New generic cosf

From: "Paul A. Clarke" <pc@us.ibm.com>

  From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
From: "Paul A. Clarke" <pc@us.ibm.com>
Date: Tue, 5 Dec 2017 09:32:56 -0600
Subject: [PATCH] New generic cosf

The same logic used in s_cosf.S version for x86 and powerpc
is used to create a generic s_cosf.c, so there is no performance
improvement in x86_64 and powerpc64.

-- 8< --
For s390, this is the improvement noted.

With patch:
  "cosf": {
   "": {
    "duration": 1.00479e+10,
    "iterations": 1.53856e+08,
    "max": 900.645,
    "min": 4.264,
    "mean": 65.3074
   }
  }
Without patch:
  "cosf": {
   "": {
    "duration": 9.93841e+09,
    "iterations": 4.63972e+08,
    "max": 1010.9,
    "min": 6.593,
    "mean": 21.4203
   }
  }

Tested on s390x, x86_64 and powerpc64le and powerpc32.

I include below a diff with recent generic s_sinf.c, as it is more
instructive than a diff with existing s_cosf.c.  There are a fair number
of cosmetic changes, a few hard differences because it's a different
computation, and adoption of changes from recent patches deemed acceptable.
--
1c1
< /* Compute sine of argument.
---
> /* Compute cosine of argument.
24,25c24,25
< #ifndef SINF
< # define SINF_FUNC __sinf
---
> #ifndef COSF
> # define COSF_FUNC __cosf
27c27
< # define SINF_FUNC SINF
---
> # define COSF_FUNC COSF
44,46c44,46
< /* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
< static const double SS0 = -0x1.555555543d49dp-3;
< static const double SS1 =  0x1.110f475cec8c5p-7;
---
> /* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
> static const double CC0 = -0x1.fffffff5cc6fdp-2;
> static const double CC1 =  0x1.55514b178dac5p-5;
52d51
< static const double SMALL = 0x1p-50; /* 2^-50.  */
78c77
< static const int ones[] = { +1, -1 };
---
> static const double ones[] = { +1, -1 };
80c79
< /* Compute the sine value using Chebyshev polynomials where
---
> /* Compute the cosine value using Chebyshev polynomials where
85,86c84
<    SIGNBIT is used to add the correct sign after the Chebyshev
<    polynomial is computed.  */
---
>    the sign of the result.  */
88,89c86
< reduced (const double theta, const unsigned long int n,
< 	 const unsigned long int signbit)
---
> reduced (double theta, unsigned int n)
91c88
<   double sx;
---
>   double sign, cx;
93,95c90
<   /* We are operating on |x|, so we need to add back the original
<      signbit for sinf.  */
<   int sign;
---
>
97c92,94
<   sign = ones[((n >> 2) & 1) ^ signbit];
---
>   n += 2;
>   sign = ones[(n >> 2) & 1];
>
101c98
<       /* Here sinf() is calculated using sin Chebyshev polynomial:
---
>       /* Here cosf() is calculated using sin Chebyshev polynomial:
103,107c100,104
<       sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
<       sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
<       sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
<       sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
<       sx = theta + theta * theta2 * sx;
---
>       cx = S3 + theta2 * S4;
>       cx = S2 + theta2 * cx;
>       cx = S1 + theta2 * cx;
>       cx = S0 + theta2 * cx;
>       cx = theta + theta * theta2 * cx;
111c108
<      /* Here sinf() is calculated using cos Chebyshev polynomial:
---
>      /* Here cosf() is calculated using cos Chebyshev polynomial:
113,117c110,114
<       sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
<       sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
<       sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
<       sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
<       sx = 1.0 + theta2 * sx;
---
>       cx = C3 + theta2 * C4;
>       cx = C2 + theta2 * cx;
>       cx = C1 + theta2 * cx;
>       cx = C0 + theta2 * cx;
>       cx = 1. + theta2 * cx;
119,121c116
<
<   /* Add in the signbit and assign the result.  */
<   return sign * sx;
---
>   return sign * cx;
125c120
< SINF_FUNC (float x)
---
> COSF_FUNC (float x)
127d121
<   double cx;
130,131c124
<   /* If |x|< Pi/4.  */
<   if (abstheta < M_PI_4)
---
>   if (isless (abstheta, M_PI_4))
133c126,127
<       if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
---
>       double cx;
>       if (abstheta >= 0x1p-5)
136,142c130,136
< 	  /* Chebyshev polynomial of the form for sin
< 	     x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
< 	  cx = S3 + theta2 * S4;
< 	  cx = S2 + theta2 * cx;
< 	  cx = S1 + theta2 * cx;
< 	  cx = S0 + theta2 * cx;
< 	  cx = theta + theta * theta2 * cx;
---
> 	  /* Chebyshev polynomial of the form for cos:
> 	   * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))).  */
> 	  cx = C3 + theta2 * C4;
> 	  cx = C2 + theta2 * cx;
> 	  cx = C1 + theta2 * cx;
> 	  cx = C0 + theta2 * cx;
> 	  cx = 1. + theta2 * cx;
145c139
<       else if (abstheta >= 0x1p-27)     /* |x| >= 2^-27.  */
---
>       else if (abstheta >= 0x1p-27)
148c142
< 	     for sin: x+x^3*(SS0+x^2*SS1).  */
---
> 	   * 1 + x^2 (CC0 + x^3 * CC1).  */
150,151c144,145
< 	  cx = SS0 + theta2 * SS1;
< 	  cx = theta + theta * theta2 * cx;
---
> 	  cx = CC0 + theta * theta2 * CC1;
> 	  cx = 1.0 + theta2 * cx;
156,160c150,151
< 	  /* Handle some special cases.  */
< 	  if (theta)
< 	    return theta - (theta * SMALL);
< 	  else
< 	    return theta;
---
> 	  /* For small enough |theta|, this is close enough.  */
> 	  return 1.0 - abstheta;
163c154
<   else                          /* |x| >= Pi/4.  */
---
>   else /* |theta| >= Pi/4.  */
165,166c156
<       unsigned long int signbit = (x < 0);
<       if (abstheta < 9 * M_PI_4)        /* |x| < 9*Pi/4.  */
---
>       if (isless (abstheta, 9 * M_PI_4))
172c162
< 	  unsigned long int n = (abstheta * inv_PI_4) + 1;
---
> 	  unsigned int n = (abstheta * inv_PI_4) + 1;
174c164
< 	  return reduced (theta, n, signbit);
---
> 	  return reduced (theta, n);
178c168
< 	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
---
> 	  if (abstheta < 0x1p+23)
180,181c170,171
< 	      unsigned long int n = __floor (abstheta * inv_PI_4) + 1.0;
< 	      double x = __floor (n / 2.0);
---
> 	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
> 	      double x = n / 2.0;
184c174
< 	      return reduced (theta, n, signbit);
---
> 	      return reduced (theta, n);
186c176
< 	  else                  /* |x| >= 2^23.  */
---
> 	  else /* |theta| >= 2^23.  */
191,192c181,182
< 	      exponent
< 	        = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
---
> 	      exponent = (exponent >> FLOAT_EXPONENT_SHIFT)
> 			 - FLOAT_EXPONENT_BIAS;
212c202
< 	          return reduced (e, l + 1, signbit);
---
> 		  return reduced (e, l + 1);
222c212
< 		      return reduced (e, l + 1, signbit);
---
> 		      return reduced (e, l + 1);
229c219
< 		      return reduced (e, l + 1, signbit);
---
> 		      return reduced (e, l + 1);
237d226
< 	  /* High word of x.  */
239,240c228,229
< 	  /* Sin(Inf or NaN) is NaN.  */
< 	  if (ix == 0x7f800000)
---
> 	  /* cos(Inf or NaN) is NaN.  */
> 	  if (ix == 0x7f800000) /* Inf.  */
247,248c236,237
< #ifndef SINF
< libm_alias_float (__sin, sin)
---
> #ifndef COSF
> libm_alias_float (__cos, cos)
-- 8< --

2017-12-05  Paul A. Clarke  <pc@us.ibm.com>

	* sysdeps/ieee754/flt-32/s_cosf.c: New implementation.
---
 sysdeps/ieee754/flt-32/s_cosf.c | 254 +++++++++++++++++++++++++++++++++-------
 1 file changed, 214 insertions(+), 40 deletions(-)

New generic cosf

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