288230376151711746, 288230376151711744) = 576460752303423488, ceiling(-288230376151711746, 288230376151711744) = 0
-ceiling(576460752303423488, 576460752303423488) = 576460752303423488, ceiling(576460752303423490, 576460752303423488) = 1152921504606846976, ceiling(-576460752303423490, 576460752303423488) = 0
-ceiling(1152921504606846976, 1152921504606846976) = 1152921504606846976, ceiling(1152921504606846978, 1152921504606846976) = 2305843009213693952, ceiling(-1152921504606846978, 1152921504606846976) = 0
-ceiling(2305843009213693952, 2305843009213693952) = 2305843009213693952, ceiling(2305843009213693954, 2305843009213693952) = 4611686018427387904, ceiling(-2305843009213693954, 2305843009213693952) = 0
-ceiling(4611686018427387904, 4611686018427387904) = 4611686018427387904, ceiling(4611686018427387906, 4611686018427387904) = -4611686018427387904, ceiling(-4611686018427387906, 4611686018427387904) = 0
-ceiling(-9223372036854775808, -9223372036854775808) = -9223372036854775808, ceiling(-9223372036854775806, -9223372036854775808) = 0, ceiling(9223372036854775806, -9223372036854775808) = 0
+ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = -4
+ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = -8
+ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = -16
+ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = -32
+ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = -64
+ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = -128
+ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = -256
+ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = -512
+ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = -1024
+ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = -2048
+ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = -4096
+ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = -8192
+ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = -16384
+ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = -32768
+ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = -65536
+ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = -131072
+ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = -262144
+ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = -524288
+ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = -1048576
+ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = -2097152
+ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = -4194304
+ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = -8388608
+ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = -16777216
+ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = -33554432
+ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = -67108864
+ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = -134217728
+ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = -268435456
+ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = -536870912
+ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = 2147483648, ceiling(-1073741826, 1073741824) = -1073741824
+ceiling(2147483648, 2147483648) = 2147483648, ceiling(2147483650, 2147483648) = 4294967296, ceiling(-2147483650, 2147483648) = -2147483648
+ceiling(4294967296, 4294967296) = 4294967296, ceiling(4294967298, 4294967296) = 8589934592, ceiling(-4294967298, 4294967296) = -4294967296
+ceiling(8589934592, 8589934592) = 8589934592, ceiling(8589934594, 8589934592) = 17179869184, ceiling(-8589934594, 8589934592) = -8589934592
+ceiling(17179869184, 17179869184) = 17179869184, ceiling(17179869186, 17179869184) = 34359738368, ceiling(-17179869186, 17179869184) = -17179869184
+ceiling(34359738368, 34359738368) = 34359738368, ceiling(34359738370, 34359738368) = 68719476736, ceiling(-34359738370, 34359738368) = -34359738368
+ceiling(68719476736, 68719476736) = 68719476736, ceiling(68719476738, 68719476736) = 137438953472, ceiling(-68719476738, 68719476736) = -68719476736
+ceiling(137438953472, 137438953472) = 137438953472, ceiling(137438953474, 137438953472) = 274877906944, ceiling(-137438953474, 137438953472) = -137438953472
+ceiling(274877906944, 274877906944) = 274877906944, ceiling(274877906946, 274877906944) = 549755813888, ceiling(-274877906946, 274877906944) = -274877906944
+ceiling(549755813888, 549755813888) = 549755813888, ceiling(549755813890, 549755813888) = 1099511627776, ceiling(-549755813890, 549755813888) = -549755813888
+ceiling(1099511627776, 1099511627776) = 1099511627776, ceiling(1099511627778, 1099511627776) = 2199023255552, ceiling(-1099511627778, 1099511627776) = -1099511627776
+ceiling(2199023255552, 2199023255552) = 2199023255552, ceiling(2199023255554, 2199023255552) = 4398046511104, ceiling(-2199023255554, 2199023255552) = -2199023255552
+ceiling(4398046511104, 4398046511104) = 4398046511104, ceiling(4398046511106, 4398046511104) = 8796093022208, ceiling(-4398046511106, 4398046511104) = -4398046511104
+ceiling(8796093022208, 8796093022208) = 8796093022208, ceiling(8796093022210, 8796093022208) = 17592186044416, ceiling(-8796093022210, 8796093022208) = -8796093022208
+ceiling(17592186044416, 17592186044416) = 17592186044416, ceiling(17592186044418, 17592186044416) = 35184372088832, ceiling(-17592186044418, 17592186044416) = -17592186044416
+ceiling(35184372088832, 35184372088832) = 35184372088832, ceiling(35184372088834, 35184372088832) = 70368744177664, ceiling(-35184372088834, 35184372088832) = -35184372088832
+ceiling(70368744177664, 70368744177664) = 70368744177664, ceiling(70368744177666, 70368744177664) = 140737488355328, ceiling(-70368744177666, 70368744177664) = -70368744177664
+ceiling(140737488355328, 140737488355328) = 140737488355328, ceiling(140737488355330, 140737488355328) = 281474976710656, ceiling(-140737488355330, 140737488355328) = -140737488355328
+ceiling(281474976710656, 281474976710656) = 281474976710656, ceiling(281474976710658, 281474976710656) = 562949953421312, ceiling(-281474976710658, 281474976710656) = -281474976710656
+ceiling(562949953421312, 562949953421312) = 562949953421312, ceiling(562949953421314, 562949953421312) = 1125899906842624, ceiling(-562949953421314, 562949953421312) = -562949953421312
+ceiling(1125899906842624, 1125899906842624) = 1125899906842624, ceiling(1125899906842626, 1125899906842624) = 2251799813685248, ceiling(-1125899906842626, 1125899906842624) = -1125899906842624
+ceiling(2251799813685248, 2251799813685248) = 2251799813685248, ceiling(2251799813685250, 2251799813685248) = 4503599627370496, ceiling(-2251799813685250, 2251799813685248) = -2251799813685248
+ceiling(4503599627370496, 4503599627370496) = 4503599627370496, ceiling(4503599627370498, 4503599627370496) = 9007199254740992, ceiling(-4503599627370498, 4503599627370496) = -4503599627370496
+ceiling(9007199254740992, 9007199254740992) = 9007199254740992, ceiling(9007199254740994, 9007199254740992) = 18014398509481984, ceiling(-9007199254740994, 9007199254740992) = -9007199254740992
+ceiling(18014398509481984, 18014398509481984) = 18014398509481984, ceiling(18014398509481986, 18014398509481984) = 36028797018963968, ceiling(-18014398509481986, 18014398509481984) = -18014398509481984
+ceiling(36028797018963968, 36028797018963968) = 36028797018963968, ceiling(36028797018963970, 36028797018963968) = 72057594037927936, ceiling(-36028797018963970, 36028797018963968) = -36028797018963968
+ceiling(72057594037927936, 72057594037927936) = 72057594037927936, ceiling(72057594037927938, 72057594037927936) = 144115188075855872, ceiling(-72057594037927938, 72057594037927936) = -72057594037927936
+ceiling(144115188075855872, 144115188075855872) = 144115188075855872, ceiling(144115188075855874, 144115188075855872) = 288230376151711744, ceiling(-144115188075855874, 144115188075855872) = -144115188075855872
+ceiling(288230376151711744, 288230376151711744) = 288230376151711744, ceiling(288230376151711746, 288230376151711744) = 576460752303423488, ceiling(-288230376151711746, 288230376151711744) = -288230376151711744
+ceiling(576460752303423488, 576460752303423488) = 576460752303423488, ceiling(576460752303423490, 576460752303423488) = 1152921504606846976, ceiling(-576460752303423490, 576460752303423488) = -576460752303423488
+ceiling(1152921504606846976, 1152921504606846976) = 1152921504606846976, ceiling(1152921504606846978, 1152921504606846976) = 2305843009213693952, ceiling(-1152921504606846978, 1152921504606846976) = -1152921504606846976
+ceiling(2305843009213693952, 2305843009213693952) = 2305843009213693952, ceiling(2305843009213693954, 2305843009213693952) = 4611686018427387904, ceiling(-2305843009213693954, 2305843009213693952) = -2305843009213693952
+ceiling(4611686018427387904, 4611686018427387904) = 4611686018427387904, ceiling(4611686018427387906, 4611686018427387904) = -9223372036854775808, ceiling(-4611686018427387906, 4611686018427387904) = -4611686018427387904
+ceiling(-9223372036854775808, -9223372036854775808) = -9223372036854775808, ceiling(-9223372036854775806, -9223372036854775808) = 0, ceiling(9223372036854775806, -9223372036854775808) = -9223372036854775808
 
 unsigned long int
@@ -1043 +1043 @@
 ceiling(1, 1) = 1, ceiling(3, 1) = 3, ceiling(-3, 1) = -3
 ceiling(2, 2) = 2, ceiling(4, 2) = 4, ceiling(-4, 2) = -4
-ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = 0
-ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = 0
-ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = 0
-ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = 0
-ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = 0
-ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = 0
-ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = 0
-ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = 0
-ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = 0
-ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = 0
-ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = 0
-ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = 0
-ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = 0
-ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = 0
-ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = 0
-ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = 0
-ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = 0
-ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = 0
-ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = 0
-ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = 0
-ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = 0
-ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = 0
-ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = 0
-ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = 0
-ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = 0
-ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = 0
-ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = 0
-ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = 0
-ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = 2147483648, ceiling(-1073741826, 1073741824) = 0
-ceiling(2147483648, 2147483648) = 2147483648, ceiling(2147483650, 2147483648) = 4294967296, ceiling(-2147483650, 2147483648) = 0
-ceiling(4294967296, 4294967296) = 4294967296, ceiling(4294967298, 4294967296) = 8589934592, ceiling(-4294967298, 4294967296) = 0
-ceiling(8589934592, 8589934592) = 8589934592, ceiling(8589934594, 8589934592) = 17179869184, ceiling(-8589934594, 8589934592) = 0
-ceiling(17179869184, 17179869184) = 17179869184, ceiling(17179869186, 17179869184) = 34359738368, ceiling(-17179869186, 17179869184) = 0
-ceiling(34359738368, 34359738368) = 34359738368, ceiling(34359738370, 34359738368) = 68719476736, ceiling(-34359738370, 34359738368) = 0
-ceiling(68719476736, 68719476736) = 68719476736, ceiling(68719476738, 68719476736) = 137438953472, ceiling(-68719476738, 68719476736) = 0
-ceiling(137438953472, 137438953472) = 137438953472, ceiling(137438953474, 137438953472) = 274877906944, ceiling(-137438953474, 137438953472) = 0
-ceiling(274877906944, 274877906944) = 274877906944, ceiling(274877906946, 274877906944) = 549755813888, ceiling(-274877906946, 274877906944) = 0
-ceiling(549755813888, 549755813888) = 549755813888, ceiling(549755813890, 549755813888) = 1099511627776, ceiling(-549755813890, 549755813888) = 0
-ceiling(1099511627776, 1099511627776) = 1099511627776, ceiling(1099511627778, 1099511627776) = 2199023255552, ceiling(-1099511627778, 1099511627776) = 0
-ceiling(2199023255552, 2199023255552) = 2199023255552, ceiling(2199023255554, 2199023255552) = 4398046511104, ceiling(-2199023255554, 2199023255552) = 0
-ceiling(4398046511104, 4398046511104) = 4398046511104, ceiling(4398046511106, 4398046511104) = 8796093022208, ceiling(-4398046511106, 4398046511104) = 0
-ceiling(8796093022208, 8796093022208) = 8796093022208, ceiling(8796093022210, 8796093022208) = 17592186044416, ceiling(-8796093022210, 8796093022208) = 0
-ceiling(17592186044416, 17592186044416) = 17592186044416, ceiling(17592186044418, 17592186044416) = 35184372088832, ceiling(-17592186044418, 17592186044416) = 0
-ceiling(35184372088832, 35184372088832) = 35184372088832, ceiling(35184372088834, 35184372088832) = 70368744177664, ceiling(-35184372088834, 35184372088832) = 0
-ceiling(70368744177664, 70368744177664) = 70368744177664, ceiling(70368744177666, 70368744177664) = 140737488355328, ceiling(-70368744177666, 70368744177664) = 0
-ceiling(140737488355328, 140737488355328) = 140737488355328, ceiling(140737488355330, 140737488355328) = 281474976710656, ceiling(-140737488355330, 140737488355328) = 0
-ceiling(281474976710656, 281474976710656) = 281474976710656, ceiling(281474976710658, 281474976710656) = 562949953421312, ceiling(-281474976710658, 281474976710656) = 0
-ceiling(562949953421312, 562949953421312) = 562949953421312, ceiling(562949953421314, 562949953421312) = 1125899906842624, ceiling(-562949953421314, 562949953421312) = 0
-ceiling(1125899906842624, 1125899906842624) = 1125899906842624, ceiling(1125899906842626, 1125899906842624) = 2251799813685248, ceiling(-1125899906842626, 1125899906842624) = 0
-ceiling(2251799813685248, 2251799813685248) = 2251799813685248, ceiling(2251799813685250, 2251799813685248) = 4503599627370496, ceiling(-2251799813685250, 2251799813685248) = 0
-ceiling(4503599627370496, 4503599627370496) = 4503599627370496, ceiling(4503599627370498, 4503599627370496) = 9007199254740992, ceiling(-4503599627370498, 4503599627370496) = 0
-ceiling(9007199254740992, 9007199254740992) = 9007199254740992, ceiling(9007199254740994, 9007199254740992) = 18014398509481984, ceiling(-9007199254740994, 9007199254740992) = 0
-ceiling(18014398509481984, 18014398509481984) = 18014398509481984, ceiling(18014398509481986, 18014398509481984) = 36028797018963968, ceiling(-18014398509481986, 18014398509481984) = 0
-ceiling(36028797018963968, 36028797018963968) = 36028797018963968, ceiling(36028797018963970, 36028797018963968) = 72057594037927936, ceiling(-36028797018963970, 36028797018963968) = 0
-ceiling(72057594037927936, 72057594037927936) = 72057594037927936, ceiling(72057594037927938, 72057594037927936) = 144115188075855872, ceiling(-72057594037927938, 72057594037927936) = 0
-ceiling(144115188075855872, 144115188075855872) = 144115188075855872, ceiling(144115188075855874, 144115188075855872) = 288230376151711744, ceiling(-144115188075855874, 144115188075855872) = 0
-ceiling(288230376151711744, 288230376151711744) = 288230376151711744, ceiling(288230376151711746, 288230376151711744) = 576460752303423488, ceiling(-288230376151711746, 288230376151711744) = 0
-ceiling(576460752303423488, 576460752303423488) = 576460752303423488, ceiling(576460752303423490, 576460752303423488) = 1152921504606846976, ceiling(-576460752303423490, 576460752303423488) = 0
-ceiling(1152921504606846976, 1152921504606846976) = 1152921504606846976, ceiling(1152921504606846978, 1152921504606846976) = 2305843009213693952, ceiling(-1152921504606846978, 1152921504606846976) = 0
-ceiling(2305843009213693952, 2305843009213693952) = 2305843009213693952, ceiling(2305843009213693954, 2305843009213693952) = 4611686018427387904, ceiling(-2305843009213693954, 2305843009213693952) = 0
-ceiling(4611686018427387904, 4611686018427387904) = 4611686018427387904, ceiling(4611686018427387906, 4611686018427387904) = -4611686018427387904, ceiling(-4611686018427387906, 4611686018427387904) = 0
-ceiling(-9223372036854775808, -9223372036854775808) = -9223372036854775808, ceiling(-9223372036854775806, -9223372036854775808) = 0, ceiling(9223372036854775806, -9223372036854775808) = 0
+ceiling(4, 4) = 4, ceiling(6, 4) = 8, ceiling(-6, 4) = -4
+ceiling(8, 8) = 8, ceiling(10, 8) = 16, ceiling(-10, 8) = -8
+ceiling(16, 16) = 16, ceiling(18, 16) = 32, ceiling(-18, 16) = -16
+ceiling(32, 32) = 32, ceiling(34, 32) = 64, ceiling(-34, 32) = -32
+ceiling(64, 64) = 64, ceiling(66, 64) = 128, ceiling(-66, 64) = -64
+ceiling(128, 128) = 128, ceiling(130, 128) = 256, ceiling(-130, 128) = -128
+ceiling(256, 256) = 256, ceiling(258, 256) = 512, ceiling(-258, 256) = -256
+ceiling(512, 512) = 512, ceiling(514, 512) = 1024, ceiling(-514, 512) = -512
+ceiling(1024, 1024) = 1024, ceiling(1026, 1024) = 2048, ceiling(-1026, 1024) = -1024
+ceiling(2048, 2048) = 2048, ceiling(2050, 2048) = 4096, ceiling(-2050, 2048) = -2048
+ceiling(4096, 4096) = 4096, ceiling(4098, 4096) = 8192, ceiling(-4098, 4096) = -4096
+ceiling(8192, 8192) = 8192, ceiling(8194, 8192) = 16384, ceiling(-8194, 8192) = -8192
+ceiling(16384, 16384) = 16384, ceiling(16386, 16384) = 32768, ceiling(-16386, 16384) = -16384
+ceiling(32768, 32768) = 32768, ceiling(32770, 32768) = 65536, ceiling(-32770, 32768) = -32768
+ceiling(65536, 65536) = 65536, ceiling(65538, 65536) = 131072, ceiling(-65538, 65536) = -65536
+ceiling(131072, 131072) = 131072, ceiling(131074, 131072) = 262144, ceiling(-131074, 131072) = -131072
+ceiling(262144, 262144) = 262144, ceiling(262146, 262144) = 524288, ceiling(-262146, 262144) = -262144
+ceiling(524288, 524288) = 524288, ceiling(524290, 524288) = 1048576, ceiling(-524290, 524288) = -524288
+ceiling(1048576, 1048576) = 1048576, ceiling(1048578, 1048576) = 2097152, ceiling(-1048578, 1048576) = -1048576
+ceiling(2097152, 2097152) = 2097152, ceiling(2097154, 2097152) = 4194304, ceiling(-2097154, 2097152) = -2097152
+ceiling(4194304, 4194304) = 4194304, ceiling(4194306, 4194304) = 8388608, ceiling(-4194306, 4194304) = -4194304
+ceiling(8388608, 8388608) = 8388608, ceiling(8388610, 8388608) = 16777216, ceiling(-8388610, 8388608) = -8388608
+ceiling(16777216, 16777216) = 16777216, ceiling(16777218, 16777216) = 33554432, ceiling(-16777218, 16777216) = -16777216
+ceiling(33554432, 33554432) = 33554432, ceiling(33554434, 33554432) = 67108864, ceiling(-33554434, 33554432) = -33554432
+ceiling(67108864, 67108864) = 67108864, ceiling(67108866, 67108864) = 134217728, ceiling(-67108866, 67108864) = -67108864
+ceiling(134217728, 134217728) = 134217728, ceiling(134217730, 134217728) = 268435456, ceiling(-134217730, 134217728) = -134217728
+ceiling(268435456, 268435456) = 268435456, ceiling(268435458, 268435456) = 536870912, ceiling(-268435458, 268435456) = -268435456
+ceiling(536870912, 536870912) = 536870912, ceiling(536870914, 536870912) = 1073741824, ceiling(-536870914, 536870912) = -536870912
+ceiling(1073741824, 1073741824) = 1073741824, ceiling(1073741826, 1073741824) = 2147483648, ceiling(-1073741826, 1073741824) = -1073741824
+ceiling(2147483648, 2147483648) = 2147483648, ceiling(2147483650, 2147483648) = 4294967296, ceiling(-2147483650, 2147483648) = -2147483648
+ceiling(4294967296, 4294967296) = 4294967296, ceiling(4294967298, 4294967296) = 8589934592, ceiling(-4294967298, 4294967296) = -4294967296
+ceiling(8589934592, 8589934592) = 8589934592, ceiling(8589934594, 8589934592) = 17179869184, ceiling(-8589934594, 8589934592) = -8589934592
+ceiling(17179869184, 17179869184) = 17179869184, ceiling(17179869186, 17179869184) = 34359738368, ceiling(-17179869186, 17179869184) = -17179869184
+ceiling(34359738368, 34359738368) = 34359738368, ceiling(34359738370, 34359738368) = 68719476736, ceiling(-34359738370, 34359738368) = -34359738368
+ceiling(68719476736, 68719476736) = 68719476736, ceiling(68719476738, 68719476736) = 137438953472, ceiling(-68719476738, 68719476736) = -68719476736
+ceiling(137438953472, 137438953472) = 137438953472, ceiling(137438953474, 137438953472) = 274877906944, ceiling(-137438953474, 137438953472) = -137438953472
+ceiling(274877906944, 274877906944) = 274877906944, ceiling(274877906946, 274877906944) = 549755813888, ceiling(-274877906946, 274877906944) = -274877906944
+ceiling(549755813888, 549755813888) = 549755813888, ceiling(549755813890, 549755813888) = 1099511627776, ceiling(-549755813890, 549755813888) = -549755813888
+ceiling(1099511627776, 1099511627776) = 1099511627776, ceiling(1099511627778, 1099511627776) = 2199023255552, ceiling(-1099511627778, 1099511627776) = -1099511627776
+ceiling(2199023255552, 2199023255552) = 2199023255552, ceiling(2199023255554, 2199023255552) = 4398046511104, ceiling(-2199023255554, 2199023255552) = -2199023255552
+ceiling(4398046511104, 4398046511104) = 4398046511104, ceiling(4398046511106, 4398046511104) = 8796093022208, ceiling(-4398046511106, 4398046511104) = -4398046511104
+ceiling(8796093022208, 8796093022208) = 8796093022208, ceiling(8796093022210, 8796093022208) = 17592186044416, ceiling(-8796093022210, 8796093022208) = -8796093022208
+ceiling(17592186044416, 17592186044416) = 17592186044416, ceiling(17592186044418, 17592186044416) = 35184372088832, ceiling(-17592186044418, 17592186044416) = -17592186044416
+ceiling(35184372088832, 35184372088832) = 35184372088832, ceiling(35184372088834, 35184372088832) = 70368744177664, ceiling(-35184372088834, 35184372088832) = -35184372088832
+ceiling(70368744177664, 70368744177664) = 70368744177664, ceiling(70368744177666, 70368744177664) = 140737488355328, ceiling(-70368744177666, 70368744177664) = -70368744177664
+ceiling(140737488355328, 140737488355328) = 140737488355328, ceiling(140737488355330, 140737488355328) = 281474976710656, ceiling(-140737488355330, 140737488355328) = -140737488355328
+ceiling(281474976710656, 281474976710656) = 281474976710656, ceiling(281474976710658, 281474976710656) = 562949953421312, ceiling(-281474976710658, 281474976710656) = -281474976710656
+ceiling(562949953421312, 562949953421312) = 562949953421312, ceiling(562949953421314, 562949953421312) = 1125899906842624, ceiling(-562949953421314, 562949953421312) = -562949953421312
+ceiling(1125899906842624, 1125899906842624) = 1125899906842624, ceiling(1125899906842626, 1125899906842624) = 2251799813685248, ceiling(-1125899906842626, 1125899906842624) = -1125899906842624
+ceiling(2251799813685248, 2251799813685248) = 2251799813685248, ceiling(2251799813685250, 2251799813685248) = 4503599627370496, ceiling(-2251799813685250, 2251799813685248) = -2251799813685248
+ceiling(4503599627370496, 4503599627370496) = 4503599627370496, ceiling(4503599627370498, 4503599627370496) = 9007199254740992, ceiling(-4503599627370498, 4503599627370496) = -4503599627370496
+ceiling(9007199254740992, 9007199254740992) = 9007199254740992, ceiling(9007199254740994, 9007199254740992) = 18014398509481984, ceiling(-9007199254740994, 9007199254740992) = -9007199254740992
+ceiling(18014398509481984, 18014398509481984) = 18014398509481984, ceiling(18014398509481986, 18014398509481984) = 36028797018963968, ceiling(-18014398509481986, 18014398509481984) = -18014398509481984
+ceiling(36028797018963968, 36028797018963968) = 36028797018963968, ceiling(36028797018963970, 36028797018963968) = 72057594037927936, ceiling(-36028797018963970, 36028797018963968) = -36028797018963968
+ceiling(72057594037927936, 72057594037927936) = 72057594037927936, ceiling(72057594037927938, 72057594037927936) = 144115188075855872, ceiling(-72057594037927938, 72057594037927936) = -72057594037927936
+ceiling(144115188075855872, 144115188075855872) = 144115188075855872, ceiling(144115188075855874, 144115188075855872) = 288230376151711744, ceiling(-144115188075855874, 144115188075855872) = -144115188075855872
+ceiling(288230376151711744, 288230376151711744) = 288230376151711744, ceiling(288230376151711746, 288230376151711744) = 576460752303423488, ceiling(-288230376151711746, 288230376151711744) = -288230376151711744
+ceiling(576460752303423488, 576460752303423488) = 576460752303423488, ceiling(576460752303423490, 576460752303423488) = 1152921504606846976, ceiling(-576460752303423490, 576460752303423488) = -576460752303423488
+ceiling(1152921504606846976, 1152921504606846976) = 1152921504606846976, ceiling(1152921504606846978, 1152921504606846976) = 2305843009213693952, ceiling(-1152921504606846978, 1152921504606846976) = -1152921504606846976
+ceiling(2305843009213693952, 2305843009213693952) = 2305843009213693952, ceiling(2305843009213693954, 2305843009213693952) = 4611686018427387904, ceiling(-2305843009213693954, 2305843009213693952) = -2305843009213693952
+ceiling(4611686018427387904, 4611686018427387904) = 4611686018427387904, ceiling(4611686018427387906, 4611686018427387904) = -9223372036854775808, ceiling(-4611686018427387906, 4611686018427387904) = -4611686018427387904
+ceiling(-9223372036854775808, -9223372036854775808) = -9223372036854775808, ceiling(-9223372036854775806, -9223372036854775808) = 0, ceiling(9223372036854775806, -9223372036854775808) = -9223372036854775808
 
 unsigned long long int