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https://github.com/UpsilonNumworks/Upsilon.git
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[liba] Import trigonometric function from OpenBSD's libm
Change-Id: Ib192451a0063388e0438bdef5e7ae776ed058e19
This commit is contained in:
Romain Goyet
@@ -5,13 +5,22 @@ liba/src/external/sqlite/mem5.o: CFLAGS += -w
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objs += $(addprefix liba/src/, assert.o errno.o malloc.o memcpy.o memset.o strcmp.o strlcpy.o strlen.o external/sqlite/mem5.o)
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objs += $(addprefix liba/src/external/openbsd/, \
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e_logf.o \
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e_log10f.o \
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e_logf.o \
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e_powf.o \
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e_rem_pio2f.o \
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e_sqrtf.o \
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k_cosf.o \
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k_rem_pio2f.o \
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k_sinf.o \
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k_tanf.o \
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s_copysignf.o \
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s_cosf.o \
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s_fabsf.o \
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s_floorf.o \
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s_scalbnf.o \
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s_sinf.o \
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s_tanf.o \
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)
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liba/src/external/openbsd/%.o: CFLAGS += -Iliba/src/external/openbsd/include -Wno-parentheses
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@@ -5,13 +5,17 @@
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LIBA_BEGIN_DECLS
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float logf(float x);
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float log10f(float x);
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float powf(float x, float y);
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float fabsf(float x);
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float sqrtf(float x);
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float scalbnf(float x, int n);
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float copysignf(float x, float y);
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float cosf(float x);
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float fabsf(float x);
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float floorf(float x);
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float log10f(float x);
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float logf(float x);
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float powf(float x, float y);
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float scalbnf(float x, int n);
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float sinf(float x);
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float sqrtf(float x);
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float tanf(float x);
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LIBA_END_DECLS
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176
liba/src/external/openbsd/e_rem_pio2f.c
vendored
Normal file
176
liba/src/external/openbsd/e_rem_pio2f.c
vendored
Normal file
@@ -0,0 +1,176 @@
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/* e_rem_pio2f.c -- float version of e_rem_pio2.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_rem_pio2f(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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* use __kernel_rem_pio2f()
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*/
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#include "math.h"
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#include "math_private.h"
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/*
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* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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*/
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static const int32_t two_over_pi[] = {
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0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
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0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
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0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
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0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
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0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
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0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
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0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
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0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
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0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
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0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
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0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
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0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
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0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
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0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
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0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
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0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
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0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
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0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
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0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
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0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
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0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
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0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
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};
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/* This array is like the one in e_rem_pio2.c, but the numbers are
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single precision and the last 8 bits are forced to 0. */
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static const int32_t npio2_hw[] = {
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0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
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0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
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0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
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0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
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0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
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0x4242c700, 0x42490f00
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};
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/*
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* invpio2: 24 bits of 2/pi
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* pio2_1: first 17 bit of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 17 bit of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 17 bit of pi/2
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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static const float
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zero = 0.0000000000e+00, /* 0x00000000 */
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half = 5.0000000000e-01, /* 0x3f000000 */
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two8 = 2.5600000000e+02, /* 0x43800000 */
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invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
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pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
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pio2_1t = 1.0804334124e-05, /* 0x37354443 */
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pio2_2 = 1.0804273188e-05, /* 0x37354400 */
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pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
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pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
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pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
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int32_t
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__ieee754_rem_pio2f(float x, float *y)
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{
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float z,w,t,r,fn;
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float tx[3];
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int32_t e0,i,j,nx,n,ix,hx;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
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{y[0] = x; y[1] = 0; return 0;}
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if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
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if(hx>0) {
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z = x - pio2_1;
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if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0])-pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z-y[0])-pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + pio2_1;
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if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z + pio2_1t;
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y[1] = (z-y[0])+pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z-y[0])+pio2_2t;
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}
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return -1;
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}
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}
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if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
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t = fabsf(x);
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n = (int32_t) (t*invpio2+half);
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fn = (float)n;
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r = t-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 40 bit */
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if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
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y[0] = r-w; /* quick check no cancellation */
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} else {
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u_int32_t high;
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j = ix>>23;
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>8) { /* 2nd iteration needed, good to 57 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>25) { /* 3rd iteration need, 74 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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else return n;
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}
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/*
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* all other (large) arguments
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*/
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if(ix>=0x7f800000) { /* x is inf or NaN */
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y[0]=y[1]=x-x; return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-7) */
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e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */
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SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
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for(i=0;i<2;i++) {
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tx[i] = (float)((int32_t)(z));
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z = (z-tx[i])*two8;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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return n;
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}
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52
liba/src/external/openbsd/k_cosf.c
vendored
Normal file
52
liba/src/external/openbsd/k_cosf.c
vendored
Normal file
@@ -0,0 +1,52 @@
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/* k_cosf.c -- float version of k_cos.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
|
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* software is freely granted, provided that this notice
|
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* is preserved.
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* ====================================================
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*/
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#include "math.h"
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#include "math_private.h"
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static const float
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one = 1.0000000000e+00, /* 0x3f800000 */
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C1 = 4.1666667908e-02, /* 0x3d2aaaab */
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C2 = -1.3888889225e-03, /* 0xbab60b61 */
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C3 = 2.4801587642e-05, /* 0x37d00d01 */
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C4 = -2.7557314297e-07, /* 0xb493f27c */
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C5 = 2.0875723372e-09, /* 0x310f74f6 */
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C6 = -1.1359647598e-11; /* 0xad47d74e */
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float
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__kernel_cosf(float x, float y)
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{
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float a,hz,z,r,qx;
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int32_t ix;
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GET_FLOAT_WORD(ix,x);
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ix &= 0x7fffffff; /* ix = |x|'s high word*/
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if(ix<0x32000000) { /* if x < 2**27 */
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if(((int)x)==0) return one; /* generate inexact */
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}
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z = x*x;
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r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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if(ix < 0x3e99999a) /* if |x| < 0.3 */
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return one - ((float)0.5*z - (z*r - x*y));
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else {
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if(ix > 0x3f480000) { /* x > 0.78125 */
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qx = (float)0.28125;
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} else {
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SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
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}
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hz = (float)0.5*z-qx;
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a = one-qx;
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return a - (hz - (z*r-x*y));
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}
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}
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194
liba/src/external/openbsd/k_rem_pio2f.c
vendored
Normal file
194
liba/src/external/openbsd/k_rem_pio2f.c
vendored
Normal file
@@ -0,0 +1,194 @@
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/* k_rem_pio2f.c -- float version of k_rem_pio2.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
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#include "math.h"
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#include "math_private.h"
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/* In the float version, the input parameter x contains 8 bit
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integers, not 24 bit integers. 113 bit precision is not supported. */
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static const int init_jk[] = {4,7,9}; /* initial value for jk */
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static const float PIo2[] = {
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1.5703125000e+00, /* 0x3fc90000 */
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4.5776367188e-04, /* 0x39f00000 */
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2.5987625122e-05, /* 0x37da0000 */
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7.5437128544e-08, /* 0x33a20000 */
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6.0026650317e-11, /* 0x2e840000 */
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7.3896444519e-13, /* 0x2b500000 */
|
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5.3845816694e-15, /* 0x27c20000 */
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5.6378512969e-18, /* 0x22d00000 */
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8.3009228831e-20, /* 0x1fc40000 */
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3.2756352257e-22, /* 0x1bc60000 */
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6.3331015649e-25, /* 0x17440000 */
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};
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static const float
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zero = 0.0,
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one = 1.0,
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two8 = 2.5600000000e+02, /* 0x43800000 */
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twon8 = 3.9062500000e-03; /* 0x3b800000 */
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int
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__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec,
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const int32_t *ipio2)
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{
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int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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float z,fw,f[20],fq[20],q[20];
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/* initialize jk*/
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jk = init_jk[prec];
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jp = jk;
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/* determine jx,jv,q0, note that 3>q0 */
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jx = nx-1;
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jv = (e0-3)/8; if(jv<0) jv=0;
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q0 = e0-8*(jv+1);
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/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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j = jv-jx; m = jx+jk;
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for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
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/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
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||||
|
||||
jz = jk;
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recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (float)((int32_t)(twon8* z));
|
||||
iq[i] = (int32_t)(z-two8*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = scalbnf(z,q0); /* actual value of z */
|
||||
z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
|
||||
n = (int32_t) z;
|
||||
z -= (float)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(8-q0)); n += i;
|
||||
iq[jz-1] -= i<<(8-q0);
|
||||
ih = iq[jz-1]>>(7-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>8;
|
||||
else if(z>=(float)0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x100- j;
|
||||
}
|
||||
} else iq[i] = 0xff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7f; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3f; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= scalbnf(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (float) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==(float)0.0) {
|
||||
jz -= 1; q0 -= 8;
|
||||
while(iq[jz]==0) { jz--; q0-=8;}
|
||||
} else { /* break z into 8-bit if necessary */
|
||||
z = scalbnf(z,-q0);
|
||||
if(z>=two8) {
|
||||
fw = (float)((int32_t)(twon8*z));
|
||||
iq[jz] = (int32_t)(z-two8*fw);
|
||||
jz += 1; q0 += 8;
|
||||
iq[jz] = (int32_t) fw;
|
||||
} else iq[jz] = (int32_t) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = scalbnf(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(float)iq[i]; fw*=twon8;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
42
liba/src/external/openbsd/k_sinf.c
vendored
Normal file
42
liba/src/external/openbsd/k_sinf.c
vendored
Normal file
@@ -0,0 +1,42 @@
|
||||
/* k_sinf.c -- float version of k_sin.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
half = 5.0000000000e-01,/* 0x3f000000 */
|
||||
S1 = -1.6666667163e-01, /* 0xbe2aaaab */
|
||||
S2 = 8.3333337680e-03, /* 0x3c088889 */
|
||||
S3 = -1.9841270114e-04, /* 0xb9500d01 */
|
||||
S4 = 2.7557314297e-06, /* 0x3638ef1b */
|
||||
S5 = -2.5050759689e-08, /* 0xb2d72f34 */
|
||||
S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
|
||||
|
||||
float
|
||||
__kernel_sinf(float x, float y, int iy)
|
||||
{
|
||||
float z,r,v;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* high word of x */
|
||||
if(ix<0x32000000) /* |x| < 2**-27 */
|
||||
{if((int)x==0) return x;} /* generate inexact */
|
||||
z = x*x;
|
||||
v = z*x;
|
||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||
if(iy==0) return x+v*(S1+z*r);
|
||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||
}
|
||||
90
liba/src/external/openbsd/k_tanf.c
vendored
Normal file
90
liba/src/external/openbsd/k_tanf.c
vendored
Normal file
@@ -0,0 +1,90 @@
|
||||
/* k_tanf.c -- float version of k_tan.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
pio4 = 7.8539812565e-01, /* 0x3f490fda */
|
||||
pio4lo= 3.7748947079e-08, /* 0x33222168 */
|
||||
T[] = {
|
||||
3.3333334327e-01, /* 0x3eaaaaab */
|
||||
1.3333334029e-01, /* 0x3e088889 */
|
||||
5.3968254477e-02, /* 0x3d5d0dd1 */
|
||||
2.1869488060e-02, /* 0x3cb327a4 */
|
||||
8.8632395491e-03, /* 0x3c11371f */
|
||||
3.5920790397e-03, /* 0x3b6b6916 */
|
||||
1.4562094584e-03, /* 0x3abede48 */
|
||||
5.8804126456e-04, /* 0x3a1a26c8 */
|
||||
2.4646313977e-04, /* 0x398137b9 */
|
||||
7.8179444245e-05, /* 0x38a3f445 */
|
||||
7.1407252108e-05, /* 0x3895c07a */
|
||||
-1.8558637748e-05, /* 0xb79bae5f */
|
||||
2.5907305826e-05, /* 0x37d95384 */
|
||||
};
|
||||
|
||||
float
|
||||
__kernel_tanf(float x, float y, int iy)
|
||||
{
|
||||
float z,r,v,w,s;
|
||||
int32_t ix,hx;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff; /* high word of |x| */
|
||||
if(ix<0x31800000) /* x < 2**-28 */
|
||||
{if((int)x==0) { /* generate inexact */
|
||||
if((ix|(iy+1))==0) return one/fabsf(x);
|
||||
else return (iy==1)? x: -one/x;
|
||||
}
|
||||
}
|
||||
if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
|
||||
if(hx<0) {x = -x; y = -y;}
|
||||
z = pio4-x;
|
||||
w = pio4lo-y;
|
||||
x = z+w; y = 0.0;
|
||||
}
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||
*/
|
||||
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
|
||||
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
|
||||
s = z*x;
|
||||
r = y + z*(s*(r+v)+y);
|
||||
r += T[0]*s;
|
||||
w = x+r;
|
||||
if(ix>=0x3f2ca140) {
|
||||
v = (float)iy;
|
||||
return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
|
||||
}
|
||||
if(iy==1) return w;
|
||||
else { /* if allow error up to 2 ulp,
|
||||
simply return -1.0/(x+r) here */
|
||||
/* compute -1.0/(x+r) accurately */
|
||||
float a,t;
|
||||
int32_t i;
|
||||
z = w;
|
||||
GET_FLOAT_WORD(i,z);
|
||||
SET_FLOAT_WORD(z,i&0xfffff000);
|
||||
v = r-(z - x); /* z+v = r+x */
|
||||
t = a = -(float)1.0/w; /* a = -1.0/w */
|
||||
GET_FLOAT_WORD(i,t);
|
||||
SET_FLOAT_WORD(t,i&0xfffff000);
|
||||
s = (float)1.0+t*z;
|
||||
return t+a*(s+t*v);
|
||||
}
|
||||
}
|
||||
45
liba/src/external/openbsd/s_cosf.c
vendored
Normal file
45
liba/src/external/openbsd/s_cosf.c
vendored
Normal file
@@ -0,0 +1,45 @@
|
||||
/* s_cosf.c -- float version of s_cos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
cosf(float x)
|
||||
{
|
||||
float y[2],z=0.0;
|
||||
int32_t n,ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cosf(y[0],y[1]);
|
||||
case 1: return -__kernel_sinf(y[0],y[1],1);
|
||||
case 2: return -__kernel_cosf(y[0],y[1]);
|
||||
default:
|
||||
return __kernel_sinf(y[0],y[1],1);
|
||||
}
|
||||
}
|
||||
}
|
||||
58
liba/src/external/openbsd/s_floorf.c
vendored
Normal file
58
liba/src/external/openbsd/s_floorf.c
vendored
Normal file
@@ -0,0 +1,58 @@
|
||||
/* s_floorf.c -- float version of s_floor.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* floorf(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floorf(x).
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const float huge = 1.0e30;
|
||||
|
||||
float
|
||||
floorf(float x)
|
||||
{
|
||||
int32_t i0,jj0;
|
||||
u_int32_t i;
|
||||
GET_FLOAT_WORD(i0,x);
|
||||
jj0 = ((i0>>23)&0xff)-0x7f;
|
||||
if(jj0<23) {
|
||||
if(jj0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0>=0) {i0=0;}
|
||||
else if((i0&0x7fffffff)!=0)
|
||||
{ i0=0xbf800000;}
|
||||
}
|
||||
} else {
|
||||
i = (0x007fffff)>>jj0;
|
||||
if((i0&i)==0) return x; /* x is integral */
|
||||
if(huge+x>(float)0.0) { /* raise inexact flag */
|
||||
if(i0<0) i0 += (0x00800000)>>jj0;
|
||||
i0 &= (~i);
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(jj0==0x80) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
}
|
||||
SET_FLOAT_WORD(x,i0);
|
||||
return x;
|
||||
}
|
||||
40
liba/src/external/openbsd/s_tanf.c
vendored
Normal file
40
liba/src/external/openbsd/s_tanf.c
vendored
Normal file
@@ -0,0 +1,40 @@
|
||||
/* s_tanf.c -- float version of s_tan.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
float
|
||||
tanf(float x)
|
||||
{
|
||||
float y[2],z=0.0;
|
||||
int32_t n, ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1);
|
||||
|
||||
/* tan(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7f800000) return x-x; /* NaN */
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2f(x,y);
|
||||
return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
|
||||
-1 -- n odd */
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user