-/** Wrapper around sin() */
-double
-_mesa_sin(double a)
-{
- return sin(a);
-}
-
-/** Single precision wrapper around sin() */
-float
-_mesa_sinf(float a)
-{
- return (float) sin((double) a);
-}
-
-/** Wrapper around cos() */
-double
-_mesa_cos(double a)
-{
- return cos(a);
-}
-
-/** Single precision wrapper around asin() */
-float
-_mesa_asinf(float x)
-{
- return (float) asin((double) x);
-}
-
-/** Single precision wrapper around atan() */
-float
-_mesa_atanf(float x)
-{
- return (float) atan((double) x);
-}
-
-/** Wrapper around sqrt() */
-double
-_mesa_sqrtd(double x)
-{
- return sqrt(x);
-}
-
-
-/*
- * A High Speed, Low Precision Square Root
- * by Paul Lalonde and Robert Dawson
- * from "Graphics Gems", Academic Press, 1990
- *
- * SPARC implementation of a fast square root by table
- * lookup.
- * SPARC floating point format is as follows:
- *
- * BIT 31 30 23 22 0
- * sign exponent mantissa
- */
-static short sqrttab[0x100]; /* declare table of square roots */
-
-void
-_mesa_init_sqrt_table(void)
-{
-#if defined(USE_IEEE) && !defined(DEBUG)
- unsigned short i;
- fi_type fi; /* to access the bits of a float in C quickly */
- /* we use a union defined in glheader.h */
-
- for(i=0; i<= 0x7f; i++) {
- fi.i = 0;
-
- /*
- * Build a float with the bit pattern i as mantissa
- * and an exponent of 0, stored as 127
- */
-
- fi.i = (i << 16) | (127 << 23);
- fi.f = _mesa_sqrtd(fi.f);
-
- /*
- * Take the square root then strip the first 7 bits of
- * the mantissa into the table
- */
-
- sqrttab[i] = (fi.i & 0x7fffff) >> 16;
-
- /*
- * Repeat the process, this time with an exponent of
- * 1, stored as 128
- */
-
- fi.i = 0;
- fi.i = (i << 16) | (128 << 23);
- fi.f = sqrt(fi.f);
- sqrttab[i+0x80] = (fi.i & 0x7fffff) >> 16;
- }
-#else
- (void) sqrttab; /* silence compiler warnings */
-#endif /*HAVE_FAST_MATH*/
-}
-
-
-/**
- * Single precision square root.
- */
-float
-_mesa_sqrtf( float x )
-{
-#if defined(USE_IEEE) && !defined(DEBUG)
- fi_type num;
- /* to access the bits of a float in C
- * we use a union from glheader.h */
-
- short e; /* the exponent */
- if (x == 0.0F) return 0.0F; /* check for square root of 0 */
- num.f = x;
- e = (num.i >> 23) - 127; /* get the exponent - on a SPARC the */
- /* exponent is stored with 127 added */
- num.i &= 0x7fffff; /* leave only the mantissa */
- if (e & 0x01) num.i |= 0x800000;
- /* the exponent is odd so we have to */
- /* look it up in the second half of */
- /* the lookup table, so we set the */
- /* high bit */
- e >>= 1; /* divide the exponent by two */
- /* note that in C the shift */
- /* operators are sign preserving */
- /* for signed operands */
- /* Do the table lookup, based on the quaternary mantissa,
- * then reconstruct the result back into a float
- */
- num.i = ((sqrttab[num.i >> 16]) << 16) | ((e + 127) << 23);
-
- return num.f;
-#else
- return (float) _mesa_sqrtd((double) x);
-#endif
-}
-
-
-/**
- inv_sqrt - A single precision 1/sqrt routine for IEEE format floats.
- written by Josh Vanderhoof, based on newsgroup posts by James Van Buskirk
- and Vesa Karvonen.
-*/
-float
-_mesa_inv_sqrtf(float n)
-{
-#if defined(USE_IEEE) && !defined(DEBUG)
- float r0, x0, y0;
- float r1, x1, y1;
- float r2, x2, y2;
-#if 0 /* not used, see below -BP */
- float r3, x3, y3;
-#endif
- fi_type u;
- unsigned int magic;
-
- /*
- Exponent part of the magic number -
-
- We want to:
- 1. subtract the bias from the exponent,
- 2. negate it
- 3. divide by two (rounding towards -inf)
- 4. add the bias back
-
- Which is the same as subtracting the exponent from 381 and dividing
- by 2.
-
- floor(-(x - 127) / 2) + 127 = floor((381 - x) / 2)
- */
-
- magic = 381 << 23;
-
- /*
- Significand part of magic number -
-
- With the current magic number, "(magic - u.i) >> 1" will give you:
-
- for 1 <= u.f <= 2: 1.25 - u.f / 4
- for 2 <= u.f <= 4: 1.00 - u.f / 8
-
- This isn't a bad approximation of 1/sqrt. The maximum difference from
- 1/sqrt will be around .06. After three Newton-Raphson iterations, the
- maximum difference is less than 4.5e-8. (Which is actually close
- enough to make the following bias academic...)
-
- To get a better approximation you can add a bias to the magic
- number. For example, if you subtract 1/2 of the maximum difference in
- the first approximation (.03), you will get the following function:
-
- for 1 <= u.f <= 2: 1.22 - u.f / 4
- for 2 <= u.f <= 3.76: 0.97 - u.f / 8
- for 3.76 <= u.f <= 4: 0.72 - u.f / 16
- (The 3.76 to 4 range is where the result is < .5.)
-
- This is the closest possible initial approximation, but with a maximum
- error of 8e-11 after three NR iterations, it is still not perfect. If
- you subtract 0.0332281 instead of .03, the maximum error will be
- 2.5e-11 after three NR iterations, which should be about as close as
- is possible.
-
- for 1 <= u.f <= 2: 1.2167719 - u.f / 4
- for 2 <= u.f <= 3.73: 0.9667719 - u.f / 8
- for 3.73 <= u.f <= 4: 0.7167719 - u.f / 16
-
- */
-
- magic -= (int)(0.0332281 * (1 << 25));
-
- u.f = n;
- u.i = (magic - u.i) >> 1;
-
- /*
- Instead of Newton-Raphson, we use Goldschmidt's algorithm, which
- allows more parallelism. From what I understand, the parallelism
- comes at the cost of less precision, because it lets error
- accumulate across iterations.
- */
- x0 = 1.0f;
- y0 = 0.5f * n;
- r0 = u.f;
-
- x1 = x0 * r0;
- y1 = y0 * r0 * r0;
- r1 = 1.5f - y1;
-
- x2 = x1 * r1;
- y2 = y1 * r1 * r1;
- r2 = 1.5f - y2;
-
-#if 1
- return x2 * r2; /* we can stop here, and be conformant -BP */
-#else
- x3 = x2 * r2;
- y3 = y2 * r2 * r2;
- r3 = 1.5f - y3;
-
- return x3 * r3;
-#endif
-#else
- return (float) (1.0 / sqrt(n));
-#endif
-}
-
-
-/** Wrapper around pow() */
-double
-_mesa_pow(double x, double y)
-{
- return pow(x, y);
-}
-
-
-/**
- * Find the first bit set in a word.
- */
-int
-_mesa_ffs(int32_t i)
-{
-#if (defined(_WIN32) ) || defined(__IBMC__) || defined(__IBMCPP__)
- register int bit = 0;
- if (i != 0) {
- if ((i & 0xffff) == 0) {
- bit += 16;
- i >>= 16;
- }
- if ((i & 0xff) == 0) {
- bit += 8;
- i >>= 8;
- }
- if ((i & 0xf) == 0) {
- bit += 4;
- i >>= 4;
- }
- while ((i & 1) == 0) {
- bit++;
- i >>= 1;
- }
- bit++;
- }
- return bit;
-#else
- return ffs(i);
-#endif
-}
-
-
-/**
- * Find position of first bit set in given value.
- * XXX Warning: this function can only be used on 64-bit systems!
- * \return position of least-significant bit set, starting at 1, return zero
- * if no bits set.
- */
-int
-_mesa_ffsll(int64_t val)
-{
-#ifdef ffsll
- return ffsll(val);
-#else
- int bit;
-
- assert(sizeof(val) == 8);
-
- bit = _mesa_ffs((int32_t)val);
- if (bit != 0)
- return bit;
-
- bit = _mesa_ffs((int32_t)(val >> 32));
- if (bit != 0)
- return 32 + bit;
-
- return 0;
-#endif
-}
-