Add fixed precision math support

git-svn-id: svn://svn.code.sf.net/p/nuttx/code/trunk@1304 42af7a65-404d-4744-a932-0658087f49c3

include/fixedmath.h

+/****************************************************************************
+ * include/fixedmath.h
+ *
+ *   Copyright (C) 2008 Gregory Nutt. All rights reserved.
+ *   Author: Gregory Nutt <spudmonkey@racsa.co.cr>
+ *
+ * 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.
+ * 3. Neither the name NuttX nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * 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 OWNER 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.
+ *
+ ****************************************************************************/
+
+#ifndef __INCLUDE_FIXEDMATH_H
+#define __INCLUDE_FIXEDMATH_H
+
+/****************************************************************************
+ * Included Files
+ ****************************************************************************/
+
+#include <sys/types.h>
+
+/**************************************************************************
+ * Definitions
+ **************************************************************************/
+
+/* Common numbers */
+
+#define b8HUNDRED       0x6400                  /* 100 */
+#define b8TEN           0x0a00                  /* 10 */
+#define b8ONE           0x0100                  /* 1 */
+#define b8HALF          0x0080                  /* 0.5 */
+#define b8ONETENTH      0x001a                  /* 0.1 (acutally 0.1015625) */
+#define b8ONEHUNDRTH    0x0003                  /* 0.01 (actualy 0.0117198765) */
+
+#define b8MAX           0x7fff                  /* Max value of b8_t */
+#define ub8MAX          0xffff                  /* Max value of rb8_t */
+#define b8MIN           0x8000                  /* Min value of b8_t */
+#define ub8MIN          0x0000                  /* Min value of ub8_t */
+
+#define b16THOUSAND     0x03e80000              /* 1000 */
+#define b16HUNDRED      0x00640000              /* 100 */
+#define b16TEN          0x000a0000              /* 10 */
+#define b16ONE          0x00010000              /* 1 */
+#define b16HALF         0x00008000              /* 0.5 */
+#define b16ONETENTH     0x0000199a              /* 0.1 (actually 0.100006..) */
+#define b16ONEHUNDRTH   0x0000028f              /* 0.01 (actually 0.0099945..) */
+#define b16ONETHOUSTH   0x00000042              /* 0.001 (actually 0.000100708..)*/
+
+#define b16MAX          0x7fffffff              /* Max value of b16_t */
+#define ub16MAX         0xffffffff              /* Max value of ub16_t */
+#define b16MIN          0x80000000              /* Min value of b16_t */
+#define ub16MIN         0x00000000              /* Min value of ub16_t */
+
+#define b32MILLION      0x000f424000000000      /* 1000000 */
+#define b32THOUSAND     0x000003e800000000      /* 1000 */
+#define b32HUNDRED      0x0000006400000000      /* 100 */
+#define b32TEN          0x0000000a00000000      /* 10 */
+#define b32ONE          0x0000000100000000      /* 1 */
+#define b32HALF         0x0000000080000000      /* 0.5 */
+#define b32ONETENTH     0x000000001999999a      /* 0.1 */
+#define b32ONEHUNDRTH   0x00000000028f5c29      /* 0.01 */
+#define b32ONETHOUSTH   0x0000000000418937      /* 0.001 */
+#define b32ONETENTHOU   0x0000000000068db9      /* 0.0001 */
+
+#define b32MAX          0x7fffffffffffffff      /* Max value of b16_t */
+#define ub32MAX         0xffffffffffffffff      /* Max value of ub16_t */
+#define b32MIN          0x8000000000000000      /* Min value of b16_t */
+#define ub32MIN         0x0000000000000000      /* Min value of ub16_t */
+
+/* Conversions between b16 and b8 *****************************************/
+
+#define b8tob16(b)      ((b16_t)(b) << 8)
+#define ub8toub16(b)    ((ub16_t)(b) << 8)
+#define b16tob8(b)      (b8_t)(((b)+0x0080)>>8)
+#define ub16toub8(b)    (ub8_t)(((b)+0x0080)>>8)
+
+#ifdef CONFIG_HAVE_LONG_LONG
+#  define b8tob32(b)    ((b32_t)(b) << 24)
+#  define ub8toub32(b)  ((ub32_t)(b) << 24)
+#  define b16tob32(b)   ((b32_t)(b) << 16)
+#  define ub16toub32(b) ((ub32_t)(b) << 16)
+#  define b32tob16(b)   (b16_t)(((b) + 0x0000000000008000)>>16)
+#  define ub32toub16(b) (ub16_t)(((b) + 0x0000000000008000)>>16)
+#  define b32tob8(b)    (b8_t)(((b) + 0x0000000000000080)>>8)
+#endif
+
+/* 16-bit values with 8 bits of precision *********************************/
+
+/* Conversions */
+
+#define b8toi(a)        ((a) >> 8)              /* Conversion to integer */
+#define itob8(i)        ((i) << 8)              /* Conversion from integer */
+#define b8tof(b)        (((float)b)/256.0)      /* Conversion to float */
+#define ftob8(f)        (b8_t)(((f)*256.0))     /* Conversion from float */
+#define b8trunc(a)      ((a) & 0xff00)          /* Truncate to integer b8 */
+#define b8round(a)      (((a)+0x0080) & 0xff00) /* Round to integer b8 */
+#define b8frac(a)       ((a) & 0x00ff)          /* Take fractional part */
+
+/* Operators */
+
+#define ub8inv(b)       (0x8000/((b)>>1))       /* Inversion (b8=b15/b7) */
+#define b8inv(b)        (0x4000/((b)>>2))       /* Inversion (b8=b14/b6) */
+#define b8addb8(a,b)    ((a)+(b))               /* Addition */
+#define b8addi(a,i)     ((a)+itob8(i))          /* Add integer from b16 */
+#define b8subb8(a,b)    ((a)-(b))               /* Subtraction */
+#define b8subi(a,i)     ((a)-itob8(i))          /* Subtract integer from b8 */
+#define b8mulb8(a,b)    b16tob8((b16_t)(a)*(b16_t)(b) /* Muliplication */
+#define ub8mulub8(a,b)  ub16toub8((ub16_t)(a)*(ub16_t)(b) /* Muliplication */
+#define b8muli(a,i)     ((a)*(i))               /* Simple multiplication by integer */
+#define b8divb8(a,b)    b8tob16(a)/(b16_t)(b)   /* Division */
+#define ub8divub8(a,b)  ub8toub16(a)/(ub16_t)(b) /* Division */
+#define b8divi(a,i)     ((a)/(i))               /* Simple division by integer */
+#define b8idiv(i,j)     (((i)<<8)/j)            /* Division of integer, b8 result */
+
+/* 32-bit values with 16 bits of precision ********************************/
+
+/* Conversions */
+
+#define b16toi(a)       ((a) >> 16)             /* Conversion to integer */
+#define itob16(i)       ((i) << 16)             /* Conversion from integer */
+#define b16tof(b)       (((float)b)/65536.0)    /* Conversion to float */
+#define ftob16(f)       (b16_t)(((f)*65536.0))  /* Conversion from float */
+#define b16trunc(a)     ((a) & 0xffff0000)      /* Truncate to integer */
+#define b16round(a)     (((a)+0x00008000) & 0xffff0000)
+#define b16frac(a)      ((a) & 0x0000ffff)      /* Take fractional part */
+
+/* Operators */
+
+#define ub16inv(b)      (0x80000000/((b)>>1))   /* Inversion (b16=b31/b15) */
+#define b16inv(b)       (0x40000000/((b)>>2))   /* Inversion (b16=b30/b14) */
+#define b16addb16(a,b)  ((a)+(b))               /* Addition */
+#define b16addi(a,i)    ((a)+itob16(i))         /* Add integer to b16 */
+#define b16subb16(a,b)  ((a)-(b))               /* Subtraction */
+#define b16subi(a,i)    ((a)-itob16(i))         /* Subtract integer from b16 */
+#define b16muli(a,i)    ((a)*(i))               /* Simple multiplication by integer */
+#define b16divi(a,i)    ((a)/(i))               /* Simple division by integer*/
+#define b16idiv(i,j)    (((i)<<16)/j)           /* Division of integer, b16 result */
+
+#ifdef CONFIG_HAVE_LONG_LONG
+#  define b16mulb16(a,b)   b32tob16((b32_t)(a)*(b32_t)(b) /* Muliplication */
+#  define ub16mulub16(a,b) ub32toub16((ub32_t)(a)*(ub32_t)(b)
+#  define b16divb16(a,b)   b16tob32(a)/(b32_t)(b)         /* Division */
+#  define ub16divub16(a,b) ub16toub32(a)/(ub32_t)(b)
+#endif
+
+/**************************************************************************
+ * Public Types
+ **************************************************************************/
+
+typedef sint16 b8_t;
+typedef uint16 ub8_t;
+typedef sint32 b16_t;
+typedef uint32 ub16_t;
+#ifdef CONFIG_HAVE_LONG_LONG
+typedef sint64 b32_t;
+typedef uint64 ub32_t;
+#endif
+
+/**************************************************************************
+ * Global Functions
+ **************************************************************************/
+
+#undef EXTERN
+#if defined(__cplusplus)
+#define EXTERN extern "C"
+extern "C" {
+#else
+#define EXTERN extern
+#endif
+
+#ifndef CONFIG_HAVE_LONG_LONG
+EXTERN b16_t  b16mulb16(b16_t m1, b16_t m2);
+EXTERN ub16_t ub16mulub16(ub16_t m1, ub16_t m2);
+EXTERN b16_t  b16divb16(b16_t num, b16_t denom);
+EXTERN ub16_t ub16divub16(ub16_t num, ub16_t denom);
+#endif
+
+#undef EXTERN
+#if defined(__cplusplus)
+}
+#endif
+#endif /* __INCLUDE_FIXEDMATH_H */

lib/Makefile

@@ -71,7 +71,7 @@ endif
 
 STDLIB_SRCS	= lib_rand.c
 
-MATH_SRCS	= lib_rint.c
+MATH_SRCS	= lib_rint.c lib_fixedmath.c
 
 UNISTD_SRCS	= lib_getopt.c
 ifneq ($(CONFIG_NFILE_DESCRIPTORS),0)

lib/lib_fixedmath.c

+/****************************************************************************
+ * lib/lib_fixedmath.c
+ *
+ *   Copyright (C) 2008 Gregory Nutt. All rights reserved.
+ *   Author: Gregory Nutt <spudmonkey@racsa.co.cr>
+ *
+ * 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.
+ * 3. Neither the name NuttX nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * 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 OWNER 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.
+ *
+ ****************************************************************************/
+
+/****************************************************************************
+ * Included Files
+ ****************************************************************************/
+
+#include <nuttx/config.h>
+#include <fixedmath.h>
+
+#ifndef CONFIG_HAVE_LONG_LONG
+
+/****************************************************************************
+ * Definitions
+ ****************************************************************************/
+
+/****************************************************************************
+ * Private Type Declarations
+ ****************************************************************************/
+
+/****************************************************************************
+ * Private Function Prototypes
+ ****************************************************************************/
+
+/****************************************************************************
+ * Public Data
+ ****************************************************************************/
+
+/****************************************************************************
+ * Private Data
+ ****************************************************************************/
+
+/****************************************************************************
+ * Name: fixsign
+ ****************************************************************************/
+
+static void fixsign(b16_t *parg1, b16_t *parg2, boolean *pnegate)
+{
+  boolean negate = FALSE;
+  b16_t arg;
+
+  arg = *parg1;
+  if (arg < 0)
+    {
+      *parg1 = -arg;
+      negate = TRUE;
+    }
+
+  arg = *parg2;
+  if (arg < 0)
+    {
+      *parg2 = -arg;
+      negate ^= TRUE;
+    }
+
+  *pnegate = negate;
+}
+
+/****************************************************************************
+ * Name: adjustsign
+ ****************************************************************************/
+
+static b16_t adjustsign(b16_t result, boolean negate)
+{
+  /* If the product is negative, then we overflowed */
+
+  if (result < 0)
+    {
+      if (result)
+        {
+          return b16MIN;
+        }
+      else
+        {
+          return b16MAX;
+        }
+    }
+
+  /* correct the sign of the result */
+
+  if (negate)
+    {
+      return -result;
+    }
+  return result;
+}
+
+/****************************************************************************
+ * Public Functions
+ ****************************************************************************/
+
+/****************************************************************************
+ * Name: b16mulb16
+ ****************************************************************************/
+
+b16_t b16mulb16(b16_t m1, b16_t m2)
+{
+  boolean negate;
+  b16_t product;
+
+  fixsign(&m1, &m2, &negate);
+  product = (b16_t)ub16mulub16((ub16_t)m1, (ub16_t)m2);
+  return adjustsign(product, negate);
+}
+
+/****************************************************************************
+ * Name: ub16mulub16
+ **************************************************************************/
+
+ub16_t ub16mulub16(ub16_t m1, ub16_t m2)
+{
+ /* Let:
+ *
+  *   m1 = m1i*2**16 + m1f                                            (b16)
+  *   m2 = m2i*2**16 + m2f                                            (b16)
+  *
+  * Then:
+  *
+  *  m1*m2 = (m1i*m2i)*2**32 + (m1i*m2f + m2i*m1f)*2**16 + m1f*m2f     (b32)
+  *        = (m1i*m2i)*2**16 + (m1i*m2f + m2i*m1f) + m1f*m2f*2**-16    (b16)
+  *        = a*2**16 + b + c*2**-16
+  */
+
+  uint32 m1i = ((uint32)m1 >> 16);
+  uint32 m2i = ((uint32)m1 >> 16);
+  uint32 m1f = ((uint32)m1 & 0x0000ffff);
+  uint32 m2f = ((uint32)m2 & 0x0000ffff);
+
+  return (m1i*m2i << 16) + m1i*m2f + m2i*m1f + (((m1f*m2f) + b16HALF) >> 16);
+}
+
+/****************************************************************************
+ * Name: b16divb16
+ **************************************************************************/
+
+b16_t b16divb16(b16_t num, b16_t denom)
+{
+  boolean negate;
+  b16_t quotient;
+
+  fixsign(&num, &denom, &negate);
+  quotient = (b16_t)ub16divub16((ub16_t)num, (ub16_t)denom);
+  return adjustsign(quotient, negate);
+}
+
+/****************************************************************************
+ * Name: ub16divub16
+ **************************************************************************/
+
+ub16_t ub16divub16(ub16_t num, ub16_t denom)
+{
+  uint32 term1;
+  uint32 numf;
+  uint32 product;
+
+ /* Let:
+  *
+  *   num = numi*2**16 + numf                                         (b16)
+  *   den = deni*2**16 + denf                                         (b16)
+  *
+  * Then:
+  *
+  *  num/den = numi*2**16 / den + numf / den                          (b0)
+  *          = numi*2**32 / den + numf*2**16 /den                     (b16)
+  */
+
+
+  /* Check for overflow in the first part of the quotient */
+
+  term1 = ((uint32)num & 0xffff0000) / denom;
+  if (term1 >= 0x00010000)
+    {
+        return ub16MAX; /* Will overflow */
+    }
+
+  /* Finish the division */
+
+  numf    = num - term1 * denom;
+  term1 <<= 16;
+  product = term1 + (numf + (denom >> 1)) / denom;
+
+  /* Check for overflow */
+
+  if (product < term1)
+    {
+        return ub16MAX; /* Overflowed */
+    }
+  return product;
+}
+
+#endif